What Drives Matching Efficiency? A Tale of Composition and Dispersion

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. What Drives Matching Efficiency? A Tale of Composition and Dispersion Regis Barnichon and Andrew Figura 2011-10 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.

What Drives Matching E¢ ciency? A Tale of Composition and Dispersion (cid:3) Regis Barnichon Andrew Figura Federal Reserve Board Federal Reserve Board January 9, 2011 Abstract This paper presents a framework to study movements in the matching e¢ ciency of the labor market and highlights two observable factors a⁄ecting matching e¢ ciency: (i) unemployment composition and (ii) dispersion in labor market conditions, the fact that tight labor markets coexist with slack ones. Using CPS micro data over 1976-2009, we (cid:133)ndthatcompositionisresponsibleformostofthemovementsinmatchinge¢ ciencyuntil 2006. In 2008-2009, only forty percent of an exceptionally low matching e¢ ciency can be attributedtocomposition. Newhighlydisaggregateddataonvacanciesandunemployment show that the unexplained decline in matching e¢ ciency coincides with an increase in dispersion. JEL classi(cid:133)cations: J6, E24, E32 Keywords: Matching Function, Matching E¢ ciency, Composition E⁄ect, Mismatch. (cid:3)We thank Shigeru Fujita, Bart Hobijn, Rob Valletta, William Wascher and seminar participants at the Chicago Fed, the National Bank of Hungary, the New York Fed and the San Francisco Fed. We thank Peter Chen for excellent research assistance. The views expressed here do not necessarily re(cid:135)ect those of the Federal Reserve Board or the Federal Reserve System. Any errors are our own. 1

1 Introduction The unemployment rate is a major indicator of economic activity. Understanding its movements is useful in assessing the causes of economic (cid:135)uctuations and their impact on welfare, as well as assessing in(cid:135)ationary pressures in the economy. An important determinant of the unemployment rate is the ability of the labor market to match unemployed workers to jobs. If aggregate matching e¢ ciency declines, i.e. if fewer job matches are formed each period conditional on unemployment and vacancies, the unemployment rate increases with adverse e⁄ects on welfare and possibly in(cid:135)ation. Further, the e⁄ects of a decline in matching e¢ ciency on the economy will depend on the forces behind this decline. A larger share of long-term unemployed, a larger fraction of permanent layo⁄s, geographic mismatch, skill mismatch, or more generous unemployment bene(cid:133)ts can all lower aggregate matching e¢ ciency but with di⁄ering degrees of persistence. In this paper, we study the determinants of aggregate matching e¢ ciency (cid:135)uctuations over the last four decades. As a (cid:133)rst pass towards capturing changes in aggregate matching e¢ ciency, we estimate an aggregatematchingfunctiontyinglevelsofvacanciesandunemploymenttothejob(cid:133)ndingrate. While the matching function appears relatively stable over time, a testimony of the success of the matching function, the regression residual, or aggregate matching e¢ ciency, displays a cyclical pattern, increasing in the later stages of expansions, and declining in the early stages of recoveries. In the 2008-2009 recession however, the decline in aggregate matching e¢ ciency startedbeforetherecessionandwasalotmorepronounced,addinganestimated11 percentage 2 points to the unemployment rate (Barnichon and Figura, 2010). The(cid:133)rstcontributionofthispaperistopresentanempiricalframeworktostudymovements in aggregate matching e¢ ciency. Under fairly general assumptions, we link movements in aggregate matching e¢ ciency to two measurable factors: (i) composition of the unemployment pool, and (ii) dispersion in labor market conditions. First, if composition changes, and a group withalowerthanaveragejob(cid:133)ndingprobability(suchasworkersonpermanentlayo⁄)becomes over-represented among the unemployed, the average job (cid:133)nding probability will decline more than what a matching function would imply. Second, changes in the location and nature (e.g., skill requirements) of new jobs can lead to a misallocation of jobs and workers across labor markets and generate dispersion in labor market conditions as tight labor markets coexist with slack labor markets. Because of the concavity of the matching function, an increase in dispersion in labor market conditions will lower matching e¢ ciency. Moreover, the e⁄ect of higherdispersiononmatchinge¢ ciencymaybeexaggeratedifworkerscan(cid:133)ndajoboutsideof theirlocallabormarket(Abraham, 1991). Toaddressthislittlestudiedissue, weintroducethe 2

concept of "permeability" between labor market segments. With higher permeability, workers are more likely to cross local labor market barriers and (cid:133)nd a job in a di⁄erent labor market segment, and dispersion has a weaker e⁄ect on matching e¢ ciency. ThesecondcontributionofthispaperistousematchedCPSmicrodataonunemploymentemployment transitions over four decades to estimate a model of job (cid:133)nding probability and to empirically relate aggregate matching e¢ ciency to composition and dispersion. In addition, because the e⁄ect of misallocation on matching e¢ ciency is a function of dispersion in labor market conditions across segments, it is crucial to observe segments at a high level of disaggregation in order to correctly assess the extent of dispersion. We thus separately consider shorter datasets that allow us to probe dispersion across more re(cid:133)ned labor market segments. Inparticular,wepresentanewdatasetonlabormarkettightnessbyoccupationandgeographic location covering a total of 564 segments, a 55-fold improvement over publicly available data suchastheJobOpeningsandLaborTurnoverSurvey(JOLTS).Further,because564segments may still be well below the true number of segments in the US, we propose a method using UK data to scale up our measure of dispersion over 564 segments to a more realistic number of labor market segments. Ourmain(cid:133)ndingscanbesummarizedasfollows: (1)Changesincompositionareimportant andgeneratenon-trivialcyclicalmovementsinmatchinge¢ ciency. Becausecyclicalmovements incompositionarepositivelycorrelatedwithaggregatelabormarkettightness, regressionsthat do not control for composition estimate the matching function elasticity with an upward bias. (2) Movements in composition are mostly due to two factors: (i) an increase in the fraction of long-term unemployed during recessions, and (ii) a larger fraction of unemployed workers on permanent (rather than temporary) layo⁄ during recessions. (3) Until 2006, changes in composition are responsible for most of the cyclical movements in matching e¢ ciency, while dispersion appears to have played a modest role. (4) Since 2006, composition explains only 40 percent of a dramatic decline in matching e¢ ciency. Instead, the unexplained decline coincides with an increase in dispersion in labor market conditions. Quantitatively, dispersion mayaccountforaquarter,andperhapsmore,oftheunexplaineddeclineinmatchinge¢ ciency. (5) Extended unemployment bene(cid:133)ts, reduced worker mobility caused by a distressed housing marketorindustryspeci(cid:133)cshocksdonotseemtohavesigni(cid:133)cantlyloweredmatchinge¢ ciency. This paper builds on a large literature studying the matching function (see Petrongolo and Pissarides (2001) for a review) and extends Bleakley and Fuhrer (1997) to identify changes in matching e¢ ciency. While that latter study focuses on aggregate labor market tightness as the main explanatory variable of the aggregate job (cid:133)nding rate, we emphasize that the aggregate job (cid:133)nding probability is an average of probabilities across heterogeneous workers working in di⁄erent segments of the labor market. Baker (1992) studies the role played by 3

composition in explaining the counter-cyclicality of average unemployment duration. This paper extends Baker (1992) by presenting a model of job (cid:133)nding probability based on the concept of a matching function that takes into account individual characteristics as well as local labor market characteristics. Finally, the literature on mismatch has typically relied on a variety of dispersion measures (Padoa Schioppa, 1991, Layard, Nickell and Jackman, 2005) to capture the extent of misallocation of jobs and workers, and absent a unifying framework, there was no consensus on the most appropriate measure. This paper (cid:133)lls the gap by providing a dispersion measure, the variance of labor market tightness across labor market segments, that can be analytically related to matching e¢ ciency and to the equilibrium unemployment rate.1 The next section takes a (cid:133)rst pass at capturing changes in matching e¢ ciency with an aggregatematchingfunctionregression. Section3presentsamorere(cid:133)nedempiricalframework to identify the driving forces of matching e¢ ciency, and Section 4 uses micro data to estimate that framework and discuss the results. Section 5 estimates the extent of dispersion across labor market conditions at a high disaggregation level and evaluates the e⁄ect on matching e¢ ciency. Section 6 concludes. 2 A (cid:133)rst look at changes in matching e¢ ciency The matching function relates the (cid:135)ow of new hires to the stocks of vacancies and unemployment. Liketheproductionfunction, thematchingfunctionisaconvenientdevicethatpartially capturesacomplexrealitywithworkerslookingfortherightjoband(cid:133)rmslookingfortheright worker. In a continuous time framework, the (cid:135)ow of hires can be modeled with a standard Cobb-Douglas matching function with constant returns to scale, and we can write m = m U(cid:27)V1 (cid:27) (1) t 0t t t (cid:0) with m , the number of new hires at instant t, U the number of unemployed, V the number t t t of vacancies, and m aggregate matching e¢ ciency.2 0t Since the job (cid:133)nding rate jf is the ratio of new hires to the stock of unemployed, we have t jf = mt so that jf = m (cid:18)1 (cid:27)with (cid:18)=v the aggregate labor market tightness, u=U=LF, t Ut t 0t t(cid:0) u v=V=LF and LF the labor force. To identify m , a simple approach is thus to estimate 0t an aggregate matching function and interpret movements in the residual as movements in 1In recent work, Sahin, Song, Topa, and Violante (2010) address the issue with a di⁄erent approach, by constructing mismatch indices based on a theoretical framework of mismatch. 2The Cobb-Douglas matching function is used in almost all macroeconomic models with search and search and matching frictions (e.g., Pissarides, 2001). 4

matching e¢ ciency. Speci(cid:133)cally, we regress lnjf = (1 (cid:27))ln(cid:18) +E (lnm )+(cid:22) (2) t t T 0t t (cid:0) with E (:) denoting the average over the estimation period so that E (lnm ) denotes the T T 0t intercept of the regression. Deviations of aggregate matching e¢ ciency from its average level are then given by (cid:22) = lnm E lnm : (3) t 0t T 0t (cid:0) We measure the job (cid:133)nding rate jf from unemployment-employment transitions from the t Current Population Survey (CPS), and we use the composite help-wanted index presented in Barnichon (2010) as a proxy for vacancy posting.3 We use non-detrended quarterly data, allow for (cid:133)rst-order serial correlation in the residual and estimate (2) over 1976-2007. Table 1 presents the results. The elasticity is estimated at 0:67. Using lagged values of v and u as t t instruments gives similar results, and the elasticity is little changed at 0:66. Figure 1 plots the empirical job (cid:133)nding rate, its (cid:133)tted value, and the residual of equation (2), i.e., (cid:22) ; the movements in aggregate matching e¢ ciency. A (cid:133)rst observation is that the t matchingfunctionappearsrelativelystableovertime,acorollaryofthesuccessofthematching function. However,aggregatematchinge¢ ciencydisplaysaclearcyclicalpattern,andtypically lagsthebusinesscycle, increasinginthelaterstagesofexpansions, peakinginthelatestagesof recessions or the early stages of recoveries, and declining thereafter. In the 2008-2009 recession however, the decline in matching e¢ ciency occurred earlier than in previous recessions and was a lot more pronounced. In the fourth quarter of 2009, the residual reached an all time low of four standard-deviations.4 The expansion period preceding the 2008-2009 recession also appears peculiar, because the increase in matching e¢ ciency that typically occurs before recessions was a lot more muted. 3 A framework to study movements in matching e¢ ciency In this section, we present a general framework to investigate the factors responsible for movements in aggregate matching e¢ ciency. In particular, we identify two observable factors that a⁄ect aggregate matching e¢ ciency: the composition of the unemployment pool, and the 3A measurement issue is that vacancies are not only (cid:133)lled from the unemployed pool (U) but also from the employment pool (E) and individuals outside the labor force (NLF). As a robustness check, we proceeded as in Blanchard and Diamond (1989) and estimated a regression over 1994-2009 of the sum of E-U (cid:135)ows, NLF-E (cid:135)owsandE-E(cid:135)ows(FallickandFleischman,2004)onvacanciesandthenumberofunemployedandindividuals outside the labor force willing to work. The behavior of m was broadly unchanged. 0t 4Elsby, Hobijn and Sahin (2010) report a similar (cid:133)nding using the unemployment out(cid:135)ow rate, and Davis, Faberman and Haltiwanger (2010) also report a dramatic decline in the vacancy yield using JOLTS data. 5

