Do Behavioral Biases Adversely Affect the Macro-Economy?

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Do Behavioral Biases Adversely Affect the Macro-Economy? George M. Korniotis and Alok Kumar 2008-49 NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Do Behavioral Biases Adversely A⁄ect the Macro-Economy? (cid:3) George M. Korniotis Board of Governors of the Federal Reserve System Alok Kumar University of Texas at Austin, McCombs School of Business Abstract This study investigates whether the adverse e⁄ects of investors(cid:146)behavioral biases extend beyond the domain of (cid:133)nancial markets to the broad macro-economy. We focus on the risk sharing (or income smoothing) role of (cid:133)nancial markets and demonstrate that risk sharing levels are higher in U.S. states inwhichinvestorshavehighercognitiveabilitiesandexhibitweakerbehavioralbiases. Further, states with better risk sharing opportunities achieve higher levels of risk sharing if investors in those states exhibit greater (cid:133)nancial sophistication. Among the various determinants of risk sharing, behavioral factors have the strongest e⁄ects. The average level of risk sharing in states with unsophisticated investors (= 0.121) is less than half of the average risk sharing level in states with (cid:133)nancially sophisticated investors (= 0.308). Collectively, our evidence indicates that the high risk sharing potential of (cid:133)nancial markets is not fully realized because the aggregate behavioral biases of individual investors impede state-level risk sharing. Keywords: Risk sharing, income risk, (cid:133)nancial markets, cognitive abilities, behavioral biases, investor sophistication. JEL: E10, G11, G12. Current version: September 12, 2008. Please address all correspondence to Alok Kumar, Department of (cid:3) Finance, McCombs School of Business, University of Texas at Austin, 1 University Station, B6600, Austin, TX 78712; Phone: 512-232-6824; email: akumar@mail.utexas.edu. George Korniotis is at the Board of Governors of the Federal Reserve System; Phone: 202-452-2581; email: george.m.korniotis@frb.gov. We thankBenBernanke,MichaelBrandt,JohnCampbell,SeanCampbell,JohnCochrane,JonathanCohn,George Constantinides, Joshua Coval, John Driscoll, Xavier Gabaix, Erik Heit(cid:133)eld, John Gri¢ n, David Hirshleifer, Ramesh Rao, Bob Shiller, Sophie Shive, Bent Sorensen, and Sheridan Titman for helpful discussions and valuable comments. We also thank Bob Shiller for the state-level stock market wealth data and Bent Sorensen forprovidingseveraldatasets,includingthestateincomedata. Weareresponsibleforallremainingerrorsand omissions. The analysis and conclusions set forth are those of the authors and should not be taken to indicate any endorsement by the research sta⁄or the Board of Governors.

Behavioral Biases and the Macro-Economy 1. Introduction One of the major challenges for the (cid:133)eld of behavioral (cid:133)nance is to convincingly establish that investors(cid:146)behavioral biases have aggregate market-wide e⁄ects (e.g., Shleifer (2000), Hirshleifer (2001), Barberis and Thaler (2003)). The recent behavioral asset pricing literature demonstrates that the aggregate forces generated by investors(cid:146)systematic behavioral biases have the ability to in(cid:135)uence stock prices and trading volume (e.g., Odean (1998), Barberis, Huang, and Santos (2001), Coval and Shumway (2005), Grinblatt and Han (2005), Statman, Thorley, and Vorkink (2006), Barberis and Huang (2008)). At a more aggregate level, behavioral mechanisms can generate high levels of market risk premium and even induce market-level misvaluations that could create a (cid:147)bubble(cid:148)(e.g., Benartzi and Thaler (1995), Scheinkman and Xiong (2003)). In this paper, we develop these insights further and examine whether the systematic e⁄ects of behavioral biases extend beyond the domain of (cid:133)nancial markets to the aggregate macro-economy. Speci(cid:133)cally,weinvestigatewhetherbehavioralfrictionsadverselya⁄ectstate-levelincomerisksharing (i.e., state-level income smoothing) that can be achieved using (cid:133)nancial markets.1 To our knowledge, this is the (cid:133)rst paper that examines whether systematic behavioral biases can in(cid:135)uence broader macro-economic phenomena such as state-level risk sharing. We focus on income smoothing for two reasons. First, this is a natural setting to examine whether the adverse e⁄ects of behavioral biases in people(cid:146)s investment decisions have far-reaching e⁄ects. One of the fundamental roles of (cid:133)nancial markets is to enhance the ability of an economy to reduce idiosyncratic income risk by facilitating the cross-ownership of productive assets. Thus, if the e⁄ects of distortions in (cid:133)nancial decisions induced by behavioral biases ripple beyond (cid:133)nancial markets, they are likely to be re(cid:135)ected in state-level income smoothing estimates. Second, through its direct e⁄ect on consumption smoothing, income smoothing has the potential to considerably a⁄ect asset prices, expected returns, and the level of social welfare. The interstate risk sharing literature reports that at the aggregate-level only 35-39% of statespeci(cid:133)c, idiosyncratic income risk can be eliminated through the (cid:133)nancial markets channel (e.g., Asdrubali, Sorensen, and Yosha (1996), Athanasoulis and Van Wincoop (2001)). These estimates are surprisingly low because (cid:133)nancial assets contain information about future economic activities (e.g., Harvey (1988), Barro (1990), Bernanke and Blinder (1992)) and have the potential to facilitate high levels of risk sharing, both within the U.S. and across countries (e.g., Brandt, Cochrane, and Santa-Clara (2006)). These aggregate-level risk sharing estimates, however, mask the substantial cross-sectional het- 1Income smoothing isdistinctfrom consumption smoothing (ortotalrisk sharing),which ismeasured by comparing the growth rates of GSP and state-level consumption (e.g, Cochrane (1991), Asdrubali, Sorensen, and Yosha (1996)). The total risk sharing measure captures the level of risk sharing that is achieved through (cid:133)nancial markets and other channels, including unemployment insurance, federal taxation, and (cid:133)scal policies. 1

Behavioral Biases and the Macro-Economy erogeneity in the state-level risk sharing estimates. For example, states such as Iowa, South Dakota andKentuckyachieveverylow(lessthan10%)levelsofrisksharingusing(cid:133)nancialassets. Incontrast, states such as Delaware, New Mexico and Oregon attain risk sharing levels of about 50%. Figure 1 providesagraphicalillustrationofthedegreeofheterogeneityinthestate-levelrisksharingestimates. We exploit this cross-sectional heterogeneity to investigate why some states are more vulnerable to local economic shocks than others. Broadly speaking, two sets of factors could in(cid:135)uence the state-level risk sharing estimates. First, thequalityofpeople(cid:146)sinvestmentdecisionswhentheychoosetoparticipatein(cid:133)nancialmarketswould determine the level of risk sharing. Merely high levels of stock market participation is unlikely to induce high levels of risk sharing. For example, if investors are motivated to participate in the stock market due to their gambling or speculative motives (Kumar (2008)), it is quite unlikely that their investment decisions will improve risk sharing. In fact, their higher propensity to trade low-priced, highly volatile stocks that promise high returns with a small probability might reduce risk sharing. Similarly, if investors trade excessively because they are overcon(cid:133)dent about their investment skills or the quality of their information sets, they will incur substantial transaction costs and underperform (e.g., Odean (1999), Barber and Odean (2000)). Such underperformance will negatively impact their total wealth and their ability to withstand adverse income shocks. Previous risk sharing studies also conjecture that distortions in people(cid:146)s investment decisions induced by various behavioral biases could limit the ability of (cid:133)nancial assets to completely eliminate state-speci(cid:133)c income risk. Speci(cid:133)cally, Athanasoulis and Van Wincoop (2001) conjecture that risk sharing levels might be low due to portfolio under-diversi(cid:133)cation induced by people(cid:146)s preference for holding stocks in their geographical vicinity (i.e., local bias). Motivatedbytheevidencefromtheserelatedstudies, weconjecturethatonlysophisticatedstock market participation can improve state-level risk sharing. In particular, investors would be able to achieve high levels of risk sharing by following the normative prescriptions of portfolio theory, where they hold well diversi(cid:133)ed portfolios that include domestic as well as foreign stocks and use buy-andhold type strategies. Even when they choose to deviate from these normative prescriptions and trade activelyorholdconcentratedportfoliosthatover-weightlocalstocks,risksharinglevelscouldincrease if those deviations are motivated by superior information instead of behavioral biases. By exploiting their superior information, those investors might develop a wealth cushion and limit their sensitivity to negative income shocks. To identify the e⁄ects of behavioral biases on state-level risk sharing, we use data on the investment decisions of a representative sample of individual investors at a large U.S. brokerage house. At present, this is the most comprehensive data set on the stock holdings and trades of U.S. individual investors. While the stock market participation levels for U.S. households can be obtained from vari- 2

Behavioral Biases and the Macro-Economy ouspublicdatasources, itisverydi¢ culttomeasurethequalityofpeople(cid:146)sinvestmentdecisionsonce they decide to participate. The brokerage sample provides a rare peek at the geographical variation in the quality of investment decisions of U.S. households.2 Using the brokerage data, we obtain the average bias measures for all investors within each state and aggregate them to de(cid:133)ne state-level proxies for several behavioral biases that are likely to in(cid:135)uence state-level risk sharing. In addition, we examine whether the cognitive abilities of state investors in(cid:135)uence the risk sharing ability of that state. This exercise is motivated by recent research inbehavioraleconomics(e.g., Frederick(2005), Benjamin, Brown, andShapiro(2006),Dohmen, Falk, Hu⁄man, and Sunde (2007)), which (cid:133)nds that lower levels of cognitive abilities are associated with stronger behavioral biases. Because direct measures of cognitive abilities of stock market participants are not available, we use the demographic characteristics of the brokerage investors (e.g., income, education, age, social networks, etc.) to de(cid:133)ne a cognitive ability or (cid:147)smartness(cid:148)proxy for each investor and use these imputed cognitive ability measures to obtain aggregated state-level measures of cognitive abilities (Korniotis and Kumar (2008)). We do not suggest that the income smoothing that is achieved through the (cid:133)nancial markets channel is induced by people(cid:146)s investment decisions in their brokerage accounts. We assume that the quality of investment decisions in brokerage accounts would be a good proxy for the overall quality of people(cid:146)sinvestmentdecisions. Withthisassumption,weexploitthebrokeragedatatoobtainmultiple proxies for the average (cid:133)nancial sophistication of market participants in individual states. In addition to the adverse e⁄ects of behavioral biases, another set of factors that can in(cid:135)uence state-level risk sharing is associated with the geographical location. Roughly speaking, investors who live in (cid:147)riskier(cid:148)regions would be more vulnerable to local economic shocks. For example, states like Alaska, North Dakota, and Wyoming have very volatile economies. As shown in Figure 4, the standard deviations of the state-speci(cid:133)c component of their real per capita gross state product (GSP) growth rates are 0.125, 0.079, and 0.067, respectively. In contrast, states like Pennsylvania, Alabama, and Illinois, appear considerably less risky. The standard deviations of the state-speci(cid:133)c component of their per capita GSP growth rate are only around 0.020. Toquantifythee⁄ectsofgeographicalfactorsonrisksharing,foreachstate,weestimatethelevel of risk sharing that could be potentially attained if the investors in that state optimally use (cid:133)nancial assets to minimize state-speci(cid:133)c income risk. The theoretical state-level risk sharing measure characterizes the investment opportunities available to the investors in the state. Speci(cid:133)cally, we use the relative gross state product to measure income before risk sharing, while the income after risk sharing is the return from a minimum variance composite portfolio that contains (cid:133)nancial assets along with a 2Although the brokerage sample has a disproportionate number of investors from California (about 21%) and New York, it contains a signi(cid:133)cant number of investors from all U.S. states. 3

Behavioral Biases and the Macro-Economy state-speci(cid:133)c (cid:147)product(cid:148)asset.3 We choose (cid:133)nancial assets from equity, bond, and treasury markets, and use the standard mean-variance optimization framework to identify the minimum variance portfolio (MVP) for each state. To measure the level of risk sharing that is potentially attainable, we use the Athanasoulis and Van Wincoop (2001) method and compare the volatility levels of the growth rate of relative GSP and the relative MVP return.4 Weexaminethee⁄ectsofbehavioralandgeographicalfactorsonrisksharingusingcross-sectional regressions in which the dependent variable is the level of risk sharing that is actually achieved by a U.S. state through the (cid:133)nancial markets channel. We measure the achieved levels of risk sharing by comparing the volatility levels of the growth rate of relative GSP and relative state income (SI).5 The relative GSP re(cid:135)ects the state-speci(cid:133)c component of income without smoothing from any risk sharing channel, while the relative SI captures the state-speci(cid:133)c component of income that incorporates the smoothing e⁄ects of (cid:133)nancial markets. Our empirical investigation is organized around three key themes. First, to set the stage, we examine the in(cid:135)uence of traditional factors such as the size and intensity of stock market participation and liquidity or borrowing constraints on state-level risk sharing.6 We (cid:133)nd that, unconditionally, states with high stock market participation rates attain high levels of risk sharing. But when we account for borrowing constraints, as captured by the state-level housing collateral ratio (Lustig and Van Nieuwerburgh (2008)), surprisingly, higher levels of participation are associated with lower levels of risk sharing. Nonetheless, states with high participation rates achieve high levels of risk sharing when a greater proportion of aggregate state-level wealth is invested in the stock market. This evidence suggests that participation by wealthier investors, who might be relatively more sophisticated, improves state-level risk sharing. The negative relation between stock market participation and risk sharing suggests that either the investment objectives of U.S. investors are not aligned with their risk sharing objectives or that their sub-optimal investment decisions generate low levels of risk sharing. In our second set of tests, we explicitly examine the e⁄ects of behavioral factors on state-level risk sharing. We (cid:133)nd that the risk sharing levels are higher in states in which the cognitive abilities of investors are higher. Investors in high risk-sharing states also trade less frequently, exhibit a lower propensity to follow gamblingmotivated strategies, exhibit a greater propensity to hold foreign stocks, and hold less concentrated portfolios. 3The state-speci(cid:133)c (cid:147)product(cid:148)asset is characterized by the growth rate of GSP. 4Relative GSP growth rate is de(cid:133)ned as the growth rate of GSP minus the growth rate of GDP. Similar to this de(cid:133)nition, the relative MVP return is the raw MVP return minus the cross-sectional mean of the raw MVP return. 5Relative GSP is GSP divided by GDP and relative SI is SI divided by national income. Both the GSP and the SI measures are in real per capita terms. 6In the absence ofany direct and publicly available data on stock market participation at the state level, we use the participation proxy proposed in Brown, Ivkovi·c, Smith, and Weisbenner (2008). 4

Behavioral Biases and the Macro-Economy Surprisingly, states in which investors tilt their portfolios disproportionately more toward local stocks also achieve higher levels of risk sharing. This result is inconsistent with the conjecture in Athanasoulis and Van Wincoop (2001). However, the evidence is consistent with the recent evidence from the retail investor literature, which demonstrates that the preference for local stocks could be induced by investors(cid:146)superior local information and could re(cid:135)ect investor sophistication (e.g., Ivkovi·c andWeisbenner(2005), MassaandSimonov(2006), Bodnaruk(2008)). Overall, theseresultsindicate that what matters for risk sharing is sophisticated stock market participation, where investors either follow the normative prescriptions of portfolio choice or attempt to exploit their superior private information. In our last set of tests, we examine the e⁄ects of geographical factors on risk sharing. We present a novel approach to quantify the potential risk sharing opportunities available to investors in a state and examine whether the potential risk sharing levels are correlated with the achieved levels of risk sharing. Our evidence indicates that states can achieve higher levels of risk sharing when the risk sharing potential is high and state investors exhibit greater (cid:133)nancial sophistication. We also (cid:133)nd that high levels of sophistication does not improve risk sharing when potential risk sharing opportunities are low, which indicates that geographical location is an important determinant of risk sharing. When we compare the e⁄ects of traditional, behavioral, and geographical factors on state-level risk sharing, we (cid:133)nd that the behavioral e⁄ects are the strongest. These results are robust and cannotbeexplainedbypotentialendogeneityofoursophisticationmeasures,heterogeneityinindustry composition (e.g., agriculture, mining, or manufacturing based state economy), size of the state economy, variation in people(cid:146)s age across states, regional di⁄erences in risk sharing, or the anomalous behavior of a handful of states. The rest of the paper is organized as follows. In the next section, we present the risk-sharing estimatesforindividualU.S.states. InSections3to5,wepresentourmainempiricalresults,wherewe examine the in(cid:135)uence of traditional, behavioral, and geographical factors on state-level risk sharing, respectively. We present robustness test results in Section 6 and conclude in Section 7 with a brief discussion. Additional details about the data sources and estimation methods are presented in a detailed appendix. 2. State-Level Risk Sharing Estimates 2.1 Risk Sharing: The Basic Idea In our paper, risk sharing refers to state-level income smoothing using (cid:133)nancial markets. The income of a U.S. state is the sum of its output and the additional income it receives from various other sources. The output or the product of a state would be in(cid:135)uenced by idiosyncratic shocks, but state 5

