The Delayed Response To A Technology Shock. A Flexible Price Explanation

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 810 July 2004 The Delayed Response to A Technology Shock A Flexible Price Explanation Robert J. Vigfusson NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/.

The Delayed Response To A Technology Shock. A Flexible Price Explanation Robert J. Vigfusson ∗† July 12, 2004 Abstract I present empirical evidence of how the U.S. economy, including per-capita hours worked, responds to a technology shock. In particular, I present results based on permanent changes to a constructed direct measure of technological change for U.S. manufacturing industries. Basedonempiricalevidence,someclaimthathoursworkeddeclinesandneverrecovers in response to a positive technology shock. This paper’s empirical evidence suggests that emphasizing the drop in hours worked is misdirected. Because the sharp drop in hours is not present here, the emphasis rather should be on the small (perhaps negative) initial response followed by a subsequent large positive response. Investment, consumption, and output have similar dynamic responses. In responseto a positive technologyshock, a standardflexible price model would have an immediate increase in hours worked. Therefore, such a model is inconsistent with the empirical dynamic responses. I show, however, that a flexible price model with habit persistenceinconsumptionandcertainkindsofcapitaladjustmentcostscanbettermatch the empirical responses. Some recent papers have critiqued the use of long run VARs to identify the dynamic responses to a technology shock. In particular they report that, when long run VARs areappliedtodatasimulatedfromparticulareconomicmodels, thepointestimatesofthe impulseresponsesmaybeimpreciselyestimated. However,basedonadditionalsimulation evidence,Ifindthat,althoughtheimpactresponsemaybeimpreciselyestimated,afinding ofadelayedresponseismuchmorelikelywhenthetruemodelresponsealsohasadelayed response. Keywords macroeconomic models, vector autoregressions, impulse responses, weak instruments, long-run identification assumption JEL Codes: D24 E24 E32 O47 Boardof Governors of theFederal Reserve System. (Emailrobert.j.vigfusson@frb.gov) ∗ Thanks to Martin Eichenbaum, Larry Christiano, Tim Conley, and John Fernald for helpful comments † in early drafts of this paper. Additional thanks for comments from Rochelle Edge, Chris Erceg, Chris Gust, William McCausland, and seminar participants at the Bank of Canada, the Bank of England, Northwestern University, the University of Alberta, UQAM, the Universit´e de Montr´eal, and the Board of Governors of the FederalReserve. AnearlierdraftofthispaperwascirculatedasThe negative response toa positive technology shock,aneoclassicalexplanation. Theviewsinthispaperaresolelytheresponsibilityoftheauthorsandshould not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of any person associatedwiththe Federal ReserveSystem. 1

1 Introduction Recent papers by Gal´ı (1999), Basu, Fernald, and Kimball (2004), and Francis and Ramey (2003) have claimed that in response to an unexpected improvement in technology, hours spent working declines. This finding challenges the standard macroeconomic flexible-price model because that model predicts a strong positive correlation between employment and technology. Thispaper’sempiricalevidencesuggeststhatemphasizingthedropinhoursworkedismisdirected. Because the sharp drop in hours is notpresent in several ofthedata seriesexamined here, the emphasis rather should be on the small (perhaps negative) initial response followed by a subsequent large positive responses. The paper also presents a flexible-price model that is broadly consistent with the empirical dynamic responses. The empirical evidence describes how the economy responds to shocks to a productivity measure that has been corrected for utilization and reallocation. For the quantities considered here (output, consumption, investment, and hours worked), a consistent pattern emerges. When the technology shock occurs, thevariablesrespondonlyslightly. Overtime, thevariables’dynamicresponsesgainstrength. To be consistent with the empirical responses, the standard quantitative dynamic flexibleprice model must be modified. The modifications pursued here are to make utility depend on past consumption (habit persistence) and to have capital adjustment costs. Gal´ı (1999) and Francis and Ramey (2003) measure productivity using aggregate labor productivity. Aggregate labor productivity, however, is a poor measure of technology because it can change for many reasons besides technological growth. In particular, in response to changes in the economy, workers sometimes vary their effort and, hence, output. Because this variation in the utilization of inputs is unobservable, changes in the utilization rate will appearaschangesinproductivity. Toobtainanaccuratemeasureofhowtechnologyincreases productivity, one must control for these changes in utilization. In addition, reallocation of laborfromanindustrywithlowlaborproductivitytoanindustrywithhighlaborproductivity will also show up as in improvement in aggregate labor productivity that may not be due to increases in technology. Combining the methods of Burnside, Eichenbaum, and Rebelo (1996) and Basu, Fernald, and Kimball (2004), the current paper constructs a quarterly measure of productivity that has been corrected for variations in utilization and also for reallocation between industries. In spiteofthestepstakentoremoveendogenousinfluences, thisproductivitymeasurestillmight be influenced by other economic variables. To control for this endogeneity, I use the long-run approach of Gal´ı (1999) to consider how the economy responds to exogenous shocks to the productivity series. The empirical results support the view that the immediate response to a technology shock is either negative or small. Although the initial responses are small, this paper shows that, within six quarters, the responses are positive and large. The empirical work is presented with an emphasis on robustness. The paper considers responses to a technology shock identified under different identification assumptions. In addition, the paper reports confidence intervals for the impact response of a technology shock that are valid under the assumption of weak instruments. Although the resulting confidence intervals are wide, compared to the possible range associated with an unidentified shock, the identification scheme does restrict the possible responses. Having documented how the economy responds to a technology shock, the challenge is to 2

construct a model that has the same dynamic responses. The empirical responses are incompatible with a standard quantitative dynamic flexible-price model; because, in the standard model, the period of the technology shock is when the variables respond most. The model needs to be modified to generate a more realistic delayed dynamic response. Gal´ı (1999) and Basu, Fernald, and Kimball (2004)propose to resolve the model’sproblemby includingsticky prices. Basu (1998) presents a sticky price model that successfully matches the immediate small empirical responses to a technology shock but fails to match the medium-term empirical responses. With both sticky prices and wages, Altig, Christiano, Eichenbaum and Linde (2004) better match these responses. The current paper does not use sticky prices. Rather it usesa flexible-price model with modificationsto both preferencesand technology. Preferences are modified such that today’s utility depends on the previous level of consumption, habit persistence. Habit persistence implies that consumption responds more slowly to an increase in technology. Just habit persistence, however, is not enough to match the data. The technology to transform investment into capital must be modified to dampen the responses by investment and output. The paper presents two specifications for the investment technology: time-to-plan and convex capital adjustment costs. When the capital adjustment costs depend on the ratio of new investment to capital, the model can match the initial period’s responses but fails to match the subsequent increases. Having the adjustment costs depend on the growth rate of investment results in a better match to the long-run response. A time-to-plan model also matches but, with only one kind of investment good, its responses are somewhat too jagged. These last two specifications work better because although they constrain the initial response by investment they allow the subsequent responses to be strong. Although these models can match the consumption, investment and hours worked responses, the models presented here have a difficult time matching the response of the real interest rate. Although there is some uncertainty with respect to the true real interest rate response, the empirical impulse responses, in general, indicate that the real interest rate increases in response to a positive technology shock. Chiefly because of habit persistence, in the reported economic models, the real interest rate instead falls in response to a positive technology shock. I show that a model with consumption adjustment costs can better match the real interest rate response. Even this model, however, does not completely capture the empirical response by the real interest rate. Recent papers by Erceg, Guerrieri and Gust (2004) and Chari Kehoe and McGrattan (2004) have critiqued the use of long-run VARs to construct impulse responses. Using simulated data from particular economic models, they show that, for these particular models, the point estimates of long run VARs are imprecisely estimated. However, when I adopt their approachofsimulatingdatafromabenchmarkmodel,Ifindfurtherevidenceinfavorofstudying the shape of the impulse responses. Although the impact response may be imprecisely estimated, a finding of a delayed response is much more likely when the true model response also has a delayed response. 2 Empirical Work This paper’s empirical work combines the two approaches taken in the literature to study productivity shocks. As in Basu Fernald and Kimball (2004), industry-level data is used to construct a utilization-corrected aggregate technology series. This series is then used as a 3

variable in a vector autoregression, where, as in Gal´ı (1998), exogenous technology shocks are identified under the assumption that only exogenous technology shocks affect the permanent level of productivity. In the first subsection, I describe how to use fluctuations in electricity usage (as in Burnside, Eichenbaum and Rebelo (1996)) and fluctuations in average hours (as in Basu Fernald and Kimball (2004)) to construct a quarterly utilization-corrected technology series. In the second subsection, I then use the same vector autoregression approach that Gal´ı (1999) and Francis and Ramey (2003) used for labor productivity to calculate impulse responses to a permanent shock to my constructed technology series. The main findings are that the response by per capita hours worked is initially small but ,within two years, hours worked experiences a large increase. 2.1 Accounting For Utilization and Reallocation Forces besides technological progress affect labor productivity. In particular, the effort expendedbyworkersandmachinescanvaryendogenouslyovertime. Onecannotalwaysobserve this time-varying utilization of inputs, which can be a serious issue in measuring technology growth because a change in utilization can be mistaken for a change in technology. This section uses methods proposed by Basu, Fernald, and Kimball (2004) [BFK] and BurnsideEichenbaumandRebelo(1996)[BER]toapproximatethechangesinutilizationwith changes in observable variables. BFK approximate changes in utilization by using changes in average hours worked. The intuition for this approximation is that a firm would choose to vary both workers’ hours and utilization until the costs and the benefits are the same.1 BER approximate changes in capital services by changes in electricity usage. In addition, because reallocation can increase aggregate productivity without requiring an increase in technology, one should also control for reallocation between industries. As is done in BFK, the aggregate productivity series is constructed by aggregating industry-level productivity series. To calculate the productivity series at the quarterly frequency requires a few strong assumptions. Because the industry-level capital stock is unobservable at the quarterly frequencies, changes in electricity usage are used to approximate the changes in capital services. Because data on material usage is unavailable at the quarterly frequency, one must assume that there is very limited substitutability between materials and a mix of capital services and labor. BFK have been critical of estimating productivity without data on materials usage. In trying to measure quarterly productivity growth, it, however, is likely better to implement partially their methods than not use them at all. Industry-Level Data The productivity equation is estimated using quarterly data at the industry level between 1972 to 2001. As in BFK, these industry-level productivity series are then aggregated to generate an economy-wide productivity series.2 The industries used here are the eighteen two-digit SIC manufacturing industries. Their names and SIC codes are reported in Table 1. 1In more formal terms, using hours to approximate for utilization implies an assumption that, at least for empirically relevant values, the output expansion path is an upward sloping line. The assumption would be satisfied if output were produced, for example, by a homothetic production function (such as Cobb-Douglas) using hours and utilization with constant costs of increasing either input. 2A lack of data requires the use of this manufacturing-based technology measure to approximate the economy-wide fluctuations intechnology. 4

