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Technology-Hours Redux: Tax Changes and the Measurement of Technology Shocks

2011; University of Chicago Press; Volume: 7; Issue: 1 Linguagem: Inglês

10.1086/658303

2150-8372

Karel Mertens, Morten O. Ravn,

Economic Policies and Impacts

Previous articleNext article FreeTechnology-Hours Redux: Tax Changes and the Measurement of Technology ShocksKarel Mertens and Morten O. RavnKarel MertensCornell University Search for more articles by this author and Morten O. RavnUniversity College London and CEPR Search for more articles by this author PDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmailPrint SectionsMoreI. IntroductionThe last decade has witnessed a lively debate on the sources of business cycles. Galí (1999), Basu, Fernald, and Kimball (2006), and Francis and Ramey (2006) provide empirical evidence for U.S. data that positive technological innovations give rise to a drop in aggregate hours worked. This finding leads to the rejection of the hypothesis of technology-driven business cycles given the observed procyclicality of hours. However, the empirical results and their implications for business cycle theories have not remained unchallenged. Christiano, Eichenbaum, and Vigfusson (2004a, 2004b) cast doubt on Galí’s (1999) assumptions regarding the trend stationarity properties of hours worked and on the exogeneity of Basu et al.’s (2006) measure of technology. They show that assuming stationary hours and taking into account possible endogeneity of Basu et al.’s technology estimates overturns the finding of a drop in hours worked. Fernald (2007) and Francis and Ramey (2009) question their arguments for stationarity of hours and show that, once low-frequency movements are removed, hours worked again decrease after a positive technology shock. Fisher (2006) questions the validity of the identifying assumption that neutral technology shocks are the only source of fluctuations in the long-run level of labor productivity and argues that permanent investment-specific technology shocks also have permanent effects on labor productivity. He finds that when one allows for investment-specific technology changes, productivity shocks account for a significant share of the in-sample variance of output and that hours worked increase after a permanent increase in investment-specific technology shocks. However, Francis and Ramey (2009) show that these results depend on how one controls for demographic and sectoral shifts.In this paper we focus on the role of permanent income tax changes on the measurement of permanent technology shocks and their effects on the economy. The potential importance of controlling for tax changes was raised earlier by Uhlig (2004, 2006), who points out that changes in capital income tax rates may give rise to long-lasting changes in labor productivity, therefore invalidating the standard identifying assumption for technology shocks. His analysis shows in particular how persistent changes in dividend taxes can have persistent effects on labor productivity as well as hours worked. Nonetheless, his empirical analysis falls short of demonstrating directly that controlling for changes in taxes leads to radically different results. Moreover, Galí (2004) refutes Uhlig’s (2006) criticism of the identifying assumption on the grounds that there is little correlation between taxes and identified technology shocks. Francis and Ramey (2005) consider a specification that includes capital income tax rates and find that this does not alter the finding of a decrease in hours.We go one step further than Uhlig (2004, 2006) and demonstrate the empirical relevance of controlling for changes in taxes when estimating technology shocks and their effects. We begin by analyzing some of the consequences of permanent changes to income taxes in the context of a simple stochastic growth model. Permanent changes in income tax rates induce permanent changes in hours worked as well as in labor productivity. This leads to a violation of the standard long-run identification strategy for technology shocks and, importantly, also implies a common stochastic trend in hours worked and labor productivity. We argue on the basis of the simple theoretical model for a vector error correction model (VECM) specification of labor productivity, hours worked, and tax revenues as a way to correctly account for a tax-induced stochastic trend in the data.Our empirical analysis uses quarterly post–World War II U.S. time series. In addition to allowing for additional sources of nonstationarity, our empirical strategy requires identification assumptions to disentangle technology shocks from tax shocks. Our approach follows Mertens and Ravn (2009) and Romer and Romer (2010) and relies on Romer and Romer’s (2008) narrative account of historical U.S. legislated federal tax liability changes, a subset of which are argued to be exogenous to business cycle conditions. We first confirm that Romer and Romer’s (2008) tax shocks bring about significant permanent changes in labor productivity, output, and hours worked, which under the assumption of exogeneity of the tax shocks casts doubt on the key identification assumption for technology shocks. We then show that orthogonalizing the data to the narrative tax shocks unambiguously changes the sign of the hours response to a long-run identified productivity shock from negative to positive. Moreover, forecast error variance decompositions reveal that tax shocks as well as permanent productivity