amount of dispersion in labor market conditions. The former arises if the characteristics of the unemployed change throughout the cycle, making job (cid:133)nding more or less likely, while the latter is caused by the concavity of the matching function and arises if tight labor markets coexist with slack labor markets. 3.1 Composition and dispersion Denote JF the job (cid:133)nding probability of an individual of type j in labor market segment i.5 ij;t Alabormarketsegmentcanbede(cid:133)nedbyitsgeographiclocation,industrygrouporoccupation group. The labor market segment i of individual type j can then be thought of as the labor market in which individual j is most likely to look for work and to (cid:133)nd a job. Typically, this will be proxied by his location and past employment history. Individual type j is de(cid:133)ned by a vector of K characteristics xk , and labor market segment i is characterized by its labor jt market tightness (or vacancy-nunemoployment ratio) (cid:18) it . Because an unemployed worker may also look outside of his labor market segment, his job (cid:133)nding probability may also depend on the aggregate labor market tightness (cid:18) .6 t Thus, we postulate that the job (cid:133)nding probability of individual type j in labor market i can be written JF = JF(X ;(cid:18) ;(cid:18) ) (4) ij;t jt it t so that the average job (cid:133)nding rate is given by U ij;t JF = JF : (5) t ij;t U t i;j X Tohighlightthee⁄ectsofcompositionanddispersionontheaveragejob(cid:133)ndingprobability, we take a second-order Taylor of expansion of JF with respect to (cid:18) around (cid:18) and X ij;t it t jt around X(cid:22) = 1 X with X = [1;x1 ;:::;xK]and xk the kth observable characteristics of T:J jt jt jt jt jt t;j X 5The job (cid:133)nding rate jf and the the job (cid:133)nding probability JF can be related from jf = ln(1 JF). 6Two other plausible determinants of the job (cid:133)nding probability are the search intensity of (cid:0) worke (cid:0) rs and the recruiting intensity of (cid:133)rms. These parameters can easily be incorporated in our framework, but we preferred to leave them out for two reasons. First, such concepts are di¢ cult to implement empirically as measuring workers(cid:146)search intensity or (cid:133)rms(cid:146)recruiting intensity is notoriously di¢ cult (See Davis, Faberman and Haltiwanger,2010forpromisingworkinthisdirection). Second,aswereportbelow,ourframeworkwithoutvarying search/recruiting intensities can successfully capture job (cid:133)nding probability movements over 1976-2006. This suggeststhataggregatelabormarkettightness(orsectoraltightness)canproxyforvaryingintensitiesandthat our framework provides a good reduced-form approximation of a model of job (cid:133)nding probability with varying intensities. After2006,varyingintensitiescould haveplayed alargerrole,andweseparatelyestimatethee⁄ect of extended unemployment bene(cid:133)ts on workers(cid:146)search intensity. 6

individual j, and we get7 (cid:18) JF = JF ((cid:18) )+ JFk MM it +(cid:17) : (6) t t t t (cid:0) t (cid:18) t t k (cid:18) (cid:19) X The (cid:133)rst term in (6), JF ((cid:18) ) = JF (X(cid:22);(cid:18) ;(cid:18) ), is the average job (cid:133)nding rate absent workers t t ij;t t t heterogeneity and dispersion. Composition: The second term in (6), JFk, captures the total composition e⁄ect with t k X JFk, the contribution of a given characteristic k to the average job (cid:133)nding probability8 t U @JF JFk = j;t xk x(cid:22)k : (7) t X j U t @xk jt(cid:12) (cid:12)(cid:18)t;X(cid:22) (cid:16) jt (cid:0) (cid:17) (cid:12) (cid:12) The composition e⁄ect arises because of wor (cid:12) ker heterogeneity. If the share Uj;t of a de- Ut mographic group (e.g. job losers) with a lower than average job (cid:133)nding probability (i.e., @JF xk x(cid:22)k < 0) increases in recessions, then the average job (cid:133)nding probability will d @ e x c k jt li (cid:12) (cid:12)n (cid:18) e t;X(cid:22) w (cid:16) ith j o t u (cid:0) t any (cid:17) change in individuals(cid:146)job (cid:133)nding probabilities. (cid:12) (cid:12) Dispersion: Thethirdtermin(6)capturesthee⁄ectofdispersioninlabormarketconditions on the average job (cid:133)nding probability with (cid:18) U (cid:18) 2 it i;t it MM = MM ((cid:18) ) 1 (8) t 0 t (cid:18) U (cid:18) (cid:0) t t t (cid:18) (cid:19) i (cid:18) (cid:19) X (cid:18) it = MM ((cid:18) )var 0 t (cid:18) t (cid:18) (cid:19) and MM ((cid:18) ) = 1(cid:18)2 @2JFij;t .9 Dispersion in labor market tightness across segments will 0 t (cid:0)2 t @(cid:18)2 it (cid:18)t;X(cid:22) negativelya⁄ecttheaverage jo(cid:12)b(cid:133)ndingprobabilityiftheindividualjob(cid:133)ndingprobabilityisa (cid:12) concavefunctionof(cid:18) (aswou (cid:12) ldbethecasewithamatchingfunction). With @2JFij;t < 0, it @(cid:18)2 it (cid:18)t;X(cid:22) an increase in dispersion across labor market segments, i.e., an increase in misallo(cid:12)cation of (cid:12) (cid:12) 7The cross-order term between X X(cid:22) and (cid:18)it 1 is omitted and only described in the Appendix. This is jt (cid:0) (cid:18)t (cid:0) done for clarity of exposition as that term is empirically very small at the level of disaggregation permitted by our data on labor market segments. 8Weomitted thesecond-orderterm forclarityofexposition,butincorporated the(small)second-orderterm in all our calculations. 9The term corresponding to (cid:18) , Uj;t @JF ((cid:18) (cid:18) ), is nil because (cid:18) = Uij;t(cid:18) : it X i;j Ut @(cid:18)it (cid:12) (cid:18)t;X(cid:22) it (cid:0) t t X i;j Ut it (cid:12) (cid:12) 7

jobs and workers, decreases the average job (cid:133)nding probability. For example, if some segments (such as health care) display a relatively tight labor market and some segments (such as manufacturing) display a slack labor market, the average job (cid:133)nding probability will be lower than in an economy where labor market tightness is identical across segments. 3.2 Postulating a functional form for JF ij;t To bring our framework to the data, we need to posit a functional form for the job (cid:133)nding probability JF . We adopt a logistic functional form ij;t JF ij;t 1 em0(cid:18)( it 1 (cid:0) (cid:27))!(cid:18)( t 1 (cid:0) (cid:27))(1 (cid:0) !) ln = (cid:12)X +ln (cid:0) +(cid:17) (9) 1 (cid:0) JF ij;t jt em0(cid:18) i ( t 1 (cid:0) (cid:27))!(cid:18)( t 1 (cid:0) (cid:27))(1 (cid:0) !) ij;t with (cid:18) = vit, X = [1;x1 ;::;xK] ! [0;1], and m a constant term. This expression has two it uit jt jt jt 2 0 constant terms: m and the constant term in X . To enable the estimation of m , we demean 0 jt 0 the X variables before estimating equation (9). jt This speci(cid:133)cation has a number of advantages: First, a logistic functional form is consistent with the fact that the job (cid:133)nding probability falls between 0 and 1. Second, in the absence of worker heterogeneity (X = X(cid:22)) and labor market dispersion jt ((cid:18) it = (cid:18) t ), (9) reduces to JF ij;t = 1 e (cid:0) m0(cid:18)1 t(cid:0) (cid:27) , the reduced-form aggregate speci(cid:133)cation (2) (cid:0) with m = m . 0t 0 Third, to relate (cid:18) and (cid:18) to the job (cid:133)nding probability of individual type j, we assume it t that the job (cid:133)nding probability is a geometric average of local labor market tightness (cid:18) and it the aggregate labor market tightness (cid:18) . Put di⁄erently, we allow for the possibility that a t worker crosses barriers between labor market segments, so that his job (cid:133)nding probability is not solely a function of tightness in his local labor market. To get some intuition, consider the simpler case without worker heterogeneity. The job (cid:133)nding rate of a worker in segment i (1 (cid:27))! (1 (cid:27))(1 !) becomes jf it = m 0 (cid:18) it (cid:0) (cid:18) t (cid:0) (cid:0) , i.e. a weighted (geometric) average of the segment labor market tightness and the aggregate labor market tightness. The weight ! [0;1] captures the 2 impermeability of the local labor market. If ! = 1, labor market segments are impossible to cross, and aggregate labor market tightness has no impact on the local job (cid:133)nding rate. In contrast, if there are no barriers between labor markets, ! = 0, a worker(cid:146)s job (cid:133)nding rate only depends on the aggregate labor market tightness. 8

3.3 A decomposition of aggregate matching e¢ ciency Thanks to our decomposition (6), we can now link movements in aggregate matching e¢ ciency to the composition of the unemployment pool and the amount of dispersion in labor market conditions. After some manipulation of (6) left for the Appendix, (cid:22) = lnm E lnm , the t 0t T 0t (cid:0) deviations of aggregate matching e¢ ciency from its average value, can be written (cid:22) em0(cid:18)1 t(cid:0) (cid:27) JFk (cid:1)mm +(cid:16) : (10) t ’ m (cid:18)1 (cid:27) t (cid:0) t t 0 t(cid:0) k X with 1 (cid:18) mm = !(1 (cid:27)) (1 !(1 (cid:27)) 1 m (cid:18)1 (cid:27) var it (11) t 2 (cid:0) (cid:0) (cid:0) (cid:0) 0 t(cid:0) (cid:18) t (cid:18) (cid:19) (cid:2) (cid:0) (cid:1)(cid:3) and (cid:1)mm = mm E mm with E (:) denoting the average over the estimation period. t t T t T (cid:0) Aggregate matching e¢ ciency m is a function of the distribution of individual charac- 0t teristics and labor market segments(cid:146)tightness. Movements in aggregate matching e¢ ciency can be decomposed into a composition e⁄ect, the (cid:133)rst term on the right-hand side of (10), a dispersion (or misallocation) e⁄ect, the second term, and an unexplained component (that includes the approximation error), the last term. Expression (11) describes the e⁄ect of misallocation (also called mismatch) on aggregate matching e¢ ciency. Three observations are worth noting. First, the e⁄ect of misallocation is roughly proportional to the variance of labor market tightness, so that one can readily estimate the e⁄ect of misallocation by looking at the dispersion in labor market conditions.10 The literature on mismatch has used various measures to quantify the e⁄ect of misallocation on the unemployment rate. For example, some use Ui Vi (e.g., Jackman and Roper U (cid:0) V X i (cid:12) (cid:12) 1987, Franz 1991, Brunello 1991), others unemployment(cid:12)rate di(cid:12)spersion measures u2 or (cid:12) (cid:12) i i X ui 2 (e.g., Jackman, Layard and Savouri (1991), Attanasio and Padoa Schioppa (1991)), u i X(cid:0) (cid:1) 1=2 2 others UiVi (Bean and Pissarides, 1991), and others Ei Ui=Ei Vi=Ei (Layard, U V E U=E (cid:0) V=E X i (cid:16) (cid:17) X i (cid:16) (cid:17) Nickell and Jackman, 1991) with E the number of employed workers in segment i and E the i total number of employed workers. Some measures were constructed using employment or labor force weights (but surprisingly, rarely unemployment weights), but other measures did notweightobservations. Whileallthesemeasurescapturetheextentofdispersion acrosslabor markets, absent a unifying framework, there was no consensus on the most appropriate measure. The measure we propose has an important advantage over these other measures: It can 10The coe¢ cient of proportionality does depend on (cid:18) but its e⁄ect is small. t 9

be directly related to aggregate matching e¢ ciency and thus to the equilibrium unemployment rate (Barnichon and Figura, 2010).11 Second, while the mismatch literature imposes tight labor market segments boundaries, our framework allows for some permeability between labor market segments. The e⁄ect of dispersion on the average job (cid:133)nding rate and matching e¢ ciency depends on !. For the range of plausible values for (cid:27) and m (cid:18)1 (cid:27), the e⁄ect of dispersion increases with barriers between 0 t(cid:0) labor market segments (i.e. when ! increases) and is strongest when labor market segments(cid:146) barriersarein(cid:133)nite. Conversely,withhigherpermeability,workersaremorelikelytocrosslocal labor market barriers and (cid:133)nd a job in a di⁄erent labor market, and this possibility weakens the e⁄ect of dispersion on aggregate matching e¢ ciency. Finally,becauseaveragedispersionispositive(var (cid:18)it 0, t),thee⁄ectofmisallocation (cid:18)t (cid:21) 8 on aggregate matching e¢ ciency movements (cid:22) t is not(cid:16)giv(cid:17)en by mm t , the level of dispersion, but by (cid:1)mm , the deviations of dispersion from its average level. t 4 Empirical results 4.1 Estimation We use matched data from the Current Population Survey (CPS) covering January 1976 to December 2007 to estimate the Unemployment-Employment (UE) transition probability for an individual j in labor market market segment i. We restrict the estimation to pre-2008 data so that any changes in matching e¢ ciency post 2007 do not a⁄ect our coe¢ cient estimates. In 1994, a major redesign of the CPS survey was implemented and introduced breaks in many important variables, such as reason for unemployment and duration of unemployment.12 To controlforthesebreaks, weestimateseparatecoe¢ cientsforthepreandpostredesignperiods. Our whole sample contains about 1.2 million observations. In this section, we present the individual characteristics that in(cid:135)uence the job (cid:133)nding probability, discuss our method for measuring labor market tightness by segment, and present results. 1. Controlling for individual characteristics The CPS data provides information allowing us to control for changes in the characteristics of the unemployed. We use three main types of information: demographic, reason for unemployment and duration of unemployment, and 11See also the recent work by Sahin, Song, Topa, and Violante (2010) who develop mismatch indices based on a theoretical framework of mismatch. 12See, for example, Polivka and Miller (1998). 10