Behavioral Biases and the Macro-Economy income can be insulated from those output (cid:135)uctuations through indirect channels such as (cid:133)nancial markets. In an ideal scenario, U.S. states could reduce income risk by directly trading claims on state income in macro-markets (e.g., Shiller (1993), Shiller (2003)). But in the absence of directly traded claims on state income, an indirect mechanism like (cid:133)nancial markets is an important income smoothing device available to a state. If a state utilizes (cid:133)nancial assets e⁄ectively, the variance of the growth rate of state income would be lower than the variance of the growth rate of its output. We compare these two variances to quantify the level of income smoothing or risk-sharing in a state. 2.2 Risk Sharing Estimation Method WeusetheAthanasoulisandVanWincoop(2001)(hereafterAVW)methodologytoestimatethelevel of risk sharing that can be achieved using (cid:133)nancial assets.7 As in AVW, we focus on idiosyncratic (or state-speci(cid:133)c) income risk. AVW quantify the level of risk sharing that can be attributed to (cid:133)nancial marketsbycomparingtheriskinessorthestandarddeviationsofthegrowthratesoftherelativegross state product (GSP) and relative state income (SI).8 The relative growth rates of the GSP and the SI for each state i between years t and t+1 are computed using the following growth rate di⁄erential: grel = g g . (1) i;t;t+1 i;t;t+1 t;t+1 (cid:0) Here, g is the per capita growth rate of either the GSP or the SI of state i between years t and i;t;t+1 t+1, while g is the per capita growth rate of either the U.S. GDP or the aggregate U.S. income.9 t;t+1 The relative GSP provides a measure of idiosyncratic or state-speci(cid:133)c income growth rate before risk sharing, while relative SI re(cid:135)ects the state-speci(cid:133)c income growth rate after risk sharing. We also de(cid:133)ne a residual growth rate measure, which represents the unexpected or the unpredictable component of the corresponding raw growth rate measure. Speci(cid:133)cally, we estimate the following regression to measure the residual growth rates of relative GSP and relative SI for state i: grel = z (cid:21)+u . (2) i;t;t+1 i;t i;t;t+1 7Previous studies have proposed correlation- and regression-based methods to measure risk sharing (e.g., Crucini (1999), Hess and Shin (2000), Asdrubali, Sorensen, and Yosha (1996), Sorensen, Wu, Yosha, and Zhu (2007)). To facilitate direct comparison with the most recent evidence, we use the risk sharing measure used in Athanasoulis and Van Wincoop (2001), which provides conservative estimates of state-level risk sharing. Nevertheless, all our results are verysimilarwhenweusethecorrelation-basedrisksharingmeasuresbecausethetworisksharingmeasuresarestrongly correlated(thecross-sectionalcorrelation=0.80). SectionA.8oftheappendixde(cid:133)nesthecorrelation-basedrisksharing measure and brie(cid:135)y discusses the results obtained using this alternative measure. 8Stateincomeisthetotalpretaxincomegeneratedbystateresidents,andstateandlocalgovernments,butdoesnot capture any federal intervention in the form of federal taxes and transfers. Because SI includes net asset income, it has been used to estimate the level of risk sharing achieved through the (cid:133)nancial markets channel. For additional details on the construction of the SI measure, see the appendix in Asdrubali, Sorensen, and Yosha (1996). 9Speci(cid:133)cally, g = ln(gsp ) ln(gsp ), or g = ln(si ) ln(si ): gsp is the per capita GSP of i;t;t+1 i;t+1 i;t i;t;t+1 i;t+1 i;t i;t (cid:0) (cid:0) state i in year t. 6

Behavioral Biases and the Macro-Economy Here, z isasetofcontrolvariablesforstateide(cid:133)nedattimetandu istheresidualgrowthrate i;t i;t;t+1 for state i de(cid:133)ned over the interval between years t and t+1. (cid:21) is a vector of coe¢ cient estimates.10 Motivated by the results in Barro and Sala-i-Martin (1991, 1992) and Athanasoulis and Van Wincoop (2001), our set of control variables includes the lagged value of the relative GSP (or SI) growth rate, the logarithm of the initial per-capita GSP (or SI), and the (cid:133)ve-year lagged population growth rate for the state.11 Last, we use these growth rate measures to obtain the risk sharing (RS) estimate: (cid:27) gRS RS = 1 . (3) (cid:0) (cid:27) g Here, (cid:27) and (cid:27) are the standard deviations of the income growth before risk sharing and after risk g gRS sharing, respectively. The RS measure takes two forms. The unconditional RS measure compares the standard deviations of the growth rates of relative GSP and relative SI. The conditional RS measure comparesthestandarddeviationsoftheresidualgrowthratesofrelativeGSPandrelativeSIobtained using equation (2). Theoretically, the RS measure must lie between zero and one. Under full risk sharing, income risk is completely eliminated, (cid:27) is zero, and the RS measure equals one. And in the absence of gRS any risk sharing, there is no reduction in the income risk, (cid:27) is equal to (cid:27) , and the RS measure gRS g equals zero. In practice, however, the RS measure could be negative due to measurement error in the state-level income data.12 2.3 Income Data and Summary Statistics We use in(cid:135)ation adjusted growth rates of per capita GSP and SI to calculate income growth rates beforeandafterrisksharing.13 Thegrossdomesticproduct(GDP)de(cid:135)atorobtainedfromtheBureau of Economic Analysis (BEA) is used to measure in(cid:135)ation. The state-level population data are from the Current Population Survey (CPS). The annual U.S. GDP and the GSP for individual states are also from the BEA. These data are available for the 1963 to 2004 period. The state income data are not provided by the BEA and they are available only for the 1963 to 1999 period. Table 1, Panel A reports the summary statistics for various annual income growth rate measures. The mean growth rates of GDP and GSP are comparable (2.2% and 2.3%, respectively). But the 10There is no intercept term in equation (2) because the relative growth rate of GSP is derived by subtracting the GDP growth rate from the raw growth rate of GSP. See AVW for more details on the regression speci(cid:133)cation. 11Athanasoulis and Van Wincoop (2001) show that the risk sharing measures are not sensitive to the choice of the speci(cid:133)c control variables. Thus, we only consider control variables for which data are easily available for the 1963 to 2004 period. 12See Appendix A.1 for a discussion on how measurement error could generate negative risk sharing estimates. Also, see Asdrubali, Sorensen, and Yosha (1996, Page 1097) or Sorensen and Yosha (2000). 13To minimize the impact of time dependence, we follow the AVW method, and use non-overlapping observations to obtain the growth rate measures used to compute RS. 7

Behavioral Biases and the Macro-Economy DE OR 0.5 NH NM WA 0.4 CO NY PA CA HI MT OH VA CT AL LA NJ OK 0.3 DC MN MO TX NC TN GA AK IL KS MD UT ID MS NV SC IN WY 0.2 MI AZ MA VT FL IA NE 0.1 AR ND KY ME SD WV 0.0 RI WI 0.1 SR lanoitidnocnU Figure 1: State-level unconditional risk sharing estimates (Time period: 1963-1999). averagestandarddeviationoftheGSPgrowthrate(=3.7%)isconsiderablyhigherthanthestandard deviation of the GDP growth rate (= 2.0%). This evidence suggests that there exists considerable scope for improving risk sharing across the U.S. states. We also (cid:133)nd that the standard deviations of SI and relative SI are lower than the standard deviations of GSP and relative GSP, respectively. These estimates indicate that (cid:133)nancial assets are able to facilitate state-level risk sharing. Examining the correlations among the growth rate measures, we (cid:133)nd that there is considerable heterogeneity in the income growth rates across the U.S. states. The mean correlation between the GDP and the GSP growth rates is 0.509, while the mean correlation between the GDP and the SI growth rates is 0.551. The mean correlations between GSP and SI are also positive and above 0.70, but the estimates are not extremely high. These correlation estimates indicate that the level of risk sharing across the U.S. states is likely to exhibit considerable cross-sectional heterogeneity. 2.4 Risk Sharing Estimates for Individual U.S. States To better illustrate the observed heterogeneity in the state-level risk sharing measures, we use the income growth data and obtain conditional and unconditional risk sharing estimates for individual U.S. states. But (cid:133)rst, in Table 2, Panel A, we report the aggregate level of risk sharing across all U.S. 8

Behavioral Biases and the Macro-Economy A. Oregon 0.07 0.05 0.03 0.01 0.01 0.03 0.05 0.07 0.09 5691 7691 9691 1791 3791 5791 7791 9791 1891 3891 5891 7891 9891 1991 3991 5991 7991 9991 Relative GSP Growth Relative SI Growth B. Kentucky 0.03 0.02 0.01 0.00 0.01 0.02 0.03 0.04 5691 7691 9691 1791 3791 5791 7791 9791 1891 3891 5891 7891 9891 1991 3991 5991 7991 9991 Relative GSP Growth Relative SI Growth C. Connecticut 0.04 0.03 0.02 0.01 0.00 0.01 0.02 0.03 0.04 5691 7691 9691 1791 3791 5791 7791 9791 1891 3891 5891 7891 9891 1991 3991 5991 7991 9991 Relative SI Growth Relative MVP Return Figure 2: Panels A and B provide examples of income smoothing in a high and a low risk sharing state, respectively. In Panel C, for an arbitrarily chosen state, we illustrate the level of smoothing that can be potentially attained using (cid:133)nancial assets. 9

Behavioral Biases and the Macro-Economy states.14 Our aggregate unconditional RS estimate of 26% and the aggregate conditional RS estimate of 23% measured over the 1963 to 1999 period are very similar to the AVW estimates obtained for the 1963 to 1999 period. In Panel B of Table 2, we report the RS estimates for the individual U.S. states. For easier visualization, we also plot these results in Figure 1. The graphical evidence indicates that there is a rich cross-sectional variation in the state-level estimates of risk sharing. States like South Dakota (RS = 0:01) and Vermont (RS = 0:14) achieve very low levels of risk sharing, while states like California (RS = 0.39) and New York (RS = 0.45) are able to substantially reduce their exposures to idiosyncratic income risk. When we examine the time-series of the GSP and the SI growth rates for individual states, the income smoothing e⁄ect is evident more clearly. In Figure 2, Panels A and B, we plot the GSP and SI growth rates for a state with a very high level of risk sharing (Oregon) and a state with a very low level of risk sharing (Kentucky). These time series plots indicate that the ability of states to smooth income using (cid:133)nancial assets varies signi(cid:133)cantly across the two risk sharing extremes. The heterogeneity in a state(cid:146)s ability to engage in risk sharing estimates raises the natural question: What factors can explain these cross-sectional di⁄erences? In the rest of the paper, we identify the key determinants of the cross-sectional variation in risk sharing by examining the e⁄ects of traditional, behavioral, and geographical factors. 3. Traditional Determinants of Risk Sharing In our (cid:133)rst set of formal tests, we examine whether traditional factors such as the size of stock market participation and borrowing or credit constraints in(cid:135)uence the ability of individuals to engage in risk sharing. We also examine whether the industry composition of a state in(cid:135)uences its risk sharing ability. Whilepreviousstudiesconjecturethatthesetraditionalfactorscoulddeterminetheaggregate RS levels, we provide new results on the cross-sectional relation between the traditional factors and the state-level risk sharing. 3.1 Risk Sharing Regression Model Our empirical analysis mainly focuses on state-level, cross-sectional risk sharing regressions. In these regressions, the dependent variable is either the unconditional or the conditional risk sharing measure (seeTable2,PanelB).Thesetofindependentvariablevariesanddependsuponthespeci(cid:133)chypothesis 14AVW calculate the aggregate RS measure by combining the data for all states. For example, to compute the aggregate unconditional RS, they (cid:133)rst stack the observations of the growth rates of relative GSP and relative SI for each state in two vectors. Then, they estimate the standard deviation of these two vectors to obtain the aggregate RS measure. 10

Behavioral Biases and the Macro-Economy to be tested. Table 3 reports the basic statistics and correlations for the main variables used in the empirical analysis. We estimate the cross-sectional regressions using ordinary least squares (OLS) and correct the standard errors for heteroskedasticity. In particular, we estimate the following regression: y y = (x x)(cid:12)+" . (4) i i i (cid:0) (cid:0) In this equation, y is either the unconditional or conditional RS measure for state i and y is the i cross-sectional average of the state-level RS measures. x is a vector of explanatory variables and x is i the cross-sectional average vector corresponding to x . (cid:12) is the vector of slope coe¢ cient estimates. i The random variable " is a zero-mean error term, which is assumed to be independent across states. i Its variance is (cid:27)2, which di⁄ers across the U.S. states. We assume that " is heteroskedastic to ensure i i that our inference is not contaminated by unobserved state-speci(cid:133)c shocks that are absorbed by the error term. The dependent variable in our risk sharing regression is a generated variable that depends on the second moments of income growth rates. It is, therefore, measured with error. Fortunately, potential measurement error in the dependent variable does not result in inconsistent or biased OLS estimates (Green (2003), Chapter 5.6). Both the dependent and independent variables in equation (4) are mean-free and, thus, our regression results do not include the estimates for the intercept.15 To allow for comparisons of coe¢ cient estimates within and across regression speci(cid:133)cations, we standardize both the dependent and the independent variables (mean is set to zero and the standard deviation is one). We also ensure that multi-collinearity does not a⁄ect our estimates. Since we have only 51 state-level observations (including Washington DC), we try to develop parsimonious regression speci(cid:133)cations by creating indices that combine multiple variables. Particularly, we de(cid:133)ne a sophistication index to capture the combined e⁄ects of all behavioral and cognitive abilities proxies. 3.2 E⁄ect of Greater Stock Market Participation If(cid:133)nancialassetshavethepotentialtofacilitaterisksharing, oneofthemainreasonswhysomestates achieve low levels of risk sharing might be related to the limited stock market participation rate in the state. To examine the relation between the state-level market participation rate and risk sharing, we consider a stock market participation proxy. Speci(cid:133)cally, following Brown, Ivkovi·c, Smith, and Weisbenner (2008), we use an annual IRS data set for the 1998 to 2005 period, which reports the 15Ofcourse, the slope coe¢ cient estimates do not change when we do not demean the variables and add an intercept term in the regression speci(cid:133)cation. 11

Behavioral Biases and the Macro-Economy percentage of tax returns in each state that contains dividend income. We compute the average of this percentage over the 1998 to 2005 period and use it as a proxy for the state-level stock market participation rate. The estimation results are reported in Table 4, Panel A. In the univariate speci(cid:133)cation, we (cid:133)nd that there is a positive but insigni(cid:133)cant relation between state-level RS and stock market participation (see columns (1) and (2)). For example, when we use the unconditional RS as the dependent variable, the estimate on the stock market participation proxy is 0.11 and its t-statistic is only 0.97. Although this coe¢ cient estimate is not statistically signi(cid:133)cant, the evidence suggests that high market participation levels might be associated with high levels of risk sharing. 3.3 Do Weaker Borrowing Constraints Improve Risk Sharing? To ensure that the stock market participation proxy is not simply capturing the ability of some investors to (cid:133)nance their investments through borrowing, we introduce a proxy for borrowing constraints in the risk sharing regression speci(cid:133)cation. We measure the severity of borrowing or liquidity constraints using the housing collateral ratio (HY) proposed in Lustig and Van Nieuwerburgh (2008). The state-level HY variable is de(cid:133)ned as the ratio of state-level housing wealth, which can serve as collateral for loans, to the state-level human wealth. We summarize the method used to estimate the state-level HY in Section A.2 of the appendix. We calculate the HY time-series for each state and use its time-series average in the risk sharing regressions. The regression results indicate that when HY is the only independent variable in the regression speci(cid:133)cation, it has a signi(cid:133)cantly positive coe¢ cient estimate (see columns (3) and (4)). This evidence is consistent with the evidence in Lustig and Van Nieuwerburgh (2008), who use data for U.S. metropolitan areas to demonstrate that borrowing constraints a⁄ect risk sharing.16 Our (cid:133)nding that state-level HY can also explain the cross-sectional variation in state-level RS is new, although it is not totally surprising. 3.4 Does the Size and Intensity of Market Participation Matter? To better understand the relative roles of market participation and borrowing constraints, we investigate whether the relative size of participation in(cid:135)uences state-level risk sharing. We measure the relative size of a state(cid:146)s stock market exposure using the ratio of the state-level stock market wealth and the aggregate U.S. stock market wealth (Wealth Ratio).17 The wealth ratio for a state is computed using the state-level stock market wealth series from Case, Shiller and Quigley (2001). We 16PradoandSorensen(2007)alsoemphasizetheimportanceofliquidityconstraints. They(cid:133)ndthatcreditconstraints a⁄ect the state-level marginal propensity to consume out of income. 17We also consider the state population as an alternative de(cid:135)ator for the state-level stock market wealth. We obtain very similar results with this per capita stock market wealth measure. 12

Behavioral Biases and the Macro-Economy use the wealth ratio as a rough proxy for the sophistication level of market participants, under the assumption that sophisticated investors would allocate a larger proportion of their wealth to (cid:133)nancial assets. TheestimationresultsarereportedinTable4, PanelA(columns(5)and(6)). We(cid:133)ndthatthere is a positive and statistically signi(cid:133)cant relation between the relative size of participation (i.e., the wealthratio)andthestate-levelRS.However, thesigni(cid:133)canceofthisvariableweakensinthepresence of HY (see columns (7) and (8)). Somewhat surprisingly, we (cid:133)nd that the coe¢ cient estimate for the stock market participation proxy turns negative, although its estimate is statistically insigni(cid:133)cant. We further quantify the importance of stock market participation for state-level risk sharing by focusing on the intensity of stock market participation. We create a high participation dummy variablethatissettooneforstatesinwhichtheparticipationrateisabovethemedian. Theregression estimates with the high stock market participation dummy are reported in Table 4, Panel B. The results in columns (1) and (2) indicate that the high participation dummy has a positive but statistically insigni(cid:133)cant coe¢ cient estimate. However, when we interact the high participation dummywiththewealthratiovariable,we(cid:133)ndthattheinteractiontermhasapositiveandstatistically signi(cid:133)cant coe¢ cient estimate. In particular, the estimation results reported in columns (3) and (4) indicate that the interaction term remains signi(cid:133)cant even in the presence of HY. The more parsimonious speci(cid:133)cations in columns (5) to (8) yield very similar and somewhat stronger results. This evidence suggests that risk sharing levels are higher in states in which investors allocate a larger proportion of their total wealth to stock investments, perhaps due to their greater (cid:133)nancial sophistication. Interestingly, when we account for the e⁄ects of HY and relative wealth-high participation interaction, the market participation proxy has a signi(cid:133)cantly negative estimate. Thus, in the presence of a rough sophistication proxy, the coe¢ cient estimate of the stock market participation variable is likely to re(cid:135)ect the adverse e⁄ects of unsophisticated participation. Examining the economic signi(cid:133)cance of the estimates of the traditional factors, we (cid:133)nd that HY has the strongest in(cid:135)uence on state-level risk sharing. For instance, in column (5) of Panel B, the coe¢ cient estimate of HY is 0.39. In economic terms, this estimate indicates that when the borrowing constraints weaken by one standard deviation, the risk sharing level increases by 0.39 standard deviation or 0:39 0:14 = 0:055: Relative to the mean state-level risk sharing estimate of (cid:3) 0.26 (see Table 3, row 1), there is a 20.22% increase in the level of risk sharing. The new RS level is 0.32, which re(cid:135)ects an economically signi(cid:133)cant jump in the level of RS. 3.5 Industry Di⁄erences Across States Last, we examine the possibility that the heterogeneity in state-level risk sharing estimates re(cid:135)ect di⁄erences in industry composition across states. It is likely that states such as California and 13