Applying the methods of BER and BFK results in the following equation whose residual is a measure of productivity growth. Output and all the inputs are expressed in logged first differences of quarterly data. For each industry j, the growth rate at quarter t of the productivity series ∆z will be the residual from the following estimated equation3: j,t ∆y =µ sv ∆k +sv (∆h +∆e ) +ξ ∆h +∆z (1) j,t j k,j j,t l,j j,t j,t j j,t j,t This output data ∆y w¡ill be measured by the Federa¢l Reserve’s measures of industrial production. The capital services variable ∆k will be approximated by data on electricity usage.4 The average hours ∆h and employment data ∆e are taken from the corresponding BLS measure. The capital sv and labor shares sv are calculated as the average value-added k l shares from the BLS KLEMS database.5 The values of µ and ξ are estimated. The values of µ and ξ are constrained to be the same for all durable good sectors and the same for all nondurable good sectors. In aggregating these industry level estimates, the aggregation equation is the same as in BFK.6 Aggregate productivity is calculated as ∆z j,t ∆z = w (2) agg,t j 1 µ s − j mj X The weight w is the share of value added by industry j. The share of materials s is j mj calculated using the materials share of gross-output reported in the KLEMS dataset. The parameters are estimated using two-step GMM under the assumption that the values of ∆z and ∆z are correlated but that there is no serial correlation. I use the three it jt instruments that are commonly used in estimating this kind of production function. One of the instruments is the previous quarter’s value of the Federal Funds shock resulting from the monetary VAR estimated in Christiano, Eichenbaum, and Evans (2001). The second instrumentisthecurrentandpreviousquarters’valuesofthedifferencebetweentheaggregateGDP price deflator and the growth rate of the price of oil.7 The third instrument is the current 3This equation is similar to that estimated in Burnside Eichenbaum and Rebelo (1996) and in Conley and Dupor(2003)exceptfortwodifferences. First,theseauthorsdon’tusetheaveragehourscorrection,represented inEquation2byξh . Second,thevalueofµisestimatedasthesumofthesharesofcapitalservicesandlabor j,t which are estimated separately. In other words, they don’t use the information on KLEMS shares but rather justestimatetheshares. Impulseresponsesgeneratedusingthisapproachweresimilartotheonesreportedin the paper. 4Somemightbeconcernedthatelectricityusagemightbeoverlysensitivetoweatherfluctuations. Because the electricity usage data is on a national basis, geographic diversification should limit any dependence on weather. 5The KLEMS dataset is used to measure multi-factor productivity as the annual frequency. It and the Canadianequivalent arefeaturedinVigfusson (2003). 6This aggregation equation calculates the increase in aggregate technology resulting from industry-level technology growth holding thedistribution of inputs among industries fixed. 7TheresultsreportedhereusetheIMFworldpriceofoil,anaverageofinternationalwell-headprices. Other researchers including Basu, Fernald, and Shapiro (2001) have used the Producer Price Index for crude oil as aninstrument. TheProducerPriceIndex,however,only measuresthepricepaidfordomestic butnotforeign oil. Notincludingforeignoilresultsinaverymisleadingpriceseriesbecause,betweenthesummerof1973and January 1981, American produced oil was under government-imposed price controls. Because of these price controls,thePPIdoesnotmeasurethetruecostofoil. Inparticular,itdoesnotcapturethedramaticeffectof theoilshocksof1973and1979thatareobservableinotherseriessuchastheIMFoilseriesortheDepartment of Energy’sseries, Refiner Acquisition Nominal Cost of ImportedCrudeOil. 5

and previous quarters’ growth rate in real defense spending.8 The GMM estimator requires an estimate of the variance-covariance matrix. Because, the estimation exercise is a system of equations for eighteen industries, the unconstrained version of the variance-covariance matrix requires a large (171) number of parameters. To reduce this number, one could place structure on the correlation between sectors. Conley and Dupor (2003) assume that the industries that use similar inputs have similar patterns of productivity. Given my interest in aggregated quantities, this correction has only a small effect on the aggregated results. 9 2.1.1 Results ThecoefficientestimatesarereportedinTable2. Forthenondurablegoodsproducingsectors, theestimateofthemark-upparameterµislessthanone. Thedifferencebetweentheestimate and constant returns, however, is not statistically significant. Some of the estimates reported in BFK were also less than one. They argue (p.29) that one possible explanation for these low estimates of µ is the omitted variable bias that would result from not including an estimate of reallocation effects. The estimates of ξ are positive and significantly different from zero. Positive coefficients imply that when utilization growth and, therefore, average hours growth are high, the growth in the utilization-corrected measure of productivity is less than the growth in the measure of uncorrected productivity. Although the work here has tried to construct a technology series that corrects for utilization and reallocation, one may be concerned that the series is still affected by measurement error. A such, this estimated technology series will be combined with a long-run identification assumption to identify the part of this series that seems to have a long-run affect on the level of technology. The next section describes how to implement such a long-run identification assumption. 2.2 Estimating A Vector Autoregression with A Long Run Identification Assumption Here, as in Gal´ı (1999), a technology shock will be identified as a permanent shock to productivity.10 These shocks and resulting impulse responses are computed in the following manner. 8To specify these variables as instruments requires an assumption that these variables are uncorrelated with the technology shocks. There are models in which this assumption would be violated. For example, if implementationcyclesmodels(Shleifer1986)wereempiricallyrelevant,thenthesevariablesmaybecorrelated. In such a model, reductions in oil prices could result in an economic expansion that would cause people to implement their ideasincreasing productivity. 9Theaggregation,however,doesobscuretheimportantroleplayedbyindustry-specificproductivitygrowth thatisfoundinUSindustrialproductiondatainConleyandDupor(2003)andagaininKLEMSdataforboth Canada and theUnitedStates in Vigfusson(2003). 10Severalrecentpapershaveidentifiedatechnologyshockusingalong-runrestriction. Thesepapersinclude Gali (1999); Francis and Ramey (2003); Altig, Christiano, Eichenbaum, and Linde (2004); and Fisher (2002). Although these methods have proven popular, some researches have critiqued these methods. In particular, FaustandLeeper(1997)describeproblemsassociatedwithconstructingconfidenceintervals(seefootnote15for morediscussion),andtheperilsofexcludingvariablesfromtheVAR.Erceg,Guerrieri,andGust(2004)present model-basedMonteCarlo evidenceon thelong-runidentification assumption. Their work will be discussed in section 4. 6

Consider the following structural vector autoregression (VAR) for a vector of variables y t εz A y =A(L)y + t (3) 0 t t 1 v − t µ ¶ The vector y consists of n elements. The first element is the growth rate of a productivity t measure, denoted by ∆z . Gal´ı measured productivity using labor productivity. Here, I will t report results for both labor productivity and also for my constructed measure of technology. The next n-1 elements are the other variables in the VAR x . t ∆z y = t (4) t x t µ ¶ The shocks εz and v (where v has n 1 elements) are assumed to be independent. Gal´ı t t t − identifies the technology shock by assuming that only the technology shock εz can have a t permanent effect on the level of productivity z . All other shocks are assumed to have no t long-run effect. To impose this restriction is to impose a restriction on the moving average representation of the data. Denote the moving average representation by: ∆z t = C 11 (L) [C 1j (L)]n j=2 εz t (5) x [C (L)]n [C (L)]n v µ t ¶ à j1 j=2 jk j,k=2 ! µ t ¶ the restriction that the long run impact on z is zero for all shocks except the first is that, for t all the other shocks, the sum of moving average coefficients equals zero. (i.e [C (1)]n = 0 1j j=2 for all j 2) ≥ ToactuallyestimatethestructuralVARwiththislong-runrestrictionrequiresarestriction on the structural VAR coefficients. To make the notation clear, I rewrite the structural VAR as a 0,11 − A 11 (L) [a 0,1j ]n j=2− [A 1j (L)]n j=2 ∆z t = εz t (6) [a ]n [A (L)]n [a ]n [A (L)]n x v à 0,j1 j=2− j1 j=2 0,jk j,k=2− jk j,k=2 ! µ t ¶ µ t ¶ Because (A A(1)) equals C(1) 1, the restriction on C(1) is equivalent11 to the following 0 − − restriction on A A(1) 0 − a A (1)=0 for all j 2 (7) 0,1j 1j − ≥ To implement this restriction we estimate the equation12 ∆z a A (L) A˜(L)(1 L) t =εz (8) 0,11 − 11 − x t t µ ¶ ¡ ¢ To estimate this equation, one has to instrument for ∆x using x . An discussed in Christ t 1 − tiano, Eichenbaum and Vigfusson (2003), if x is non-stationary, then x will be a weak t 1 t 1 instrument.13 Section 2.4 considers the weak in − strument problem. − 11Theequivalency canbeseenby examinationof the co-factor formula for the inverse of a matrix. 12This specification is the “doubledifference” approachdescribed inKing andWatson (1997). 13If the VAR is correctly specified, lagged ∆x ’s cannot be used as instruments for ∆x . For a VAR t i t withplags,thefirstpvaluesof∆x ∆x p − willalsobeintheequation. Hence,theycannotserveas t − i { t − i }i=1 instruments. Othervalues { ∆x t − i } ∞i=p+¡1 arenotvali ¢ dinstrumentsbythedefinitionoftheVARbeingcorrectly specified. Beingcorrectlyspecifiedimpliesthatthesevaluescannotcontainanyinformationabout∆x beyond t that containedin ∆x p . { t − i }i=1 7

