Fiscal Policy Asymmetries

Transcription

1 Fiscal Policy Asymmetries Steven Fazzari James Morley Irina Panovska May 23, 2011 Abstract We investigate the eects of government spending and taxes on U.S. economic activity using a threshold version of a structural vector autoregressive model. Our empirical ndings support state-dependent eects of scal policy. In particular, the eects of government spending on output are signicantly larger and more persistent when the economy has a high degree of underutilized resources than when the economy is close to capacity. This evidence is consistent with an underlying structure of the economy in which insucient aggregate demand often constrains the level of economic activity. JEL Codes: C32, E32, E62 Keywords: Fiscal Policy, Threshold, Vector Autoregression, Nonlinear Models Preliminary draft Washington University in St. Louis University of New South Wales ; Washington University in St. Louis. Corresponding author: ipanovsk@wustl.edu 1

2 1 Introduction The Great Recession" and the concomitant American Recovery and Reinvestment Act (ARRA) scal stimulus package of more than $700 billion dollars has reignited interest, academic and otherwise, in the ecacy of scal policy. More broadly, these developments have raised questions about the relevance of aggregate demand and government spending as engines of economic activity. Many recent studies have sought to determine whether government spending has signicant eects on output and components of output, such as consumption and investment, as a way to address these questions. This debate is of central importance not only for economic policy, but also for the insights it provides on the underlying structure of modern developed economies. Theoretical models in which resources are fully employed predict that the direct eect of a positive shock to government spending, given preferences and technology, should completely crowd out private economic activity. The government spending multiplier arising from such models is zero, at least as a rst approximation. 1 In contrast, Keynesian models predict that the economy may not fully employ available resources, possibly for extended periods of time, because of insucient demand. If output is below its potential level due to insucient aggregate demand, an increase in government spending can motivate the employment of idle resources and raise output. Much of the recent empirical research on scal policy considers the eects of spending shocks on dierent components of output. On the one hand, a baseline neoclassical model predicts crowding out of both consumption and investment, and therefore implies negative responses of these variable to a positive shock to government spending. On the other hand, if government spending raises resources use through Keynesian channels, consumption and investment should respond positively to spending shocks. Indeed, these spillovers create the possibility that the government spending multiplier exceeds unity because higher government spending induces increases in other components of demand. Most of the existing empirical research on scal policy has been done in the context of linear time-series models in which the size of the response of output or other macro components to government spending is independent of the state of the economy (important recent exceptions include Mittnik and Semmler, 2009, and Auerbach and Gorodnichenko, 2010; see the following section). The results from such models are useful, especially if the maintained null hypothesis is the neoclassical baseline of zero eects on output and crowding out of consumption and investment. But the Keynesian alternative suggests an important nonlinearity in the eect of any demand shock, government spending in particular, on output. Higher demand eects cannot raise output indenitely. Eventually, resource constraints bind: even a Keynesian economy behaves like a neoclassical system if demand is suciently high. Threshold models provide a natural econo- 1 These models can generate indirect allocational eects of spending on output, but of ambiguous sign. For example, the higher interest rate induced by a rise in government spending could encourage intertemporal substitution in labor supply that raises output but also reduced capital accumulation that lowers output. 2

3 metric framework for exploring this basic asymmetry. If government spending shocks aect output through Keynesian demand channels, we expect such effects to be larger when the economy has a signicant resource slack than when it is operating at or near full capacity. The purpose of this paper, then, is to test this simple, but fundamentally important hypothesis. We estimate a nonlinear structural vector autoregressive (SVAR) models that allow for threshold eects. In our analysis, we consider several alternative measures of economic slack to dene the threshold. Various statistical and economic criteria identify capacity utilization (adjusted for structural breaks) as the best measure of slack, but the main results are robust to other choices for the threshold variable. The analysis also provides estimates of the values of the thresholds at which the dynamic eects of a government spending shock switch from a low-utilization regime with substantial slack in resource use to a regime with high resource utilization. Our results provide strong evidence in favor of nonlinearity; that is, government spending shocks have larger eects on output when they occur with relatively low resources utilization than when they appear at times of high resources use. Indeed, in our benchmark model, the estimated threshold for capacity utilization places a majority of observations in the low-utilization regime. The evidence implies, therefore, that the normal" state of the U.S. economy is a regime in which positive demand shocks have a signicantly positive and persistent eects on output and its components. We also employ generalized impulse response functions (GIRF) to isolate the dierent eects of scal policy under particular economic conditions. We nd that the responses of output and output components depend signicantly on the state of the economy when a policy shock occurs. For example, the responses of output to government spending are much larger during the Great Recession" than during the less severe 2001 recession. The rest of the paper is organized as follows. Section 2 reviews previous research that has estimated the aggregate eects of scal policy in a timeseries context. Section 3 introduces the baseline empirical model, the estimation method, and the test for linearity. Section 4 presents the empirical results obtained using the estimated model and extends the baseline model to models that include consumption, investment, components of investment, and interest rates. Section 5 concludes. 2 Related Literature The empirical literature that explores the eects of government spending on macroeconomic variables, both old and new, is divided in its ndings. Most papers fall in one of four main strands: models based on traditional Keynesian models, SVAR models, DSGE models, and models based on the narrative approach introduced by Ramey and Shapiro (1998). Traditional Keynesian models usually relate target variables such as output to dierent components of spending, typically with a reduced-form, linear spec- 3