Behavioral Biases and the Macro-Economy New York with more diversi(cid:133)ed economies would be able to withstand income shocks better than states with more concentrated economies (e.g., the Dakotas or Alaska). Certain industries such as agriculture and manufacturing are more sensitive to local economic shocks (Asdrubali, Sorensen and Yosha (1996)) than industries such as mining. Alternatively, states with greater ability for risk sharing would achieve greater industrial specialization and could have a more concentrated economy (Kalemli-Ozcan, Sorensen, and Yosha (2003)). We examine the potential link between industry composition and risk sharing following the Asdrubali, Sorensen and Yosha (1996) approach. Speci(cid:133)cally, we examine whether the GSP weights of the agricultural, mining and manufacturing sectors are related to the level of income risk sharing in a state. These speci(cid:133)c industries are also used in Kalemli-Ozcan, Sorensen and Yosha (2003), who examine the determinants of regional specialization. In addition, we measure the industry concentration of each state using a Her(cid:133)ndahl index. Using data for the 1966 to 1997 period, for each state, we compute the proportion of GSP that a state derives from ten broad industry categories.18 We use these industry weights to compute the state-level Her(cid:133)ndahl index. When we consider only the industry concentration measure in the regression speci(cid:133)cation, it has a positive but insigni(cid:133)cant coe¢ cient estimate (see Table 4, Panel C, columns (1) and (2)). This evidenceindicatesthatdi⁄erencesinindustryconcentrationcouldin(cid:135)uencethelevelofrisksharing.19 When we include the three industry weights in the risk sharing regression speci(cid:133)cation, consistent with the previous evidence, we (cid:133)nd that states with an agriculture-based economies have lower levels of risk sharing (see columns (3) and (4)). However, when we include the stock market participation, stockmarketwealthratio,andtheHYmeasuresintheregressionspeci(cid:133)cation,neitheroftheindustry measures is signi(cid:133)cant. This evidence indicates that the relation between industry composition and risk sharing is likely to re(cid:135)ect the heterogeneity in stock market participation rates, stock market wealth, and borrowing constraints (as captured by HY) across the states. Collectively, the results summarized in Table 4 indicate that higher stock market participation ratesarenotsu¢ cienttoimprovestate-levelrisksharing. Thenegativerelationbetweenparticipation andrisksharingsuggeststhateithertheinvestmentobjectivesofU.S.investorsareimproperlyaligned with the goal of risk sharing or that stock market participants(cid:146)sub-optimal investment decisions lead to low levels of risk sharing.20 This evidence is consistent with our conjecture that what is really 18Thetenindustriesareagriculture(includingforestryand(cid:133)shing),mining,construction, manufacturing,transportation and utilities, retail trade, wholesale trade, FIRE ((cid:133)nance, insurance and real estate), services, and government. The GSP data are obtained from http://www.bea.gov/regional/gsp. 19To account for the possibility that the initial industry endowment rather than the average industry concentration during the sample period might in(cid:135)uence the state(cid:146)s ability to enagage in risk sharing, we measure the industry concentration at the beginning of our sample period using data for the 1963 to 1965 period. We (cid:133)nd that the coe¢ cient estimates for the industry concentration measure obtained using 1963-65 data are even weaker. 20Another alternative interpretation of the negative participation-risk sharing relation is that, after we include a proxy for sophisticated participation, our stock participation proxy de(cid:133)ned using dividend income reported in tax returns re(cid:135)ects the participation rates of investors who prefer dividends. Because the clienteles of dividend paying 14

Behavioral Biases and the Macro-Economy needed for improving state-level risk sharing is sophisticated participation, where individuals invest broadly and signi(cid:133)cantly in the stock market. 4. Behavioral Biases and Risk Sharing Inoursecondsetoftests,weexaminewhetherfrictionsinducedbyinvestors(cid:146)behavioralbiasesprevent U.S. states from achieving high levels of risk sharing. 4.1 Main Testable Hypotheses We attempt to characterize the relation between the cognitive abilities and behavioral biases of individual investors and state-level risk sharing using two distinct hypotheses. The (cid:133)rst hypothesis focuses on the direct relation between behavioral biases and state-level risk sharing. Speci(cid:133)cally, we posit that: Hypothesis 1: Risk sharing levels are higher in states in which investors have higher cognitive abilities, exhibit weaker behavioral biases, and possess greater overall (cid:133)nancial sophistication. In our second hypothesis, we examine whether behavioral biases also in(cid:135)uence the relation between geographical location and the achieved levels of risk sharing. Hypothesis 2: Risk sharing opportunities vary geographically across the U.S. states but higher state-level risk sharing opportunities can be exploited only when state investors are (cid:133)nancially sophisticated. We test the (cid:133)rst hypothesis in the current section and provide empirical results to support the second hypothesis in Section 5. 4.2 Positive E⁄ects of Cognitive Abilities We begin by investigating whether higher levels of cognitive abilities of state investors are associated with higher levels of state-level risk sharing. This test is motivated by recent research in behavioral economics(e.g.,Frederick(2005),Benjamin,Brown,andShapiro(2006),Dohmen,Falk,Hu⁄man,and Sunde(2007)),which(cid:133)ndsthatlowerlevelsofcognitiveabilitiesareassociatedwithmore(cid:147)anomalous(cid:148) preferences (e.g., greater level of impatience and stronger short-stakes risk aversion) and stronger stocksarerelativelylesssophisticated(e.g.,older,low-incomeinvestors;seeGrahamandKumar(2006)),highermarket participation rates need not necessarily improve risk sharing. When we do not account for sophisticated participation, our participation proxy captures both sophisticated and unsophisticated participation. As a result, we observe a weak positive relation between participation and state-level risk sharing. 15

Behavioral Biases and the Macro-Economy behavioralbiases. Ifinvestors(cid:146)cognitiveabilitiesarenegativelyassociatedwiththeirbehavioralbiases, the investment decisions of low ability investors might not be aligned with the goal of minimizing total risk, which could in turn induce low levels of risk sharing. Since it is extremely di¢ cult to obtain direct measures of the cognitive abilities of stock market participants within each of the U.S. states, we adopt the imputation procedure to obtain state-level estimatesofinvestors(cid:146)cognitiveabilities. Speci(cid:133)cally, weusetheempiricalmodelofcognitiveabilities (CAB) estimated in Korniotis and Kumar (2008). The dependent variable in the model is a direct measureofcognitiveabilities(theaverageofverbal,quantitativeandmemorytestscores)andagroup ofdemographicvariables, whichhavebeenidenti(cid:133)edbythepsychologyliteratureasthekeycorrelates ofcognitiveabilities, aretheindependentvariables. Theempiricalmodelindicatesthatinvestorswith higher cognitive abilities are younger, wealthier, more educated, and more socially connected.21 We use the demographic characteristics of a sample of brokerage investors distributed across the U.S. to obtain the imputed CAB for all investors in that sample.22 The state-level CAB estimate is the equal-weighted average of imputed CAB estimates of all brokerage investors located in a state.23 In our sample, investors in states like Kansas, Colorado, Missouri, Virginia, and Connecticut have high CAB estimates, while investors in states such as Arkansas, Maine, New Mexico, Florida, and South Carolina have low imputed CAB. We do not use the state-level Census data directly to obtain imputed cognitive abilities for individual states because the Census data provide the characteristics of both market participants and non-participants. Direct measures of state-level IQ have a similar disadvantage. Because we want to quantify the CAB of only the market participants, the use of brokerage data seems most appropriate. We re-estimate several speci(cid:133)cations of the risk sharing regression after adding the state-level CABmeasuretothesetoftheindependentvariables,whichalsocontainsthetraditionaldeterminants of state-level risk sharing. The estimation results are reported in Table 5 (columns (1) to (4)). In univariatespeci(cid:133)cations, we(cid:133)ndthatstateswithhighcognitiveabilityinvestorsachievehighlevelsof risk sharing. For example, in column (2), the coe¢ cient estimate of CAB is 0.25 and its t-statistic is 2.24. Even when we include the stock market participation proxy, the HY, and the wealth ratio-high participation interaction term in the regression speci(cid:133)cation, the relation between cognitive abilities and risk sharing remains strong (estimate = 0.25, t-statistic = 2.77).24 Consistent with our (cid:133)rst hypothesis, these results indicate that the investment decisions of in- 21See Section A.3 of the appendix for details about the imputation method and the empirical model of cognitive abilities used to obtain the state-level cognitive abilities estimates. 22The brokerage data set is described in Appendix A.4. 23The results are similar when we de(cid:133)ne a value-weighted state-level CAB measure, where portfolio size is used to obtain the weights. 24The results in Table 4 indicate that among the traditional determinants of risk sharing, the variables that are consistentlystatisticallysigni(cid:133)cantarethestockparticipationproxy,theHY,andtherelativewealth-highparticipation interactionterm. Forparsimony,intherestofthepaper,thesetoftraditionalfactorsincludesonlythesethreevariables. 16

Behavioral Biases and the Macro-Economy vestors with higher cognitive abilities are more closely aligned with the goal of risk reduction, which eventuallyleadtohigherlevelsofrisksharing. Sinceweuseimputedvaluesofinvestors(cid:146)cognitiveabilities instead of direct measures of their cognitive abilities, a more conservative interpretation of these (cid:133)ndings is that states in which investors are younger, wealthier, better educated, and more strongly socially connected achieve higher levels of risk sharing, perhaps due to their weaker behavioral biases. 4.3 Adverse E⁄ects of Behavioral Biases To gather additional support for the (cid:133)rst hypothesis, we examine the quality of investment decisions ofindividualinvestorsdirectly. Usingtheinvestmentdecisionsofbrokerageinvestors,weobtainstatelevel estimates for the main behavioral biases identi(cid:133)ed in the recent behavioral (cid:133)nance literature. Likethestate-levelcognitiveabilitiesmeasure, weobtainthestate-levelestimatesofbehavioralbiases by computing an equal-weighted average of the behavioral bias measures of all investors within the state. Speci(cid:133)cally, for each state, we obtain estimates for the average portfolio turnover (an overcon(cid:133)dence proxy), the average percentage of local owners divided by our state-level participation proxy (participation-adjusted local bias proxy)25, the portfolio weights in foreign stocks (home bias or diversi(cid:133)cation preference proxy), proportion of all trades that are in stocks with lottery-type features (gambling or speculation proxy)26, and the normalized portfolio variance, which is the ratio of portfolio variance and the average correlation of stocks in the portfolio (portfolio concentration proxy).27 We also consider the state-level cognitive abilities proxy. Together, these measures capture investor sophistication and serve as proxies for various behavioral biases such as overcon(cid:133)dence (e.g., Odean (1999),BarberandOdean(2000)),localbias(e.g.,Huberman(2001),GrinblattandKeloharju(2001), Ivkovic and Weisbenner (2005), Massa and Simonov (2006)), home bias (e.g., Lewis (1999)), gambling or speculation (e.g., Kumar (2008)), and under-diversi(cid:133)cation (e.g., Barber and Odean (2000), Goetzmann and Kumar (2008)). As before, we estimate the risk sharing regressions using either the unconditional or the conditional RS measure as the dependent variable. The set of independent variables contain the behavioral bias proxies, the cognitive abilities proxy, and several control variables, including the traditional determinants of risk sharing. The results are presented in Table 5 (columns (5) to (8)). 25The percentage of local owners for a stock is de(cid:133)ned as the proportion of all brokerage investors who are located in the same state in which the (cid:133)rm is headquartered. Because a state with a high level of stock market participation willmechanicallyhaveahighpercentageoflocalowners,wede(cid:135)atethispercentagewiththestockmarketparticipation proxy. The ratio re(cid:135)ects the level of local bias, conditional upon participation. 26Lottery-typestocksarelow-pricedstockswithhighidiosyncraticvolatilityandhighidiosyncraticskewness(Kumar (2008)). 27We also considered a state-level measure of the disposition e⁄ect (investors(cid:146)reluctance to sell stock investments with lossesand a strong propensity to sellpositionswith gains; e.g.,Shefrin and Statman (1984),Odean (1998b)). We (cid:133)nd that it is not signi(cid:133)cantly related to state-level risk sharing. 17

Behavioral Biases and the Macro-Economy The evidence indicates that risk sharing levels are higher when investors follow the normative prescriptions of portfolio theory. Across all speci(cid:133)cations, we (cid:133)nd that states in which investors do not trade very actively and hold relatively better diversi(cid:133)ed portfolios (i.e., hold less concentrated portfoliosandincludeforeignstocks)achievehigherlevelsofrisksharing. Inaddition,thesigni(cid:133)cantly positive coe¢ cient of the cognitive abilities proxy remains signi(cid:133)cant in these speci(cid:133)cations. We also (cid:133)nd that the estimates for the lottery preference proxy are negative, although their statistical signi(cid:133)cance is weak. This evidence indicates that a strong preference for speculative stocks that provide cheap bets but are risky is likely to reduce the level of risk sharing. Interestingly, a stronger preference for local stocks is associated with higher levels of risk sharing. This (cid:133)nding is consistent with the recent evidence from the local bias literature, which supports the conjecture that local bias is induced by better information about local (cid:133)rms rather than pure familiarity (e.g., Ivkovi·c and Weisbenner (2005), Massa and Simonov (2006)). Because high local bias is associated with superior performance, the local bias measure can also be interpreted as another proxy for investor sophistication, which we (cid:133)nd to be positively related to risk sharing. Taken together, the regression results in Table 5 provide strong support for our (cid:133)rst hypothesis. They indicate that the sensitivity to state-speci(cid:133)c income shocks is reduced considerably when investors within a state follow the normative prescriptions of portfolio theory. Somewhat surprisingly, we also (cid:133)nd that informed deviations from the normative prescriptions of portfolio theory (i.e., information-induced local bias) facilitate risk sharing. 4.4 Quantifying the Behavioral E⁄ects Using a Sophistication Index In this section, we attempt to quantify the combined e⁄ects of all behavioral bias and cognitive abilities proxies on risk sharing. We also investigate whether the behavioral e⁄ects are stronger than the traditional determinants of risk sharing (i.e., market participation rate, size of participation, and borrowing constraints). Because we have a limited number of state-level observations (only 51), we aggregate the behavioral bias and cognitive abilities proxies into one composite sophistication index and choose parsimonious risk sharing regression speci(cid:133)cations. We construct the sophistication index as follows. First, for each behavioral bias proxy (e.g., portfolio turnover), we create a dummy variable. The dummy variable takes the value of one for states in which the bias proxy is above the qth percentile (q = 25, 50, or 75). We then add the dummy variables corresponding to the measures that are positively related to RS (cognitive ability, local preference, and percentage of foreign stock) and subtract the dummy variables for the measures thatarenegativelyrelatedtoRS(portfolioturnover,portfolioconcentration,andlotterypreferences). The resulting total is divided by six. This linear combination of the behavioral bias proxies is our sophistication index. For robustness, we de(cid:133)ne a continuous sophistication index using standardized 18

Behavioral Biases and the Macro-Economy 0.33 0.28 0.23 0.18 0.13 0.08 0.03 0.02 0.33 0.17 0.00 0.17 0.33 Sophistication Index SR egarevA Unconditional RS Conditional RS Figure 3: Investor sophistication and state-level risk sharing. (mean = 0, std. dev. = 1) bias measures instead of the six behavioral bias dummy variables. We also de(cid:133)ne an (cid:147)unsophistication(cid:148)index, which is computed just like the sophistication index. In this instance, however, the dummy variable associated with a behavioral bias proxy takes the value of one if the state-level bias proxy is below the 25th percentile. Asexpected, we(cid:133)ndapositiverelationbetweenstate-levelinvestorsophisticationandstate-level risk sharing. This positive relation is evident in Figure 3. For q = 75, the (cid:133)gure shows the average level of RS for the distinct values of the sophistication index. Consistent with our previous evidence, we(cid:133)ndthatamongstateswithlowlevelsofsophistication(indexvalue= 0.33or 0.17),theaverage (cid:0) (cid:0) RS is 0.121. But, for states with higher levels of sophistication (index 0), the average RS estimate (cid:21) is 0.308. In economic terms, a jump in the sophistication level of investors from the low to the high value of the sophistication index corresponds to a 154% increase in the level of risk sharing. We also re-estimate the risk sharing regressions, where the sophistication index is the main independent variable and the traditional determinants of risk sharing serve as control variables. The estimation results reported in Table 6, Panel A show that the sophistication index is a signi(cid:133)cant determinant of risk sharing across all speci(cid:133)cations. Further, the higher the value of q, the higher is the estimate and the t-statistic for the sophistication index. The monotonic increase in the estimate and the t-statistic con(cid:133)rms our conjecture that states with the most sophisticated investors are able to reduce the sensitivity to state-speci(cid:133)c idiosyncratic income risk most e⁄ectively. We (cid:133)nd similar results with the continuous sophistication index. When we compare the estimate for the sophistication index to the estimates for the traditional 19

Behavioral Biases and the Macro-Economy determinants of risk sharing, we (cid:133)nd that the coe¢ cient estimate of the sophistication index is comparable to the estimates of strong traditional factors such as HY. For instance, in column (6), the sophistication index has a coe¢ cient estimate of 0.56 (t-statistic = 5.81) while HY has an estimate of 0.42 (t-statistic = 4.79). This evidence indicates that both traditional and behavioral factors are important determinants of state-level risk sharing. 4.5 State-Level Education: An Alternative Sophistication Proxy For robustness, we consider the average education level of individuals in a state as an alternative proxy for investor sophistication. This variable is de(cid:133)ned as the proportion of residents in a state with a Bachelor(cid:146)s or higher educational degree. The education data are obtained from the 1990 U.S. Census. We (cid:133)nd that the correlation between the education measure and our sophistication index is 0.40. Thisestimateindicatesthatoursophisticationindexestimatedusingthebrokeragedataisreasonable because it has the expected positive correlation with an aggregate state-level measure obtained from a completely di⁄erent source. We also re-estimate the risk sharing cross-sectional regressions with the education measure as an additional independent variable and report the results in Panel B of Table 6. We (cid:133)nd that, like the estimates for the sophistication index, education has positive coe¢ cient estimates. However, their statistical signi(cid:133)cance is weak (see columns (1)-(4)). For instance, in column (2), the education variable has a coe¢ cient estimate of 0.18 and a t-statistic of 1.71. When we include both the sophistication index and the education variable in the regression speci(cid:133)cation, the sophistication index has a signi(cid:133)cantly positive coe¢ cient estimate, while the estimates for education become statistically insigni(cid:133)cant (see columns (5) and (6)). Theserobustnesscheckresultsindicatethatoursophisticationindex,whichcapturesthe(cid:133)nancial sophistication of only the stock market investors within a state, is more strongly associated with the state-level risk sharing than the education variable, which re(cid:135)ects the sophistication level of both market participants and non-participants. Nonetheless, the weakly positive estimate for education in the risk sharing regression is comforting. This evidence also highlights the strengths of the brokerage data set, which we use to measure the quality of investment decisions of individuals who choose to participate in the market.28 Collectively, the risk sharing regression results with the behavioral bias proxies indicate that the levels of risk sharing are higher in states in which investors have higher cognitive abilities and exhibit weaker behavioral biases. Even when the size of market participation is large, lack of (cid:133)nancial 28Our attempt to measure the (cid:133)nancial sophistication of only the market participants instead of the entire statepopulation is in spirit of the consumption-based asset pricing models that estimate the consumption choices of stock holders (e.g., Malloy, Moskowitz, and Vissing-Jorgensen (2008)). 20