we include a set of monthly dummies to control for seasonality in job (cid:133)nding probabilities.13 Demographicinformationincludestheageandsexoftheunemployedindividual. Wemodel the e⁄ect of age on the job (cid:133)nding probability using a quadratic in age. The CPS distinguishes between5mainreasonsforunemployment: permanentlayo⁄,temporarylayo⁄,newlaborforce entrant, reenteringthelaborforce, andquitjob. Weusedummyvariablesforeachreason. The CPS records the duration (in weeks) of individuals(cid:146)current spells of unemployment, which we allow to linearly a⁄ect the probability of exit. Prior research suggests that the job (cid:133)nding probability declines with duration, and two reasons are often cited. First, prolonged unemployment may lower individuals(cid:146)skills relative tootherjobseekers,makingthemlessdesirabletoemployers,oritmayreducetheircontactsin job(cid:150)(cid:133)ndingnetworks, makingitharderto(cid:133)ndemployment. Henceforth, wedescribethise⁄ect asscarring. Second, prolongedunemploymentmaysignalthattheindividualshaveunobserved characteristics that make it di¢ cult to (cid:133)nd employment. Prolonged unemployment may also capture unobserved circumstances. For instance, an individual may be looking for work in a toonarrow(relativetodataavailabilities), andhenceunobservable, labormarketsegmentwith averylowvacancy-to-unemploymentratio. Assuchworkersremainintheunemploymentpool longer, the unobserved circumstances will be correlated with unemployment duration. Thus, unobservedcharacteristicsorcircumstancesmayberesponsibleforduration(cid:146)sabilitytopredict the job (cid:133)nding probability. Average unemployment duration is also likely a⁄ected by aggregate labor market conditions. Whenlabordemandislow, ittypicallytakesunemployedindividualslongerto(cid:133)ndjobs, anddurationsrise.Thus,thesignalaboutjob(cid:133)ndingprospectsfromanindividual(cid:146)sunemployment duration may be weaker when average durations are higher. To allow the signal from an individual(cid:146)s unemployment duration to change as aggregate conditions change, we interact an individual(cid:146)s duration with the average duration, which is highly countercyclical. In e⁄ect, this speci(cid:133)cation allows the slope of the relationship between job (cid:133)nding and duration to change as aggregate conditions change. 2. Measuring labor market tightness by segment To estimate the e⁄ect of dispersion in (cid:18) on aggregate matching e¢ ciency, we need vacancy posting data by industry and region it going back to 1976. Moreover, since the e⁄ect of misallocation arises out of the concavity of the matching function, it is important to reach a good level of disaggregation as dispersion increases with the number of observed segments. Unfortunately, the two data sources with vacancy posting data, the JOLTS and the Help-Wanted Indexes (HWI) from the Conference 13Wealsoexperimentedwitheducationlevelandrace/ethnicitybutfoundthatthesecharacteristicsplaylittle roleinthecyclicalityofmatchinge¢ ciency,consistentwiththe(cid:133)ndingsofBaker(1992). Wethusomittedthese characteristics for clarity of exposition. 11

Board do not satisfy these criteria. JOLTS is only available since December 2000, and while the JOLTS measure of job openings can be disaggregated into 10 industry groups, the survey(cid:146)s sample size is too small to allow for a disaggregation by regions and industries.14 The HWI can be disaggregated by regions (the nine US Census divisions), but not by industry. Instead, we use the unemployment rate to proxy for the labor market tightness in a particular segment. Regional and industry data on vacancy posting from the JOLTS over 2000-2010 show that vacancies and unemployment rates are highly negatively correlated across regions (cid:11) or industries, and that uit is a very good proxy for (cid:18)it with no apparent break over 2008ut (cid:18)t 2009.15 We use the CPS(cid:16)mi(cid:17)cro data to estimate unemployment rates for each segment. Since new entrants to the labor force cannot be easily classi(cid:133)ed in a particular industry, we use the average unemployment rate in their state of residence. While the CPS sample is large (about 60,000households)andallowsforahigherlevelofdisaggregationover1976-2009thanavailable vacancy data, we nonetheless face some limitations regarding the degree of disaggregation we can achieve. We de(cid:133)ne 150 segments based on the cross product of 50 states and three broad industry groups.16 Our three broad industry groups roughly correspond to goods producing, business/health care/educational services, and other services.17 Accordingly, we estimate the slightly modi(cid:133)ed form of equation (9) JF ij;t 1 e m0 u u i t t (cid:13) (cid:18)1 t(cid:0) (cid:27) ln 1 (cid:0) JF i U j; E t = (cid:12)X jt +ln (cid:0) e m0 u u (cid:16) i t t (cid:13) (cid:17) (cid:18)1 t(cid:0) (cid:27) +" ijt (12) (cid:16) (cid:17) by maximum likelihood with (cid:13) = (cid:11)(1 (cid:27))!. To be able to infer an estimate of permeability, (cid:0) !, from our estimate (cid:13), we will posit that (cid:11) = 1:5, a value in the middle of the plausible (cid:0) range of our estimates for (cid:11).18 14TheJOLTSisproducedbytheBLSandcontainsmonthlydataonjobopeningsfrom16,000establishments since December 2000. 15Formally, we used JOLTS and Conference Board vacancy data by region or industry to regress ln(cid:18)it = (cid:11)lnuit +(cid:12). The regression results are shown in Table A1 in the Appendix. (cid:18)t ut 16AtthelevelofdisaggregationpermittedbytheCPS,initialregressionsanddispersionindexesbyindustryor statesuggestthatstatedi⁄erencesinunemploymenthavemuchstrongere⁄ectsonjob(cid:133)ndingprobabilitiesthan di⁄erences across industries. Therefore, we allow for as much state-level unemployment variation as possible. 17De(cid:133)ning segments by occupation rather than industry does not qualitatively change our results. The industry groups are (1) manual workers-agriculture, mining, construction, manufacturing, transportation and public utilities, (2) professional workers-(cid:133)nance, professional and business services, health care and education, informationandpublicsector,and(3)serviceworkers-retailandwholesaletrade,leisureandhospitalityservices, other services. 18The value of (cid:11) only matters for our estimate of !. Using the extreme values of 1.7 and 1.3 makes little di⁄erence to our conclusions, with ! ranging from 0.35 to 0.45. 12

4.2 Results 4.2.1 Coe¢ cient estimates Table2reportsourcoe¢ cientestimates. Thecoe¢ cientontheaggregatevacancy-unemployment ratio is highly signi(cid:133)cant but is lower than the coe¢ cient estimated in Section 2 using only aggregate labor market tightness. This suggests that characteristics and/or dispersion are on average procyclical, and that failing to control for those parameters biases estimates of the aggregate matching function elasticity upward. The impermeability coe¢ cient of labor market segments is signi(cid:133)cantly smaller than one (! = :16=(1:5 :28) 0:4). While barriers between labor market segments appear to be non (cid:3) ’ trivial, they are also not insurmountable. As a result, the e⁄ect of labor market tightness on exit hazards within a segment (!(1 (cid:27)) = 0:16) is not as great as the e⁄ect of aggregate labor (cid:0) market tightness ((1 (cid:27))(1 !) = 0:22). (cid:0) (cid:0) Turningtoindividualcharacteristics,JFisdecreasinginunemploymentduration. Using(6) and(7),thecoe¢ cientonunemploymentdurationimpliesthathavingaspellofunemployment lasting6monthsisassociatedwithadecreaseinanindividual(cid:146)sjob(cid:133)ndingprobabilityofabout 1-11 percentage point. However, the coe¢ cient on the interaction of individual and aggregate 2 durationimpliesthatthise⁄ectismitigatediftheaverageunemploymentdurationisalsohigh. In other words, the slope of the relationship between job (cid:133)nding and unemployment duration becomes (cid:135)atter in downturns. As a result, increases in duration in a cyclical downswing do not sendasstrongasignalaboutreducedjob(cid:133)ndingprobabilitiesasinotherperiodsbecausethese increases re(cid:135)ect, in part, changes in aggregate conditions, which we have already controlled for. The estimates of the e⁄ect of the reason for unemployment on the job (cid:133)nding probability are relative to that of a job leaver. The estimates reveal that it is particularly di¢ cult for permanent job losers and new entrants to the labor force to (cid:133)nd employment. Unsurprisingly, workers on temporary layo⁄ have an easier time becoming reemployed. As expected, the CPS redesign, by restricting temporary layo⁄s to individuals expecting to be recalled within 6 months, increased the di⁄erence in exit hazards for permanently and temporarily laid o⁄ workers. Turning to demographics, the coe¢ cient on the male dummy indicates that males are more likelyto(cid:133)ndjobsthanfemales. However,acomparisonofthepreandpostredesigncoe¢ cients shows that this relative advantage has lessened over time. The estimated coe¢ cients on the age variables indicate that the probability of job (cid:133)nding initially increases and then decreases with age. In the pre redesign period, the age with the highest job (cid:133)nding probability is around 30. In the post redesign period, it is close to 17. 13

4.2.2 The e⁄ect of individual characteristics and dispersion on the job (cid:133)nding probability Next, we use our decomposition (6) to estimate the e⁄ect of individual characteristics and labor market dispersion on the average job (cid:133)nding probability over 1976-2009. Figure 2 graphs JFk , the contributions of characteristics (cid:150)reason for unemployment, unemployment durat tion, demographics(cid:150), and MM , the contribution of dispersion in labor market tightness, to (cid:8) (cid:9) t JF . t The contribution of reason for unemployment is procyclical, falling in recessions and rising in recoveries. This pattern owes, in part, to an increasing share of permanent job losers and a declining share of temporary job losers during recessions. The contribution of duration is also procyclical. Although the coe¢ cient on the interaction term suggests that the e⁄ect of duration on job (cid:133)nding probabilities is reduced in recessions, longer duration always implies a lower job (cid:133)nding probability. This indicates that some of the increase in individual durations during cyclically weak periods re(cid:135)ects scarring or unfavorable unobserved circumstances. Demographics generate a downward trend in the average job (cid:133)nding probability over the sample period, as the labor force ages and women(cid:146)s share of the labor force increases, before leveling out at the end of the sample, as the share of men in the unemployment pool increases. Consistent with Baker (1992), demographic characteristics have little in(cid:135)uence on the cyclical behavior of the job (cid:133)nding probability. Finally, the e⁄ect of dispersion on the job (cid:133)nding probability, given by (8), is very small because the cross-sectional variance of relative labor market tightness is too small, at least for the segments we observe, for misallocation to have a noticeable e⁄ect on aggregate matching e¢ ciency. 4.2.3 Movements in aggregate matching e¢ ciency Using decomposition (10), the lower panel of Figure 2 presents movements in aggregate matching e¢ ciency, in a similar fashion to Figure 1, but allowing for a richer speci(cid:133)cation than the reduced-form approach (2) from Section 2. The plain thick line is analogous to the residual of Figure 1 and shows (cid:22) , the total movements in aggregate matching e¢ ciency, given by (10). t The plain thin line plots em0(cid:18)1 t(cid:0) (cid:27) JFk (cid:1)mm , the e⁄ect of composition and dispersion on m0(cid:18)1 t(cid:0) (cid:27) t (cid:0) t k X (cid:22) . Finally, the dotted line plots the di⁄erence between the two other lines, i.e. (cid:16) , the changes t t in aggregate matching e¢ ciency that cannot be accounted for by composition or dispersion. Up until 2006, composition accounted for most of the cyclical movements in aggregate matching e¢ ciency. Changes in composition make aggregate matching e¢ ciency procyclical because, as noted above, (i) the fraction of long-term unemployed increases during recessions, and (ii) a larger fraction of unemployed workers is on permanent layo⁄ during recessions. 14