4 ication. The interest rate is usually held xed close to zero over the whole forecasting horizon, and the multipliers obtained from those models are often very large (always greater than 1, sometimes as big as 4). In particular, the ARRA scal stimulus package was designed based on a study along these lines by Romer and Bernstein (2009) that estimated a short-run scal multiplier eect that was approximately equal to. Studies based on SVAR models in which government spending is assumed to be predetermined typically nd that output, consumption, and real wages increase after a positive government spending shock. Blanchard and Perotti (2002) and Perotti (2008) nd that the response of output and consumption to government spending is positive and persistent, although, somewhat surprisingly, they nd a negative response of investment. The magnitude of the estimated eects depends on the identication of the model. Blanchard and Perotti (2002) and Perotti (2008), use institutional information to identify the shocks, and they get multipliers that are about 1.3. Mountford and Uhlig (2005) use an alternative approach based on sign restrictions, and they get a small positive government spending multiplier (0.5) and a consumption multiplier that is very close to zero. These SVAR studies are sometimes criticized because they do not allow for state-dependent responses, an issue addressed here. Most DSGE studies are based on a New Keynesian model with Calvo pricing frictions and the model usually allows the interest rate to revert to the natural" interest rate determined by standard neoclassical rst-order conditions in the long run. Papa (2005) uses an RBC model with Calvo pricing and xed interest rates and she nds that output, real wages, and consumption rise, while investment falls, but the magnitude of the responses is very sensitive to the parameterization of the model. Cogan et al. (2009) employ the same model with interest rates that are xed for four quarters and nd an output multiplier that is only. Although Barro and Redlick (2010) use a simple linear regression model with annual data instead of a DSGE model, they nd that the impact multiplier of government spending is just 0.3, similar to the DSGE results. Notably, some DSGE models allow for asymmetric dierent responses to government spending shocks depending on the interest rate. In particular, some studies consider the importance of interest rate responses to scal policy by holding the interest rate pegged at zero for a certain period and then comparing the resulting impulse responses to when interest rates are not xed. Simulations based on these models tend to yield multipliers that are above 1 only when the interest rate is xed exogenously. When the interest rate is allowed to increase, the multiplier is well below unity. Another strand of the literature uses the narrative approach to identify exogenous government spending shocks. Ramey and Shapiro (1998), Eichenbaum et al. (1999), and Ramey (2010) show that when using the Ramey-Shapiro or the Ramey military spending variables as proxies for government spending, the estimated multiplier is small and the increase in consumption is very temporary. Ramey (2009) argues that the SVAR-based multipliers are large only because they fail to capture the importance of timing of government shocks and because the combined narrative data Granger-causes the government spending shocks. 4