Behavioral Biases and the Macro-Economy 0.12 0.10 0.08 0.06 0.04 0.02 0.00 0.010 0.005 0.000 0.005 0.010 0.015 0.020 Mean of Growth Rate of Relative GSP PSG evitaleR fo etaR htworG fo noitaiveD dradnatS AK ND WY IL PA AL Figure 4: Mean and standard deviation of income before risk sharing. sophistication could hurt risk sharing. These (cid:133)ndings provide strong empirical support for our (cid:133)rst hypothesis and indicate that both traditional and behavioral factors are important determinants of state-level risk sharing. Of course, these results should be interpreted with some degree of caution because the timeperiodsusedtomeasureinvestors(cid:146)levelof(cid:133)nancialsophisticationandrisksharingdonotfullyoverlap. The investment decision measures are estimated using data from 1991 to 1996, while the state-level risk sharing estimates are obtained for the 1963 to 1999 period. However, the evidence of a signi(cid:133)cant relation between the investor sophistication measures estimated using the retail brokerage data and the risk sharing measures estimated using state-level macro-economic data is quite remarkable. We suspect that the relation between risk sharing and investor sophistication would be stronger if more accurate measures of people(cid:146)s investment decisions using a longer panel on the stock-holdings and trades of U.S. households are employed in the analysis. 5. Does Geographical Location In(cid:135)uence Risk Sharing? If some U.S. states are inherently riskier, in addition to the traditional and the behavioral factors, the geographicallocationcouldin(cid:135)uencethemagnitudeofstate-levelrisksharing.Thegraphicalevidence in Figure 4 indicates that the standard deviations of relative GSP growth rates for states like Alaska, North Dakota, and Wyoming are signi(cid:133)cantly higher than the standard deviations of relative GSP growth rates for Alabama, Illinois, and Pennsylvania. For riskier states, reducing the sensitivity to 21

Behavioral Biases and the Macro-Economy idiosyncratic state-speci(cid:133)c income risk would be very di¢ cult, unless the sophistication level of state investors is very high. Inthissection, (cid:133)rst, wequantifytheextenttowhichgeographicallocationdeterminesthelevelof risk sharing opportunities that are available to investors within a state. Next, we investigate whether the geographical, behavioral, and traditional e⁄ects interact to generate the overall level of interstate risk sharing. Together, these empirical tests allow us to gather support for the second hypothesis. 5.1 Potential Risk Sharing Estimation Method To quantify the role of location on risk sharing, for each state, we compute a state-speci(cid:133)c theoretical benchmark. This benchmark re(cid:135)ects the potential risk sharing opportunities o⁄ered by (cid:133)nancial markets to the individuals in that state. Thus, it quanti(cid:133)es the degree of di¢ culty that investors in a particular state might face when attempting to reduce their exposure to the idiosyncratic, statespeci(cid:133)c income risk. We compute the level of risk sharing that a U.S. state can potentially attain by minimizing the total variance of a composite portfolio that contains the (cid:147)product asset(cid:148)of the state (i.e., a perpetual claim to GSP) and a broad set of (cid:133)nancial assets. As in Fama and Schwert (1977) and Jagannathan and Wang (1996), we assume that the return from the product asset is the growth rate of GSP.29 We require the total return of the composite portfolio to be at least as high as the return from the state(cid:146)s income asset (i.e., the growth rate of SI).30 Ourpotentialrisksharingcomputationmethodadoptsageneralequilibriumapproach. Toensure that the equilibrium returns of (cid:133)nancial assets are not a⁄ected by the risk sharing induced trading strategies, we set the weight on the product asset to be equal to the ratio of GSP to the total state wealth. Further, we constrain the total weight on (cid:133)nancial assets to be equal to the average ratio of the state (cid:133)nancial wealth and the total state wealth. Using the mean-variance optimization framework, for each state, we compute a set of portfolio weights that characterizes the minimum variance portfolio (MVP) of that state. To calculate the MVP weights, we use the GSP and the asset return data for the 1966 to 2004 period.31 The MVP weights allow us to obtain the return of the MVP portfolio (r ), which re(cid:135)ects the income growth pt rate associated with the potential level of risk sharing. The state-speci(cid:133)c income after risk sharing is 29Inunreportedrobustnesstests,wealsoconsiderthecaseinwhichthegrowthrateofGSPispredictable. Whenthe growth rate is predictable, Shiller (1995) and Campbell (1996) argue that the return to the perpetual claim on GSP shouldnotjustincludethegrowthrateofGSP,butitshouldalsoincludeanyrevisionsaboutthepathoffuturegrowth rates. Whenwede(cid:133)nethereturntotheproductassetfollowingBaxterandJermann(1997),we(cid:133)ndverysimilarresults. 30Without this restriction, we could almost mechanically reduce income risk and increase risk sharing by simply investing in less risky (cid:133)nancial assets that would also yield low returns. See Sections A.5 to A.7 of the appendix for a detailed description of our mean-variance portfolio optimization procedure. 31Although the state income data used to compute the actualrisk sharing levels are available only until1999, we use the 1996-2004 GSP data for calculating the MVP weights to reduce estimation error. 22

Behavioral Biases and the Macro-Economy 0.12 Relative GSP Growth Rate Relative MVP Return 0.10 0.08 0.06 0.04 0.02 0.00 0.010 0.005 0.000 0.005 0.010 0.015 0.020 Mean noitaiveD dradnatS Figure5: Meanandstandarddeviationofincomebefore(relativeGSPgrowthrate)andafter(relative MVP return) potential level of risk sharing. the di⁄erence between r and the mean of r across all states in year t. We denote the deviation of pt pt the r from its cross-sectional mean as relative MVP return. pt To calculate the level of risk sharing that can be potentially attained, we use the risk sharing measure de(cid:133)ned in equation (3), where we replace the standard deviation of growth rate of relative SI ((cid:27) ) by the standard deviation of relative MVP return ((cid:27) ). As before, the state-speci(cid:133)c income SI MVP before risk sharing is the relative growth rate of GSP. Therefore, the denominator in the RS equation (= (cid:27) ) remains unchanged. g Since we use all the available data to estimate one set of (cid:133)xed weights for each state, the weights exploit all the in-sample variation in the GSP and (cid:133)nancial asset returns. Thus, they should be interpretedasfullinformation,ex-postweights. Similarly,thepotentialRSestimateshouldbeviewed as a benchmark that captures the potential level of risk sharing under full information.32 5.2 Potential Risk Sharing Estimates The MVP computation requires a set of (cid:133)nancial assets. For feasibility, we consider a set of broad stock market and debt indices that can e⁄ectively quantify the investment opportunities o⁄ered by 32We choose the in-sample approach to obtain more accurate weight estimates and, consequently, more accurate risk sharing estimates. This methodological choice is aimed at minimizing the errors-in-variables problem. Our approach is di⁄erent from the method used in recent portfolio choice papers (e.g. Jagannathan and Ma (2003)). Those studies adopt an out-of-sample approach and update the portfolio weights at the end of each time period. In contrast, we are mainly interested in identifying a theoretical benchmark that characterizes the potential risk sharing opportunities availabletotheinvestorsinagivenU.S.state. Nevertheless,weobtainqualitativelysimilarresultsevenwhenweadopt animplementablestrategywithnolookaheadbias,althoughinthisinstance,theMVPweightsaresomewhatunstable. 23

Behavioral Biases and the Macro-Economy 0.12 Relative SI Growth Relative MVP Return 0.10 0.08 0.06 0.04 0.02 0.00 0.010 0.005 0.000 0.005 0.010 0.015 0.020 Mean noitaiveD dradnatS Figure6: Meanandstandarddeviationofincomeafterachieved(relativeSIgrowthrate)andpotential (relative MVP return) levels of risk sharing. (cid:133)nancial markets. Our choice is based on the evidence from the existing literature, which shows that (cid:133)nancial assets contain information about the state of the aggregate economy (e.g., Lamont (2001)). If economic activities across U.S. states are correlated, (cid:133)nancial assets might also contain information abouttheincomegrowthratesofindividualstatesandcouldprovideopportunitiesforriskreduction. Speci(cid:133)cally,ourbroadstockmarketindicesincludethemonthlyreturnsofthethreeFama-French factors (Fama and French (1992, 1993)) and the momentum factor (Jegadeesh and Titman (1993), Carhart (1997)). The set of debt instruments include the monthly yields for the 30-day Treasury Bill and 10-year government bond. We also use the monthly yields for Aaa and Baa rated corporate bonds. In Section A.6 of the appendix, we discuss our choice of (cid:133)nancial assets in considerable detail. Table 1, Panel B presents the basic summary statistics for all (cid:133)nancial assets and their correlations with the income growth measures. Figure 5 reports the mean and the standard deviation of income before and after potential level of risk sharing for all U.S. states. It is evident from the plot that (cid:133)nancial assets have the potential to reduce the risk levels of product assets substantially. The average standard deviation can potentially be reduced from 0.0272 to 0.0121, which corresponds to a more than a 50% decline. Even riskier states like Alaska, North Dakota, and Wyoming have large opportunities for risk sharing using (cid:133)nancial assets. For instance, in Alaska, (cid:133)nancial assets can reduce the risk by almost one-third (from 0.125 to 0.067). Further, the mean estimates of the relative MVP return for all states are 24

Behavioral Biases and the Macro-Economy similar and closer to zero, which indicates that all states would grow at the national rate.33 Table7reportsthepotentialrisksharingestimates. InPanelA,wereporttheaggregatepotential RS across all states. The aggregate potential RS estimate is 0.62, which is more than twice the aggregate level of RS that is actually achieved (= 0.26). Similarly, the potential RS for individual states reported in Panel B are always higher than the corresponding achieved RS levels (see Table 2, Panel B). For some states, the di⁄erence between the potential and the achieved RS levels is quite large. In particular, states like Nebraska, South Dakota and Vermont are able to achieve less than 15% risk sharing even though the potential RS estimates for those states are above 65%. In sum, the state-level potential risk sharing estimates indicate that existing (cid:133)nancial markets o⁄er signi(cid:133)cant risk sharing opportunities. If investors exploit the available risk sharing potential, there would be a signi(cid:133)cant reduction in the level of standard deviation of the income growth rate. Comparing the potential risk sharing estimates with the actual levels of risk sharing, we (cid:133)nd that althoughstatesareabletoreducetheincomerisk, thepotentialforfurtherimprovementissigni(cid:133)cant (see Figure 6). 5.3 Potential versus Actual Levels of Risk Sharing To understand why states with large risk sharing opportunities are unable to exploit them, we reestimate risk sharing regressions with enhanced speci(cid:133)cations. As before, in the regressions, the achieved RS level for a state is the dependent variable. The set of independent variables contains the potential level of RS, along with the traditional and the behavioral determinants of risk sharing. The results are reported in Table 8. The estimation results indicate that the potential RS is not a signi(cid:133)cant predictor of achieved RS. Speci(cid:133)cally, in columns (1) and (2), the coe¢ cient estimates for potential RS are 0:10 (t-statistic = 0:72) and 0:00, (t-statistic = 0:01), respectively.34 This evidence indicates that the investment decisions of state investors might not be aligned with the goal of improving risk sharing. To further examine the relation between the potential and the achieved levels of risk sharing, we replace the potential RS variable in the risk sharing regression with a high potential RS dummy variable. The dummy variable takes the value of one if a state(cid:146)s potential RS estimate is above the median, and zero otherwise. It tests whether investors exploit risk sharing opportunities and achieve high levels of RS when the potential RS level is high.35 The results in columns (3) and (4) indicate 33In an earlier (cid:133)gure (Figure 2, Panel C), we further illustrate the sharp contrast between the volatility levels of income growth rate before risk sharing and after risk sharing that can be potentially attained. 34In unreported results, we (cid:133)nd that potential RS is not a signi(cid:133)cant predictor of achieved RS even in univariate regressions. 35There is also a statistical reason why we use the high potential RS dummy variable. Because the potential RS is uniformly high for all states, its cross-sectional variation is low. In untabulated results we (cid:133)nd that its cross-sectional standard deviation is about 0.07, whereas the cross-sectional standard deviation of the achieved RS is about 0.12. 25

Behavioral Biases and the Macro-Economy that when the potential risk sharing opportunities are high, the achieved RS levels are also high.36 Next, we formally test our second hypothesis, which posits that high risk sharing opportunities are more (less) e⁄ectively exploited when the level of investor sophistication is high (low). We de(cid:133)ne two interaction terms to test the hypothesis. First, we interact the sophistication index with the high potentialRS(abovemedian)dummyvariable. Second,weinteractthesophisticationindexwithalow potential RS (below the 25th percentile) dummy variable. If sophisticated investors are better able to exploit the high risk sharing opportunities o⁄ered by (cid:133)nancial markets, then the (cid:133)rst interaction term would be positively correlated with the achieved levels of RS, while the second interaction term would either be uncorrelated or negatively correlated with the achieved RS variable. We estimate the risk sharing regressions after including the two interaction terms in the set of independent variables and report the estimates in Table 8 (columns (5) to (8)). Consistent with our conjecture, we (cid:133)nd that the sophistication-high potential RS interaction term has a positive and statistically signi(cid:133)cant estimate (see columns (5) and (6)). In addition, the sophistication-low potentialRSinteractiontermhasanegativecoe¢ cientestimate, althoughitisstatisticallysigni(cid:133)cant in the conditional risk sharing regression (see columns (7) and (8)). This evidence indicates that even high levels of (cid:133)nancial sophistication cannot improve risk sharing when the potential risk sharing opportunities are modest. In sum, the state-level potential risk sharing estimates indicate that existing (cid:133)nancial markets o⁄er signi(cid:133)cant risk sharing opportunities. If investors exploit the available risk sharing potential e⁄ectively, there would be a signi(cid:133)cant reduction in the level of standard deviation of the income growth rate and even the mean of the income growth rate would be signi(cid:133)cantly higher.37 6. Robustness Checks and Alternative Explanations In this section, we carry out additional tests to entertain alternative explanations and examine the robustness of our results. We use speci(cid:133)cations (5) and (6) from Table 8, which summarize the key resultsinourpaper,andincludeadditionalcontrolvariablestoexaminethesensitivityandrobustness of those main (cid:133)ndings. The results from these additional tests are summarized in Table 9. Because of the low cross-sectional variation in the potential RS measure, its parameter estimates can be imprecisely estimated. The dichotomy created with the dummy variable between low potential RS and high potential RS allows us to side-step some of the these econometric issues. 36We obtain similar results when the high potential RS variable takes the value of one for states above the 75th percentile of potential RS. 37Thepotentialrisksharingestimatesusedinourtestsallowforshorting(seeTableA.1intheappendix). Ourresults are very similar when we do not allow shorting. The aggregate risk sharing estimate drops from 0.62 to 0.57, but we (cid:133)nd that the cross-sectional variation in the potential risk sharing measure remains virtually unchanged. As a result, the cross-sectional regression estimates reported in Table 8 remain very similar. Thus, even in the presence of short sales constraints, sophisticated investors would be able to improve state-level risk sharing when the potential level of risk sharing is high. 26

Behavioral Biases and the Macro-Economy 6.1 Size of the State Economy Inthe(cid:133)rsttest,weexaminewhethertherisksharinglevelsarelowerinsmaller(i.e.,lowerGSP)states that might have riskier economies. We use the state-level GSP at the beginning of the sample period as a proxy for the size of the state economy and include it in the risk sharing regression speci(cid:133)cation. The results indicate that larger states achieve higher levels of risk sharing, but the size-risk sharing relation is statistically very weak (see columns (1) and (2)). 6.2 Do Smarter Investors Move to High Risk Sharing States? A potential concern with our baseline risk sharing regression speci(cid:133)cation is that the sophistication index might be endogenous. It is possible that sophisticated investors self-select into states in which risk sharing opportunities are higher and smoothing income shocks is relatively easier. To account for this potential endogeneity, in the second test, we estimate our baseline regressions using an instrumental variable (IV) estimator. We instrument the sophistication index with initial per capita GSP. We also instrument the interaction term between high potential risk sharing and sophistication with an interaction term between high potential risk sharing and initial GSP. Initial GSP is a valid instrument for at least two reasons. First, because the initial GSP is measured in 1966 (the beginning of our sample period), it should be uncorrelated with the error term of the regression. Second, it is highly correlated with the sophistication index. In unreported results we (cid:133)nd the correlation coe¢ cient is 0.50.38 The IV estimation results are presented in Table 9, columns (3) and (4). We (cid:133)nd that the coef- (cid:133)cient estimates for the sophistication index are 0.51 (t-statistic = 3.08) and 0.56 (t-statistic = 2.67) in the unconditional and conditional risk sharing regressions. These estimates are very similar to the OLS estimates reported in Table 8, column (5) (estimate = 0.53, t-statistic = 4.76) and column (6) (estimate=0.48, t-statistic=4.26). Further, muchliketheOLSresults, thesigni(cid:133)canceofthepotentialrisksharing-sophisticationinteractiontermislowerthanthatofthenon-interactedsophistication index. For example, when the dependent variable is the conditional risk sharing measure, the OLS estimate and t-statistic are 0.20 and 2.10, respectively (Table 8, column (6)), while the IV estimate and t-statistic are 0.47 and 1.74, respectively (Table 9, column (4)). These IV estimates indicate that our key results are unlikely to be induced by the potential endogeneity of the sophistication index. 6.3 Age Composition of the State In the next test, we examine whether the age composition of the population in a state in(cid:135)uences 38Findinganappropriateinstrumentisnottrivialforavarietyofreasons. Tobeginwith,attheaggregatelevelthere are common shocks that a⁄ect most macroeconomic series. Therefore, in most macroeconomic studies lagged values of theindependentvariablesareusedasinstruments. Duetothecross-sectionalnatureofourstudy,wecannotadoptthis approach. Our only option is to use instruments dated at the beginning of our sample period, which is 1966. The only comprehensivedataonU.S.statesavailablepriorto1966areprovidedbytheBureauofEconomicAnalysisfrom which we obtain the per capita GSP at 1966. 27