Estimating this equation results in a time series of the technology shocks. To calculate the impulse responses requires the moving average representation of y in terms of εz and v . t t t One approach to calculate this moving average representations starts with the reduced form VAR14 y =B(L)y +u (9) t t 1 t − where u is the vector of the n reduced-form residuals. A regression of u on εz results in γ, t t t thefirstcolumnofA 1. Theresidualsfromtheseregressionswouldbealinearcombinationof −0 the other fundamental error terms v that are un-correlated with εz. The impulse response to t t aone standard-deviation technology shockσ can beconstructedusingthecolumnγ andthe εz inverted reduced-form VAR coefficients. The formula for the impulse responses Γ is therefore Γ=(I B(L)L) 1γσ (10) − εz − To summarize, the impulse responses can be calculated using the following four steps. ∆z a A (L) A˜(L)(1 L) t = εz (11) 0,11 − 11 − x t t µ ¶ ¡ ¢ y = B(L)y +u t t 1 t − u = γεz +v t t t Γ = (I B(L)L) 1γσ − εz − 2.3 Impulse Responses The next section reports the dynamic responses to an exogenous shock to productivity. The measure of productivity is the result of using Equation 2 to aggregate the industry-level estimates calculated using Equation 1. Two sets of results are reported. The first results correspond exactly to the methods used by Gal´ı (1999) and Francis and Ramey (2003) except that I replace their use of labor productivity with my productivity measure. Compared to the initial response by hours when usinglabor-productivity,theinitialresponsehereismuchmorepositive. Eitherhoursdeclines less or it does not decline at all. The result reported here do not overturn earlier critiques of the standard quantitative dynamic flexible-price model. Hours still do not respond positively to the shock for the first year. The second set of results report the dynamic responses by investment, output, and consumption as well as hours. These results are useful becausethey provide the basisupon which to characterize the ability of the macroeconomic model to match the data. These variables do not respond much in the period of the shock. In subsequent periods, the variables start to increase in response to the technology shock. 14Becausetherearenootherrestrictionontheequation,theresultscalculatedusingthereducedformVAR areidenticaltoresultscalculatedusingthestructuralVARwithcoefficientsA andA(L). Imposingadditional 0 restrictions on A such as also identifying a monetary policy shock, as in Altig, Christiano, Eichenbaum, and 0 Linde (2003), wouldrequireusing the structural VARto calculate impulse responses. 8

2.3.1 Bivariate VAR with Hours Worked AsinGal´ı(1999)andFrancisandRamey(2003),theimpulseresponsearefromatwo-variable VAR on the growth rates of a productivity series and the growth rates of hours worked. Productivity is measured using two different time series: labor productivity and my constructed aggregate productivity series. In addition, impulse responses are calculated from a VAR of the constructed productivity series and the levels of per-capita hours worked. Christiano, Eichenbaum and Vigfusson (2003) argue that estimating the long-run VAR with hours in first differences is mis-specified relative to estimating a VAR with per-capita hours in levels. This section, however, reports both sets of results to maximize comparability with the earlier literature. Confidence intervals around the estimate are calculated using a bootstrapped approach. Sampling from the residuals with replacement, the estimated VAR is used as a data generating process to simulate time series. Using the simulated data, the VAR is estimated and the responses to a permanent positive increase in technology are calculated. After simulating the data 500 times, the variance of each period’s impulse response is calculated. The resulting confidence interval is the estimated response plus or minus 1.96 times the standard deviation.15 Figure1reportstheresponseofthethreedifferentVARs. Thethreedifferentspecifications havesimilarresponses. Nothingmuchhappensonimpact. Subsequently, hoursworkedbegins to increase. For all three VARs, the response on impact is much greater than that reported in Gal´ı or in Francis and Ramey. These results, however, are not large enough to overturn the conclusions of previous work. Hours still do not respond much initially to a positive productivity shock. Therefore, the evidence is still against models that predict a large initial response to increases in productivity. 2.3.2 VAR with Hours Worked and Other Variables To compare the model to the data, one needs to know how other variables in the economy respond to a technology shock. This section describes how other variables (output y , t consumptionc , investment i , and the real interest rate r )16 respond to a technology shock. t t t The approach taken here is to estimate the set of equations described in Section 2.2 . The 15Faust and Leeper (1997) note that the standard confidence intervals for impulse responses are not valid unless restrictive assumptions are made concerning the data generating process. For the bootstrapped confidenceintervalsconsiderehere,theimplicitassumptionisthetruedatageneratingprocessactuallyisasixlag bivariate vector autoregression. Under such a restrictive assumption, the confidence intervals reported here would bevalid. 16Allvariablesareexpressedinlogs. Thevariablesspanthesecondquarterof1972totheendof2001andare takenfromtheDRIBASICEconomics(neeCitibase)database. Theserieswiththeirmnemonicsareasfollows: real consumption (the sum of consumption of services GCS, nondurables GCN and government consumption divided by the gross output price deflator GDPD and consumption of durables GCD), real investment (gross private investment (GPI) and government investment divided by the output price deflator GDPD), output (nominalconsumptionandinvestmentdividedbyGDPD),realinterestrate(3monthTreasuryBillrateminus thegrowthrateoftheGDPpricedeflator),andhoursworked(nonfarmbusinesshoursLBMNU).Allquantities areexpressedinper-capitatermbydividingbythepopulationover16. Deflatingconsumptionandinvestment bythesamepricemeasureratherthanusingtheseparatepublisheddeflatorsforinvestmentandconsumption isdeliberate. SeeWhelan (2000) for a discussion of using chain-weighteddata. 9

vector of other variables is constructed as follows h t r t   x = ∆y (12) t t  i y  t t  −   c y  t t  −    Cointegrating relationships are defined between investment and output, and consumption and output. Thereisno assumption ofa cointegratingrelationship between per-capita output and the technology series, in order to allow for other shocks to have a permanent effect on per-capita output. Besides this baseline VAR, I also report impulse responses for two other VARs. One uses the same reduced form VAR but identifies the technology shock not with a long-run identifying assumption but rather uses a standard recursiveness assumption with technology ordered first. In other words I estimate the same reduced form VAR but identify my technology shock εz as the first element in u . I then regress u on εz to find γ and then t t t t calculatetheimpulseresponsesasdoneearlier. Finally,IreportanotherVARwhereIconsider permanent shocks to labor productivity rather than to my constructed productivity series.17 Figure 2 reports the data used in the VAR. The log of per-capita hours worked increases over this time period. This increase in hours worked is the result of two opposite trends. An increase in the labor force participation rate (from 60 to 67 percent over this time period) offsets the decline in average hours worked, (for production workers, the average work week has declined from 36 hours to 34 hours). Figure 3 reports the implications for the technology growth series by applying the longrun identification assumption. The constructed technology series is presented along with the technology series implied by the VAR and allowing only permanent shocks to technology. In ordertoemphasizetheroleofthelongrunidentificationassumption,bothseriesarepresented withmeanzero. Perhapsnotsurprisingtheseriesthatresultsfromthelongrunidentification series is much less volatile than the original series. Impulse responses for the baseline long-run VAR are reported in Figure 4. In general, quantities take time to respond to the technology shock. Hours worked responds only slightly in the impact period of the shock. It takes several quarters before hours worked has a strong response. Consumptiononlyrespondsgraduallyovertime. Intheimpactperiod, theresponse is only about half of what it will be 10 quarters later. In percentage terms, the investment response is stronger on impact but the strongest investment response is about four quarters later. The real interest rate, however, has a very different response. The real rate jumps 80 basis points on impact. It then steadily declines but it does take six years before the real rate returns to normal. TheresultsforthetwootherVARsaresimilar. Identifytechnologyshockswithashort-run recursiveness assumption produces a few small differences. The largest difference is that the 17The labor productivity output series considers total output divided by business hours. As such, this definition of labor productivity is more like the work by Gali (1999) than the definition used in Francis and RameyandChristiano,Eichenbaum,andVigfusson(2003). AsinCEV,Icouldhavedefinedlaborproductivity as the ratio of business output to business hours worked. This has the advantage of avoiding the problem of increases in government spending being misconstrued as a technology shock. However, it comes at the cost of being less transparent concerning theimposed cointegration results. 10

real interest rate response is much weaker. Also, the consumption response is not as strong but the investment response is of greater size and duration. For this dataset, identifying a technology shock as a permanent shock to labor productivity again produces a very similar set of responses. 2.3.3 The Shape of the Impulse Responses I have claimed that the delayed response to a positive technology shock is a robust feature of the data. The following section characterizes this robustness. Using the baseline VAR as the DGP process, Figure 5 reports that in the majority of cases the response by hours six quarters after a shock is greater than the response on impact. Table 3 reports that for the majority of simulations, the impact period response for consumption, investment, or hours worked is much smaller than responses several periods later. 2.4 Weak Instruments And the Delay in the Hours Response To identify a permanent change in technology requires estimating an instrumental variables regression. One may be concerned about whether the above conclusions concerning the shape of the impulse responses are robust to weak instruments. Although the actual instrumental variables regression may have problems with weak instruments, the evidence is that the conclusions concerning shape are more robust.18 When instruments are only weakly correlated with the explanatory variables, confidence intervals can often be much wider than those calculated using standard methods. In the equation estimated here, the lagged level of hours worked is used to instrument for the growth rate of hours worked. If hours worked has either a unit root or else approaches a unit root asymptotically, then hour worked would be a weak instrument.19 Valid confidence intervals for estimation using weak instruments, however, were established by Anderson and Rubin (1949). In the present context, their method can be implemented as follows. Begin with the IVregressionwhereanydependenceonlaggedvalueshasbeenremovedbyalinearprojection. All that is left is to estimate a , in the following equation, 0 ∆z ∆x a =εz t t 0 t − with the instruments x . The Anderson Rubin confidence interval can be described (Wright t 1 − 2002) as the values of a that satisfy the following condition: 0 1 (∆z ∆xa 0 ) 0 x 1 x 0 1 x 1 − x 0 1 (∆z ∆xa 0 ) a : − − − − − − F (k,α)  0 (∆³z ∆¡xa 0 ) 0 (∆¢z ∆x´a 0 ) ≤ χ2   − −  where ∆z,∆x and x are the vectors of ∆z , ∆x and x and F is the α percent critical 1 t t t 1 − − value from a chi-squared distribution with k degrees of freedom, where k is the number of instruments. Figure 6 plots the results when ∆z is the growth rate of the constructed 18Complementary to this work is a paper by Pesavento and Rossi (2003) where they calculate confidence intervals for impulse responses at long horizons. 19Addition detail is provided in Christiano, Eichenbaum and Vigfusson for the weak instruments problem that occurs when hours has a unit root. 11