Interestingly, the muted increase in aggregate matching e¢ ciency in the run-up to the 2008- 2009 recession can also be explained by composition, with both (i) and (ii) playing a role and demographics contributing to a downward trend in matching e¢ ciency. Prior to 1994, the ability of composition to account for matching e¢ ciency movements is not as good, and this is probably due to the quality of the data and the loose distinction between temporary and permanent layo⁄before 1994.19 Since 2007, a large fraction of the decline in aggregate matching function e¢ ciency has been due to unobserved factors. Initially, the deterioration in late 2007 and 2008 owed almost entirelytounobservablefactors,asobservablecomponentswererelativelyconstant. Thereafter, observable factors, especially unemployment duration and reason for unemployment, began to contributetothedeterioration,andthiscontributionhasgrownsteadily,whiletheunexplained component has been relatively constant. As a result, as of 2009Q4, observable factors account forabout40percentofthedeclineinaggregatematchinge¢ ciencysince2007,whileunobserved factors account for the remainder. After controlling for dispersion and observed characteristics, the unexplained decline in matching e¢ ciency amounts to about 0:15 log points in end 2009, compared to 0:20 log points (Figure1)usingareduced-formregression(2)thatonlyconditionedonaggregatelabormarket tightness. It is perhaps surprising that the di⁄erence between these two numbers is not larger giventhatchangesinthecompositionoftheunemployedhaveledtoadeteriorationinmatching e¢ ciency and are responsible for 40 percent of the total decline. The reason is that the deterioration in matching e¢ ciency caused by changes in observed characteristics is in line with what one would have predicted conditioning on aggregate labor market tightness. As a result, thesee⁄ectswerealreadycaptured(inareducedformsense)bytheaggregatematching function regression. As mentioned above, the coe¢ cient in the aggregate regression is larger than in a regression using micro data, because it re(cid:135)ects the correlation between aggregate labor market tightness and the characteristics of the unemployed. 4.2.4 Digging further: matching e¢ ciency in the 2008-2009 recession To try to understand the unexplained portion of the recent decline in aggregate matching e¢ ciency, we explore several other estimation speci(cid:133)cations. Allowing for a break after 2007 First, we estimate (12) over 1976-2009 and allow for breaks in the coe¢ cients on the right-hand-side variables after 2007. Speci(cid:133)cally, each right- 19TheCPSredesign,byrestrictingtemporarylayo⁄stoindividualsexpectingtoberecalledwithin6months, made the distinction a lot sharper (as seen from the evolution of the coe¢ cient on temporary layo⁄s pre and post-1994 in Table 2), which certainly improved our measure of composition. 15

hand-side variable is interacted with a dummy variable equal to 1 after 2007. If the deterioration in matching e¢ ciency is related to a larger contribution of permanent job losers or older workers, for example, then the post-2007 coe¢ cients on permanent job loss or age should change to re(cid:135)ect this fact. If, however, the deterioration is not related to the observed characteristics of the unemployed, then it will be re(cid:135)ected by changes in the coe¢ cients of the aggregate matching function. Table 3 shows our estimation results, while Figure 3 shows the contributions of the righthand-sidevariablesafterallowingforabreakinthepost2007coe¢ cients. Thedeteriorationin matching e¢ ciency appears mostly as a higher aggregate elasticity (from 0.28 to 0.36) and as a larger e⁄ect of unemployment duration. As shown in Figure 3, the increase in unemployment durationhasbeenassociatedwithalargedecreaseinmatchinge¢ ciency. Thecoe¢ cientonthe interaction between average duration and individual duration has decreased signi(cid:133)cantly post 2007. Whereas in previous recessions, the contribution of individual duration to a reduction in job (cid:133)nding was attenuated (because it likely re(cid:135)ected aggregate labor market conditions, already controlled for, rather than individual circumstances) in the most recent recession, this was not the case and the e⁄ect of duration on matching e¢ ciency was stronger. Changes in other characteristics have had little e⁄ect. The lower panel of Figure 3 repeats the lower panel of Figure 2, which shows the explained and unexplained components of the deterioration in matching e¢ ciency, except that Figure 3 includes in the explained component the part explained by a break in post-2007 coe¢ cients. The explained component now accounts for somewhat more (50 versus 40 percent) of the deterioration in matching e¢ ciency. Moreover, the fraction of explained variation seems to grow overtime, due largely to the duration component. This pattern suggests that duration is capturing the e⁄ect of unobserved circumstances, rather than scarring, on the job (cid:133)nding probability. Indeed, if unobserved circumstances lowered the job (cid:133)nding probability of some individuals, the contribution of the unexplained component to lower matching e¢ ciency would belargeinitially. Butwithtime,itwouldfadeasthe(increasing)unemploymentdurationofthe a⁄ected individuals began to capture the e⁄ect of the unobserved circumstances. This pattern is not what one would expect, however, if scarring were the explanation for the explanatory power of duration. The e⁄ect of extended emergency unemployment bene(cid:133)ts Next, we study whether the increases in the maximum length of eligibility for unemployment insurance, which went into e⁄ect at the onset of the recession, have had any e⁄ect on worker(cid:146)s search intensity and thus on matching e¢ ciency. To identify the e⁄ect of extended and emergency unemployment bene(cid:133)ts (EEB) on job (cid:133)nding probabilities, we follow a strategy used by Kuang and Valletta 16

(2010) who note that job losers are predominantly eligible for unemployment insurance (UI) bene(cid:133)ts while job leavers and new labor force entrants are not. While Kuang and Valletta (2010) study the e⁄ect of EEB on unemployment durations, we identify the e⁄ect of EEB on the job (cid:133)nding probability by interacting a job loser dummy with a post-2008 dummy (the period when EEB was in full e⁄ect) in our regression (12). We (cid:133)nd that EEB has little e⁄ect on job (cid:133)nding probabilities.20 The coe¢ cient on the interaction between the job loser dummy and the post 2008 dummy is nearly identical to that on the interaction between the other unemployed dummy and the 2008 dummy. Is the deterioration in matching e¢ ciency concentrated by sector or region? Next, we look at whether the deterioration in matching e¢ ciency has been concentrated by industry or by location.21 To do so, we estimate two separate speci(cid:133)cations of (12), where we interact a post-2007 dummy with, respectively, dummies for an individual(cid:146)s last industry of employment, and dummies for an individual(cid:146)s current state of residence. If the deterioration in matching e¢ ciencyisconcentrated,thentherewillbesigni(cid:133)cantdi⁄erencesintheinteractioncoe¢ cients across industries or states. One can think of these interaction terms as shifts in local labor market or industry Beveridge curves. Turning (cid:133)rst to concentration by industry, we (cid:133)nd that there is no signi(cid:133)cant di⁄erence across our three broad industry categories. The coe¢ cients on the post-2007 interaction terms arealmostidentical,andthedeclineinmatchinge¢ ciencyappearstobepresentinallindustry groups. In contrast, there are statistically signi(cid:133)cant di⁄erences in the deterioration in matching e¢ ciency across states. However, there is no apparent pattern to the di⁄erences. The top 5 states (in terms of deterioration) are (in order) Florida, South Carolina, New Hampshire, Minnesota, and Missouri. The presence of Florida is perhaps unsurprising as that state has su⁄eredalargedropinhomepricesandalargenumberofforeclosures. Thedropinhomeprices may have increased the number of homeowners who are underwater on their mortgages and 20The results are reported in Table A2 in the Appendix. Our results do not necessarily contradict Kuang and Valletta(cid:146)s (cid:133)ndings or Mo¢ tt (1985), Katz and Meyer (1990) and Meyer (1990) conclusion that extending bene(cid:133)tsdoesincreaseunemploymentduration. Thereasonisthatunemploymentdurationisdeterminedbythe unemployment-employment (UE) transition rate and by the unemployment-nonparticipation (UN) transition rate. In the Appendix, we also estimate a logistic regression for the UN transition probability after controlling for characteristics of the unemployed. We do (cid:133)nd a signi(cid:133)cant e⁄ect of EEB on UN transitions as job losers(cid:146) probability of remaining in the labor force increased signi(cid:133)cantly more than the UN probability of other unemployedafter2008. SeealsoFujita(2010)whousesadi⁄erentidenti(cid:133)cationschemethanKuangandValettaand (cid:133)nds that EEB signi(cid:133)cantly lowered male workers(cid:146)job (cid:133)nding probability in the 2008-2009 recession. 21The results are shown in Table A3 and Table A4 in the Appendix. We also looked at education groups. While highereducationalattainmentis generally associated with higherjob (cid:133)nding probabilities, the change in job(cid:133)ndingprobabilityafter2007wasfairlywidespread. Allcategoriesexcepttheleasteducated(lessthanhigh schooldegree)andthemosteducated(graduatedegree)su⁄eredsigni(cid:133)cantdeclinesinjob(cid:133)ndingprobabilities. 17

therefore less mobile than other households. At the same time, large numbers of foreclosures may signal the presence of many homeowners with scarce (cid:133)nancial resources and little ability to borrow, which might also impede mobility. Still, three other states often mentioned with Florida as states with particularly bad housing markets, Nevada, Arizona and California, are not in the top 10 (Nevada is 14th, Arizona 18th and California 28th), and the remaining states in the top 5 have no apparent similarities.22 Discussion From these results we take away two main conclusions. First, many of the popular explanations for the deterioration in aggregate matching e¢ ciency (cid:133)nd little support in the data. For example, some observers have speculated that job (cid:133)nding di¢ culties of unemployed workers from the construction industry, which was particularly hard hit in the last recession, were behind the deterioration in matching e¢ ciency. We (cid:133)nd the deterioration in matching e¢ ciency to be widespread across industries, consistent with Barnichon, Elsby, Hobijn and Sahin(cid:146)s (2010) (cid:133)ndings based on JOLTS data that the decline in the vacancy yield is relatively broad-based across industries. Other observers suggested that underwater mortgages and their detrimental e⁄ect on mobility were responsible for the deterioration in match e¢ ciency. Although Florida, a state with particularly hard hit real estate markets, did appear to su⁄er particularly large deteriorations in matching e¢ ciency, three other states with problem real estate markets(cid:151)Nevada, Arizona and California(cid:151)did not. More generally, the geographic distribution of match e¢ ciency did not suggest real estate, or any other factor, as a single cause. Finally, the advent of EEB does not appear responsible for the deterioration in matching e¢ ciency, although it does appear to have dissuaded some individuals from dropping out of the labor force. Second, much of the deterioration in aggregate matching e¢ ciency seems to be associated with long-duration spells of unemployment. Moreover, the timing pattern of the decline in e¢ ciency, in which the fraction of the decline that is unexplained has rapidly decreased over time, suggests that unobserved characteristics, rather than scarring, explain the correlation between duration and deterioration in matching e¢ ciency. These unobserved characteristics could be related to a mismatch between workers(cid:146)skills and location and the skills/location required by available jobs. Although we have found little evidence of misallocation, our dispersion measure has been highly aggregated, and dispersion may be occurring at a much more disaggregated level. We explore this possibility in the next section. 22Farber (2010), Molloy, Smith and Wozniac (2010) and Kaplan and Schulhofer-Wohl (2010) also (cid:133)nd little evidence that a "house-lock" is impeding migration or driving up unemployment. 18

5 More evidence on dispersion Our empirical exercise has so far relied on the unemployment rate by state and industry to proxy for labor market tightness and capture the extent of dispersion across labor market segments. In this section, we instead use direct measures of vacancy posting, and, using three di⁄erent datasets, we consider three measures of dispersion: (i) dispersion by industry, (ii) dispersion by region, and (iii) dispersion by occupation and geographic location. Availabledispersionmeasuresareconfrontedwithtwolimitations. First,notallhiresoccur with the formal posting of a vacancy, and the fraction of informal hiring is not necessarily identical across occupation, industry or geographic location. As a result, dispersion in labor market tightness need not solely capture misallocation of jobs and workers but also the fact that some segments have a higher level of informal hiring than others. Second, the level of disaggregation allowed by direct measures of labor market tightness is probably too coarse to capture the full extent of dispersion. To address these two measurement issues, we rely on a simpler framework which abstracts from worker heterogeneity and allows us to (i) estimate the fraction of informal hiring by segment, and (ii) use UK data to infer the extent of dispersion at a very (cid:133)ne level of disaggregation. 5.1 A simpler empirical framework Toexplorewhetherdispersioncanaccountforthe0.15logpointsdeclineinmatchinge¢ ciency notaccountedforbycomposition, wesimplifyourempiricalframeworkbyconsideringthecase without worker heterogeneity but using the elasticity estimated after controlling for composition, i.e., (cid:27)=0:72. Without worker heterogeneity, the job (cid:133)nding rate in segment i absent worker heterogeneity is given by !(1 (cid:27)) (1 !)(1 (cid:27)) jf it = m 0 (cid:18) it (cid:0) (cid:18) t (cid:0) (cid:0) (13) and the e⁄ect of dispersion on aggregate matching e¢ ciency movements is given by 1 (cid:18) (cid:18) it it (cid:1)mm !(1 (cid:27))(1 !(1 (cid:27))) var E var : (14) t T ’ 2 (cid:0) (cid:0) (cid:0) (cid:18) (cid:0) (cid:18) t t (cid:20) (cid:18) (cid:19) (cid:18) (cid:19)(cid:21) 5.2 Data on labor market tightness by segment We consider three datasets. First, the JOLTS measure of job openings can be disaggregated into 10 industry groups over 2000-2010.23 Second, the Conference Board Help-Wanted Index 23These groups are Trade (wholesale and retail), Information, Construction, Manufacturing, Professional/Business Services, Education and Health, Leisure and Hospitality, Financial Activities, Transportation. 19