Behavioral Biases and the Macro-Economy our results. For example, risk sharing levels could be high in states such as Florida with a large concentration of older investors just because those older investors have accumulated more (cid:133)nancial assets over their lifetime.39 But older investors might also make worse investment decisions (e.g., Korniotis and Kumar (2007)), which can reduce the level of risk sharing. When we include average age of the state population as an additional independent variable in the speci(cid:133)cation, we (cid:133)nd that it has a statistically insigni(cid:133)cant coe¢ cient estimate (see columns (5) and (6)). Thus, age di⁄erences across states do not have an incremental ability to explain the cross-sectional variation in the level of risk sharing. 6.4 Regional Variation in Risk Sharing In the fourth robustness test, we examine whether our results re(cid:135)ect the known regional variation in the level of risk sharing (e.g., Sorensen and Yosha (2000)). Using the regional classi(cid:133)cation scheme from the U.S. Census, we de(cid:133)ne three regional dummy variables and include them in the risk sharing regressions. We (cid:133)nd that relative to the Southern states, the states in the West are able to achieve higher levels of risk sharing, while Mid-Western states have somewhat lower levels of risk sharing (see columns (7) and (8)). The North-East region dummy has negative coe¢ cient estimates, but they are insigni(cid:133)cant. More importantly, the inclusion of these regional dummy variables do not signi(cid:133)cant lower the statistical or the economic signi(cid:133)cance of the behavioral and geographical factors. Among the traditional factors, the HY variable is no longer signi(cid:133)cant, which indicates that the variation in state-level HY that matters for risk sharing is regional. This evidence is not surprising because thereisastrongregionalcomponentintherealestatemarket. Inuntabulatedresults, consistentwith this conjecture, we (cid:133)nd that when we de(cid:133)ne HY at the regional level, it has a signi(cid:133)cant coe¢ cient estimate (estimate = 0.23, t-statistic = 2.14). 6.5 Finite Sample Bias and the E⁄ect of Outliers Last,weconducttworandomizationteststoensurethatourregressionestimatesarenotin(cid:135)uencedby the (cid:133)nite sample bias or the abnormal behavior of only a handful of states. First, we re-estimate the risk sharing regression (speci(cid:133)cation (6) from Table 8) after randomly excluding (cid:133)ve states from the sample. Werepeattheprocess1,000timesandexaminethedistributionsofthecoe¢ cientestimatesof the independent variables considered in Table 8, column (6). In untabulated results, we (cid:133)nd that the coe¢ cient estimates from the randomized sub-samples are very similar to the full-sample estimates. Both the mean and the median estimates are almost identical to the estimates reported in Table 8, column (6). This evidence indicates that our results are not driven by outliers. In the next randomization test, we create 2,500 bootstrapped samples by choosing states randomly with replacement. We (cid:133)nd that, in most iterations, the coe¢ cient estimates reported in Table 39We thank John Campbell for suggesting this test. 28

Behavioral Biases and the Macro-Economy 8 (column (6)) are higher in magnitude than the bootstrap estimates. Thus, we are able to reject the null hypothesis that the traditional, behavioral, and geographical factors are insigni(cid:133)cant determinants of the cross-sectional variation in state-level risk sharing. The p-values corresponding to these independent variables are all below 0.08. Taken together, the results from these additional tests indicate that our risk sharing regression estimates are robust. The main results cannot be fully explained by potential endogeneity of our sophistication measures, heterogeneity in the size of the state economy and people(cid:146)s age across states, regional di⁄erences in risk sharing, or the anomalous behavior of a handful of states. 7. Summary and Conclusion This study presents the (cid:133)rst comprehensive analysis of the determinants of state-level income risk sharing (or income smoothing). We focus on the aggregate e⁄ects of behavioral biases, but we also study the e⁄ects of traditional and geographical factors on the level of risk sharing across the U.S. states. Wepresentthreekeyresults. First, weshowthatmerelyhighlevelsofstockmarketparticipation rates do not generate high levels of risk sharing. In fact, after accounting for borrowing constraints, on average, states in which individuals participate more in the stock market achieve low levels of risk sharing. Therisksharinglevelsarehighwhenindividualsinvestbroadlyandsigni(cid:133)cantlyinthestock market, perhaps due to their greater (cid:133)nancial sophistication. Second, we show that risk sharing levels are higher in states in which investors trade less frequently, exhibit a lower propensity to follow gambling-motivated strategies, exhibit a greater propensity to hold foreign stocks, and hold less concentrated portfolios. In other words, investors who follow the normative prescriptions of portfolio theory facilitate risk sharing at the aggregate level. Surprisingly, risk sharing is also enhanced when investors deviate from the theoretical benchmarks and tilt their portfolios toward local stocks due to an informational advantage. Third,weshowthatthepotentialtoachievehighlevelsofrisksharingvariesgeographicallyacross the U.S. states. However, the available opportunities for risk sharing are exploited e⁄ectively when investors within a state have higher levels of cognitive abilities and exhibit weaker behavioral biases. The geographical location is also important because even very sophisticated investors are unable to improve risk sharing when the potential risk sharing opportunities are modest. Collectively, our results indicate that the in(cid:135)uence of investors(cid:146)cognitive abilities and behavioral biases extend beyond the domain of (cid:133)nancial markets to the aggregate macro-economy. These empirical (cid:133)ndings make several useful contributions. First, our study integrates three distinct and somewhat unconnected strands of literature on interstate risk sharing, the ability of (cid:133)nancial assets to capture current and future economic activities, and the growing literature on 29

Behavioral Biases and the Macro-Economy household (cid:133)nance. We show that people(cid:146)s sub-optimal investment decisions aggregate up and the adverse e⁄ects of the associated biases can be detected even in the aggregate, state-level macroeconomic data. Although we do not attempt to quantify the total welfare cost of these biases, unlike the evidence in Calvet, Campbell, and Sodini (2007), our results suggest that aggregate behavioral biases could adversely e⁄ect social welfare. Beyond the contributions to the behavioral (cid:133)nance and the risk sharing literatures, our potential risk sharing estimates are useful because they provide a more precise characterization of the degree of market incompleteness, which in turn has important implications for asset pricing.40 Because market incompleteness is a statement about the investment environment and is not necessarily related to the decisions of investors, the potential risk sharing estimates that only re(cid:135)ects the characteristics of the investment environment could provide a more accurate assessment of the degree of market incompleteness. Our results indicate that, at least from the perspective of interstate risk sharing, (cid:133)nancial markets are more complete than previously believed, although they appear more incomplete due to people(cid:146)s sub-optimal investment decisions. In light of this evidence, consumption-based asset pricing models employed to investigate the implications of market incompleteness should be extended to account for investors(cid:146)behavioral biases. Our (cid:133)ndings also have distinct policy implications. First, they indicate that state-level risk sharing would not improve by simply increasing stock market participation rates. E⁄orts to increase stock market participation should also attempt to increase sophisticated participation. In particular, improvements in (cid:133)nancial literacy might be needed to improve state-level risk sharing. Second, since very high levels of income risk sharing can be potentially attained through the (cid:133)nancial markets channel, federal policies should encourage the development of state-speci(cid:133)c mutual funds. If used e⁄ectively, those funds could allow people to have smoother income stream, and hence smoother consumption, thereby improving social welfare. Thus, in broader terms, our results reinforce the notion that increased and sophisticated (cid:133)nancial market participation can improve social welfare. 40Forexample,ConstantinidesandDu¢ e(1996)showthatwhenincomeriskisnotfullydiversi(cid:133)able,theconsumption growth rates across investors are not identical and their cross-sectional di⁄erences could a⁄ect asset prices. Extending this insight, Korniotis (2008) (cid:133)nds that cross-sectional variances in the growth rates of U.S. state consumption are important asset pricing factors for explaining the cross-section of expected returns. Jacobs and Wang (2004) provide similar results using household-level data. 30

Behavioral Biases and the Macro-Economy References Amemiya,T.,1985,(cid:147)AdvancedEconometrics,(cid:148)HarvardUniversityPress,Cambridge,Massachusetts. Asdrubali, P., B. E. Sorensen, and O. Yosha, 1996, (cid:147)Channels of Interstate Risk Sharing: United States 1963-1990,(cid:148)Quarterly Journal of Economics, 111, 1081(cid:150)1110. Athanasoulis, S. G., and E. Van Wincoop, 2001, (cid:147)Risk Sharing Within the United States: What do Financial Markets and Fiscal Federalism Accomplish?,(cid:148)Review of Economics and Statistics, 83, 688(cid:150)698. Barber, B. M., and T. Odean, 2000, (cid:147)Trading is Hazardous to Your Wealth: The Common Stock Investment Performance of Individual Investors,(cid:148)Journal of Finance, 55, 773(cid:150)806. Barber, B.M., andT.Odean, 2001, (cid:147)BoyswillbeBoys: Gender, Overcon(cid:133)dence, andCommonStock Investment,(cid:148)Quarterly Journal of Economics, 116, 261(cid:150)292. Barber, B. M., T. Odean, and N. Zhu, 2008, (cid:147)Do Noise Traders Move Markets?,(cid:148)Review of Financial Studies, Forthcoming. Barberis, N., and M. Huang, 2008, (cid:147)Stocks as Lotteries: The Implications of Probability Weightings for Security Prices,(cid:148)American Economic Review, Forthcoming. Barberis, N., M.Huang, andT.Santos, 2001, (cid:147)ProspectTheoryandAssetPrices,(cid:148)Quarterly Journal of Economics, 116, 1(cid:150)53. Barberis, N., and R. Thaler, (cid:147)A Survey of Behavioral Finance,(cid:148) Handbook of the Economics of Finance, G. M. Constantinides, M. Harris, and R. M. Stulz, eds., Elsevier B.V., Amsterdam, Netherlands. Barro, R. J., 1990, (cid:147)The Stock Market and Investment,(cid:148)Review of Financial Studies, 3, 115(cid:150)131. Barro, R.J., andX.Sala-i-Martin, 1991, (cid:147)ConvergenceAcrossStatesandRegions,(cid:148)Brookings Papers on Economic Activity, 1991, 107(cid:150)182. Barro, R. J., and X. Sala-i-Martin, 1992, (cid:147)Convergence,(cid:148)Journal of Political Economy, 100, 223(cid:150)251. Baxter, M., and U. J. Jermann, 1997, (cid:147)The International Diversi(cid:133)cation Puzzle Is Worse Than You Think,(cid:148)American Economic Review, 87, 170(cid:150)180. Benjamin, D. J., S. A. Brown, and J. M. Shapiro, 2006, (cid:147)Who is (cid:145)Behavioral(cid:146)? Cognitive Ability and Anomalous Preferences,(cid:148)Working Paper (May), University of Chicago and Harvard University. Benartzi, S., and R. Thaler, (cid:147)Myopic Loss Aversion and the Equity Premium Puzzle,(cid:148)Quarterly Journal of Economics, 110, 73(cid:150)92. Bernanke, B. S., and A. S. Blinder, 1992, (cid:147)The Federal Funds Rate and the Channels of Monetary Transmission,(cid:148)American Economic Review, 82, 901(cid:150)921. Bodnaruk, Andriy, 2008, (cid:147)Proximity Always Matters: Local Bias when the Set of Local Companies Changes,(cid:148)Working Paper (April), University of Notre Dame. Bottazzi, L., P. Pesenti, and E. Van Wincoop, 1996, (cid:147)Wages, Pro(cid:133)ts and the International Portfolio Puzzle,(cid:148)European Economic Review, 40, 219(cid:150)254. 31

Behavioral Biases and the Macro-Economy Brandt, M.W., J.H.Cochrane, andP.Santa-Clara, 2006, (cid:147)InternationalRiskSharingisBetterThan You Think, or Exchange Rates are Too High,(cid:148)Journal of Monetary Economics, 53, 671(cid:150)698. Brown, J. R., Z. Ivkovi·c, P. A. Smith, and S. Weisbenner, 2008, (cid:147)Neighbors Matter: Causal Community E⁄ects and Stock Market Participation,(cid:148)Journal of Finance, 63, 1509(cid:150)1531. Browning, M., and S. Leth-Petersen, 2003, (cid:147)Imputing Consumption From Income and Wealth Information,(cid:148)Economic Journal, 113, F282(cid:150)301. Calvet, L. E., J. Y. Campbell, and P. Sodini, 2007, (cid:147)Down or out: Assessing the Welfare Costs of Household Investment Mistakes,(cid:148)Journal of Political Economy, 115, 707(cid:150)747. Campbell, J. Y., 1996, (cid:147)Understanding Risk and Return,(cid:148)Journal of Political Economy, 104, 298(cid:150) 345. Campbell, J. Y., 2006, (cid:147)Household Finance,(cid:148)Journal of Finance, 61, 1553(cid:150)1604. Campbell, J. Y., and J. H. Cochrane, 1999, (cid:147)By Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior,(cid:148)Journal of Political Economy, 107, 205(cid:150)251. Carhart, M., 1997, (cid:147)On Persistence of Mutual Fund Performance,(cid:148)Journal of Finance, 52, 57(cid:150)82. Cochrane J., 1991, (cid:147)A Simple Test of Consumption Insurance,(cid:148)Journal of Political Economy, 99, 957(cid:150)976. Constantinides, G. M., and D. Du¢ e, 1996, (cid:147)Asset Pricing with Heterogeneous Consumers,(cid:148)Journal of Political Economy, 104, 219(cid:150)240. Coval, J. D., and T. Shumway, 2005, (cid:147)Do Behavioral Biases A⁄ect Prices?,(cid:148)Journal of Finance, 60, 1(cid:150)34. Crucini,M.,1999,(cid:147)OnInternationalandNationalDimensionsofRiskSharing,(cid:148)Review of Economics and Statistics, 81, 73(cid:150)84. Davis, S. J., and P. Willen, 2000a, (cid:147)Occupation-Level Income Shocks and Asset Returns: Covariance and Implications for Portfolio Choice,(cid:148)NBER Working Paper # 7905. Davis, S. J., and P. Willen, 2000b, (cid:147)Using Financial Assets to Hedge Labor Income Risk: Estimating the Bene(cid:133)ts,(cid:148)Working Paper (March), University of Chicago. Davis, S. J., and P. Willen, 2002, (cid:147)Risky Labor Income and Portfolio Choice,(cid:148)Innovations for Financing Retirement, Z. Bodie, O. S. Mitchell, B. Hammond, and S. Zeldes, eds., University of Pennsylvania Press. Dohmen, T., A. Falk, D. Hu⁄man, and U. Sunde, 2007, (cid:147)Are Risk Aversion and Impatience Related to Cognitive Ability?,(cid:148)IZA Discussion Paper No. 2735. Fama, E. F., and G. W. Schwert, 1977, (cid:147)Human Capital and Capital Market Equilibrium,(cid:148)Journal of Financial Economics, 4, 95(cid:150)125. Fama, E. F., and K. R. French, 1992, (cid:147)The Cross-Section of Expected Returns,(cid:148)Journal of Finance, 47, 427(cid:150)456. 32

Behavioral Biases and the Macro-Economy Fama, E. F., and K. R. French, 1993, (cid:147)Common Risk Factors in the Returns on Stocks and Bonds,(cid:148) Journal of Financial Economics, 33, 3(cid:150)56. Frederick, S., 2005, (cid:147)Cognitive Re(cid:135)ection and Decision Making,(cid:148)Journal of Economic Perspectives, 19, 25(cid:150)42. Friedman, B. M., and K. N. Kuttner, 1992, (cid:147)Money, Income, Prices, and Interest Rates,(cid:148)American Economic Review, 82, 472(cid:150)492. Gertler, M., and C. S. Lown, 1999, (cid:147)The Information in the High Yield Bond Spread for the Business Cycle: Evidence and Some Implications,(cid:148)Oxford Review of Economic Policy, 15, 132(cid:150)150. Graham, J. R., and A. Kumar, 2006, (cid:147)Do Dividend Clienteles Exist? Evidence on Dividend Preferences of Retail Investors,(cid:148)Journal of Finance, 61, 1305(cid:150)1336. Graham, J. R., C. R. Harvey, and H. Huang, 2006, (cid:147)Investor Competence, Trading frequency, and Home Bias,(cid:148)Working Paper (May), Fuqua School of Business, Duke University. Greene, W. H., 2003, Econometric Analysis, 5th Edition, Prentice Hall, New Jersey. Grinblatt, M., and B. Han, 2005, (cid:147)Prospect Theory, Mental Accounting, and Momentum,(cid:148)Journal of Financial Economics, 78, 311(cid:150)339. Grinblatt, M., and M. Keloharju, 2001, (cid:147)What Makes Investors Trade?(cid:148)Journal of Finance, 56, 589(cid:150)616. Harvey, C. R., 1988, (cid:147)The Real Term Structure and Consumption Growth,(cid:148)Journal of Financial Economics, 22, 305(cid:150)333. Harvey, C. R., 1989, (cid:147)Forecasts of Economic Growth from the Bond and Stock Markets,(cid:148)Financial Analysts Journal, 45, 38(cid:150)45. Hess, G. D., and K. Shin, 2000, (cid:147)Risk Sharing by Households Within and Across Regions and Industries,(cid:148)Journal of Monetary Economics, 45, 533(cid:150)560. Hirshleifer, D., 2001, (cid:147)Investor Psychology and Asset Prices(cid:148)Journal of Finance, 56, 1533(cid:150)1597. Huberman, G., 2001, (cid:147)Familiarity Breeds Investment,(cid:148)Review of Financial Studies, 14, 659(cid:150)680. Ivkovi·c, Z., J. Poterba, and S. Weisbenner, 2005, (cid:147)Tax-Motivated Trading by Individual Investors,(cid:148) American Economic Review, 95, 1605(cid:150)1630. Ivkovi·c, Z., C. Sialm, and S. Weisbenner, 2008, (cid:147)Portfolio Concentration and the Performance of Individual Investors,(cid:148)Journal of Financial and Quantitative Analysis, Forthcoming. Ivkovi·c, Z., and S. Weisbenner, 2005, (cid:147)Local Does as Local Is: Information Content of the Geography of Individual Investors(cid:146)Common Stock Investments,(cid:148)Journal of Finance, 60, 267(cid:150)306. Jacobs, K., and K. Wang, 2004, (cid:147)Idiosyncratic Consumption Risk and the Cross Section of Asset Returns,(cid:148)Journal of Finance, 59, 2211(cid:150)2252. Jagannathan, R., and Z. Wang, 1996, (cid:147)The Conditional CAPM and the Cross-Section of Expected Returns,(cid:148)Journal of Finance, 51, 3(cid:150)53. 33