technology series and x is the level of per-capita hours. The first panel of Figure 6 plots the criterion function. A 95 percent confidence interval for a is very large ranging between -7 0 and 6.2. However, the value of a is only important as it affects the measure of γ. Each a 0 0 maps into a value γ, the response by hours to a one standard deviation shock. The second panel plots the mapping from a to γ. The third panel shows that this mapping implies that 0 the confidence interval for the impact response of hours to a one-standard deviation shock is between -0.05 percent and 0.11 percent. Although this confidence interval is large, it does contain information. In particular, if the coefficient were unidentified, the confidence interval would be between [ σ ,σ ], the variance of the reduced form residual.20 u u − These confidence intervals are constructed holding as fixed the values of the reduced form VAR coefficients. Hence if we combine these estimates of the possible values of γ with the reduced form VAR, the resulting hours response six quarters later is between 0.05 and 0.27. Similar calculations can be done for the six variable system. A grid search on all the possible values of a would be particularly laborious for the larger system. For example, a five 0 dimensional space with 100 grid points per dimension would be ten billion points. However, onecanapproximatethegridsearchbyinsteadsamplingovertheparameterspace. Arandom sample of the same space should be sufficiently informative.21 Table 4 reports confidence intervals for γ that result from those values of a that belong to the AR confidence interval. 0 0 Going from the bivariate autoregression to the multivariate regression seems to have both tightened and shifted upwards the confidence intervals on the hours worked response. There appears to be a great deal of uncertainty of investment’s response on impact. This uncertainty does not seem to be reflected in the standard bootstrap confidence intervals reported above. Perhaps the most surprising thing is the improvement of identification that results from using the constructed technology series. Theemphasisontheshapeofthehoursworkedresponsecanalsobestudiedinthecontext of weak instruments. Consider Figure 7, which shows the connection between the response by hours on impact combined with its response six quarters later. The oval indicates all observed responses, holding the reduced form VAR coefficients B(L) fixed. The grey area indicates those values that are associated with a value of the Anderson Rubin statistic less than the 95 percent critical value of 9.488. Although this oval does not take into account the sampling uncertainty of B(L), the figure is supportive of placing a greater emphasis on the shape of responses. The evidence from the weak instruments reinforces the view that the robust finding is 20The proof of this claim is straightforward. By definition the part of x that does not depend on lagged t x is u . Given thepreviously describedidentity, t i t − u =γεz+v t t t theresponsebyx toaone-standarddeviationshocktoεz isγσ . Butbecauseεz andv areuncorrelated,the t t z t t variance of uis thefollowing σ2 =γ2σ2+σ2 u z v and therefore,we have theresult that γσ σ z u | |≤ completing the proof. 21Thefollowingtableisbasedon20,000samplesovertheparameterspace. Theseresultswerethenchecked bymakinganadditional30,000simulations. Innocasedidtheseadditionalsampleschangetheresultsreported here. 12

that the hours response is initially small but grows over time. Models therefore should be constructed to attempt to match this finding. 2.5 Sensitivity of Results The following sections report on the sensitivity to using different data and also to using different sample periods. 2.5.1 Ex ante Real Interest Rate To check for data sensitivity, the empirical VAR is estimated using an ex ante measure of the real interest rate in place of the ex post measure. The ex ante real interest rate is based on the difference between the three month treasury rate and the forecasted inflation in the GDP deflator for the next quarter. The forecasted inflation is the median forecast from the Survey ofProfessional Forecasters. Theresults arepresented inFigure8. Onimpact, theex ante real interest rate only increase 50 basis points rather than the ex post real interest rate increase of 100 basis points. However, all of the quantities experience responses that are similar to those reported in the baseline VAR. 2.5.2 Shorter Sample, Starting in 1983 One might wonder if the strong-interest rate response is stable over time. In particular, Gal´ı, L´opez-Salido and Vall´es (2003) argue that monetary policy changed in the United States with Paul Volker and that therefore the responses to a technology shock look very different after 1983 than they did earlier. There are two ways to test the stability. The first is to calculate γ from a regression of just a subsample of the identified technology series on the reduced form residuals, estimated from the full-sample VAR. This method holds the VAR fixed but sees whether a particular episode drove the estimation results. These results, although not reported, are almost identical to the results in Figure 8. Therefore, we have evidence against any particular technology shock episode driving the results. The second approach, which was used by Gal´ı L´opez-Salido and Vall´es, is to re-estimate theentireVARbutbeginin1983. TheimpulseresponsesfromthisVARarereportedinFigure 8. For the first year after impact, these responses are quite different from the responses in the baseline VAR. For the shorter sample VAR, the variables are less responsive on impact. After two years, the responses by quantities are quite similar. These results emphasizes the robustness of describing the response to a technology shock as being a delayed response. One important difference between the two sets of results is that, with the shorter sample, the real interest rate does not respond to the technology shock. The shocks identified using the post-1982 VAR are very different from the same shocks identified using the full sample of data. The full sample shocks are much more volatile. In addition, they are not closely related to the post-1982 shocks. The post-1982 shocks are the same sign as the full sample shocks only about 50 percent of the time. Thequestioniswhetherthefullsampleorthetruncatedsamplecorrectlyidentifiesthetrue technology shocks. Determining which is the correct set of responses is a difficult question. A simple likelihood ratio test would support using the truncated sample. However, to exclude three of the four recessions in the covered time period throws away a lot of information. As 13

such, the analysis here will continue to use the benchmark responses, but with the caveat that other responses are possible. 3 Models Having described the empirical responses, the next step is to develop a model that can match the data. The model presented here has two features that are different from a standard quantitative dynamic flexible-price model. The first is that the economic agent has habit persistence in the utility function. Thus, the previous period’s level of consumption affects current utility. Habit persistence results in a slower response by consumption. (In order to match the real interest rate response, a model with consumption adjustment costs is also presented.) The second feature and the focus of the paper is how investment is transformed into capital. I consider two different specifications of this transformation: time-to-build and capital-adjustment-cost models. Both specifications have the property of preventing capital from adjusting quickly.22 The time-to-build model has a lag between the decision to increase the capital stock and the actual increase in the capital stock. Likewise in the capital adjustment model, increasing investment is expensive and therefore an economic agent will have an incentive to smooth out investment. All of these features have been used previously to explain other economic phenomena. In particular, Christiano and Todd (1995) and Christiano and Vigfusson (2003) document the propertiesofaparticularparameterizationofthetime-to-buildmodel,thetime-to-planmodel, whereinvestmentcannotrespondmuchinthefirstperiodofashock. ChristianoandVigfusson showthatthismodelismuchbetterthanastandardquantitativedynamicflexible-pricemodel in matching the output growth dynamics and the lead-lag relationship between output and business investment.23 Models with capital adjustment costs that depend on the ratio of investment to capital have been used extensively in the Tobin’s Q literature. (See Chirinko (1993) for a survey.) Boldrin, Christiano, and Fisher (2000) and Beaudry and Guay: (1996) document how adding capital adjustment costs and habit persistence allows a macroeconomic model to explain both business cycle facts and asset pricing issues. Topel and Rosen (1988) make capital adjustment costs depend on the growth rate of investment to explain housing investment. Christiano, Eichenbaum, and Evans (2001) use a similar specification to generate improved dynamics in a sticky price model. Francis and Ramey (2003) also consider a capital adjustment model to explain the low correlations between productivity and employment. In their model, capital adjustment costs depend on the ratio of investment to capital. 22Modelswithcapitaladjustmentcostsdohaveasimilaritywithmodelsofmarginalefficiencyshocks(Dejong Ingram and Whiteman 2000). In both models, the amount of output required to produce a unit of capital (themarginalefficiencyofinvestment)variesovertime. Themodelsdifferinhowtheydeterminethemarginal efficiency. Inmodelswithcapital adjustmentcosts,themarginal efficiencyvariesendogenously asagents vary howmuchtheyinvest. InDejongIngramandWhiteman(2000),themarginalefficiencyisanexogenousrandom variable. 23Additional support for time-to-build models comes from Kovea (2000), which presents firm-level evidence of time-to-build being a feature of investment in structures. Based on reports from newspapers and trade journals on 106 randomly chosen firms, she estimates an average time-to-build for structures of about two years. Furthermore, shereports that very few of the projectsthat she examines were cancelled. 14

3.1 The Utility Function The model has a representative agent who chooses consumption C and the fraction of time spent working H to maximize utility, where utility is defined as E βj(log(C bC )+ηlog(1 H )) (13) t t+j t+j 1 t+j − − − X Thecoefficientbdescribesthedegreeofhabitpersistenceinthemodel.24 Theagentmaximizes utilitysubjecttotwoconstraints. Thefirstconstraintistheaggregateresourceconstraintthat for any period t+j, the resources used in that period must be no more than the amount of output produced. The constraint is: C +I F (θ ,K ,H ) (14) t+j t+j t+j t+j t+j ≤ The amount of output produced depends on the amount of labor H, the amount of capital K, and the level of technology θ . t As an alternative to habit persistence, I also consider a model that features consumption adjustmentcosts. Inthismodel,thehabitpersistencecoefficientissettozeroandtheresource constraint is the following. C 2 t C +I +ξ x C +A(U )K F (θ ,K ,H ) (15) t+j t+j t 1 t+j t+j t+j t+j t+j C t 1 − − ≤ µ − ¶ As will be discussed in the section on the real interest rate, consumption adjustment costs 2 ξ Ct x C are a useful alternative to habit persistence. This feature results in the Ct 1 − t − 1 sa³me−dampe´ned consumption response without driving down the response of the real interest rate. Two different production functions are considered here. As is common in the macroeconomic literature, I use a Cobb Douglas technology function. F (θ ,K ,H )=θ (K )α(H )1 α t+j t+j t+j t+j t+j t+j − In addition, because of the strong interest rate response reported above, I also consider the following CES production function.25 1/ψ F (θ ,K ,H )= α1 ψ(K )ψ +θ (1 α)1 ψ(Hψ t+j t+j t+j − t+j t+j − − t+j h i The second constraint specifies how investment is transformed into capital and will be described in Section 3.3 OnedifferencebetweenthismodelandFrancisandRameyisthespecificationoftheutility for leisure. They used an indivisible labor model; whereas, here, the model has the standard 24The specification of habit persistence used here is standard in the literature. One drawback of this specification is that it requires that the level of consumption c must always be greater than the habit stock bc t t to avoid marginal utility being infinite. Carroll, Overland, and Weil (2000) discuss a different specification, where what matters is the ratio of current consumption to the lagged habit stock. Using the ratio avoids the problemsof infinite marginal utility aslong as consumptionis positive. 25For the CES production function, technology is labor augmenting. This assumption is important for the normalizationrequiredwhen technology is a randomwalk. 15