originally proxied for the number of help-wanted advertisements in 51 major newspapers. While the print index is not disaggregated by industries, the index can be disaggregated by region, and an index of newspaper help-wanted advertising for the nine US census divisions is available. Thesenewspaperindexeshavebecomeincreasinglyunrepresentativewiththeadvent of online advertising, and the Conference Board began collecting data on online job posting in 2005.24 By splicing the regional print help-wanted indexes with online job openings by regions as in Barnichon (2010), we build composite indexes of print and online vacancy posting for the nine US census divisions over 2000-2010. Third, since November 2006, the Conference Board has published the number of helpwanted online ads by state and occupation, as well as the number of ads by metropolitan statistical areas (MSA) and occupation. The coverage of these two datasets is unique as it allows us to build a direct counterpart of vit at a high level of disaggregation. To the best uit of our knowledge, these datasets are the (cid:133)rst ones to contain information on vacancy posting in the US by occupation and geographic location. Moreover, we expand the coverage of each dataset by combining the state-level information with the MSA-level information to produce series of vacancy posting by occupation and geographic areas across the US. With 50 states and 52 MSAs, we get a total of 94 geographic areas.25 The Conference Board reports online ads for six occupation groups.26 After combining these vacancy series with the number of unemployed by geographic area and occupation estimated from the CPS, we can survey the extent of dispersion over 94 6 = 564 labor market segments during the 2008-2009 recession. (cid:3) Oneconcernaboutusingvacancydatabysegmentisthatsomesegmentsmayhaveahigher share of informal hiring. For example, it is likely that a lot of hiring in construction occurs without the formal posting of a vacancy. While the aggregate vacancy-unemployment ratio from Conference Board data averaged 1.1 in 2006, the vacancy-unemployment ratio averaged 0.5 in construction and maintenance but about 4 in management and business/(cid:133)nancial. Similarly, because a broad industry group may contain industries with di⁄erent levels of informal hiring, the levels of job openings may not be comparable across regions with di⁄erent industry 24The online data collected by the Conference Board correspond to the number of new, (cid:133)rst-time online jobs and jobs reposted from the previous month on more than 1200 major Internet job boards. These data provide a direct measure of online job posting. 25Morespeci(cid:133)cally,weproceed asfollows: when astatecomprisesnMSAs,wedecomposethenumberofads for that state into n+1 geographic areas. The additional area is the di⁄erence between total ads in the state and the total number of ads across the MSAs from that state. We obtain less than 50+52 areas because some MSAs span di⁄erent states (such as New York City). When this is the case, we group these states together. The additional area is then the di⁄erence between total ads in those states and the total number of ads in the MSAs of those states. A list of the geographic areas is presented in Table A5 in the Appendix. 26ThesegroupsareManagement&Business/Financial,Professional&Related,Services,Sales&O¢ ce,Construction & Maintenance, Production & Transportation. They correspond to the SOC high level aggregations, except Management & Business/Financial and Professional & Related which split the high-level aggregation group "Management, Business, Science and Arts" into two subgroups. 20

specializations. Forexample,labormarkettightnessinservicesisonaveragethreetimeshigher in Denver than in New York. Similarly, rural areas and urban areas need not display the same fraction of informal hiring. Becauseofsuchdi⁄erencesininformalhiring,dispersioninobservedlabormarkettightness need not solely capture misallocation of jobs and workers but also the fact that some segments haveahigherlevelofinformalhiringthanothers. Formally, informalhiringisakintomeasurementerrorinvacancyposting,aswedonotmeasure(cid:18) but~(cid:18) with(cid:18) = (cid:11) ~(cid:18) and(cid:11) theshare it it it i it i offormalhiring.27 With(cid:18) = Uit(cid:18) , wethenget(cid:18) = (cid:11) ~(cid:18) with(cid:11) = Vit(cid:11) . According t i Ut it t 0t t 0t i Vt i to (14), the e⁄ect of dispersion on matching e¢ ciency is thus a function of var (cid:11)i ~(cid:18)it . P P (cid:11)0t ~(cid:18)t To estimate (cid:11)i for each dataset, we use data on the job (cid:133)nding rate by seg(cid:16)ment. (cid:17)Taking (cid:11)0t !(1 (cid:27)) (1 !)(1 (cid:27)) the log of jf it = m 0 (cid:18) it (cid:0) (cid:18) t (cid:0) (cid:0) for segment i and an arbitrarily chosen segment 1, we can back-out ln (cid:11)i from the regression (cid:11)1 (cid:11) lnjf lnjf = !(1 (cid:27))ln i +!(1 (cid:27)) ln~(cid:18) ln~(cid:18) +(cid:24) (15) it (cid:0) 1t (cid:0) (cid:11) (cid:0) it (cid:0) 1t t 1 (cid:16) (cid:17) wherewetakethelog-di⁄erencebetweentwosegmentstoremovethenon-observableparameter (cid:11) : We then obtain (cid:11)0t from (cid:11)0t = Uit (cid:11)i, and we get (cid:11)i = (cid:11)i=(cid:11)0t. For the online help- 0t (cid:11)1 (cid:11)1 i Ut (cid:11)1 (cid:11)0t (cid:11)1 (cid:11)1 wantedadsbyoccupationandgeography,thelevelofdisaggregationissuchthatthesamplesize P of the CPS is a limitation and the monthly measures of the job (cid:133)nding rate and unemployment over 564 segments are noisy. We thus use variables at their average values over 2006-2010 and, assuming a value for !(1 (cid:27)) (we take !=0.4 and (cid:27)=0.72), we can compute (cid:11)i from (14).28 (cid:0) (cid:11)1 5.3 Dispersion measures Figure 4 plots the dispersions in labor market tightness over 2000-2010 using our three data sources. JOLTSdataindicatethatdispersionacrosstenindustrygroupsincreasedinthe2008- 2009 recession by about twice as much as during the 2001 recession, but that it receded in 2009. Dispersion across the 9 census divisions also rose in the 2008-2009 recession, but the increase started in late 2006, earlier than for sectoral dispersion. In comparison, the increases in regional dispersion in the 2001 recession were small. Dispersion by geography and occupation shows a clear increase in the 2008-2009 recession, 27We assume that, apart from measurement error, there are no di⁄erences in matching e¢ ciency across occupation and geographic area so that m = m , i (an assumption we implicitly made in Seci 0 8 tion 3 with our functional form (9)). With di⁄erent matching e¢ ciency levels, (13) becomes jf = it m i (cid:11)! i (1 (cid:0) (cid:27))~(cid:18) ! it (1 (cid:0) (cid:27)) (cid:11)( 0 1 t(cid:0) !)(1 (cid:0) (cid:27))~(cid:18) ( t 1 (cid:0) !)(1 (cid:0) (cid:27)) : With (cid:11) i and m i both a⁄ecting matching e¢ ciency in observationally equivalent, it is not possible to disentangle the two phenomena from information on the job (cid:133)nding rate and measured labor market tightness alone. 28Using a di⁄erent value for ! makes little di⁄erence to our results. 21

and Figure 4 shows that the behavior of the series matches very well with the behavior of the unexplained component of Figure 2. In fact, the correlation between the two series is high at 0:82. Over 2007-2008, the increase in dispersion coincides with the decline in match e¢ ciency, while composition was (cid:135)at (Figure 2). In 2009, both dispersion and the unexplained component of matching e¢ ciency peaked before declining slightly. Geography/occupationdispersionwasconstantin2009whilebothdispersionacrossregions anddispersionacrossindustrygroupsdeclined. Thesedi⁄erentresultshighlighttheimportance of looking simultaneously at geography and occupation or industry when studying the e⁄ect of dispersion. Thus in the rest of the paper, we will concentrate on dispersion by geography and occupation, which we think provides the most accurate description of dispersion in labor market conditions. 5.4 Inferring the true amount of dispersion from UK data Becausethee⁄ectofdispersionarisesoutoftheconcavityofthematchingfunction,itiscrucial to reach a good level of disaggregation. Our highest level of disaggregation covers only 564 labor market segments, probably a small amount compared to the true number of segments in the US. As Shimer (2007) emphasized, the Occupational Employment Statistics (OES) counts about 800 occupations, and there are 362 metropolitan statistical areas and 560 micropolitan statistical areas, so a total of about 740,000 labor market segments.29 Thus, we now present a method using UK data to scale up our measure of dispersion over 564 segments to a more realistic number of labor market segments. De(cid:133)ne an elementary labor market segment as the smallest segment in which the matching function is still well described by (13). We will refer to an elementary segment as a unit. The e⁄ect of misallocation on matching e¢ ciency is thus given by the dispersion in labor market conditions across such units. We cannot observe labor market tightness at the unit level. Instead, we observe (cid:22)(cid:18) = jt 1 (cid:18) , the average value of the (cid:18) s over segment j, consisting of m N(cid:22) units indexed m jk t i (cid:17) N jk Ij by IP 2 = j ;::;j [1;N(cid:22)] with N(cid:22) the total number of units and N the number of observed j 1 m f g (cid:26) (larger)segments. Thus, wecannotmeasure var (cid:18)it , thedispersionovertheN(cid:22) units, butwe (cid:18)t can measure var (cid:22)(cid:18)jt , the variance in labor m(cid:16)arke(cid:17)t tightness over N larger segments with n (cid:18)t n N 1.30 (cid:16) (cid:17) (cid:17) N(cid:22) (cid:20) To relate these two quantities and get an estimate of var (cid:18)it from var (cid:22)(cid:18)jt , we turn (cid:18)t n (cid:18)t (cid:16) (cid:17) (cid:16) (cid:17) 29740,000isanextremeexampleusedforillustrationasdispersionacrossthatmanysegmentswouldexaggerate the e⁄ect of mismatch. When the set of classi(cid:133)cations is too (cid:133)ne, the boundaries between segments are less clearly de(cid:133)ned, and workers are more likely to cross segments to (cid:133)nd a job. 30As we re(cid:133)ne the level of disaggregation and n=N 1, var (cid:18)(cid:22) j var (cid:18)it : N(cid:22) ! n (cid:18)t ! (cid:18)t (cid:16) (cid:17) (cid:16) (cid:17) 22

to UK data. Unlike the US, the UK public employment o¢ ce collects vacancies by occupation and geography at very di⁄erent levels of disaggregation, from low levels of disaggregation to very high levels of disaggregation (as high as 80,000 segments). These numbers can in turn be matched to the number of job seekers(cid:146)allowance claimants to construct measures of labor market tightness across various occupation and geographic segments.31 With these data, we can then establish an empirical (cid:147)scaling law(cid:148)that captures how var (cid:22)(cid:18)jt increases when we n (cid:18)t raise the number of observations N and consider smaller labor marke(cid:16)t seg(cid:17)ments. The UK data by occupation are available at the one- to four- digits SOC levels, consisting of respectively 9, 25, 81 and 353 groups, and we use data by geographic region at three disaggregation levels; government o¢ ce regions (11 segments), Job Center plus Districts (48 segments), and Travel to Work Areas (232 segments). Thanks to these di⁄erent levels of disaggregation, wecanprobehowvar (cid:22)(cid:18)jt variesasweincreasetheprecisionofobservations n (cid:18)t from N = N occ N geo = 9 11 = 99 s(cid:16)egm(cid:17)ents to 353 232 = 81;896 segments. To increase (cid:3) (cid:3) (cid:3) the sample size, we took averages of unemployment and vacancy data over the whole sample period July 2006-July 2010.32 A simple theoretical framework left for the Appendix shows that we could expect a relation of the form (cid:22)(cid:18) (cid:18) N N jt it geo occ var = var f(n ;n ) with n = ;n = (16) n (cid:18) (cid:18) geo occ geo N(cid:22) occ N(cid:22) (cid:18) t (cid:19) (cid:18) t (cid:19) geo occ with f(n ;n ) 1, f(:) increasing and f 1 when (n ;n ) (1;1), and where f(:) geo occ geo occ (cid:20) ! ! can be assumed to be time invariant. Empirically, a power law lnvar ( (cid:22)(cid:18)jt) = lna + a lnn + a lnn (cid:133)ts the UK data n (cid:18)t 0 1 geo 2 occ extremely well with an R2 of 0:98 (Table 4).33 This encouragingly suggests that one need not probe the data at a very high level of disaggregation to estimate the e⁄ect of dispersion on matching e¢ ciency, but can instead use f(n geo ;n occ ) = na ge 1 o na oc 2 c to scale up our estimate var (cid:22)(cid:18)jt . To illustrate the empirical relation, Figure 5 plots the relationship between the n (cid:18)t total(cid:16)num(cid:17)ber of observed segments and var (cid:22)(cid:18)jt as we increase the number of occupation n (cid:18)t categories from 9 (comparable with the 6 occu(cid:16)pati(cid:17)ons observed using Conference Board data) to 353, and holding the number of geographic areas constant at 48 (comparable with the 94 areas observed using Conference Board data). Assuming that f(:) is similar in the UK and in the US (i.e. that the scaling law parameters 31See Sahin, Song, Topa, and Violante (2010) for a detailed study of mismatch in the UK. 32We do not use data prior to May 2006 because of a break in methodology. 33Estimatingthescalinglaw usingonlyyearlydata(andleavingoutthehighestdisaggregation levelsN = occ 353) gives similar a and a but di⁄erent intercepts a , supporting our assumption that f(:) is time invariant. 1 2 0 23