Behavioral Biases and the Macro-Economy Jagannathan, R., and T. Ma, 2003, (cid:147)Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps,(cid:148)Journal of Finance, 58, 1651(cid:150)1684. Jegadeesh, N., and S. Titman, 1993, (cid:147)Returns to Buying Winners and Selling Losers: Implications for Stock Market E¢ ciency,(cid:148)Journal of Finance, 48, 65(cid:150)91. Kalemli-Ozcan, S., B. E. Sorensen, and O. Yosha, 2003, (cid:147)Risk Sharing and Industrial Specialization: Regional and International Evidence,(cid:148)American Economic Review, 93, 903(cid:150)918. Kanazawa, S., 2006, (cid:147)IQ and the Wealth of States,(cid:148)Intelligence, 34, 593(cid:150)600. Kashyap, A. K., J. C. Stein, and D. W. Wilcox, 1993, (cid:147)Monetary Policy and Credit Conditions: Evidence from the Composition of External Finance,(cid:148)American Economic Review, 83, 78(cid:150)98. Korniotis, G., 2008, (cid:147)Habit Formation, Incomplete Markets, and the Signi(cid:133)cance of Regional Risk for Expected Returns,(cid:148)Review of Financial Studies, Forthcoming. Korniotis,G.,andA.Kumar,2007,(cid:147)DoOlderInvestorsMakeBetterInvestmentDecisions?(cid:148)Working Paper (September), McCombs School of Business, University of Texas at Austin. Korniotis, G., and A. Kumar, 2008, (cid:147)Superior Information or a Psychological Bias? A Uni(cid:133)ed FrameworkwithCognitiveAbilitiesResolvesThreePuzzles,(cid:148)WorkingPaper(March),McCombs School of Business, University of Texas at Austin. Kumar, A., 2008, (cid:147)Who Gambles in the Stock Market?,(cid:148)Journal of Finance, Forthcoming. Lamont, O. A., 2001, (cid:147)Economic Tracking Portfolios,(cid:148)Journal of Econometrics, 105, 161(cid:150)184. Lettau, M., and S. Ludvigson, 2001, (cid:147)Resurrecting the (C)CAPM: A Cross-Sectional Test When Risk Premia are Time-Varying,(cid:148)Journal of Political Economy, 109, 1238(cid:150)1287. Lewis, K., 1999, (cid:147)Trying to Explain Home Bias in Equities and Consumption,(cid:148)Journal of Economic Literature, 37, 571(cid:150)608. Liew, J., and M. Vassalou, 2000, (cid:147)Can Book-To-Market, Size and Momentum be Risk Factors That Predict Economic Growth?,(cid:148)Journal of Financial Economics, 57, 221(cid:150)245. Lustig, H., and S. Van Nieuwerburgh, 2008, (cid:147)How Much Does Household Collateral Constrain RegionalRiskSharing?,(cid:148)WorkingPaper(July),DepartmentofEconomics,UCLA,andDepartment of Finance, NYU. MalloyC., T.Moskowitz, A.Vissing-Jorgensen, 2008, (cid:147)Long-RunStockholderConsumptionRiskand Asset Returns,(cid:148)Journal of Finance, Forthcoming. Mark, N. C., and D. Sul, 2003, (cid:147)Cointegration Vector Estimation by Panel DOLS and Long-run Money Demand,(cid:148)Oxford Bulletin of Economics and Statistics, 66, 655(cid:150)680. Massa, M., and A. Simonov, 2006, (cid:147)Hedging, Familiarity and Portfolio Choice,(cid:148)Review of Financial Studies, 19, 633(cid:150)685. Mehra, R., and E. C. Prescott, 1985, (cid:147)The Equity Premium: A Puzzle,(cid:148)Journal of Monetary Economics, 15, 145(cid:150)161. 34

Behavioral Biases and the Macro-Economy Odean,T.,1998,(cid:147)Volume,Volatility,Price,andPro(cid:133)tWhenAllTradersareAboveAverage,(cid:148)Journal of Finance, 53, 1887(cid:150)1934. Odean, T., 1998b, (cid:147)Are Investors Reluctant to Realize Their Losses?,(cid:148)Journal of Finance, 53, 1775(cid:150) 1798. Odean, T., 1999, (cid:147)Do Investors Trade Too Much?,(cid:148)American Economic Review, 89, 1279(cid:150)1298. Saito, Y., and Y. Takeda, 2000, (cid:147)Predicting the U.S. Real GDP Growth Using Yield Spreads of Corporate Bonds,(cid:148)Working Paper # 00-E-3, International Department, Bank of Japan. Sangvinatsos, A., 2005, (cid:147)Portfolio Choice: The Hedging Role of Corporate Bonds?,(cid:148)Working Paper (June), University of Southern California. Scheinkman, J., and W. Xiong, 2003, (cid:147)Overcon(cid:133)dence and Speculative Bubbles,(cid:148)Journal of Political Economy, 111, 1183(cid:150)1219. Shefrin, H. M., and M. Statman, 1985, (cid:147)The Disposition to Sell Winners Too Early and Ride Losers Too Long,(cid:148)Journal of Finance, 40, 777(cid:150)790. Shiller, R. J., 1993, Macro Markets: Creating Institutions for Managing Society(cid:146)s Largest Economic Risks, Oxford University Press, Oxford, UK. Shiller, R. J., 1995, (cid:147)Aggregate Income Risks and Hedging Mechanisms,(cid:148)Quarterly Review of Economics and Finance, 35, 119(cid:150)152. Shiller, R. J., 2003, The New Financial Order: Risk in the 21st Century, Princeton University Press, Princeton, NJ. Shleifer, A., 2000, Ine¢ cient Markets: An Introduction to Behavioral Finance, Oxford University Press, Oxford, UK. Skinner, J., 1987, (cid:147)A Superior Measure of Consumption From the Panel Study of Income Dynamics,(cid:148) Economic Letters, 23, 213(cid:150)216. Sorensen, B.E., andO.Yosha, 2000, (cid:147)IsRiskSharingintheUnitedStatesaRegionalPhenomenon?(cid:148) Federal Reserve Bank of Kansas City Economic Review, Summer 2000, 33(cid:150)47. Sorensen, B. E., Y.-T. Wu, O. Yosha, and Y. Zhu, 2007, (cid:147)Home Bias and International Risk Sharing: Twin Puzzles Separated at Birth,(cid:148)Journal of International Money and Finance, 26, 587(cid:150)605. Statman, M., S. Thorley, and K. Vorkink, 2006, (cid:147)Investor Overcon(cid:133)dence and Trading Volume,(cid:148) Review of Financial Studies, 19, 1531(cid:150)1565. Stock, J.H., andM.W.Watson, 1993, (cid:147)ASimpleEstimatorofCointegratingVectorsinHigherOrder Integrated Systems,(cid:148)Econometrica, 61, 783(cid:150)820. Vassalou, M., 2003, (cid:147)News Related To Future GDP Growth as a Risk Factor in Equity Returns,(cid:148) Journal of Financial Economics, 68, 47(cid:150)73. Zhang, Z., 2002, (cid:147)Corporate Bond Spreads and the Business Cycle,(cid:148)Working Paper 2002-15, Bank of Canada. Ziliak, J. P., 1998, (cid:147)Does the Choice of Consumption Measure Matter? An Application to the Permanent-Income Hypothesis,(cid:148)Journal of Monetary Economics, 41, 201(cid:150)216. 35

Behavioral Biases and the Macro-Economy Table 1 Correlations and Summary Statistics for Income Growth Rates and Asset Returns Panel A reports the sample period summary statistics for the annual, per capita growth rates of the U.S. gross domestic product (GDP), gross state product (GSP), and state income (SI) for individual states. The GSP, SI, and GDP are measured in real terms. The GSP and GDP data are available for the 1964 to 2004 period, while the SI data are available for the 1963 to 1999 period. The summary statistics for annual returns of (cid:133)nancialassetsarereportedinPanelB.Thesetof(cid:133)nancialassetsincludesthemarketindex(MKT),theSMB (small-minus-big) factor, the (high-minus-low) HML factor (Fama and French (1992, 1993)), the momentum factor(JegadeeshandTitman(1993),Carhart(1997)),the30-dayTreasuryBill,the10-yeargovernmentbond, and the Aaa and Baa rated corporate bonds. Univariate Statistics Correlation Coefficients Panel A: Income Growth Rates Rel Rel Mean Std Dev g g g g g GDPusa GSP GSP SI SI (1964 04) (1964 04) (1964 04) (1964 99) (1964 99) g 0.022 0.020 0.509 0.046 0.551 0.048 GDPusa g 0.023 0.037 0.837 0.731 0.580 GSP Rel g 0.002 0.032 0.502 0.704 GSP g 0.025 0.033 SI Rel g 0.001 0.024 SI Panel B: Financial Assets MKT 0.120 0.170 0.049 0.065 0.044 0.216 0.054 SMB 0.039 0.148 0.114 0.070 0.009 0.131 0.010 HML 0.061 0.145 0.111 0.029 0.037 0.108 0.034 UMD 0.110 0.138 0.037 0.008 0.033 0.023 0.023 30 Day T Bill 0.059 0.028 0.182 0.122 0.026 0.126 0.010 10 Year Gov. Bond 0.078 0.097 0.318 0.203 0.034 0.200 0.004 Aaa Corp. Bond 0.083 0.023 0.281 0.187 0.039 0.187 0.018 Baa Corp. Bond 0.093 0.026 0.316 0.208 0.040 0.205 0.015 36

Behavioral Biases and the Macro-Economy Table 2 State-Level Risk Sharing Achieved Through Financial Markets This table reports unconditional (UnRS) and conditional (ConRS) risk sharing (RS) estimates for the 1966 to 1999 period. The aggregate income risk without any risk sharing is measured using the in(cid:135)ation adjusted relative GSP. The aggregate income risk after risk sharing through the (cid:133)nancial markets channel is measured using the in(cid:135)ation adjusted relative SI. GSP and SI are measured in per capita real terms. We use the Athanasoulis and van Wincoop (2001) methodology to obtain the RS estimates and measure their statistical signi(cid:133)cance. Section 2.1 de(cid:133)nes the income measures and presents details of the AVW risk sharing estimation method. In Panel A, we report the aggregate RS measures calculated by pooling the observations from all states. Thet-statisticsoftheestimatesarereportedinsmallerfontbelowtheestimates. InPanelB,wereport the RS measures for individual U.S. states. Panel A: Aggregate RS Estimates UnRS 0.26 ConRS 0.23 21.65 15.87 Panel B: RS Estimates for Individual U.S. States State UnRS ConRS State UnRS ConRS State UnRS ConRS AL 0.33 0.33 KY 0.06 0.14 ND 0.10 0.10 AK 0.32 0.24 LA 0.33 0.36 OH 0.37 0.39 AZ 0.16 0.15 ME 0.03 0.04 OK 0.33 0.33 AR 0.10 0.11 MD 0.27 0.22 OR 0.51 0.48 CA 0.39 0.39 MA 0.18 0.19 PA 0.40 0.41 CO 0.40 0.40 MI 0.30 0.34 RI 0.07 0.06 CT 0.34 0.37 MN 0.30 0.34 SC 0.24 0.21 DE 0.52 0.52 MS 0.30 0.27 SD 0.01 0.05 DC 0.30 0.32 MO 0.31 0.29 TN 0.29 0.29 FL 0.12 0.14 MT 0.36 0.33 TX 0.31 0.21 GA 0.28 0.24 NE 0.12 0.14 UT 0.25 0.22 HI 0.37 0.37 NV 0.23 0.37 VT 0.14 0.08 ID 0.24 0.23 NH 0.45 0.42 VA 0.38 0.36 IL 0.26 0.26 NJ 0.37 0.37 WA 0.45 0.43 IN 0.22 0.21 NM 0.45 0.44 WV 0.01 0.06 IA 0.11 0.07 NY 0.45 0.47 WI 0.06 0.23 KS 0.25 0.24 NC 0.28 0.32 WY 0.22 0.14 37

Behavioral Biases and the Macro-Economy Table 3 Summary Statistics: Risk Sharing Measures and Determinants of Risk Sharing The table includes cross-sectional summary statistics for the state-level unconditional and conditional risk sharing (RS) measures and the main variables used to explain the cross-sectional heterogeneity in the RS measures. The state-level RS estimates are calculated for the 1966 to 1999 period using the AVW method. The stock market participation proxy is calculated using IRS data and it measures the percentage of tax returns in each state with dividend income. HY is the state-level housing collateral ratio computed using the Lustig and Van Nieuwerburgh (2008) method. Section A.2 of the appendix summarizes the method used for estimating the state-level HY. We use the state stock market wealth series of Case, Shiller and Quigley (2001) to compute the ratio of state to U.S. stock market wealth. The state-level behavioral bias measures are obtained by aggregating the biases of a sample of brokerage investors (see Appendix A.4). The set of behavioralproxiesincludestheaverageportfolioturnover, ameasureoflocalpreference(averagepercentageof localownersdividedbystate-levelparticipation),theportfolioweightsinforeignstocks,portfolioconcentration (normalized portfolio variance, which is the ratio of portfolio variance and the average correlation of stocks in the portfolio), and the proportion of all trades that are in stocks with lottery-type features. We also de(cid:133)ne a state-levelcognitiveabilitiesproxy,whichistheaverageimputedcognitiveabilitiesofinvestorsinagivenstate (see Section A.3 of the appendix). The potential risk sharing estimates are reported in Table 7. Sections A.5 to A.7 describe the potential RS computation procedure in detail. The state-level education is from the 1990 Census, and it refers to the proportion of state inhabitants with Bachelor(cid:146)s or higher educational degree. The average age is the average age of the inhabitants of each state according to the 1990 Census. The industry concentration of each state is measured with the Her(cid:133)ndahl index. To compute the index, we obtain the GSP decomposition data from the Bureau of Economic analysis (1966 - 1997) for ten broad industry categories, de(cid:133)ne industry weights using the contribution of each industry to the GSP, take a time-series average of these weights,andusethemtocomputethestate-levelHer(cid:133)ndahlindex. Theagricultural,mining,andmanufacturing industry weights are calculated using the same GSP decomposition data. 38

Behavioral Biases and the Macro-Economy Panel A: Basic Statistics and Correlations with RS Measures Mean St. Dev. Correlation Coefficients 1 2 3 4 5 6 7 8 1 Unconditional RS 0.26 0.14 1 2 Conditional RS 0.25 0.16 0.95 1 3 STK Participation 24.12 4.56 0.11 0.08 1 4 HY 5.68 0.31 0.33 0.31 0.49 1 5 S to U.S. STK Wealth 0.02 0.02 0.26 0.27 0.32 0.23 1 6 Cognitive Ability 0.08 0.23 0.26 0.25 0.35 0.10 0.25 1 7 Portfolio Turnover 6.30 1.35 0.16 0.07 0.24 0.09 0.14 0.15 1 8 Local Preference(x 100) 0.60 0.38 0.21 0.19 0.25 0.18 0.26 0.13 0.30 1 9 % Foreign Stocks 14.41 3.40 0.33 0.35 0.20 0.24 0.13 0.21 0.03 0.03 10 Portfolio Concentration 0.54 0.04 0.03 0.02 0.25 0.17 0.13 0.00 0.06 0.05 11 Lottery Preference 11.55 1.90 0.09 0.05 0.24 0.18 0.22 0.09 0.12 0.13 12 Potential Un. RS 0.66 0.06 0.08 0.03 0.22 0.54 0.08 0.05 0.06 0.07 13 Potential Con. RS 0.66 0.07 0.07 0.03 0.25 0.56 0.06 0.02 0.04 0.08 14 Education 27.13 6.20 0.18 0.18 0.70 0.29 0.27 0.67 0.27 0.30 15 Average Age 50.33 1.86 0.14 0.18 0.20 0.15 0.06 0.28 0.26 0.30 16 Industry Concentration 0.15 0.03 0.12 0.16 0.14 0.13 0.03 0.32 0.16 0.15 17 Agric. GSP weight 0.03 0.03 0.38 0.33 0.02 0.42 0.28 0.26 0.12 0.20 18 Mining GSP weight 0.04 0.07 0.02 0.06 0.27 0.16 0.25 0.14 0.18 0.02 19 Manuf.GSP weight 0.19 0.08 0.03 0.03 0.02 0.15 0.13 0.08 0.03 0.04 Panel B: Correlation Matrix (continued) 9 10 11 12 13 14 15 16 17 18 10 Portfolio Concentration 0.04 1 11 Lottery Preference 0.18 0.28 1 12 Potential Un. RS 0.09 0.04 0.04 1 13 Potential Con. RS 0.10 0.03 0.05 0.99 1 14 Education 0.16 0.16 0.13 0.05 0.12 1 15 Average Age 0.16 0.04 0.27 0.04 0.03 0.32 1 16 Industry Concentration 0.26 0.35 0.06 0.24 0.19 0.43 0.03 1 17 Agric. GSP weight 0.20 0.18 0.03 0.05 0.04 0.13 0.21 0.48 1 18 Mining GSP weight 0.02 0.21 0.16 0.10 0.06 0.39 0.19 0.17 0.01 1 19 Manuf.GSP weight 0.14 0.23 0.07 0.38 0.40 0.04 0.04 0.15 0.24 0.47 39

Behavioral Biases and the Macro-Economy Table 4 Traditional Determinants of Risk Sharing: Cross-Sectional Regression Estimates This table reports cross-sectional risk sharing regression estimates, where either the unconditional or the conditional risk sharing (RS) measure is the dependent variable. The set of independent variables includes the traditional determinants of risk sharing. The stock market participation proxy is the percentage of tax returns in each state that reported dividend income. These data are from the Internal Revenue Service (IRS). We use the state-level stock market wealth series of Case, Shiller and Quigley (2001) to compute the ratio of state to U.S. stock market wealth. The HY is the state-level housing collateral ratio computed as in Lustig and Van Nieuwerburgh (2008). Section A.2 of the appendix summarizes the method used for estimating statelevel HY. The high participation dummy variable takes the value of one for states in which the stock market participation proxy is above its median value, and zero otherwise. The industry concentration of each state is measured using the Her(cid:133)ndahl index. To compute the index, we obtain the GSP decomposition data from the Bureau of Economic analysis (1966 - 1997) for ten broad industry categories, de(cid:133)ne industry weights using the contribution of each industry to the GSP, take a time-series average of these weights, and use them to compute the state-level Her(cid:133)ndahl index. The agricultural, mining, and manufacturing industry weights are calculated using the same GSP decomposition data. The cross-sectional regressions are estimated using OLS. TheAVWrisksharingestimationmethodisdescribedinSection2.1andtherisksharingregressionspeci(cid:133)cation is described in Section 3.1. The t-statistics reported in smaller font underneath the coe¢ cient estimates are calculated using standard errors corrected for heteroskedasticity. The dependent and independent variables have been standardized (mean is set to zero and the standard deviation is one). Panel A: Basic Specifications (1) (2) (3) (4) (5) (6) (7) (8) UnRS ConRS UnRS ConRS UnRS ConRS UnRS ConRS STK Participation Proxy 0.11 0.08 0.12 0.16 0.97 0.65 0.96 1.19 HY 0.33 0.31 0.34 0.34 2.92 3.08 2.64 2.87 State to U.S. STK Wealth 0.26 0.27 0.23 0.25 2.61 2.93 1.80 2.05 Adjusted R squared 0.01 0.01 0.09 0.08 0.05 0.06 0.10 0.11 40