shocks are important contributors to business cycle fluctuations. These results are shown to be robust to adopting alternative measures of tax shocks and to distinguishing between anticipated and unanticipated tax changes.The finding that controlling for tax shocks changes the sign of the hours response is, however, sensitive to assumptions made about stochastic trends. It does not obtain in specifications that assume stationarity of hours worked (such as a vector autoregression [VAR] with hours in levels) or in specifications that do not take into account cointegration (such as a VAR with hours in differences). We generate artificial data from the theoretical model and show that, as the importance of permanent shocks to tax rates increases, specifications that do not control for taxes and/or make erroneous assumptions about underlying stochastic trends produce negative responses of hours to productivity shocks in finite samples. The VECM specification that controls for tax shocks instead produces accurate estimates on average regardless of the importance of changes in taxes.The remainder of the paper is organized as follows: Section II presents a simple real business cycle model with permanent tax shocks and discusses the implications for the time-series properties of output and hours worked. Section III presents the empirical analysis of U.S. time series. Section IV evaluates the small-sample performance of different estimators in simulations of a theoretical model. Finally, Section V presents conclusions.II. TheoryBefore turning to the empirical analysis, we start by introducing permanent exogenous changes in tax rates in a standard real business cycle (RBC) model. Our aim is to bring out three insights. The first is that, as pointed out by Uhlig (2004, 2006) and Francis and Ramey (2005), permanent changes in tax rates affect capital-labor ratios in the long run, therefore violating the long-run identification assumption for a technology shock in Galí (1999). Second, with permanent tax shocks, hours worked become nonstationary, which causes problems for empirical specifications that ignore low-frequency movements in labor supply that are due to changes in tax rates. Finally, we use the model as motivation for our empirical specification in Section III and as a data-generating process for simulations in Section IV.Households. Household preferences are given by where denotes the expectation of xt given all information available at date s ≤ t, 0 < β < 1 is the subjective discount factor, ψt > 0 is a taste shock that follows a stationary stochastic process with mean ψ, 1/κ ≥ 0 is the Frisch labor supply elasticity, ct denotes consumption in period t, and nt denotes hours worked. The household faces the flow budget constraints where kt is the household’s capital stock, ks is given, 0 < δ ≤ 1 is the depreciation rate, τt is the income tax rate, wt is the real wage, rt is the capital rental rate, and mt are lump-sum government transfers.Firms. Competitive firms produce output yt using a Cobb-Douglas technology where 0 < α < 1 is the elasticity of output with respect to the input of capital, and Xt denotes the level of labor-augmenting technology. Firms rent capital and labor from the households at given prices rt and wt , and firm profits in period t areTechnology evolves according to where γ ≥ 0 and is mean zero random variable.Government. The government is in charge of fiscal policy. The income tax rate is subject to random but permanent changes, that is, where is a mean zero random variable. We assume that the only source of government expenditures is lump-sum transfers mt that adjust to ensure a balanced budget: Equilibrium. A competitive equilibrium is a sequence of allocations and a price system such that, given initial condition ks and processes for ψt , Xs , and τt , (i) households maximize utility (1) subject to the budget constraints in (2), (ii) firms maximize profits (4) in every period, (iii) the government budget constraint in (7) is satisfied every period, and (iv) all markets clear.Equilibrium sequences are solutions to the following set of conditions: The log of labor productivity can be expressed as Equation (9) implies that a permanent increase in τt decreases the capital-output ratio and therefore labor productivity in the long run. In a deterministic setting, the capital-output ratio converges to which depends on the income tax rate τ. Thus, permanent technology shocks and permanent tax rate changes will both have effects on labor productivity in the long run. This invalidates the identifying assumption made by Galí (1999) that permanent neutral technology shocks are the only source of fluctuations in long-run labor productivity. Moreover, there are also long-run effects on hours worked through permanent changes in before- and after-tax wages and lifetime wealth. In a deterministic setting, hours worked converges to which depends negatively on the income tax rate τ. The recent literature has highlighted the importance of the stationarity properties of hours worked in estimating the effects of technology shocks. In practice, tax reforms are likely sources of low-frequency changes in labor supply. Accounting for tax changes in the data may therefore be important not only for correct identification but also for the choice of specification of empirical models. To see this more clearly, we proceed by deriving an approximate linear representation of the data that will motivate our empirical specification in the next section.Assume for