a and a are not country speci(cid:133)c)34 and given an estimate of the number of labor market 1 2 units N(cid:22) and N(cid:22) , we can use the UK scaling law to build an estimator of var (cid:18)it : geo occ (cid:18)t (cid:16) (cid:17) var (cid:22)(cid:18)jt var (cid:18) it n (cid:18)t : (17) n (cid:18) (cid:17) f(n (cid:16);n (cid:17)) t geo occ (cid:18) (cid:19) Assuming that there are 353 disdtinct occupations in the US and 232 geographic segments, probably a conservative estimate given Shimer(cid:146)s (2007) aforementioned observation and the fact that the US is, geography-wise, much larger than the UK, we get that f( 94 ; 6 ) 1=20, 232 353 ’ so that an increased in measured dispersion in online HWI from 0:25 to 0:5 between November 2006 and December 2009 for (N =6, N =94) translates into an increase from 5 to 10 when occ geo (N =353, N =232). occ geo 5.5 E⁄ects of dispersion on matching e¢ ciency To translate our estimated increase in dispersion into lower matching e¢ ciency, we need to address one (cid:133)nal issue. The previous section suggests that the increase in dispersion in labor market conditions lead to a high value of var (cid:18)it at about 10 in 2009. With such high (cid:18)t dispersion, the Taylor expansion (14) need not p(cid:16)rov(cid:17)ide a good approximation of the e⁄ect of dispersion on matching e¢ ciency. Instead, we resort to numerical simulations to calculate the exact e⁄ect of dispersion on matching e¢ ciency. If the job (cid:133)nding rate in segment i is described by (13), mm, the e⁄ect of dispersion on matching e¢ ciency is given by the di⁄erence in the average job (cid:133)nding rate when (cid:18)i always equals 1 and when (cid:18)i is distributed with variance (cid:27)2. Speci(cid:133)cally, (cid:18) (cid:18) (cid:18) U mm = ln U i m 0 (cid:18) ! i (1 (cid:0) (cid:27)) (cid:18)(1 (cid:0) !)(1 (cid:0) (cid:27)) (cid:0) lnm 0 (cid:18)1 (cid:0) (cid:27) (18) i X and we calculate mm = mm((cid:27)2) by positing that ln (cid:18)i N((cid:0) ln(1+(cid:27)2 (cid:18) ) ;ln 1+(cid:27)2 ), so that (cid:18) (cid:18) (cid:24) 2 (cid:18) E(cid:18)i=1 and var((cid:18)i)= (cid:27)2. Figure 6 shows how changing (cid:27)2 a⁄ects mm and aggregate matching (cid:18) (cid:18) (cid:18) (cid:18) (cid:0) (cid:1) e¢ ciency. Moreover, because it is di¢ cult to estimate the permeability of labor market segments, Figure 6 also plots the e⁄ect of ! on the relationship between dispersion and matching e¢ ciency. That way, we can report the e⁄ect of dispersion on matching e¢ ciency for di⁄erent values of !: Withthevarianceof (cid:18)it increasingfromabout5inNovember2006toabout10inDecember (cid:18)t 34In the Appendix, we show that one can apply the UK scaling law to US data if the average correlation in labor market conditions within an occupation group and/or a geographic area is similar in both countries. 24

2009, misallocation can explain 26 percent (0:04 log-points out of the 0:15 unexplained logdeclineinjf, cf. Figure2)ofthedeclineinmatchinge¢ ciencywhen! = 0:4, about36percent (:055logpoints)when! = 0:6,andabout20percent(:03log-points)when! = 0:3:35 Asavery conservativeestimate, wecantaketheincreaseindispersionfromonlineHWIatfacevalue(an increase from 0.25 to 0.5) and not use the UK scaling law. In that case, dispersion accounts for about 10 percent (0.015 log-points) of the unexplained decline in matching e¢ ciency (using ! = 0:4). Thus, we conclude that an increase in labor market dispersion likely led to a noticeable decline in matching e¢ ciency, though a signi(cid:133)cant fraction of the overall decline remains unexplained.36 5.6 Taking stock It is di¢ cult to estimate the e⁄ect of dispersion on matching e¢ ciency because data on vacancies and unemployment at high levels of disaggregation are not available. However, with some assumptions, one can use the available data to estimate the e⁄ect of dispersion at high levels of disaggregation. These assumptions are: (1) most of the di⁄erences in matching ef- (cid:133)ciency across segments are due to di⁄erent fractions of informal hiring, (2) the UK scaling relationship linking var (cid:18)it , the actual dispersion in labor market conditions, to var (cid:22)(cid:18)jt , (cid:18)t n (cid:18)t thedispersionmeasured(cid:16)over(cid:17)anumberoflargersegments, istimeinvariantandcanbea(cid:16)pplie(cid:17)d to the US. Given these assumptions, it is likely that greater dispersion has accounted for a substantial portion (cid:150)about a quarter but possibly more(cid:150)of the unexplained drop in matching e¢ ciency over the past three years. 6 Conclusion In this paper, we study the determinants of aggregate matching e¢ ciency (cid:135)uctuations over the last four decades. 35While these numbers are derived using N(cid:22) =353 and N(cid:22) =232, in practice, for N(cid:22) large enough, the occ geo choice of N(cid:22) makes little di⁄erence to our conclusion. Doubling the number of units (i.e., setting N(cid:22) =706 occ and N(cid:22) =464) only increases the contribution of misallocation from 26 to 27 percent, while halving N(cid:22) only geo decreases it to 24 percent. 36Note that our calculation implicitly assumed that the estimated value of var (cid:18)it in November 2006 (cid:18)t corresponds to E var (cid:18)it , the average dispersion level over 1976-2007. This se(cid:16)ems(cid:17)plausible given that T (cid:18)t Figures 1 and 2 show t(cid:16)hat(cid:17)aggregate matching e¢ ciency was at its average level in late 2006, suggesting that dispersionwasatitsaveragelevel. Interestingly,iftheaveragelevelofdispersionisgivenbytheNovember2006 reading of 5, this implies that, on average, dispersion in labor market conditions depresses the US job (cid:133)nding rate by about 15 percent (using !=0:4 and Figure 6). 25

Under fairly general assumptions, we link movements in aggregate matching e¢ ciency to two measurable factors: (i) composition of the unemployment pool, and (ii) dispersion in labor market conditions. We also show that the e⁄ect of misallocation on aggregate matching e¢ ciency is a function of the dispersion in conditions across labor markets segment and of the segments(cid:146)permeability. While a number of dispersion measures have been proposed in the literature, our framework provides a dispersion measure (cid:150)the variance of labor market tightness(cid:150) that can be analytically related to matching e¢ ciency and to the equilibrium unemployment rate. Using CPS micro data over 1976-2009, we (cid:133)nd that changes in composition of the unemploymentpoolgeneratenon-trivialprocyclicalmovementsinmatchinge¢ ciency,implyingthat estimates of the aggregate matching function elasticity are biased upwards. Until 2006, the composition of the unemployment pool (mostly the share of job losers on permanent layo⁄s and the share of long-term unemployed) is responsible for most of the cyclical movements in matching e¢ ciency, while dispersion in labor market conditions appears to have played a modest role. Since 2006, composition explains only 40 percent of a dramatic decline in matching e¢ ciency. Instead, the behavior of the unexplained decline is highly (negatively) correlated with dispersion in labor market conditions. Quantitatively, misallocation of workers and jobs may account for a quarter, and perhaps more, of the unexplained decline. We also test a number of popular explanations but (cid:133)nd no evidence that matching e¢ ciency was a⁄ected by the extension of unemployment coverage, by a (cid:147)house-lock(cid:148)or by industry speci(cid:133)c shocks. A remaining question is what accounted for the remaining unexplained decline in matching e¢ ciency. An obvious possibility, given the di¢ culty to assess dispersion at high levels of disaggregation, is that our UK scaling law lead us to understate the extent of the increase in dispersion and hence the e⁄ect of dispersion on matching e¢ ciency. Another possibility, not tested in this paper, is that part of the decline in matching e¢ ciency was caused by a compositional change in vacancy posting. For example, because the construction sector has a high fraction of informal hiring (and hence an apparently high matching e¢ ciency), a decline in the fraction of construction ads among vacancies will lower matching e¢ ciency. However, Barnichon, Elsby, Hobijn and Sahin (2010) do not (cid:133)nd that vacancy composition signi(cid:133)cantly contributed to the decline in the vacancy yield. A related hypothesis raised by Davis, Faberman and Haltiwanger (2010) is that (cid:133)rms vary recruiting intensity during recessions. Despite the fact that our empirical framework does not allow for varying recruiting intensity, it can successfully capture job (cid:133)nding probability movements over 1976-2006. This suggests that aggregate labor market tightness (orsectoral tightness)can proxy for varying recruiting intensity over that period. Thus, if the recent unexplained decline in matching e¢ ciency was caused by lower recruiting intensity, this would imply that recruiting intensity was exceptionally low 26

in the current recession. Assessing this hypothesis would be an interesting goal for future research. 27

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[14] Fujita, S. (cid:147)E⁄ects of the UI Bene(cid:133)t Extensions: Evidence from the Monthly CPS,(cid:148) Philadelphia Fed Working Paper 10-35, 2010. [15] Jackman, R. and S. Roper. (cid:147)Structural Unemployment,(cid:148)Oxford Bulletin of Economics and Statistics, 49(1), 9-36, 1987. [16] Jackman, R., R. Layard, and S. Savouri. (cid:147)Mismatch: a framework for thought,(cid:148)in Mismatch and Labor Mobility, Cambridge, Cambridge University Press, 1991. [17] Layard R., S. Nickell, and R. Jackman. Unemployment: Macroeconomic Performance and the Labour Market, 2nd Edition, Oxford University Press, 2005. [18] Kaplan, G. and S. Schulhofer-Wohl. (cid:147)Interstate migration has fallen less than you think: Consequences of hot deck imputation in the Current Population Survey,(cid:148)Working Paper, 2010. [19] Katz, Lawrence, and Bruce Meyer. (cid:147)The Impact of the Potential Duration of Unemployment Bene(cid:133)ts on the Duration of Unemployment,(cid:148)Journal of Public Economics, 41 pp. 45-72, 1991. [20] Kuang,K.andR.Valletta.(cid:147)ExtendedUnemploymentandUIBene(cid:133)ts,(cid:148)FRBSSEconomic Letter, 2010. [21] Meyer,Bruce.(cid:147)UnemploymentInsuranceandUnemploymentSpells,(cid:148)Econometrica,58:4, pp. 757-82, 1990. [22] Mo¢ tt, Robert. (cid:147)Unemployment Insurance and the Distribution of Unemployment Spells,(cid:148)Journal of Econometrics, 28, pp. 85-101, 1985 [23] Molloy, R., C. Smith and A. Wozniac. (cid:147)Internal Migration in the US: Updated Facts and Recent Trends,(cid:148)mimeo, University of Notre Dame, 2010. [24] Padoa Schioppa, F. Mismatch and Labor Mobility, Cambridge, Cambridge University Press, 1991. [25] Petrongolo, B. and C. Pissarides. (cid:147)Looking into the black box: A survey of the matching function,(cid:148)Journal of Economic Literature, 39: 390-431, 2001. [26] Pissarides, C. Equilibrium Unemployment Theory, 2nd ed, MIT Press, 2000. [27] Sahin A., J. Song, G. Topa, and G. Violante. (cid:147)Mismatch in the Labor Market: Evidence from the UK and the US," mimeo, 2010. [28] Shimer, R. (cid:147)Mismatch,(cid:148)American Economic Review, 97(4): 1074-1101, 2007. 29