divisiblelabor utilityfunction. Thetwospecificationsimply verydifferentvalues for thelabor supply elasticity. The labor supply elasticity is much greater for the indivisible labor model, where the labor supply is infinitely elastic. With divisible labor, the labor supply would have an elasticity of about three.26 Therefore, the labor supply will be less responsive in the specification studied here. 3.2 The Technology Shocks Inordertomatchthedata,themodelshouldhavegrowthandthereforetheleveloftechnology should be nonstationary. The level of technology θ has the following functional form t lnθ =µ+lnθ +ε (16) t t 1 t − where ε has mean zero. The standard assumption is that the shock to the growth rate ε of t t technology is independent over time. An alternative specification allows the growth rate to be autoregressive ε =ρ ε +u (17) t z t 1 t − where ρ is strictly less than one and u is independent over time. Although most of the z t | | reported results are for a shock where ρ equals zero, some results reported in Section 3.6 are z considered where ρ equals 0.7. The standard deviations of u is chosen so that the standard t deviation of ε is 0.01. t 3.3 Transforming Investment into Capital This section describes how investment is transformed into capital. Three different specifications are considered. The first is the time-to-build model of Kydland and Prescott (1982). In this model, several quarters pass before a desired increase in the capital stock is realized. The second is the convex capital adjustment costs where the costs are a function of the ratio of investment to capital. The third has adjustment costs that depend on the growth rate of investment.27 3.3.1 Time-to-Build In the time-to-build model (Kydland and Prescott 1982), the investment technology has two features. The first is that the time between the decision to increase the capital stock and the actual increase is greater than a quarter. In the current application, four quarters pass between making a decision to increase the capital stock and the actual increase. The second feature is that the increase in the capital stock is paid for over time. In other words, a project x initiated at quarter t results in an increase in the capital stock K (1 δ)K four t t+4 t+3 − − quarter later. The total cost of the project x equals the increase K (1 δ)K , but the t t+4 t+3 − − 26Microeconomic evidence suggests that the labor supply elasticities aremuch smaller. The labor literature reports labor supply elasticities near zero for males and about 1 for females. Most macroeconomic models, however, require theselarger estimates inorder to match the data. 27Theemphasisinthispaperisonconvexadjustmentcosts. CooperandHaltiwanger(2000)emphasizethat including firm-level non-convex costs (such as fixed costs) also matters for aggregate investment. Including suchnon-convexities is a goal for futurework. 16

project is paid for in installments. Thus, investment consists of several different projects that are at various stages of completion. In particular, period t investment equals: I =φ x +φ x +φ x +φ x (18) t 1 t 2 t 1 3 t 2 4 t 3 − − − where φ 0 for i=1,2,3,4, and i ≥ φ +φ +φ +φ 1. 1 2 3 4 ≡ Resources in the amount φ x must be applied in period t, φ x must be applied in period 1 t 2 t t+1,φ x must be applied in period t+2, and finally, φ x must be applied in period t+3. 3 t 4 t Once initiated, the scale of an investment project cannot be expanded or contracted. 3.3.2 Capital Adjustment Costs Two versions of capital adjustment costs are described here. The first, (which I will refer to as CIK), is the more common version where the cost of capital adjustment is a function of the ratio of current investment to capital I 2 t K +γ δ K (1 δ)K I (19) t+1 t t t K − − − − t µ ¶ The second (which I will refer to as CII) is less common but it allows the adjustment costs to depend on the ratio of current investment to the previous period’s investment. I 2 t K +γ expµ I (1 δ)K I (20) t+1 t 1 t t I t 1 − − − − − µ − ¶ For the specifications given here, adjustment costs parameterized by γ, will not affect the steady state properties of the model. For the two models, these parameters, however, should be calibrated at different values. For comparable costs of adjustment, the value of γ for the investment growth rate specification should be δ times the value of γ in the investment to capital ratio specification 28 3.4 Model Parameterization At calibrated values, the standard RBC model fails to match the main facts discussed in the empirical section. In particular, all the variables respond to a positive technology shock most strongly on impact. Therefore, they completely miss the delayed response observed in the data. Recent model estimation has often tried to match impulse responses by using a GMM weighting function. However, the goal of this paper is to show the flexibility of these macroeconomic models to match estimated technology impulse responses. As such, rather than attempting to match any particular set of responses, I will present a comparative analysis 28The difference in the two specifications can be seen by examining the cost of the investment adjustments costswheninvestmentis(1+r)timesgreaterthanthesteadystatevalue. Fortheinvestmenttocapitalratio case, the adjustment costs would equal γ(rδ)2K. For the investment growth rate case, the adjustment costs would equal γ(r)2δK. Hence, the values of γ must be different for the two specifications. 17

that will clarify how the flexible-price models are compatible with the responses observed both in this paper and in many of the other papers in the literature. Figure 9 reports results for just the response of hours on impact and how the different models are able to capture the response of hours to a positive technology shock. For each of the different models, some of the model’s coefficients were fixed and others were allowed to vary. The coefficients that were allowed to vary were the ones that characterize the newer features of the model. In particular, results are reported for different values of both the degree of habit persistence and the coefficients related to how investment is translated into capital, (i.e. the degree of investment adjustment costs γ or time-to-build weights φ.). The other coefficients were held constant.29 The models were log-linearized and solved using the undetermined coefficients method of Christiano (2001).30 In Figure 9, there are several things to note. First, all three models have parameterization that are consistent with hours worked falling in response to a positive technology shock. Many, including Gal´ı and Basu, Fernald, and Kimball, have argued that the earlier empirical claims of negative hours responses to a technology shock is evidence against flexible-price models. Clearly, the flexible-price models reported here can imply that hours fall on impact of a positive technology shock. Therefore, these previous criticism of flexible-price models, althoughvalidforthestandardRBCmodel,donotapplytothesemodels. Furthermore,forall threemodels, differentcombinationsofinvestmentadjustmentcostsandhabitpersistencecan generate a given hours response. Habit persistence and investment adjustment costs actually work against each other. Investment adjustment costs decrease the investment response and increase the consumption response, and habit persistence increases the investment response and decreases the consumption response. Figure 10 illustrates these trade offs for the CII model and how consumption and investment impact responses depend on the degree of habit persistence and investment adjustment costs. The shaded areas indicate the bootstrap confidence intervals around the empirical impact effect. For investment, the width of the area suggest that the investment response is not very informative about the best values of habit persistence and the investment adjustment cost. 3.5 Dynamic Responses Figure 11 reports on the ability of all three models to capture the dynamic response of hours worked, consumption, and investment. The benchmark empirical results from Figure 2 are reproduced here. Thefirstpanelreportsresponsesforamodelwithhabitpersistenceandinvestmentadjustment costs that depend on the growth rate of investment, the CII model. As seen in Figure 10, it isfairly easy to findmodel parameterization thatmatch theconsumption response. The investment response is somewhat more difficult with the response being too strong compared to the empirical response. The hours worked response is delayed. However, hours actually do not respond enough on impact and then responds too strongly afterwards. The differences in 29The value of η is 1.5.The following coefficients were taken from Christiano and Eichenbaum (1992). The vector (β,α,δ) equals 1.03 0.25,0.36,0.02 . − 30Because the model is assumed to have a unit root in the technology, in calculating a solution, the vari- ¡ ¢ ables will be normalized by dividing through by the level of technology. Hence the model will be solved for c ,i ,k ,H where c ,i ,k equals C /θ ,I /θ ,K /θ . t t t t t t t t t t t t t 1 { } { } { − } 18

responses, however, are within the standard bootstrapped confidence intervals, indicated by the shaded regions. The second panel reports results from the time-to-build and CIK models. The CIK model can match the initial responses. However the CIK model can not match the increases in responses because the ratio of investment to capital does not quickly change. Without a changeintheratioofinvestmenttocapital,theinvestmentadjustmentcostsremainhigh. The time-to-buildmodeldoesbetteratcreatingresponsesthataresmallinitiallybutthenincrease. The main problem with the time-to-build model is that the responses are too jagged. The jaggedness results from there being only one kind of capital with only a four period building period. A time-to-build model with much smoother responses can be found in Edge (2000) where there are many different kinds of capital goods, with each kind of capital requiring a different number of periods to build.31 3.6 Real Interest Rate Response Although both the investment growth rate model and the time-to-plan model have done well infittingtheresponsesofconsumption, investmentandhoursworked, thissectionmakesclear that the models have a much harder time matching the strong interest rate response observed in the benchmark results. Figure 12 reports the real interest rate results from the empirical VAR and from the economic models. Given that consumption only slowly increases in both the CII and time-to-build models, it may seem puzzling that the real interest rate actually falls on impact. The explanation, however, involves the definition of marginal utility with habit persistence. First, the real interest rate can be expressed in terms of a ratio of marginal utilities. In particular, ignoring uncertainty, the real interest rate can be written as u (C ) 0 t (1+R )= t βu (C ) 0 t+1 Assumingnogrowth, theinterestratewouldbebelowthesteadystateinterestrateonlyifthe current marginal utility is less than next period’s marginal utility. For log utility and without habit persistence, we have that C t+1 (1+R ) = t βC t and so the interest rate only falls below steady state if current consumption is more than future consumption. With positive investment adjustment costs but no habit persistence, consumption does spike on impact and then declines somewhat. Therefore, in this case, the real interest rate declines on impact. Adding habit persistence, however, deepens the puzzle because then consumption increases over time. With consumption increasing over time and log utility, the interest rate would increase. However, with habit persistence, marginal utility depends on both the level and the growth rate of consumption. Because the growth rate of consumption increase with the impact of a technology shock, the real interest rate falls. 31As is evident in Christiano and Vigfusson (2003), this jaggedness is not a problem when examining the spectrumimpliedby thetime-to-planmodel. 19