now that there are no taste shocks, that is, ψt = ψ for all t. Define , , and . Equilibrium sequences are solutions to the following set of conditions: Consider a log-linear approximation of the equilibrium dynamics of the variables , , nt , and , τt by the linear system around a point , , n, (defined in app. A) and γ, τ, yielding decision rules of the form where hat variables denote log deviations of the point of approximation, the ϕ’s are scalar coefficients, and |ϕkk| < 1 . We wish to study the time-series properties of a trivariate vector of observables that includes the log growth rates of labor productivity Δln (yt/nt) , hours worked Δln (nt) , and government tax revenues Δln (Tt) ≡ Δln (τtyt) . In appendix B, we show that the decision rules in (16) and (17) yield the following moving average representation (we omit constants for brevity): where and L is the lag operator.This representation permits the Beveridge-Nelson decomposition where Equation (19) decomposes the time series into a sum of initial conditions (first two terms), a bivariate random walk component (third term), and a bivariate stationary process (last term). The matrix Ξ captures the long-run effects on the variables of the structural shocks. Since rank (Ξ) = 2 , it is clear that permanent shocks to taxes introduce a second stochastic trend in the data. As the first element in the second column of Ξ is generally not zero, permanent tax shocks affect labor productivity in the long run. As the second element of the second column in Ξ is in general not zero, permanent tax shocks also introduce a stochastic trend into hours worked. The latter implies that an appropriate empirical specification should allow for nonstationary hours. Given the focus on the role of taxes, it is compelling to include data on tax revenues, which in practice requires one additional shock to avoid stochastic singularity. We assume that this additional shock has no long-run impact on either labor productivity or hours worked. It therefore also does not affect tax revenues in the long run, as is the case for the stationary taste shock ψt in the theoretical model. In that case, the long-run impact matrix Ξ has deficient rank, and there is a cointegration relationship described by the null space of Ξ′ . A vector ζ is a cointegrating vector if Ξ′ζ = 0 . However, a vector stochastic process with cointegrating variables does not admit a pure VAR representation in first differences, which is why we will adopt a VECM. For the null space to be of the correct dimension one, we need to include variables in the system that ensure that rank (Ξ) = 2 . One reason why tax revenues are a good choice for the third variable in the specification is that the long-run impact on tax revenues of permanent tax changes is likely to have the opposite sign of the impact on the other variables.Discussion. The analysis above assumes that a tax change gives rise to a simultaneous change in both labor income and capital income tax rates. Alternatively, one might consider changes in only one of these two tax rates. In a simple model like the one studied above, permanent shocks to labor income taxes alone affect hours worked but leave labor productivity unchanged in the long run. Permanent changes in capital income taxes instead have effects similar to those that we derived above. The apparent differential impact of changes in labor income taxes and capital income taxes is not general and results from many simplifying assumptions. In settings with educational choices, human capital accumulation, or other sources of endogenous changes in labor productivity (such as learning by doing), permanent changes in labor income taxes can affect the long-run level of labor productivity through the impact on the incentive to accumulate skills. In particular, increases in labor income taxes lower the return on skills and therefore decrease measured labor productivity as long as skills are productive. Similarly, changes in labor income taxes can affect the retirement decisions of older workers, and this participation choice may in turn affect labor productivity if skills are accumulated over the life cycle.An alternative mechanism that can induce a link between labor income taxes and labor productivity is the government budget constraint. If the government adjusts capital income taxes to changes in the primary deficit to ensure long-run solvency (or, more extremely, to balance the budget period by period), then, for a given level of government spending, a cut in labor income taxes can lead to an increase in (future) capital income taxes, which affects the long-run level of labor productivity.1In summary, the model above highlights that permanent changes in taxes invalidate the standard identifying assumption for productivity shocks and induce a common stochastic trend in hours worked and labor productivity. While simple models suggest that only capital income taxes have long-run effects on labor productivity, in more general settings permanent changes in labor income tax rates can affect hours worked as well as labor productivity in the long run.III. Empirical AnalysisIn this section we estimate structural VARs and VECMs in which, using the insights from the previous section, we impose identifying assumptions and cointegration relationships that allow for the estimation of the impact of technology shocks while controlling for tax shocks. As a side product, this also allows us to estimate the impact of tax changes.The empirical analysis uses U.S. quarterly