Behavioral Biases and the Macro-Economy Panel B: Extended Specifications (1) (2) (3) (4) (5) (6) (7) (8) UnRS ConRS UnRS ConRS UnRS ConRS UnRS ConRS STK Participation Proxy 0.07 0.06 0.29 0.32 0.29 0.32 0.26 0.31 0.50 0.43 1.90 2.23 1.89 2.25 1.77 2.08 High Participation Dummy 0.12 0.06 0.13 0.06 0.09 0.03 ( > 50 Pctl.) 0.46 0.25 0.56 0.30 0.40 0.14 HY 0.37 0.37 0.39 0.39 0.38 0.39 2.86 3.29 3.03 3.52 3.04 3.51 State to U.S. STK Wealth 0.12 0.11 0.91 1.03 High Part. x State to U.S. Wealth 0.23 0.27 0.31 0.35 0.32 0.36 1.56 2.07 2.84 3.38 3.06 3.60 Adjusted R squared 0.02 0.03 0.10 0.11 0.11 0.12 0.13 0.14 Panel C: Industry Effects (1) (2) (3) (4) (5) (6) (7) (8) UnRS ConRS UnRS ConRS UnRS ConRS UnRS ConRS STK Participation Proxy 0.11 0.26 0.14 0.24 0.67 1.68 0.85 1.37 HY 0.23 0.30 0.26 0.31 1.26 1.76 1.71 2.06 High Part. x State to U.S. Wealth 0.24 0.32 0.23 0.30 1.71 2.50 1.85 2.47 Industry Concentration 0.12 0.16 0.02 0.08 1.20 1.64 0.15 0.66 Agricultural GSP weight 0.41 0.38 0.25 0.11 0.21 0.12 4.59 4.83 1.25 0.59 1.58 0.97 Mining GSP weight 0.06 0.15 0.05 0.03 0.49 1.28 0.43 0.27 Manufacturing GSP weight 0.15 0.20 0.06 0.09 1.16 1.46 0.43 0.58 Adjusted R squared 0.01 0.01 0.10 0.09 0.09 0.08 0.14 0.13 41

Behavioral Biases and the Macro-Economy Table 5 Behavioral Determinants of Risk Sharing: Cross-Sectional Regression Estimates This table reports cross-sectional risk sharing regression estimates, where either the unconditional or the conditional risk sharing (RS) measure is the dependent variable. The set of independent variables contains the behavioral determinants of risk sharing and the traditional determinants of risk sharing de(cid:133)ned in Table 4. We de(cid:133)ne the state-level behavioral bias proxies by aggregating the investment decisions of a sample of brokerage investors (see Section A.6 of the appendix). We also consider the state-level cognitive abilities proxy in the regression speci(cid:133)cation. Sections 4.2 and 4.3 provide details on the cognitive abilities and behavioral bias measures, respectively. The cross-sectional regressions are estimated using OLS. The t-statistics reported in smaller font underneath the coe¢ cient estimates are calculated using standard errors corrected for heteroskedasticity. Thedependentandindependentvariableshavebeenstandardized(meanissettozeroandthe standard deviation is one). (1) (2) (3) (4) (5) (6) (7) (8) UnRS ConRS UnRS ConRS UnRS ConRS UnRS ConRS STK Participation Proxy 0.34 0.39 0.39 0.41 2.32 2.51 2.66 2.63 HY 0.40 0.41 0.35 0.35 3.46 3.89 2.98 2.88 High Part. x State to U.S. Wealth 0.29 0.33 0.39 0.39 2.81 3.38 4.20 4.43 Cognitive Ability 0.26 0.25 0.26 0.25 0.16 0.16 2.22 2.24 2.93 2.77 1.91 1.94 Portfolio Turnover 0.24 0.15 0.32 0.23 1.90 1.03 3.11 2.02 Local Preference 0.32 0.27 0.24 0.18 3.39 2.69 2.66 1.82 Percentage in Foreign Stocks 0.39 0.39 0.29 0.29 4.00 3.95 2.71 2.65 Portfolio Concentration 0.11 0.04 0.14 0.07 0.76 0.28 1.21 0.62 Lottery Preference 0.21 0.15 0.24 0.17 1.59 1.24 1.97 1.57 Adjusted R squared 0.05 0.04 0.17 0.18 0.18 0.12 0.32 0.24 42

Behavioral Biases and the Macro-Economy Table 6 Investor Sophistication and Risk Sharing: Cross-Sectional Regression Estimates This table reports cross-sectional risk sharing regression estimates, where either the unconditional or the conditional risk sharing (RS) measure is the dependent variable. The set of independent variables in Panel A containsanindexofinvestorsophisticationandthetraditionaldeterminantsofrisksharingde(cid:133)nedinTable4. Section 4.4 describes the method used to compute the sophistication index. In Panel B, we report regression estimates with the state-level education measure (an alternative sophistication proxy), which is de(cid:133)ned as the proportion of state inhabitants with Bachelor(cid:146)s or higher educational degree. The state-level education data are from the 1990 Census. The cross-sectional regressions are estimated using OLS. The AVW risk sharing estimationmethodisdescribedinSection2.1andtherisksharingregressionspeci(cid:133)cationisdescribedinSection 3.1. Thet-statisticsreportedinsmallerfontunderneaththecoe¢ cientestimatesarecalculatedusingstandard errorscorrectedforheteroskedasticity. Thedependentandindependentvariableshavebeenstandardized(mean is set to zero and the standard deviation is one). Panel A: Sophistication Index of Stock Holders (1) (2) (3) (4) (5) (6) (7) (8) UnRS ConRS UnRS ConRS UnRS ConRS UnRS ConRS STK Participation Proxy 0.26 0.31 0.30 0.34 0.42 0.46 0.40 0.43 1.78 2.06 2.20 2.47 3.33 3.52 2.99 2.88 HY 0.34 0.37 0.37 0.38 0.42 0.42 0.34 0.36 2.43 2.69 3.15 3.40 4.76 4.79 3.51 3.40 High Part. x State to U.S. Wealth 0.32 0.36 0.33 0.37 0.27 0.31 0.38 0.41 3.23 3.66 3.12 3.79 2.61 3.29 4.24 4.75 Sophistication Index (above 25 Pctl.) 0.17 0.06 1.17 0.34 Sophistication Index (above median) 0.24 0.19 1.90 1.35 Sophistication Index (above 75 Pctl.) 0.60 0.56 5.88 5.81 Sophistication Index (Continuous) 0.51 0.42 5.26 4.18 Adjusted R squared 0.14 0.12 0.29 0.35 0.46 0.42 0.37 0.30 43

Behavioral Biases and the Macro-Economy Panel B: Census Demographic Variables (1) (2) (3) (4) (5) (6) UnRS ConRS UnRS ConRS UnRS ConRS STK Participation Proxy 0.38 0.46 0.41 0.49 2.20 2.37 2.77 2.90 HY 0.40 0.40 0.42 0.42 3.14 3.52 4.70 4.72 High Part. x State to U.S. Wealth 0.30 0.33 0.27 0.30 2.80 3.27 2.64 3.26 Sophistication Index (> 75 Pctl.) 0.60 0.55 5.73 5.54 Education 0.18 0.18 0.19 0.23 0.02 0.04 1.71 1.71 1.44 1.65 0.19 0.32 Adjusted R squared 0.01 0.01 0.13 0.15 0.45 0.41 44

Behavioral Biases and the Macro-Economy Table 7 Risk Sharing Levels Potentially Attainable Through Financial Markets Thistablereportsunconditional(UnRS)andconditional(ConRS)risksharing(RS)levelsthatarepotentially attainable using a set of (cid:133)nancial assets. The sample period is from 1966 to 2004. The set of (cid:133)nancial assets includesthethreeFama-Frenchandmomentumfactors,the30-dayTreasuryBill,the10-yeargovernmentbond, and the Aaa and Baa rated corporate bonds. The income before risk sharing is the relative GSP, measured in per capita real terms. The income after risk sharing is based on the returns from an optimal composite portfolio containing the growth rate of GSP and (cid:133)nancial asset returns. Sections A.7 to A.9 of the appendix provides details of the procedure used to obtain the potential RS estimates. We use the Athanasoulis and van Wincoop (2001) methodology to obtain the RS estimates and measure their statistical signi(cid:133)cance. Section 2.1 de(cid:133)nes the income measures and presents details of the AVW risk sharing estimation method. In Panel A, we report the aggregate RS measures calculated by pooling the observations from all states. The t-statistics of the estimates are reported in smaller font below the estimates. In Panel B, we report the RS measures for individual U.S. states. Panel A: Aggregate Risk Sharing Estimates UnRS 0.62 ConRS 0.62 130.88 140.54 Panel B: RS Estimates for Individual States State UnRS ConRS State UnRS ConRS State UnRS ConRS State UnRS ConRS AL 0.64 0.62 IN 0.60 0.59 NE 0.68 0.67 SC 0.57 0.59 AK 0.60 0.59 IA 0.65 0.65 NV 0.72 0.71 SD 0.71 0.71 AZ 0.77 0.77 KS 0.61 0.60 NH 0.75 0.75 TN 0.65 0.64 AR 0.61 0.59 KY 0.59 0.58 NJ 0.68 0.69 TX 0.73 0.72 CA 0.66 0.67 LA 0.58 0.57 NM 0.72 0.71 UT 0.72 0.72 CO 0.72 0.70 ME 0.70 0.71 NY 0.64 0.64 VT 0.69 0.69 CT 0.70 0.70 MD 0.66 0.67 NC 0.61 0.61 VA 0.65 0.65 DE 0.70 0.70 MA 0.70 0.70 ND 0.58 0.59 WA 0.73 0.72 DC 0.60 0.62 MI 0.60 0.59 OH 0.49 0.48 WV 0.63 0.61 FL 0.71 0.72 MN 0.69 0.70 OK 0.67 0.66 WI 0.66 0.63 GA 0.69 0.70 MS 0.54 0.53 OR 0.73 0.72 WY 0.80 0.79 ID 0.74 0.72 MO 0.59 0.59 PA 0.54 0.53 IL 0.64 0.64 MT 0.70 0.69 RI 0.63 0.64 45

Behavioral Biases and the Macro-Economy Table 8 Geographical Location and Risk Sharing: Cross-Sectional Regression Estimates Thistablereportscross-sectionalrisksharingregressionestimates,whereeithertheunconditionalortheconditionalrisksharing(RS)measureisthedependentvariable. Thesetofindependentvariablescontainspotential risksharingmeasures(seeTable7),anindexofinvestorsophistication(seeTable6),andthetraditionaldeterminants of risk sharing (see Table 4). We use the potential RS measure to de(cid:133)ne two dummy variables. The high potential RS dummy variable (denoted by (cid:147)RS Potential > 50 Pctl.(cid:148)) takes the value of one for states in which the potential RS is above its median value, and zero otherwise. The low potential RS dummy variable (denoted by (cid:147)RS Potential < 25 Pctl.(cid:148)) takes the value of one for states in which the potential RS is below its 25th percentile, and zero otherwise. The AVW risk sharing estimation method is described in Section 2.1 andtherisksharingregressionspeci(cid:133)cationisdescribedinSection3.1. Thecross-sectionalregressionsareestimated using OLS. The t-statistics reported in smaller font underneath the coe¢ cient estimates are calculated using standard errors corrected for heteroskedasticity. The dependent and independent variables have been standardized (mean is set to zero and the standard deviation is one). (1) (2) (3) (4) (5) (6) (7) (8) UnRS ConRS UnRS ConRS UnRS ConRS UnRS ConRS STK Participation Proxy 0.43 0.47 0.46 0.51 0.49 0.53 0.46 0.51 3.35 3.32 3.73 3.56 4.00 3.75 3.82 3.69 HY 0.36 0.42 0.27 0.29 0.27 0.28 0.28 0.33 3.68 4.51 2.75 2.95 2.91 2.85 2.91 3.53 High Part. x State to U.S. Wealth 0.29 0.31 0.34 0.37 0.35 0.37 0.32 0.35 2.63 2.94 3.23 3.47 3.29 3.56 2.92 3.13 Sophistication Index 0.62 0.56 0.64 0.60 0.53 0.48 0.70 0.68 5.76 5.42 6.99 6.36 4.76 4.26 5.83 6.48 RS Potential 0.10 0.00 0.72 0.01 RS Potential > 50 Pctl. 0.26 0.22 0.28 0.23 0.24 0.19 2.30 1.42 2.38 1.51 2.06 1.31 (RS Pot. > 50 Pctl.) x Soph. Index 0.21 0.20 1.84 2.10 (RS Pot. < 25 Pctl.) x Soph. Index 0.10 0.17 1.02 2.11 Adjusted R squared 0.46 0.41 0.50 0.44 0.51 0.46 0.49 0.45 46

Behavioral Biases and the Macro-Economy Table 9 Results from Additional Robustness Checks This table reports cross-sectional risk sharing regression estimates reported in Table 8 with additional control variables. Speci(cid:133)cally, we include initial GSP per capita, which is the GSP at the beginning of our sample period (1966). Average age is the average age of the state population according to the 1990 Census. The three regional dummy variables correspond to the three U.S. Census regions. The South region dummy is excluded from the speci(cid:133)cation. The cross-sectional regressions (1), (2), and (5) to (8) are estimated using OLS. The regressions (3) and (4) are estimated using an instrumental variable (IV) estimator, which instruments the sophistication index with the initial per capita GSP. The t-statistics reported in smaller font underneath the coe¢ cient estimates are calculated using standard errors corrected for heteroskedasticity. The dependent and independent variables have been standardized (mean is set to zero and the standard deviation is one). (1) (2) (3) (4) (5) (6) (7) (8) IV IV UnRS ConRS UnRS ConRS UnRS ConRS UnRS ConRS STK Participation Proxy 0.49 0.55 0.53 0.64 0.50 0.52 0.28 0.39 3.96 3.76 3.56 3.23 3.84 3.24 2.56 2.98 HY 0.27 0.27 0.27 0.25 0.28 0.27 0.07 0.15 2.77 2.49 2.68 1.83 3.00 2.79 0.53 0.95 High Part. x State to U.S. Wealth 0.34 0.37 0.35 0.38 0.35 0.37 0.36 0.38 3.30 3.62 3.08 3.01 3.28 3.43 3.35 3.78 Sophistication Index 0.52 0.45 0.51 0.56 0.53 0.48 0.53 0.48 3.92 3.28 3.08 2.67 4.74 4.34 5.39 4.25 RS Potential > 50 Pctl. 0.28 0.25 0.30 0.33 0.28 0.24 0.20 0.18 2.37 1.52 2.15 1.62 2.38 1.50 1.97 1.20 (RS Pot. > 50 Pctl.) x Soph. Index 0.21 0.22 0.37 0.47 0.20 0.21 0.17 0.18 1.78 2.07 1.38 1.74 1.80 2.16 1.69 1.93 Initial GSP per capita (1966) 0.01 0.07 0.10 0.74 Average Age 0.03 0.02 0.31 0.26 North Eastern State Dummy 0.20 0.14 0.79 0.55 Mid Western State Dummy 0.41 0.26 1.54 0.80 Western State Dummy 0.46 0.35 2.37 1.80 Adjusted R squared 0.50 0.45 0.49 0.35 0.50 0.44 0.53 0.44 47

Behavioral Biases and the Macro-Economy Appendix Inthisappendix, weprovideadditionaldetailsaboutthedatasourcesandthemethodologyemployed to estimate the risk sharing regressions. We also further explain some of our methodological choices. A.1 Mesaurement Error and Negative Risk Sharing Estimates A negative risk sharing (RS) measure can arise when the information (i.e., the signal) is weaker than the noise (i.e., the measurement error) in the observed values of GSP and SI growth rates. The following example illustrates this possibility. Suppose g and gRS denote growth rates before and after risk sharing, respectively. Due to measurement error, the observed values of g and gRS are given by the sum of the true g (i.e., g ) (cid:3) and true gRS (i.e., gRS ) plus an additive measurement error e and eRS, respectively: g = g + e, (cid:3) (cid:3) gRS = gRS + eRS. The variables g and gRS contain the information, while e and eRS contain (cid:3) (cid:3) (cid:3) the noise in g and gRS, respectively. Due to risk sharing, the volatility of gRS should be lower than (cid:3) that of g and the true RS measure (= 1 gRS =g ) would be positive. However, if the volatility of (cid:3) (cid:3) (cid:3) (cid:0) eRS is signi(cid:133)cantly greater than that of gRS , i.e., when the noise in gRS is too high, the volatility (cid:3) of gRS could exceed the volatility of g, and the measured RS (= 1 gRS=g) can be negative. (cid:0) A.2 State-Level Housing Collateral Ratio TheHYratioisthecointegratingresidualofloghousingwealth(h)fromitslongrunrelationshipwith log human wealth (y), i.e., HY= h by, where the parameter b is extracted from the cointegrating (cid:0) vector [1;b] between h and y. We measure the annual housing wealth of each state using the Lustig andVanNieuwerburgh(2008)approach. Duetodatalimitations, theseriesforthestate-levelhousing collateral cannot be constructed before 1980. Therefore, the estimation period for HY is from 1980 to 1999. We measure the annual human wealth using the BEA data on state income from wages and salaries and personal transfers. Using the panel dynamic ordinary least square estimator of Mark and Sul (2003), we estimate b = 0:103. We use a panel estimator because we do not have enough annual observations per state to reliably estimate a cointegrating vector for each state. A.3 Imputation Method and the Model of Cognitive Abilities Theimputationmethodusedtoobtainthecognitiveabilitiesproxyiscommonlyusedtolinkmultiple data sets (e.g., Skinner (1987), Ziliak (1998), Browning and Leth-Petersen (2003)). Graham, Harvey, and Wei (2006) and Korniotis and Kumar (2008) use this approach in a Finance setting. Speci(cid:133)cally, Graham, Harvey, and Wei (2006) use investor characteristics to estimate models of perceived competence and optimism. They estimate the models in one setting and use the predicted values of 48