For further intuition, consider the real interest rate in a model of internal habit which drops the forward looking part of the external habit specification used here.32 1(C bC ) t+1 t (1+R )= − t β(C bC ) t t 1 − − If the difference between C and bC is greater than the difference between C and bC t t 1 t+1 t − then the model projects that the real interest rate will fall. Modeling the production function as a CES production function, rather than Cobb- Douglas, does strengthen the growth rates of investment. However, this feature does not overcome the negative interest rate response generated by the habit persistence. Another optionwouldbetohavehabitpersistencedependonthedifferencebetweencurrentconsumption and a habit stock that only slowly evolved with current consumption. In other words, the new utility function is U(C ,X ,H ) = ln(C bX ) ηln(1 H ) t t t t t 1 t − − − − X = (1 τ)X +τC t 1 t 2 t 1 − − − − Althoughaddingahabitstockamelioratesthedeclineintherealinterestrate,therealinterest rate still falls in response to a positive technology shock. Onepartialremedytothefallingrealrateistoreplacehabitpersistencewithconsumption adjustment costs. With consumption adjustment costs, one continues to delay the consumption response but, unlike habit persistence, consumption adjustment costs do not introduce the growth rate of consumption into marginal utility. As such, the real interest rate increases on impact. However, as seen in Figure 12, the rise is not as much or as persistent as the empirical point estimates. Consumption adjustment costs may seem particularly ad-hoc. However, like investment adjustment costs, they help macroeconomic models match the empirical impulse response functions. Future work will be required to find a more structural mechanism to reduce how quickly both the level and the marginal utility of consumption increases in response to a positive technology. Anotherpossiblesolutionwouldbetohaveseriallycorrelatedtechnologyshocks. Although serially correlated shocks can result in a model with a stronger real interest rate response. Figure13reportsresultswiththeassumptionthattheautoregressivecoefficientonthegrowth rateoftechnologyρ equals0.7. AsshowninFigure13,inmodelswithinvestmentadjustment z costs, the real interest rate increases almost 50 basis points on impact. 33 However, this real interest rate response is less than the estimated response. In addition, the responses of the other variables particularly investment and hours worked are now too weak compared to the 32Withexternal habit,the real interest rate is a somewhat less tractable 1 +β − bexp( − εt+1 ) (1+R t )= β 1 (ct− bexp( 1 − εt)ct − 1 ) +β (ct+1− − b b e e x x p p ( ( − − ε ε t t + + 1 2 ) ) ct ) (ct+1− bexp( − εt+1 )ct ) (ct+2− bexp( − εt+2 )ct ) 33With serially correlated shocks,the standard flexible price model has a delayed response to the onset of a technology shock. The response on impact however seem to be too negative with both investment and hours workedfalling sharply. 20

estimated responses. So any gain in better real interest rate fit is lost in worse fit of hours worked and the real interest rate. Therealinterestrateresponseisaproblemforthesemodels. Asmentionedintheempirical section, the interest rate response is somewhat uncertain with both a wide confidence interval and being sensitive to the sample period. Therefore, some may question the seriousness of a failure to match this response. In fact, many researchers have felt that a fall in real interest rates followed by a positive increase in output is a desirable characteristic in a technology driven model. 4 Criticisms of Long Run VARs Recent papers by Erceg, Guerrieri and Gust (2004) and Chari Kehoe and McGrattan (2004) have criticized the use of long-run VARs to construct impulse response. Both papers have shown that, for particular model parameterizations, the point estimates of the impulse responses may be estimated imprecisely. This section provides some additional simulation evidence concerning the responses. I show for a particular set of models that, although, these authors do have a valid concern about the possible imprecision of the point estimates, the impulse responses are informative about the shape of the responses. Of specific relevance to the current paper, simulation evidence shows that these impulse responses can distinguish between a model where hours responds most on impact and a model where hours have a delayed (hump shaped) response. However, sign restrictions are not as informative. For the models considered here, the finding of a positive response is unlikely to allow us to discriminate between a model that has a positive hours response on impact and a model that has a negative hours response on impact. The simulation evidence presented here comes from three models: a standard quantitative dynamic flexible-price model (where hours responds positively and with the largest response being immediate), a model with CII investment adjustment costs (where hours responds positively and with a delayed response), and a model with CII investment adjustment costs and habit persistence. In order to estimate a non-trivial bivariate VAR, each model has an additional shock εη that affects the labor preference parameter η. Hence the utility function t becomes E βj(log(C bC )+η(1+ε η )log(1 H )) (21) t t+j t+j 1 t t+j − − − and the shock εη isXassumed to be independent of the technology and shock and have the t following autoregressive structure. εη =ρ εη +υ t η t 1 t − where υ is i.i.d normal with variance σ2. Using the standard quantitative dynamic flexiblet η price model and holding the standard deviation of the technology shock σ fixed at 0.01, z the standard deviation and the persistence of the preference shock is estimated by maximum likelihood (as described in Christiano and Vigfusson (2003)), by matching the model-based spectrum of labor productivity growth and the log level of hours worked to the empirical spectrum of nonfarm business labor productivity and per capita hours worked.34 Based on 34Appendix A describes briefly theestimationprocedure. 21

data between 1959q1-2000q4, the standard deviation of the labor supply shock equals 0.0093 with a persistence coefficient of 0.975.35 Giventheseestimates,Ithenusedeachmodeltogenerate500datasetsof200observations each on labor productivity and hours worked. For each simulated data set, I then estimated a long run VAR on the growth rate of labor productivity and the log level of hours worked. Figure 14 reports the theoretical model response for hours worked and also the average response estimated from the simulated data. For all models, the average responses are biased upwards, but the average responses are reasonably close. However, an interval that contains 90 percent of the simulated responses is very large. Figure 14 plots such an interval for the CII model. Given these wide intervals, one may be concerned that one could not distinguish between the models. Some measures but not others are able to distinguish between the models. Figure 15 reports the probability of observing two results in each model. The top panel reports the probability of observing a positive impact response. Because of the wide confidence intervals and the upward bias in the hours response, all three models, including the model where the true response is negative, have a high probability of observing a positive value. Therefore, a finding of a positive response is not very informative about the true data generating model. AscanbeseeninthebottompanelofFigure15, theshaperesultsaremuchmoreinformative. In the standard RBC model, the downward trend in the hours response is apparent in the small fraction of responses that are greater than the impact response. Likewise, in the model with investment adjustment costs, the hump-shaped response is readily apparent by the large fraction of responses that are greater than the impact response. One way to quantify the difference between models would be with a posterior odds ratio. In particular given the observed data y, one would calculate the odds of model one M being 1 preferred over model two M as follows. 2 P (M y) P(y M )P(M ) 1 1 1 | = | P (M y) P (y M )P(M ) 2 2 2 | | Supposingthatmodelonehascoefficientsθ ,wecoulddefinetheposteriorprobabilityP(y M ) 1 1 | as follows P(y M )= P(y θ ,M )P(θ M )dθ 1 1 1 1 1 1 | | | Z where P(y θ,M ) is the likelihood of observing y in model one given parameters θ and 1 | P(θ M ) is the prior belief about the distribution of θ. Instead of a full fledged Bayesian 1 1 | analysis, I will suppose that the data y is the fact that we observed a hump-shaped response and that our prior belief about the distribution P(θ M ) is that P(θ M ) equals zero for 1 1 1 1 | | all θ except for the calibrated values used here. Given these assumptions, one can calculate 1 the odds ratio as being the ratio of the percentages reported in Figure 15. Therefore, based on the hump-shaped response, the odds in favor of the CII model relative to the standard quantitative dynamic flexible-price model are well over two to one. A similar calculation on the sign of the impact response is not as informative. Because of both the bias and the 35These values were calculated for the version of the flexible price model without any adjustment costs. As such, a richer structure might result in different parameter estimates. However, the goal of this section is to providesomeevidenceontheusefulnessoflongrunVARstodiscriminatebetweenmodels,notafullmaximum likelihood estimation. 22

imprecision of the point estimates, the observation of a positive impact response favors the standard quantitative dynamic flexible-price model over the CII model with habit persistence with odds of only 1.22 to one. These calculations should be taken as only a guideline. Other models with more features or other shocks might give different results for both the identification of point estimates and response shapes. However, at least for these simple models where the criticisms of EGG and CKM are valid, studying the shape of the responses seems to be a valid way to use long-run VARS to learn about the economy.36 5 Conclusions The main empirical conclusion of this paper is that, for the U.S. economy, the response by per-capita hours worked to a technology shock is initially small but subsequently increases. The small initial response is evidence against any model, including the standard quantitative dynamic flexible-price model, that predicts a large immediate response by employment to a technology shock. These results do not, however, completely invalidate the use of real technologyshocks to explainbusinesscyclessince variables dorespond in the mediumtermto these shocks. Therefore, the task is to develop models that can explain both the short-term and long-term responses to technology shocks. The current paper presents quantitative dynamic flexible-price models that can be reconciled with the observed responses by quantities to a technology shock. Of course, this reconciliation is not a rejection of other possible explanations. These other possible explanations might includetheexamplesprovidedby Basu, Fernald, and Kimball (2004): sticky-price models, multi-sector reallocation models, and cleansing models of recessions. All of these explanations should be scrutinized further to determine their relative merits. The current paper has done three things. First, it has presented new empirical dynamic responses for models to match. Second, it has shown that the estimated shape of these dynamic responses may be more informative than the sign of the impact response. Third, it has put forward flexible-price models that better explain these delayed responses. In effect, it has raised the standard for criticisms of the flexible-price model. It was easy to show that the small initial response by hours worked was inconsistent with the standard flexibleprice model. With the additional features discussed here, a flexible-price model can be made consistent with these observations concerning hours worked. The new challenge will be to build upon the improved fits described here. 36In the above results, I did not consider the effect of using the growth rate of hours in the long-run VAR. In these models, hours worked is stationary. As is discussed in CEV (2003), estimating a VAR after first differencing a stationary variable is a form of specification error. Hence using the first difference VAR on model-simulateddatawouldbeusingamisspecficiedVAR.AswasfoundinCEVandCKM,Ialsofoundthat applying the first difference VARs would result in a very high probability of a negative response by hours on impact. 23

A A Summary of Model Estimation by Maximum Likelihood in the Frequency Domain In order to make the paper somewhat more self-contained, this appendix summarizes how to estimate a model by maximum likelihood in the frequency domain. For more details and application,. see Christiano and Vigfusson (2003). Begin with a time series of data, y = [y ,...,y ], where y is a finite-dimensional column 1 T t vector with zero mean. In this paper’s analysis, the vector y is defined as t ∆log(Y /H ) y = t t , (22) t log(H ) t · ¸ where Y denotes output and H denotes hours worked. t t It is well known (Harvey, 1989, p. 193) that for T large, the Gaussian likelihood for such a time series of data is well approximated by: T 1 1 − L(y,Φ)= 2log2π+log[det(F(ω ;Φ))]+tr F(ω ;Φ) 1I(ω ) (23) j j − j −2 j=0 X© ¡ ¢ª where tr() and det( ) denotes the trace and determinant operators, respectively. Also, I(ω) · · is the periodogram of the data: T 1 I(ω)= y(ω)y( ω), y(ω)= y exp( iωt), (24) 0 t 2πT − − t=1 X and 2πj ω = , j =0,1,...,T 1. j T − Finally, F(ω;Φ) is the spectral density of y at frequency ω, and Φ is a vector of unknown parameters.37 To estimate a model by frequency domain maximum likelihood, one needs the mapping from the model’s parameters, Φ, to the spectral density matrix of the data, F(ω ;Φ). The j following describes this mapping. The first step is to solve a linearized version of the macroeconomic model. One can then use the linearized solution to write a linear approximation of the y process t y =α(L;Φr)ε =α (Φr)ε +α (Φr)ε +α (Φr)ε +..... (25) t t 0 t 1 t 1 2 t 2 − − In the two-shock model, y is defined in (22), α(L;Φr) is 2 2 matrix polynomial in L, t × and η σ2 0 ε = t , V(Φr) = η . t u 0 σ2 µ t ¶ · u ¸ 37Let C(k;Φ)=Ey y , for integer valuesof k. Then, t t0 k − F(ω;Φ)= 1 ∞ C(k;Φ)e− iωk, 2π k= X−∞ for ω (0,2π). ∈ 24