time series for the sample period 1948:Q1–2007:Q4 on labor productivity and hours worked from Francis and Ramey (2009). The Francis-Ramey time series on per capita hours worked (denoted by nt ) is obtained by dividing an average hourly worked estimate corrected for demographic changes by the civilian population aged 16 and above. We also use data on U.S. tax revenues from the Bureau of Economic Analysis.2 Figure 1 plots the time series used.Fig. 1. Time seriesView Large ImageDownload PowerPointOur approach to identifying tax changes makes use of the narrative account of U.S. federal tax liability changes provided by Romer and Romer (2008). We study only those tax changes that Romer and Romer classify as “exogenous due to long-term growth objectives” or exogenous due to “deficit concerns.” The former of these are tax changes that were introduced with no explicit concerns about the current state of the economy and the latter are tax changes introduced to address inherited budget deficits. The tax shocks are depicted in figure 2. This approach has the advantage that tax shocks can be treated as observable and therefore easily controlled for but rests crucially on the assumption that the tax liability changes identified by Romer and Romer can be assumed exogenous. Mertens and Ravn (2009) and Favero and Giavazzi (2010) test this assumption formally and show that it cannot be rejected.3Fig. 2. Romer and Romer’s (2008) tax shocksView Large ImageDownload PowerPointA. A Two-Dimensional VARAs a first step we replicate existing estimates of the impact of permanent productivity shocks using the conventional long-run restrictions without controlling for tax changes. We estimate the following bivariate VAR: where A(L) = I2 − A1L − ⋯ ApLp is a p-order lag polynomial and zt is the vector of observables that consists of the first difference of (the logarithm of) labor productivity, Δln (yt/nt) , and either the level or first difference of (the logarithm of) hours worked, that is, ln (nt) or Δln (nt) . The term ut is the vector of reduced-form errors.4 These are related to the structural shocks through the relationship where et denotes the vector of orthogonal structural shocks. We identify the technology shocks by imposing Galí’s (1999) identifying assumption that only technology shocks have a long-run impact on the level of labor productivity. Let Ξ = A(1)−1B denote the long-run total impact matrix and Σu the variance-covariance matrix of ut . Productivity shocks are identified through the restriction Figure 3a shows the estimated impulse response functions for p = 4 of labor productivity, output per capita, and hours worked to a one-standard-deviation productivity shock when we enter hours worked in differences for a forecast horizon of 10 years. The shaded areas show 68% and 95% confidence intervals computed with a nonparametric bootstrap. Figure 3b illustrates the impulse responses when the VAR includes the level of hours worked.Fig. 3. Productivity shock in a VAR with labor productivity and hoursView Large ImageDownload PowerPointThe results confirm the findings of Francis and Ramey (2009). Regardless of the stationarity assumptions made on hours worked, a permanent technology shock gives rise to a temporary drop in hours worked and output and labor productivity rise permanently. The two-dimensional specifications therefore cast doubt on the importance of technology shocks as a source of business cycle fluctuations.B. A Three-Dimensional VECM SpecificationWe now consider a slightly more general specification in which the vector of observables includes also tax revenues. We specify the empirical model as a VECM: where zt = [ln (yt/ nt), ln nt, ln Tt]′ , C(L) = C0 + C1L + ⋯ + CpLp is a p-order lag polynomial, α is a 3 × r loading matrix, β is a 3 × r cointegration vector, and the rank of αβ′ is equal to r (the cointegration rank). Formal tests of cointegration rank consistently reject the null of r = 0 , which would correspond to running a VAR with all variables in first differences.5 The tests proved inconclusive on whether r = 1 or r = 2 .6 Motivated by the discussion in the previous section, we impose one cointegrating relationship r = 1 , which means we allow for two shocks that have potentially permanent effects on all variables, including hours worked, and one shock that is restricted to have only transitory effects. As before we assume that ut is linked to the structural shocks et through (21). The long-run total impact matrix in the VECM is where it follows, owing to the cointegration restriction, that rank(Ξ) = 2 . In this equation α⊥ and β⊥ denote the orthogonal complements of α and β, respectively. The last column of this matrix, which corresponds to the impact of the transitory shock, is equal to the null vector. The productivity shock is again identified as the only shock with a long-run impact on the level of labor productivity. We estimate the VECM with p = 4 .The results are illustrated in figure 4. A positive permanent productivity shock gives rise to a permanent increase in output and in labor productivity. The shapes and size of these responses are very similar to those of the bivariate VARs in (20) when we entered hours worked in differences and not very different from the specification that entered hours worked in levels. As is the case in the VARs, hours worked fall in response to a productivity shock.7Fig. 4. Productivity shock in a VECM with labor productivity, hours, and tax revenuesView Large ImageDownload PowerPointWe believe, however,