Appendix A second-order Taylor expansion of the job (cid:133)nding probability Rewriting (9), the individual job (cid:133)nding probability is given by 1 e m0 (cid:18) (cid:18) i t t (1 (cid:0) (cid:27))! (cid:18)1 t(cid:0) (cid:27) e(cid:12)Xjt (cid:0) (cid:16) (cid:17) ! JF = +(cid:17) : ij;t it e m0 (cid:18) (cid:18) i t t (1 (cid:0) (cid:27))! (cid:18)1 t(cid:0) (cid:27) + 1 e m0 (cid:18) (cid:18) i t t (1 (cid:0) (cid:27))! (cid:18)1 t(cid:0) (cid:27) e(cid:12)Xjt (cid:16) (cid:17) (cid:0) (cid:16) (cid:17) ! Expanding with respect to X around X(cid:22) and (cid:18) around (cid:18) to a second-order, JF becomes jt it t t (cid:18) JF = JF ((cid:18) )+ JFk MM it +f +(cid:17) t t t t (cid:0) t (cid:18) t t t k (cid:18) (cid:19) X with JF t k = e (cid:0) m0(cid:18)1 t(cid:0) (cid:27) 1 (cid:0) e (cid:0) m0(cid:18)1 t(cid:0) (cid:27) U U j;t [(cid:12) k xk jt (cid:0) x(cid:22)k (cid:0) 2 1 1 (cid:0) 2e (cid:0) m0(cid:18)1 t(cid:0) (cid:27) (cid:12)2 k xk jt (cid:0) x(cid:22)k 2 t (cid:16) (cid:17)X j (cid:16) (cid:17) (cid:16) (cid:17) (cid:16) (cid:17) 1 + 2 1 (cid:0) 2e (cid:0) m0(cid:18)1 t(cid:0) (cid:27) (cid:12) k xk jt (cid:0) x(cid:22)k (cid:12) l xl jt (cid:0) x(cid:22)l ] X l 6 =k(cid:16) (cid:17) (cid:16) (cid:17) (cid:16) (cid:17) the (second-order) composition e⁄ect from characteristic k on the average job (cid:133)nding rate, (cid:18) U (cid:18) 2 it i;t it MM = MM ((cid:18) ) 1 t 0 t (cid:18) U (cid:18) (cid:0) t t t (cid:18) (cid:19) i (cid:18) (cid:19) X the term capturing the e⁄ect of dispersion on the average job (cid:133)nding rate with MM ((cid:18) ) = 0 t 1 2 (cid:27)+(1 (cid:0) (cid:27))m 0 (cid:18)1 t(cid:0) (cid:27) m 0 (cid:18)1 t(cid:0) (cid:27)e (cid:0) m0(cid:18)1 t(cid:0) (cid:27) and (cid:0) (cid:1) U (cid:18) f = !(1 (cid:27)) ij;t m (cid:18)1 (cid:27) 2m (cid:18)1 (cid:27) 1 it 1 (cid:12) xk x(cid:22)k : t (cid:0) U 0 t(cid:0) 0 t(cid:0) (cid:0) (cid:18) (cid:0) k jt (cid:0) t t X i;j X k (cid:0) (cid:1) (cid:18) (cid:19) (cid:16) (cid:17) capturing the interaction of composition and dispersion.37 37This e⁄ect comes from the concavity of the matching function, as above average workers would have a stronger positive impact on matching e¢ ciency than below average workers if above average workers were located in looser labor markets. Interestingly, this also implies that matching e¢ ciency is lower when workers with above average characteristics are concentrated in tighter labor markets. 30

Decomposing movements in aggregate matching e¢ ciency To establish a link between aggregate movements in matching e¢ ciency and changes in composition and dispersion, we write the job (cid:133)nding rate jf as a function of the job (cid:133)nding t probability JF , and use (6) to get t jf = ln(1 JF ) t t (cid:0) (cid:0) (cid:18) = ln 1 JF ((cid:18) )+ JFk MM it +(cid:17) (cid:0) (cid:0) t t t (cid:0) t (cid:18) t t !! k (cid:18) (cid:19) X 1 (cid:18) = ln 1 JF ((cid:18) ) ln 1 JFk MM it +(cid:17) (cid:0) (cid:0) t t (cid:0) (cid:0) 1 (cid:0) JF t ((cid:18) t ) k t (cid:0) t (cid:18) (cid:18) t (cid:19) t !! (cid:0) (cid:1) X 1 (cid:18) jf((cid:18) )+ JFk MM it +(cid:17) ’ t 1 (cid:0) JF t ((cid:18) t ) k t (cid:0) t (cid:18) (cid:18) t (cid:19) t ! X with jf((cid:18) ) ln 1 JF ((cid:18) ) : t t t (cid:17) (cid:0) (cid:0) Usingthefunctionalform(9), wehavejf((cid:18) ) = m (cid:18)1 (cid:27), andtakingthelogoftheprevious (cid:0) (cid:1) t 0 t(cid:0) expression gives us lnjf lnm +(1 (cid:27))ln(cid:18) t 0 t ’ (cid:0) +ln 1+ em0(cid:18)1 t(cid:0) (cid:27) JFk MM (cid:18) it +(cid:17) m 0 (cid:18) t 1 (cid:0) (cid:27) k t (cid:0) t (cid:18) (cid:18) t (cid:19) t !! X lnm +(1 (cid:27))ln(cid:18) 0 t ’ (cid:0) + em0(cid:18)1 t(cid:0) (cid:27) JFk MM (cid:18) it +(cid:17) (19) m 0 (cid:18)1 t(cid:0) (cid:27) k t (cid:0) t (cid:18) (cid:18) t (cid:19) t ! X At | {z } whereforthelastexpression,weusedthefactthatm 0 (cid:18)1 t(cid:0) (cid:27)e (cid:0) m0(cid:18)1 t(cid:0) (cid:27) (cid:29) JF t k (cid:0) MM t (cid:18) (cid:18) i t t + X k (cid:16) (cid:17) (cid:17) : Expression (19) has the same form as our aggregate regression (2). t Thus, the deviations of aggregate matching e¢ ciency from its average level can be written (cid:22) = lnm E lnm t 0t T 0t (cid:0) = lnjf (1 (cid:27))ln(cid:18) E (lnjf (1 (cid:27))ln(cid:18) ) t t T t t (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) A E A using (19) t T t ’ (cid:0) em0(cid:18)1 t(cid:0) (cid:27) JFk (cid:1)mm +(cid:16) ’ m (cid:18)1 (cid:27) t (cid:0) t t 0 t(cid:0) k X 31

with mm = em0(cid:18)1 t(cid:0) (cid:27) MM (cid:18)it and (cid:1)mm = mm E mm .38 Using the expression for t m0(cid:18)1 t(cid:0) (cid:27) t (cid:18)t t t (cid:0) T t MM (cid:18)it , the e⁄ect of dis (cid:16) pers (cid:17) ion on matching e¢ ciency movements is then given by t (cid:18)t (cid:16) (cid:17) 1 (cid:18) (cid:18) (cid:1)mm !(1 (cid:27)) (1 !(1 (cid:27)) 1 m (cid:18)1 (cid:27) var it E var it : t ’ 2 (cid:0) (cid:0) (cid:0) (cid:0) 0 t(cid:0) (cid:18) (cid:0) T (cid:18) t t (cid:20) (cid:18) (cid:19) (cid:18) (cid:19)(cid:21) (cid:2) (cid:0) (cid:1)(cid:3) A theoretical link between actual labor market dispersion and observed dispersion Assume that the (cid:18) are independently distributed across N(cid:22) elementary labor market segments i of equal size (i.e., with the same number of unemployed). For clarity of exposition, we will refer to the elementary segments as units. Denote h the distribution of (cid:18) across units so that i (cid:18) h((cid:18);(cid:27)2) (mean (cid:18) and variance (cid:27)2) with i [1;N(cid:22)]. We cannot observe the value of (cid:18) i (cid:24) (cid:18) (cid:18) 2 i for the N(cid:22) units, but we do observe the average value of (cid:18) over many units. Speci(cid:133)cally, for i N segments that consist of m N(cid:22) units, we observe (cid:22)(cid:18) = N (cid:18) , the average value of (cid:17) N j N(cid:22) jk jk Ij 2 the (cid:18) s over segment j indexed by I = j ;::;j [1;N(cid:22)], a se P gment consisting of m = N(cid:22) i j f 1 m g (cid:26) N observations of (cid:18) : To estimate the true amount of dispersion in the labor market, we want to i recover (cid:27)2 from the observed variance across larger segments, i.e., var((cid:22)(cid:18) ): (cid:18) j If the observed segments were random samples of the (cid:18) s (i.e., if the (cid:18) s were independently i i distributed across units in each observed segment), we would have a linear relation linking the true dispersion to the observed variance N var((cid:22)(cid:18) ) = (cid:27)2 : (20) j (cid:18)N(cid:22) which converges to (cid:27)2 when N N(cid:22). (cid:18) ! In fact, however, the segments that we observe are not random samples of the (cid:18) s. Instead, i because the segments that we observe correspond to an occupation group or/and a geographic location, the labor market units inside those segments are likely to be correlated. Denote (cid:26) the average correlation between labor market units within a segment. Speci(cid:133)cally, (cid:26) = 1 corr((cid:18) ;(cid:18) ), and, for simplicity, we assume that the average correlation (cid:26) is the n 1 m=n jm jn (cid:0) 6 same for all observed segments. (cid:26) is likely to increase as we re(cid:133)ne our de(cid:133)nition of a segment. P For example, the average correlation between labor markets across the large US Census region "West" is certainly lower than the average correlation between labor markets across the city of 38Forthelastexpression,weassumedthatE JFk issmall,whichisempiricallythecasesincethesecond- T t k orderapproximationofJFk isverysmallandsin X cewedemeanedtheX variablesbeforeestimating(9)sothat t jt the (cid:133)rst-order term of JFk is nil. t 32

Los Angeles. Denoting N the number of observed geographic locations and N the number geo occ of observed occupations, we have N = N N , and we assume that (cid:26) = (cid:26)( Ngeo; Nocc) with geo occ N(cid:22) geo N(cid:22) occ (cid:26) > 0, (cid:26) > 0 and (cid:26)( Ngeo; Nocc) 1 when N N(cid:22) = N(cid:22) N(cid:22) . A little bit of algebra gives us 01 02 N(cid:22) geo N(cid:22) occ ! ! geo occ N N N N var((cid:22)(cid:18) ) = (cid:27)2 1+(cid:26)( geo ; occ ) 1 (21) j (cid:18) N(cid:22) N(cid:22) (cid:0) N(cid:22) N(cid:22) (cid:18) geo occ (cid:18) (cid:19)(cid:19) N N = (cid:27)2f( geo ; occ ) (cid:18) N(cid:22) N(cid:22) geo occ which also converges to (cid:27)2 when N N(cid:22). With (cid:26)( Ngeo; Nocc) = 0, this generalization of (20) (cid:18) ! N(cid:22) geo N(cid:22) occ 6 is not linear. Instead, because (cid:26)( Ngeo; Nocc) 1 when N N(cid:22), one can show that, as N N(cid:22) geo N(cid:22) occ ! ! converges to N(cid:22), @2var((cid:22)(cid:18)j) < 0 and the curve (cid:135)attens out, in line with the UK evidence. @N2 Thus, we can build an estimator of (cid:27)2 (cid:18) var (cid:22)(cid:18) n j var ((cid:18) ) : (22) n i (cid:17) f(n ;n ) geo(cid:0) oc(cid:1)c Thistheoreticalframeworkisusefuldtoclarifywhatkindofassumptionsarenecessarytousethe UKscalinglawandtheestimatorvar withUSdata. Notethatf( Ngeo; Nocc)isindependentof n N(cid:22) geo N(cid:22) occ (cid:27)2. Thus, f( Ngeo; Nocc) will be identical in the US and the UK, if both countries have identical (cid:18) N(cid:22) geo N(cid:22) occ d (cid:26)( Ngeo; Nocc), i.e., if, within a segment of size N(cid:22) , the average correlation in labor market N(cid:22) geo N(cid:22) occ NgeoNocc tightness between units of that segment is the same for both countries.39 For example, within the"West"regionofeachcountry, theaverage correlationbetweentwoneighboringgeographic unitsmustbethesameintheUSandtheUK.Or,withintheoccupationgroup"Construction", the average correlation between subcategories of construction must the same. Assuming as a (cid:133)rst approximation that the average correlations across occupation and geographic are time invariant and similar in the US and the UK, we can apply the UK scaling law to US data. N Finally, we do not observe var((cid:22)(cid:18) ) but the sample variance 1 (cid:22)(cid:18) (cid:18) 2 : As a result, j N j (cid:0) j=1 N P (cid:0) (cid:1) we can only use (22) if N is large enough to ensure 1 (cid:22)(cid:18) (cid:18) 2 var((cid:22)(cid:18) ). For low values N j (cid:0) ’ j j=1 of N (as would be the case with JOLTS data with onlPy 1(cid:0)0 indus(cid:1)try groups and 1 area), the sample variance may not be a good approximation of the actual variance, and the scaling law could give misguided results. 39The condition to use the UK law (21) with US data becomes more stringent as N increases. Since only the average correlation enters (21), one only needs that, within a segment of size n = N(cid:22), the average correlation N betweenunitsisidenticalintheUSandtheUK.ButasN increasestoN(cid:22),thenumberofunitswhichonetakes the average gets smaller, and the condition is more restrictive. 33