In this case, α(L;Φr) is the infinite moving average representation corresponding to a vector ARMA model with 2 autoregressive and 2 moving average lags, i.e., a VARMA(2,2). In all cases, I restrict Φr so that ∞ α (Φr)V(Φr)α (Φr) < , i i 0 ∞ i=0 X guaranteeingthatthespectraldensityofy exists. WealsorestrictΦr sothatdet[α(z;Φr)] =0 t implies z 1, where denotes the absolute value operator. | | ≥ |·| The spectral density of y at frequency ω is t 1 Fr(ω;Φr)= α(e iω;Φr)Vα(eiω;Φr), − 0 2π where the superscript, r, on F indicates that the form of α(L;Φr) is restricted by the model. Using this expression, one can then maximize the likelihood function with respect to the values of Φr. Christiano and Vigfusson (2003) describe the usefulness of the frequency domain approach in studying model fit. References Altig, David, LawrenceJ. Christiano, MartinEichenbaumandJesperLinde, 2004, “AnEstimated Dynamic, General Equilibrium Model for Monetary Policy Analysis,” Manuscript. Anderson, T.W. and H. Rubin 1949 “Estimation of the Parameters of A Single Equation in A Complete System of Stochastic Equations”, Annals of Mathematical Statistics, 20, pp. 46-63 BasuSusanto1998“TechnologyandBusinessCycles: HowWellDoStandardModelsExplain the Facts?” Beyond Shocks: What Causes Business Cycles? Federal Reserve Bank of Boston, Conference Series No. 42 Basu Susanto John G. Fernald 2000 “Why is Productivity Procyclical? Why do we care?” NBER Working Paper 7940 Basu Susanto, John G. Fernald, and Miles S. Kimball. 2004. “Are Technology Improvements Contractionary” NBER Working Paper 10592 Basu Susanto John G. Fernald and Matthew D. Shapiro 2001 “Productivity Growth in the 1990s Technology Utilization or Adjustment” NBER Working Paper 8359 Beaudry Paul, Alain Guay. 1996 “What Do Interest Rates Reveal about the Functioning of Real Business Cycle Models?”, Journal of Economic Dynamics and Control, 20,.1661- 1682 Boldrin, Michele, Lawrence J. Christiano and Jonas D.M. Fisher, 2001 “Habit Persistence, Asset Returns and the Business Cycle” American Economic Review 91 149-166. BurnsideCraig1996“ProductionFunctionRegressions, ReturnstoScaleandExternalities,” Journal of Monetary Economics, 37, 177-201. Burnside Craig, Martin Eichenbaum and Sergio Rebelo, 1996 “Sectoral Solow Residuals,” European Economic Review, 40, 861-869. Carroll Christopher D. , Jody Overland, and David N. Weil 2000 “Saving and Growth with Habit Formation” American Economic Review, 90(3), 341-355 25

Chari, V.V., Patrick Kehoe, and Ellen McGrattan 2004 “An Economic Test of Structural VARs” FederalReserveBankofMinneapolisResearchDepartmentWorkingPaperNumber 631 Chirinko Robert S. 1993 “Business Fixed Investment Spending” Journal of Economic Literature 31 1875-1911. Christiano, Lawrence J., 2001, “Solving Dynamic Equilibrium Models by a Method of Undetermined Coefficients”, forthcoming. See also, NBER Technical Working paper 225. ChristianoLawrenceJ.MartinEichenbaumandCharlesEvans2001“NominalRigiditiesand theDynamicEffectsofaShocktoMonetaryPolicy”manuscriptNorthwesternUniversity Christiano, Lawrence J. and Martin Eichenbaum, 1992, “Current Real-Business-Cycle Theories and Aggregate Labor-Market Fluctuations”, American Economic Review, 82(3), June, 430-50. Christiano Lawrence J. and Jonas D. M. Fisher 1998 “Stock Market and Investment Good Prices: Implications for Macroeconomics,” Federal Reserve Bank of Chicago Working Paper Christiano, Lawrence J. and Richard M. Todd, 1996, ‘Time to Plan and Aggregate Fluctuations’, Federal Reserve Bank of Minneapolis Quarterly Review, Winter, 14-27. Christiano, Lawrence J. and Robert J. Vigfusson 2001 “Maximum Likelihood in the Frequency Domain: The Importance of Time-to-plan” manuscript Northwestern University Conley Timothy G. William D. Dupor 2003 “A Spatial Analysis of Sectoral Complementarity” Journal of Political Economy 111(2) p 311-52 Cooper, Russell W. and John C. Haltiwanger 2000 “On the Nature of Capital Adjustment Costs” manuscript DeJong David N., Beth F. Ingram, and Charles H. Whiteman, 2000 “Keynesian Impulses versus Solow Residuals: Identifying Sources of Business Cycle Fluctuations”, Journal of Applied Econometrics, 15(3), pp. 275-287. Edge, Rochelle M. 2000 “Time-to-build, time-to-plan, habit-persistence, and the liquidity effect,” Board of Governors International Finance Discussion Paper 673 Erceg,Christopher, Luca Guerrieri and Christopher Gust. 2004 “Can Long-Run Restrictions Identify TechnologyShocks?”, Federal Reserve Boardof Governors International Finance Discussion Paper 792 Faust, Jon andEricLeeper 1997“When Do Long-RunIdentifying Restrictions GiveReliable Results?” Journal of Business and Economic Statistics 15(3) 345-53 Francis, Neville and Valerie A. Ramey 2003 “Is the Technology-Driven Real Business Cycle Hypothesis Dead? Shocks and Aggregate Fluctuations Revisited” manuscript October Fuhrer,JeffreyC.2000“HabitFormationinConsumptionandItsImplicationsforMonetary- Policy Models” American Economic Review 90(3) 371-390 Gal´ı, Jordi, 1999 “Technology, Employment, and the Business Cycle: Do Technology Shocks Explain Aggregate Fluctuations,” American Economic Review, 89 249-271. Gal´ı, Jord, J. David Lo´pez-Salido and Javier Vall´es 2003 “Technology shocks and monetary policy: assessing the Fed’s performance” Journal of Monetary Economics, 50(4), 723-743 Harvey, Andrew, 1989, Forecasting Structural Time Series Models and the Kalman Filter, Cambridge University Press. 26

Jermann, Urban J., 1998 “Asset Pricing in Production Economies,” Journal of Monetary Economics 41 257-276. King,RobertG.,Charles.I.Plosser,JamesH.Stock,andMarkW.Watson.1991.“Stochastic Trends and Economic Fluctuations.” American Economic Review. 81(4) 819-840. King Robert G. and Mark W. Watson 1997 “Testing long-run neutrality” Federal Reserve Bank of Richmond Economic Quarterly 69-101 Koeva, Petya 2000 “The Facts About Time-to-Build” IMF Working Paper August Kydland, Finn E. and Edward C. Prescott, 1982, “Time to Build and Aggregate Fluctuations’, Econometrica, 50, November, 1345-70. Lum Sherlene K.S. and Brian C. Moyer 1998 “Gross Product by Industry 1995-97” Survey of Current Business November Pesavento, Elena and Barbara Rossi 2003 “Do Technology Shocks Drive Hours Up or Down? A Little Evidence From an Agnostic Procedure” Duke University manuscript Shleifer, Andrei 1986 “Implementation Cycles”,Journal of Political Economy, 94(6) 1163-90 Topel, Robert and Sherwin Rosen 1988 “Housing Investment in the United States”, Journal of Political Economy 96:4 718-740. Vigfusson, RobertJ.2003“HowDoestheBorderAffectProductivity? EvidencefromAmerican and Canadian Manufacturing Industries ”, Federal Reserve Board of Governors, International Finance Discussion Papers 788 Whelan, Karl 2000 “A Guide to the Use of Chain Aggregated NIPA Data” Federal Reserve Board of Governors Finance and Economics Discussion Series 2000-35 (June) Wright, Jonathan H. 2002 “Testing the Null of Identification in GMM”, Federal Reserve Board of Governors, International Finance Discussion Papers 732 27

A Tables Table 1: Manufacturing Industries Durable Good Producers SIC Code Nondurable Good Producers SIC Code Lumber 24 Food 20 Furniture 25 Textiles 22 Glass Stone & Clay 32 Apparel 23 Primary Metals 33 Paper 26 Fabricated Metals 34 Printing 27 Industrial Machinery 35 Chemicals 28 Electrical Machinery 36 Petroleum 29 Transportation 37 Rubber and Plastics 30 Instruments 38 Miscellaneous 39 Table 2: Coefficient Estimates Coef T-stat Coef T-stat NonDurable Durable µ 0.82 -1.13 1.04 0.28 ξ 0.31 2.45 0.17 1.65 Results: 18 Manufacturing Industries 1972-2001 GMM Estimation with Asymptotic Standard Errors T-stat for µ is test of µ equal to one. T-stat for ξ is test of ξ equal to zero. Degrees of Freedom Equal to 167 28

Table 3 Percent of Simulations where the response x periods after the shock is greater than the response on impact x Periods After Shock H C I 1 90.1 77.4 94.1 2 90.7 68.0 92.0 3 91.4 77.0 93.4 4 87.8 74.4 88.4 5 88.5 79.4 88.2 6 90.3 84.7 87.6 7 89.7 83.8 86.3 8 89.0 85.6 85.1 9 88.6 86.0 83.1 Table 4: Estimated Confidence Intervals and Theoretical Bounds on Impact Response to A Technology Shock Estimate Confidence Intervals Theoretical Bounds Technology Labor Productivity Technology Labor Productivity VAR VAR Labor Productivity (-0.06, 0.38) (-0.22, 0.36) 0.518 0.55 ± ± Hours Worked (-0.007, 0.084) (-0.09, 0.11) 0.108 0.124 ± ± Real Interest Rate (28, 98) (-38, 100) 101.1 102.6 ± ± Output (-0.05, 0.42) (-0.31, 0.45) 0.564 0.62 ± ± Consumption (0.07, 0.32) (-0.03, 0.20) 0.469 0.46 ± ± Investment (-0.69, 1.08) (-1.09, 1.30) 1.32 1.41 ± ± Notes: Confidence Intervals Constructed using 95 percent critical value of 11.07 for tech and 9.488 for labor productivity 29