Behavioral Biases and the Macro-Economy competence and optimism from their models in another setting in which competence and optimism measures are unavailable. The CAB model we use for obtaining the imputed CAB is estimated in Korniotis and Kumar (2008). The model is estimated using a large European data set (Survey of Health and Retirement in Europe or SHARE), which contains 22,000 observations spread across eleven countries. We obtain similar results when we use the cognitive abilities model estimated using the 2004 Health and Retirement Survey (HRS) data set from the U.S. To assess the appropriateness of the state-level cognitive abilities estimates, we compute the correlation between state-level CAB estimates and state IQ estimates reported in Kanazawa (2006). While the state-level IQ estimates are noisy, somewhat controversial, and do not match with our sample period, it is comforting to know that the correlation between our state-level CAB estimates and the state-level IQ estimates is signi(cid:133)cantly positive (correlation = 0.207, t-statistic = 2.15). A.4 Retail Investor Data Set We use a data set containing the portfolio holdings and trades of a large sample of individual investors at a large U.S. discount brokerage house for the 1991 to 1996 time period. There are 77,995 households in the database. These investors hold and trade a variety of securities including common stocks, mutual funds, options, American depository receipts (ADRs), etc. The data also contain demographic information such as age, occupation, income, self-reported net worth, gender, marital status, and the zip code of household(cid:146)s primary residence. To our knowledge, at present, this is the most comprehensive data on the stock-holdings of U.S. individual investors. Additional details on the investor database are available in Barber and Odean (2000). ComparisonswithotherrepresentativedatasetssuchastheSurveyofConsumerFinances(SCF), TradeandQuote(TAQ),andInternalRevenueServices(IRS)indicatethatthereisareasonablygood match between the portfolio and trading characteristics of sample investors and representative U.S. households. Ivkovi·c, Poterba, and Weisbenner (2005) (cid:133)nd that the distribution of stock holding periods in the IRS and the brokerage data sets is very similar. Barber, Odean, and Zhu (2008) (cid:133)nd that the characteristics of trades by brokerage investors are very similar to the small trades time series in TAQ. Graham and Kumar (2005) and Ivkovi·c, Sialm, and Weisbenner (2008) make comparisons with the SCF and provide additional evidence on the representativeness of the brokerage data. Overall,theindividualinvestorsamplecloselyresemblestheU.S.individualinvestorpopulation along many important dimensions. A.5 Mean-Variance Portfolio Optimization Framework Tomeasurethelevelofrisksharingthatcanbepotentiallyattainedusing(cid:133)nancialassets,weminimize thetotalvarianceofacompositeportfoliothatcontainsa(cid:147)productasset(cid:148)(aperpetualclaimtoGSP) and the (cid:133)nancial assets. The income growth rate after risk sharing is the return from this composite 49

Behavioral Biases and the Macro-Economy portfolio. Speci(cid:133)cally, we use the standard mean-variance optimization method to solve: (cid:13) min w 0 Vw; subject to 1 0 w = 1, r 0 w = (cid:22), and w y = w y . w=(w1; :::; ws; wy) 0 2 Here, (cid:13) is the coe¢ cient of risk aversion, which is set to three. This choice is consistent with the existing consumption-based asset pricing literature (e.g., Mehra and Prescott (1985), Campbell and Cochrane (1999)). w is is a vector of size (S +1) 1 and contains the portfolio weights. Its (cid:133)rst (cid:2) S elements correspond to the weights on (cid:133)nancial assets. Its last element (w ) is the weight on the y product asset. The set of (cid:133)nancial assets include broad stock market indices and debt instruments. The vector r contains the mean return of the (cid:133)nancial assets and the mean growth rate of GSP. V is the variance-covariance matrix between the returns of the (cid:133)nancial assets and the growth rate of GSP. (cid:22) is the mean growth rate of SI for the state. To determine the return from the product asset, we follow Fama and Schwert (1977) and Jagannathan and Wang (1996), and assume that the growth rate of the GSP is unpredictable. When the growth rate is unpredictable, the return from the product asset is appropriately captured by the GSP growth rate. As mentioned earlier, we also consider the case in which the growth rate of GSP is predictable. Speci(cid:133)cally, we de(cid:133)ne the return to the product asset following Baxter and Jermann (1997) and (cid:133)nd similar results. We impose three restrictions on the minimum variance portfolio (MVP) calculations. First, the weights are restricted to sum to one, i.e., 1w = 1. Second, we add restrictions on the mean return 0 of the composite portfolio of the product asset and (cid:133)nancial assets for each state. We require it to be higher or equal to each state(cid:146)s average SI growth rate, which we denote by (cid:22), i.e., r 0 w = (cid:22). We impose this restriction because we do not want the MVP weights to simply prescribe a portfolio that over-weights low risk assets and, thus, almost by construction, generates high levels of risk-sharing. Third, the weight on the product asset is set equal to the ratio of GSP to the total state wealth, which we denote by w , i.e., w = w . The total wealth of a state is the sum of state-level (cid:133)nancial y y y wealth and the GSP, where (cid:133)nancial wealth is de(cid:133)ned as (cid:133)nancial assets minus (cid:133)nancial liabilities. This constraint ensures that the weight on the product asset is always positive and re(cid:135)ects the actual stock market participation level in the state.41 When participation in (cid:133)nancial markets increases, the level of (cid:133)nancial wealth in the state increases relative to the level of GSP, and the weight on the product asset decreases. For example, if the annual GSP is $10,000 and the weight on the product asset is 0.4, the total weight on (cid:133)nancial assetsshouldbe0.6. Thus, toensureanoptimallevelofrisksharing, thesizeofthe(cid:133)nancialportfolio should be 0:6=0:4 = 1:5 times the size of the product asset (= $15,000). We calculate the total state wealth in the vector w as follows. First, because wealth data per y state are not available, we construct a proxy for state wealth following Case, Shiller and Quigley 41Thechoiceofapositiveweightre(cid:135)ectsthefactthattheproductassetisnon-tradableandcannotbeshortedbecause macro-markets, in which claims on GSP could be traded, do not exist (Shiller (1993, 1996)). 50

Behavioral Biases and the Macro-Economy (2001). Speci(cid:133)cally, we compute the (cid:133)nancial wealth of a state by multiplying the aggregate U.S. (cid:133)nancial wealth level with a proxy for the ratio of state (cid:133)nancial wealth to national (cid:133)nancial wealth (i.e., state-to-national (cid:133)nancial ratio). We obtain the U.S. wealth series from the (cid:135)ow of funds accounts.42 To proxy for the state-to-national (cid:133)nancial ratio, we use a data set from the Internal Revenue Services (IRS), which are available at an annual frequency for the 1998 to 2005 period.43 Using the IRS data, we calculate the ratio of reported (cid:133)nancial income (= dividends plus net capital gains) in a state to the reported (cid:133)nancial income in the U.S. The average of this ratio in a state over the 1998 to 2005 is our proxy for the state-to-national (cid:133)nancial ratio. This proxy is multiplied with U.S. (cid:133)nancial wealth to obtain the state (cid:133)nancial wealth series. For each year and each state, we also calculate the ratio of the state GSP and the total state wealth (= GSP plus state (cid:133)nancial wealth). We use the time-series average of this ratio over the 1966 to 2004 period as the weight w on the product asset. This constraint further ensures that the y equilibrium asset returns are not a⁄ected by risk sharing prescribed trading strategies. The results reported in the (cid:147)GSP(cid:148)columns of Table A.1 indicate that the minimum weight on the product asset across all states is 0.14 (for Nevada), the maximum is 0.54 (for Louisiana), and the average weight across all states is 0.36. A.6 Choice of Financial Assets Our MVP calculations utilize a set of bond and equity indices. We identify these indices based on the evidence from the existing literature, which shows that (cid:133)nancial assets contain information about the state of the aggregate economy (e.g., Lamont (2001)). If economic activities across U.S. states are correlated,(cid:133)nancialassetscouldalsocontaininformationabouttheincomegrowthratesofU.S.states and could provide opportunities for reducing risk. Particularly, those assets could also successfully predict the variation in the growth rate of the gross state product (GSP) relative to the national growth rate. The previous literature has shown that the aggregate stock market returns and stock market spreads such as the small-minus-big (SMB) and high-minus-low (HML) factors contain information about the future economic activity (e.g., Barro (1990), Liew and Vassalou (2000), Lettau and Ludvigson (2001), Vassalou (2003)). Similarly, Harvey (1988, 1989) shows that bond market instruments contain more accurate information about the national growth rates. Spreads based on bills and bonds are also good indicators of current and future economic activities. Speci(cid:133)cally, the paper-bill spread is an indicator of future economic activities, including the real output growth rate, the unemployment rate, and the income growth rate (e.g., Bernanke and Blinder (1992), Friedman and Kuttner (1992), Kashyap, Stein, and Wilcox (1993)). The predictive power of the paper-bill spread comes from its relation to the monetary policy. In particular, tighter monetary 42The funds data are available at http://www.federalreserve.gov/releases/z1/Current/data.htm. 43The IRS data are available at http://www.irs.gov/taxstats/article/0,,id=171535,00.html. 51

Behavioral Biases and the Macro-Economy policy might prevent smaller (cid:133)rms from getting credit, thereby curtailing economic activity. In this setting, the widening spread could serve as an indicator of future recession. Furthermore, the corporate bond spread is likely to be more sensitive to changes in economic conditions and could contain information about the business cycle (e.g., Gertler and Lown (1999), Saito and Takeda (2000), Zhang (2002), Sangvinatsos (2005)). Last, Harvey (1988) (cid:133)nds that real term structure measures such as the term spread can predict future aggregate consumption (or GSP) growth. Motivated by these earlier papers, our broad stock market indices include the monthly returns of the three Fama-French factors (Fama and French (1992, 1993)) and the momentum factor (Jegadeesh and Titman (1993), Carhart, 1997)) from Kenneth French(cid:146)s data library.44 Our debt instruments include the monthly yields for the 30-day Treasury Bill and 10-year government bond obtained from the Center for Research on Security Prices (CRSP). We also use the monthly yields for Aaa and Baa rated corporate bonds obtained from the Federal Reserve Economic Data library.45 Because the GSP data are at the annual frequency, we calculate annual returns by compounding the monthly returns. Table 1, Panel B includes summary statistics for the (cid:133)nancial assets as well as correlations with GSP and SI growth rates. Examining the correlations, we (cid:133)nd that the GSP growth rate measures and equity asset returns are moderately correlated. For instance, the maximum correlation between the growth rate of GSP (g ) and equity returns is 0.070. The correlations with debt instruments GSP (cid:0) . For example, the correlation of the GSP growth rate with the 10-year government bond is 0.203. (cid:0) The correlations are negative and signi(cid:133)cantly lower (in absolute value) for the relative GSP measure (g g ). For this series, the maximum correlation, in absolute value, is only 0.040. Our GSP GDP (cid:0) correlation estimates are consistent with previous studies that (cid:133)nd moderate correlations between the GDP growth rates and (cid:133)nancial asset returns (e.g., Fama and Schwert (1977), Bottazzi, Pesenti, and Van Wincoop (1996), Davis and Willen (2000b)).46 A.7 MVP Weights For Individual U.S. States We compute the minimum-variance portfolio (MVP) weights separately for each state. To calculate the weights, we use GSP and return data for the period 1966 to 2004. Although our SI data end in 1999, for calculating the MVP weights, we use all the available data to minimize estimation errors in the weights. The vector of mean returns r is the average of the (cid:133)nancial asset returns and growth rate of GSP over 1966 to 2004. The estimate of the variance-covariance matrix V is the sample variance-covariance matrix for the period 1966 to 2004. We report the estimated weights in Table A.1. The type of portfolio prescribed by the weights is similaracrossmoststatesandconformswiththe(cid:133)ndingsfromtheexistingliterature. First, theMVP 44The web site is http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html. 45The web site is http://liber8.stlouisfed.org/. 46Previousstudieshavereportedthemoderatecorrelationsbetween(cid:133)nancialmarketreturns(primarilytheaggregate stock market returns) and the GDP growth rate. However, our evidence of moderate correlations among returns from (cid:133)nancial assets and state-level GSP growth rates is new. 52

Behavioral Biases and the Macro-Economy strategies recommend borrowing using the 30-day Treasury bill (average weight is 0:11) and holding (cid:0) the 10-year bond (average weight is 0:06). This strategy exposes the composite portfolio returns to termstructurerisk,whichisconsistentwithHarvey(cid:146)s(1988)(cid:133)ndingthatrealtermstructuremeasures can predict future aggregate consumption (or GDP) growth. Second,theMVPstrategiesprescribeshortpositionsinthestockmarketindices(averageweights on MKT, HML and UMD are 0:02, 0:03, 0:02, respectively). The only exception is the SMB (cid:0) (cid:0) (cid:0) index, which has an average weight of 0.04. Last, the MVP strategies prescribe short positions in the corporate bond spread. The average weights on the Aaa and Baa bonds are 3:09 and 2:39, (cid:0) respectively. Thisevidenceindicatesthattheprevious(cid:133)ndingthatthecorporatebondspreadcontains information about the U.S. business cycle (e.g., Gertler and Lown (1999), Saito and Takeda (2000), Zhang (2002) and Sangvinatsos (2004)) carries over to the state-level macro-economy. A.8 Correlation-Based Risk Sharing Measure For robustness, we examine whether our main results change signi(cid:133)cantly when we use an alternative, correlation-based methodology to measure risk sharing (Asdrubali, Sorensen, and Yosha (1996), Sorensen, Wu, Yosha, and Zhu (2007)). This alternative risk sharing measure formalizes the key idea that under full risk sharing, the growth rates of income before and after risk sharing would be uncorrelated. Speci(cid:133)cally, the risk sharing estimate is (1 (cid:12)), where (cid:12) is the coe¢ cient estimate (cid:0) from a regression speci(cid:133)cation that is estimated after pooling data from all states. The dependent variable in the regression speci(cid:133)cation is the growth rate of relative SI and the independent variable is the growth rate of relative GSP. In comparison to the RS estimates obtained using the AVW method, the correlation-based RS estimates are uniformly higher (almost double). For example, the average unconditional RS estimates with the correlation-based and AVW methods are 0.50 and 0.26, respectively. Although the levels di⁄er signi(cid:133)cantly, both measures exhibit similar cross-sectional variations. The cross-sectional correlation between the two RS measures is about 0.80. When we re-estimate the risk-sharing regressions using the correlation-based RS measure, we obtain very similar results. In particular, we (cid:133)nd that the geographical factor is still the weakest of thethreedeterminantsofrisksharingincludedinthespeci(cid:133)cation. Theregressionestimatesreported in previous tables are also similar when we use the correlation-based RS measure. Given the high correlationbetweentheAVWandcorrelation-basedRSmeasures, thisevidenceisnotverysurprising. But nonetheless, they indicate that our risk sharing regression estimates are robust. 53

Behavioral Biases and the Macro-Economy Table A.1 MVP Weights For Individual U.S. States This table report the MVP weights computed by minimizing the total variance of a composite portfolio that contains the growth rate of per capita real GSP and a set of (cid:133)nancial assets. GSP MKT SMB HML UMD 30d Bill 10y B Aaa Baa AL 0.42 0.01 0.03 0.02 0.00 0.03 0.05 2.45 1.88 AK 0.52 0.01 0.00 0.06 0.02 1.88 0.17 7.86 5.62 AZ 0.24 0.01 0.04 0.02 0.01 0.09 0.05 3.66 2.85 AR 0.41 0.01 0.04 0.03 0.01 0.00 0.06 2.14 1.60 CA 0.26 0.02 0.04 0.02 0.02 0.14 0.05 4.16 3.31 CO 0.23 0.02 0.04 0.02 0.02 0.18 0.04 4.29 3.36 CT 0.25 0.02 0.04 0.03 0.02 0.10 0.04 4.17 3.34 DE 0.37 0.04 0.06 0.01 0.02 0.01 0.05 3.05 2.46 DC 0.50 0.01 0.01 0.02 0.01 0.03 0.00 1.83 1.39 FL 0.17 0.01 0.04 0.02 0.02 0.12 0.05 4.62 3.72 GA 0.32 0.03 0.04 0.03 0.02 0.06 0.06 3.40 2.68 HI 0.36 0.02 0.01 0.02 0.02 0.26 0.01 3.03 2.19 ID 0.31 0.02 0.05 0.05 0.04 0.03 0.10 2.89 2.27 IL 0.35 0.02 0.04 0.03 0.01 0.03 0.05 2.79 2.15 IN 0.46 0.04 0.07 0.06 0.03 0.23 0.10 1.47 1.19 IA 0.47 0.02 0.07 0.05 0.02 0.09 0.11 1.01 0.66 KS 0.42 0.01 0.04 0.03 0.01 0.16 0.06 2.74 2.04 KY 0.46 0.01 0.04 0.01 0.00 0.03 0.04 1.53 1.08 LA 0.54 0.01 0.01 0.01 0.01 0.70 0.10 2.50 1.39 ME 0.33 0.02 0.05 0.04 0.03 0.03 0.06 3.66 2.99 MD 0.32 0.01 0.04 0.02 0.01 0.07 0.04 3.73 3.02 MA 0.25 0.03 0.04 0.03 0.02 0.05 0.06 4.33 3.55 MI 0.46 0.05 0.06 0.08 0.04 0.40 0.12 1.47 1.34 MN 0.35 0.02 0.05 0.05 0.03 0.05 0.08 3.00 2.33 MS 0.47 0.02 0.03 0.05 0.03 0.01 0.09 1.94 1.43 MO 0.42 0.03 0.04 0.04 0.02 0.01 0.05 2.49 1.89 MT 0.33 0.01 0.05 0.04 0.03 0.14 0.08 3.19 2.42 NE 0.38 0.00 0.04 0.01 0.01 0.12 0.06 2.47 1.83 NV 0.14 0.01 0.04 0.02 0.01 0.10 0.05 4.76 3.85 NH 0.23 0.02 0.04 0.03 0.02 0.05 0.05 4.45 3.64 NJ 0.33 0.02 0.04 0.02 0.01 0.02 0.04 3.70 3.04 NM 0.39 0.00 0.01 0.01 0.03 0.09 0.08 3.44 2.79 NY 0.31 0.02 0.03 0.02 0.01 0.10 0.04 3.76 3.00 NC 0.38 0.02 0.05 0.04 0.02 0.02 0.07 2.71 2.15 ND 0.48 0.01 0.09 0.08 0.06 0.41 0.19 2.37 1.57 OH 0.48 0.03 0.05 0.04 0.02 0.07 0.06 1.33 0.92 OK 0.45 0.01 0.01 0.03 0.03 0.45 0.06 3.32 2.32 OR 0.31 0.03 0.05 0.04 0.02 0.07 0.06 2.63 2.02 PA 0.40 0.01 0.04 0.02 0.01 0.00 0.05 2.29 1.72 RI 0.35 0.03 0.03 0.04 0.02 0.04 0.05 3.45 2.75 SC 0.37 0.01 0.04 0.02 0.01 0.12 0.04 2.64 1.93 SD 0.34 0.00 0.05 0.04 0.04 0.02 0.08 2.78 2.14 TN 0.37 0.01 0.04 0.03 0.01 0.09 0.06 2.63 2.12 TX 0.34 0.02 0.02 0.04 0.02 0.36 0.07 3.74 2.74 UT 0.32 0.02 0.05 0.02 0.01 0.06 0.04 3.43 2.73 VT 0.29 0.01 0.03 0.03 0.01 0.04 0.05 3.70 2.98 VA 0.32 0.02 0.04 0.02 0.01 0.11 0.04 3.62 2.86 WA 0.25 0.02 0.04 0.02 0.02 0.06 0.05 3.82 3.05 WV 0.58 0.02 0.02 0.01 0.01 0.03 0.01 0.44 0.09 WI 0.38 0.02 0.04 0.03 0.02 0.08 0.06 2.56 2.05 WY 0.25 0.02 0.00 0.01 0.02 0.35 0.08 4.44 3.41 Avg 0.36 0.02 0.04 0.03 0.02 0.11 0.06 3.09 2.39 54