Figure 1: Empirical job (cid:133)nding rate, job (cid:133)nding rate predicted by an aggregate matching function and (log) aggregate matching e¢ ciency, the (log) di⁄erence between the empirical and the predicted job (cid:133)nding rate, 1976-2009. For aggregate matching e¢ ciency, the plotted series is the 4-quarter moving average. Grey bars indicate NBER recession dates. 34

Reason for Unemployment Demographics 0.02 0.02 ytilaborp 0.01 ytilaborp 0.01 F 0 F 0 J ni segnah 0.01 J ni segnah 0.01 C C 0.02 0.02 1976 1980 1984 1988 1992 1996 2000 2004 2008 1976 1980 1984 1988 1992 1996 2000 2004 2008 Duration Dispersion 0.02 0.02 ytilaborp 0.01 ytilaborp 0.01 F 0 F 0 J ni segnah 0.01 J ni segnah 0.01 C C 0.02 0.02 1976 1980 1984 1988 1992 1996 2000 2004 2008 1976 1980 1984 1988 1992 1996 2000 2004 2008 Decomposition of changes in matching efficiency 0.1 0.05 0 fj fo stniop goL 0 . 0 0 . 5 1 Aggregate 0.15 Composition/Dispersion Residual 0.2 0.25 1976 1980 1984 1988 1992 1996 2000 2004 2008 Figure2: Upperpanel: decompositionofthetotale⁄ectofcompositionanddispersionintoreasonforunemployment,demographics,unemploymentdurationanddispersion. Thedashedline representsthetotale⁄ectofcomposition/dispersion. Lowerpanel: decompositionofchangesin aggregate matching e¢ ciency into composition e⁄ect/dispersion and an unexplained aggregate e⁄ect. Regression estimated over 1976-2007. All series are 4-quarter moving averages. 35

Reason for Unemployment Demographics 0.015 0.015 0.01 0.01 ytilaborp 0.005 0 ytilaborp 0.005 0 F F J ni segnah 0 0 . . 0 0 0 . 1 0 0 5 5 1 J ni segnah 0 0 . . 0 0 0 . 1 0 0 5 5 1 C C 0.02 0.02 0.025 0.025 1976 1980 1984 1988 1992 1996 2000 2004 2008 1976 1980 1984 1988 1992 1996 2000 2004 2008 Duration Dispersion 0.015 0.015 0.01 0.01 ytilaborp 0.005 0 ytilaborp 0.005 0 F F J ni segnah 0 0 . . 0 0 0 . 1 0 0 5 5 1 J ni segnah 0 0 . . 0 0 0 . 1 0 0 5 5 1 C C 0.02 0.02 0.025 0.025 1976 1980 1984 1988 1992 1996 2000 2004 2008 1976 1980 1984 1988 1992 1996 2000 2004 2008 Decomposition of changes in matching efficiency 0.1 0.05 0 fj fo stniop goL 0 0 . . 0 1 0 . 5 5 1 A C g o g m re p g o a s t i e tion/Dispersion Residual 0.2 0.25 1976 1980 1984 1988 1992 1996 2000 2004 2008 Figure3: Upperpanel: decompositionofthetotale⁄ectofcompositionanddispersionintoreasonforunemployment,demographics,unemploymentdurationanddispersion. Thedashedline representsthetotale⁄ectofcomposition/dispersion. Lowerpanel: decompositionofchangesin aggregate matching e¢ ciency into composition e⁄ect/dispersion and an unexplained aggregate e⁄ect. Regression estimated over 1976-2009, allowing for a break in the coe¢ cients in 2008. All series are 4-quarter moving averages. 36

Figure 4: Left scale: dispersion in labor market tightness across 9 regions, 10 industry groups and564occupation/regiongroups. Rightscale: Unexplainedmovementsinmatchinge¢ ciency (y-axis in reverse order). 2001-2010. 37

Figure 5: Relationship between var((cid:18)it) and the number of observed labor market segments in (cid:18) the UK over 2006-2007, keeping the number of geographic units (cid:133)xed (48) but increasing the numberofobservedoccupations(9, 25, 81, 353). Labormarkettightnessmeasuresconstructed from jobseekers allowance claimants and vacancy posting data from Jobcentre Plus. 0.35 0.3 0.25 )F J (g 0.2 o l fo 0.15 s tin U 0.1 0.05 0 1 8 0.8 6 0.6 4 Varianceq (i)/q 0.4 2 0.2 0 Impermeabilityw Figure 6: The e⁄ect of labor market tightness dispersion var (cid:18)i and impermeability ! on (cid:18) matching e¢ ciency. (cid:16) (cid:17) 38

Table 1: Estimating a Cobb-Douglas matching function Dependent variable: λUE λUE Sample (quarterly frequency) 1976-2007 1976-2007 Regression (1) (2) Estimation OLS GMM 1-σ 0.33*** 0.34*** (0.01) (0.01) R2 0.87 -- Note: Standard-errors are reported in parentheses. In equation (2), we use 3 lags of v and u as instruments. We allow for first-order serial correlation in the residual. Table 2 Estimated Coefficients for Job Finding probability regression, 1976-2007 Explanatory Variable Pre-redesign Post-redesign 1976-1993 1994-2007 Matching Function parameter Aggregate elasticity: 1-σ 0.28 (0.01) Constant: ln(m) -1.43 0 (0.003) Local elasticity: γ 0.16 (0.01) Other parameters Age 0.0026 0.0004 (0.001) (0.001) Age squared -0.0002 -0.0002 (0.00002) (0.00002) Male dummy 0.20 0.12 (0.01) (0.01) Permanent layoff dummy -0.27 -0.27 (0.01) (0.01) Temporary layoff dummy 0.38 0.67 (0.001) (0.01) Reentrant dummy -0.26 -0.32 (0.01) (0.01) New Entrant dummy -0.58 -0.88 (0.01) (0.02) Unemployment duration -0.025 -0.021 (0.001) (0.002) Duration interacted with 0.0006 0.0003 average duration (0.0001) (0.0001) Pseudo R2 0.0455 Note. Explanatory variables also include monthly dummies. All variables, except age after 1993, are significant at conventional levels. Standard errors are in parentheses. 39

Table 3 Estimated Coefficients for Job Finding probability regression, 1976-2009 Explanatory Variable 1976-2007 Post 2007 Matching Function parameter Aggregate elasticity: 1-σ 0.28 0.36 (0.01) (0.23) Constant: ln(m) -1.43 -1.54 0 (0.002) (0.002) Local elasticity: γ 0.16 0.19 (0.01) (0.02) Other parameters 1994-2007 Age 0.0004 0.0036 (0.001) (0.002) Age squared -0.0002 -0.0002 (0.00002) (0.0001) Male dummy 0.12 0.059) (0.01) (0.02) Permanent layoff dummy -0.28 -0.26 (0.01) (0.03) Temporary layoff dummy 0.68 0.93 (0.01) (0.04) Reentrant dummy -0.32 -0.25 (0.01) (0.04) New Entrant dummy -0.88 -0.80 (0.02) (0.05) Unemployment duration -0.021 -0.019 (0.002) (0.003) Duration interacted with 0.0003 0.0001 average duration (0.0001) (0.0001) Pseudo R 0.0457 Note. Explanatory variables also include monthly dummies. All variables, except duration interacted with average duration after 2007 and age, are significant at conventional levels. Standard errors are in parentheses. Table 4: Estimating a functional form for the UK scaling law θ  Dependent variable: var n  θ jt    t  a 5.08 0 (0.50) a 0.67 occ (0.03) a geo 0.13 (0.04) R2 0.98 Note: The sample includes 12 observations, with Ngeo=11, 48, 232 and Nocc=9, 25, 81, 353. 40

Appendix NOT FOR PUBLICATION α θ u  Table A1: Proxying it with  it  θ u  t t Dependent θ it θ it θ it θ it variable: θ θ θ θ t t t t Sample (quarterly 2000-2010 2000-2009 2006-2010 2006-2010 frequency) Data source JOLTS JOLTS Conference Board Conference Board Industry groups US Census Regions Occupations State/MSA regions α -1.34*** -1.32*** -1.71*** -1.29*** (0.03) (0.11) (0.08) (0.02) Number of 1170 444 234 3510 observations R2 0.76 0.73 0.89 0.83 Note: Standard-errors are reported in parentheses. All panel regressions include industry or region fixed effects. The first two regressions include a quadratic trend. The first two columns use vacancy measures from the JOLT, and the last two columns use data on online advertising from the Conference Board. Table A2: Effects of EEB on UE and UN transition probabilities in the 2008-2009 recession UE probability UN probability -0.12 -0.22 Job loser (0.02) (0.02) -0.16 -0.05 Non job loser (0.02) (0.02) Note: The two rows report the coefficients on the interaction term between a post-2008 dummy and, respectively, a job loser and non-job loser dummy. In the first column, the dependent variable is the UE transition probability, and in the second column, the dependent variable is the UN transition probability. Table A3: Coefficients on post-2007 last industry of employment dummy Industry Coefficients -0.11 Goods production (0.02) -.13 Professional services (0.02) -0.12 Sales and other services (0.02) -0.15 No industry (new entrant) (0.04) Note: Except for the industry dummy, the regression is identical to Table 3. Other coefficients are little changed and are available upon request. 41

Table A4: Coefficients on post-2007 state of residence dummy State of State of Coefficients Coefficients residence residence FL -0.41 KS -0.16 SC -0.37 CA -0.15 NE -0.30 IL -0.15 MN -0.29 HI -0.15 MO -0.28 IA -0.15 UT -0.28 KY -0.15 AL -0.27 TN -0.12 NH -0.27 VA -0.11 IN -0.26 RI -0.11 OR -0.25 WY -0.09 AR -0.25 SD -0.08 OH -0.25 PA -0.08 MI -0.24 MS -0.07 NV -0.22 VT -0.07 GA -0.22 CT -0.07 MA -0.21 ND -0.01 OK -0.21 NY -0.01 AZ -0.20 ID 0.00 DE -0.20 TX 0.00 ME -0.19 NJ 0.01 MD -0.18 DC 0.02 NC -0.16 LA 0.06 CO -0.16 AK 0.06 WI -0.16 WV 0.06 WA -0.16 NM 0.14 MT -0.16 Note: Except for the state of residence du mmy, the regress ion is identical to Table 3. Other coefficients are little changed and are available upon request. 42

Table A5: List of geographic areas AK FL LA WA SD Other, AK Jacksonville, FL New Orleans, LA Other, WA Other, SD AL Miami, FL Other, LA Seattle-Tacoma, WA TN Birmingham, AL Orlando, FL MA/RI WI Memphis, TN Other, AL Other, FL Boston, MA Milwaukee, WI Nashville, TN AR Tampa, FL Other, MA/RI Other, WI TD Other, AR GA Providence, RI WV Other, TD AZ Atlanta, GA MD Other, WV TX Other, AZ Other, GA Baltimore, MD WY Austin, TX Phoenix, AZ HI Other, MD Other, WY Dallas, TX Tucson, AZ Honolulu, HI ME NH Houston, TX CA Other, HI Other, ME Other, NH Other, TX Los Angeles, CA IA MI NM San Antonio, TX Other, CA Other, IA Detroit, MI Other, NM UT Riverside, CA ID Other, MI NV Other, UT Sacramento, CA Other, ID MN Las Vegas, NV Salt Lake City, UT San Diego, CA IN/IL/KS/MO Minneapolis-St. Paul, MN Other, NV VA San Francisco, CA Chicago, IL Other, MN OK Other, VA San Jose, CA Indianapolis, IN MS Oklahoma City, OK Richmond, VA CO Kansas City, MO Other, MS Other, OK Virginia Beach, VA Denver, CO Other, IN/IL/KS/MO MT OR VT Other, CO St. Louis, MO Other, MT Other, OR Other, VT CT KY/OH NC/SC Portland, OR Hartford, CT Cincinnati, OH Charlotte, NC PA/NJ/NY Other, CT Cleveland, OH Other, NC/SC Buffalo, NY DC Columbus, OH ND New York, NY Washington, DC Louisville, KY Other, ND Other, PA/NJ/NY DE Other, KY/OH NE Philadelphia, PA Other, DE Other, NE Pittsburgh, PA Rochester, NY 43