B Figures Figure 1: Hours Response 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 -0.05 0 5 10 15 20 25 30 35 Thick Line VAR with Constructed Productivity Series and Hours In Levels ’X’s: VAR with Constructed Productivity Series and Hours In Difference Stars VAR with Labor Productivity and Hours in Differences Grey Area: 95 Percent Bootstrapped Confidence Interval Centered Around VAR with Constructed Productivity Series and Hours In Levels 30

Figure 2: Data Used In the VAR Analysis Productivity Growth Log of Percapita Hours 0.03 1.54 0.02 0.01 1.53 0 -0.01 1.52 -0.02 -0.03 1.51 -0.04 1975 1980 1985 1990 1995 2000 1975 1980 1985 1990 1995 2000 Real Interest Rate Output Growth 0.02 6 4 0.01 2 0 0 -0.01 -2 -0.02 -4 -0.03 1975 1980 1985 1990 1995 2000 1975 1980 1985 1990 1995 2000 Consumption Share of Output Investment Share of Output 0.83 0.22 0.82 0.21 0.81 0.2 0.8 0.19 0.79 0.18 0.78 0.17 1975 1980 1985 1990 1995 2000 1975 1980 1985 1990 1995 2000 31

Figure 3: The Result of Applying The Long Run Identification Assumption 0.04 0.03 0.02 0.01 0 -0.01 -0.02 -0.03 1975 1980 1985 1990 1995 2000 Thin Line Constructed Technology Growth Rate Series (Demeanded) Thick Line: Technology Growth Rate Series (Demeanded) implied by the Long Run Identification Assumption 32

Figure 4: Responses To Productivity Shock Labor Productivity Hours Worked 0.25 1 0.2 0.8 0.15 0.6 0.1 0.4 0.05 0.2 0 0 0 5 10 15 0 5 10 15 Real Interest Rate Output 1 100 50 0.5 0 0 0 5 10 15 0 5 10 15 Consumption Investment 2 1 1 0.5 0 -1 0 0 5 10 15 0 5 10 15 Thick Line VAR with Constructed Productivity Series and Hours In Levels, with Long Run Identification Assumption Grey Area: 95 Percent Bootstrapped Confidence Interval Centered Around VAR with Constructed Productivity Series and Hours In Levels Circles VAR with Constructed Productivity Series and Hours In Levels, with Short Run Identification Assumption ’Stars’s VAR with Labor Productivity and Hours in Differences with Long Run Identification Assumption 33

Figure 5: Shape of The Response of Hours 0.25 0.2 71 % 0.15 0.1 r 18 % 4 % e at L s 0.05 r e rt a u Q 0 x Si e n s -0.05 o p s R e 1 % 3 % -0.1 -0.15 3 % -0.2 -0.25 -0.2 -0.1 0 0.1 0.2 Response on Impact 34

Figure 6: Confidence Intervals for a , Impact Response on Hours, and the Response Six Periods Later 0 Anderson-Rubin Confidence Set for a Mapping from a to γ 0 0 10 0.15 9 0.1 8 7 0.05 6 a s c t t t i i S 5 γ 0 R A 4 -0.05 3 -0.1 2 -0.15 1 0 -0.2 -30 -20 -10 0 10 20 -40 -30 -20 -10 0 10 20 30 Coefficient Estimate Coefficient Estimate Anderson-Rubin Confidence Set Anderson-Rubin Confidence Set for Hours Response On Impact for Hours Response Six Periods Later 10 10 9 9 8 8 7 7 6 6 a s c t t t i i S 5 a s c t t t i i S 5 R R A 4 A 4 3 3 2 2 1 1 0 0 -0.1 -0.05 0 0.05 0.1 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 Hours Response On Impact Response Six Periods After Impact 35

Figure 7: Anderson-Rubin Confidence Set 0.14 0.12 0.1 r e t a L 0.08 s r e t a r 0.06 u Q x Si 0.04 e s n o 0.02 p s e R 0 -0.02 -0.04 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 Response on Impact Thin Line indicated all possible combinations of γH and γH 0, 6, The grey area indicates those combinations with an Anderson-Rubin statistic less than the 95 percent critical value. 36

Figure 8: Robustness of Impulse Responses to Different Subsamples. Labor Productivity Hours Worked 0.3 1 0.25 0.2 0.15 0.5 0.1 0.05 0 0 0 5 10 15 0 5 10 15 Real Interest Rate Output 1.5 150 1 100 0.5 50 0 0 0 5 10 15 0 5 10 15 Consumption Investment 2 1 1 0.5 0 0 -1 0 5 10 15 0 5 10 15 Thick Line VAR and Grey Area: Baseline Results replicated from Figure 4 ‘X’s VAR with exante Real Interest Rate, full sample 1973-2001. Squares VAR with exante Real Interest Rate, short sample 1983-2001. 37

Figure 9: How Hours Responds on Impact I/K Adjustment ∆I Adjustment 0.9 -0.4 0.9 0.8 0.8 -0.4 0.7 n e e c s st i P e b r 0 0 0 . . . 4 5 6 -0 - . 0 2 .3 e b n e c t e s s r i 0 0 0 0 . . . . 4 5 6 7 0 1 5 0 . 1 0 . 0 50 - 0 .1 -0 .2 -0 .3 a b ti H 0 0 . . 2 3 0 1 0 . 0 50 -0.1 P ti H a b 0 0 . . 2 3 0.1 0.1 20 40 60 80 100 0.2 0.4 0.6 0.8 InvestmentAdjustmentCosts InvestmentAdjustmentCosts γ Time to Build Notes ThickBlackLine: PointEstimateofResponse of Hours on Impact Grey Area: 95 percent weak-instrument con- 0.8 fidence interval as reported in Table 4. 0.7 b 0.6 e c n e 0.5 st 4 s r i 0.4 - 0. e P 3 b ti 0.3 - 0. a H 0.2 0. 2 5 0.1 - 0. 1 00. 0 5 0. 1 0 . 1 0 . 2 - 0.1 0.2 0.3 FirstPeriodTime-to-BuildWeight 38

Figure 10: The Trade-off Between Investment Adjustment Costs and Habit Persistence Consumption Investment Response 0.9 0.9 0.1 0.8 0.15 0.8 2 0.7 0.2 0.7 1 . 5 1. 2 1. 1 1 b 0.25 b 5 e c 0.6 0.3 e c 0.6 0. 7 n n e st 0.5 0.35 e st 0.5 e s r i 0.4 0.4 0.45 e s r i 0.4 P P b ti 0.3 0.5 b ti 0.3 a a H 0.55 H 5 5 0.2 0.2 0. 0.6 0.1 0.1 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 InvestmentAdjustmentCosts γ InvestmentAdjustmentCosts γ 39

Figure 11: Dynamic Responses Comparing Models and Data Investment Adjustment Costs as Function of Investment Growth Consumption Investment Hours Worked 0.25 2.5 1 2 0.2 0.8 1.5 0.15 0.6 1 0.1 0.4 0.5 0.05 0.2 0 0 0 0 5 10 0 5 10 0 5 10 Thick Solid Line: Empirical Response, Thin Line, Standard flexible-price model (b,φ) =0 Squares: Model with habit persistence and investment adjustment Costs (b,φ)=(0.4,0.09) ’*’s Model with investment adjustment Costs (b,φ)=(0,0.09) Consumption Investment Hours Worked 0.3 2.5 1 0.2 2 0.8 0.1 1.5 0 0.6 1 -0.1 0.4 -0.2 0.5 0.2 -0.3 0 -0.4 0 0 5 10 0 5 10 0 5 10 Thick Solid Line: Empirical Response, Stars: Model with habit persistence and Time to Plan (b,φ)=(0.5,0.05) Thin Solid: Model with habit persistence and Time to Build (b,φ)=(0.5,0.20) Line with Solid Circles, CIK model with habit persistence (b,φ)=(0.28,5) 40

Figure 12: Real Interest Rate Response Real Interest Rate 1 0.5 0 -0.5 -1 -1.5 -2 -2.5 0 2 4 6 8 10 Thick Solid Line: Empirical Response, Thin Line, Standard flexible-price model (b,φ)=0 Squares: Model with habit persistence and investment adjustment Costs (b,φ) =(0.4,0.09) Stars: Model with habit persistence and Time to Plan (b,φ) =(0.5,0.05) Diamonds: Model with consumption adjustment costs and investment adjustment costs. (b,φ) =(0.4,0.2) 41

Figure 13: Model Responses with Correlated Shocks. Consumption Investment 1.2 1 2 0.8 1 0.6 0.4 0 0.2 -1 0 0 5 10 0 5 10 Hours Worked Real Interest Rate 0.2 100 0.1 0 50 -0.1 0 0 5 10 0 5 10 Thick Solid Line: Empirical Response, Thin Line, Standard flexible-price model (b,φ)=0 with ρ =0.7 z Squares: Model with habit persistence and investment adjustment Costs (b,φ) =(0.4,0.09) with ρ =0.7 z 42

Figure 14: Hours Response to A Technology Shock 1 0.5 0 -0.5 0 2 4 6 8 10 Thick Lines, Model Responses, Plain Standard RBC, Diamonds CII Adjustment Cost, Squares, CII Adjustment and Habit Thin Lines, Average Estimated Response, Plain Standard RBC, Diamonds CII Adjustment Cost, Squares, CII Adjustment and Habit Dashed Lines, 90 Percent of all estimated responses for the CII Model are contained within dashed lines 43

Figure 15: Simulations Results Responses that Are Positive 100 No Adj Costs Inv Adj Cost 80 Plus Habit t 60 n e c r e P 40 20 0 0 1 2 3 4 5 6 7 8 9 Periods After Shock Responses that Are Larger than Impact Response 100 No Adj Costs Inv Adj Cost 80 Plus Habit t 60 n e c r e P 40 20 0 1 2 3 4 5 6 7 8 9 Periods After Shock No Adj Costs: Standard flexible-price model with no investment adjustment costs or habit persistence. Inv Adj Costs: flexible-price model with CII-type investment adjustment costs (γ =0.01) Plus Habit flexible-price model with CII-type investment adjustment costs (γ =0.01) and with habit persistence coefficient (b =0.6) 44