5 However, Perotti (2007) shows that lagged government spending, tax, and GDP shocks also predict the Ramey-Shapiro narrative dates. Van Brusselen (2009) and Leigh et. al. (2010) provide a very extensive surveys of the empirical literature. Consistent with the summary above, they show that the estimated government spending multipliers are very sensitive to the choice of the parameters and to the selection of the model. Van Brusselen (2009) points out that even within the same class of models (i.e., DSGE models with Calvo pricing), the government multiplier can vary between -3.7 and 3.7, depending on how the increase in spending is nanced, how long is the interest rate pegged, and whether the economy is closed or open. Building on the existing literature, we adopt a nonlinear SVAR-based approach that allows the impact of shocks to depend on the level of resource utilization at the time of the shock. We do not impose any assumptions about the response of interest rates or about the degree of price or wage stickiness. Our approach nests the possibility of empirical results consistent with equilibrium models which predict to small or even negative responses of output and other macro variables to positive government spending shocks. But to the extent that the data identify Keynesian eects, our model allows these eects to vary with the state of the economy that prevails at the time of the shock; that is, we test whether positive responses are stronger when there is substantial slack in the economy. In particular, we employ a threshold SVAR model in which the system's dynamics change back and forth between low-utilization and a highutilization regimes. Our main goal is to examine if the eects of government spending and tax cuts are dierent when the economy has a lot of slack compared to times when the economy is close to capacity. The size and dierence in the multipliers across regimes is of fundamental interest and we also consider what the data tell us about the amount of time the economy spends in the dierent regimes. Our analysis is similar in spirit to recent papers by Auerbach and Gorodnichenko (2010) and Mittnik and Semmler (2009). Auerbach and Gorodnichenko (2010) estimate a smooth transition threshold SVAR model for government spending, taxes, and output, in which they impose the restrictions that government spending has dierent eects during recessions and expansions, and that the economy spends 20% of the time in recessions. They estimate that the eects of government spending are large and positive (1.7 over 20 quarters) when the economy is in a recession and smaller (very close to unity) when the economy is not in a recession. They control for the state of the business cycle by using a moving average of output growth as the switching variable, and they impose that the threshold around which the behavior changes is equal to the mean of output growth. Mittnik and Semmler (2009) estimate a bivariate threshold model for output and employment where the switching output is lagged output growth and threshold is predetermined and equal to the mean output growth. In their model, the responses of employment to output shocks are much larger in the low regime than in the high regime. Our paper diers from these papers because we do not impose that the economy behaves dierently during recessions and expansionswe estimate the threshold from the data without assuming it a 5

6 priori and by formally testing if the behavior changes across regimes. Also, we explicitly take into account capacity constraints by including a measure of slack in our baseline model. 3 Empirical Methods 3.1 Model Traditional vector autoregressive (VAR) models do not capture nonlinear dynamics such as regime switching and asymmetric responses to shocks. For our analysis, we consider a threshold version of a VAR model that extends the model proposed by Tong (1978,1983) to a multivariate setting. Threshold models work by splitting the time series process endogenously into dierent regimes. Within each regime the process is described by a linear model. Specically, we specify a threshold version of a reduced-form VAR model as follows: Y t = Φ Φ1 1 (L)Y t 1 + (Φ Φ 2 1 (L)Y t 1)I[q t d > γ] + ε t (1) where Y t is a vector containing the rst dierence of the logarithm of real government spending, the rst dierence of the logarithm of net taxes, the rst dierence of the logarithm of real GDP, and a measure of economic slack. The lag polynomial matrices Φ 1 1(L) and Φ 2 1(L) capture the dynamics of the system; ε t is independent Gaussian vector of disturbances with mean zero and covariance matrix equal to λω until 1984Q1 and equal to Ω afterwards (i.e., rather than assuming that the errors are strictly iid, we introduce a scaling parameter for the variance-covariance matrix that captures the Great Moderation). Because the focus of this paper is not on determining the exact break date in volatility and there is some consensus in the literature about the general timing of the volatility break (see, for example Kim and Nelson (1999) or Mc- Connell and Perez-Quiros(2000)), we set the break date exogenously. By using a scale factor λ and a constant variance-covariance matrix Ω, we are also assuming that the correlations between the endogenous variables do not change over time or over regimes. The switching variable q t d determines the prevailing regime; γ is the threshold parameter at which the regime switching occurs. The indicator function I[ ] equals 1 when the q t d exceeds the threshold γ and 0 when q t d < γ.the integer d is the delay lag for the threshold switch; that is, if the threshold variable q t d crosses γat time t d, the dynamics actually change at time d. 3.2 Data We consider several alternative denitions of the threshold variable q t d : capacity utilization, capacity utilization adjusted for structural breaks, the CBO output gap, the unemployment rate, the unemployment rate adjusted for structural breaks, and the change in the unemployment rate. The basic Keynesian 6

7 theory summarized above implies that the threshold variable should measure the level of economic activity and intensity of resource use. For this purpose, the output gap, the level of capacity utilization or the unemployment rate would seem to be the best choices. However, we also considered rst dierences, however, to check the robustness of the results and to explore whether threshold eects might relate to growth rather than levels. Government spending and net taxes are dened as in Blanchard and Perotti (2002). The full sample period considered is 1967Q1-2010Q4. All output components are measured in real terms and are seasonally adjusted by the source. The monthly capacity utilization series was converted to quarterly frequency using simple arithmetic means, and we used the last observation for the quarter to convert the interest rate on 10-year treasury constant maturity bonds to quarterly frequency. To get the real interest rate, we subtracted ination from the nominal interest rate. The series for output, its components, and government spending were obtained from NIPA-BEA, and the capacity utilization series was obtained from the Federal Reserve Statistical Releases website. The interest rate and CPI series were obtained from the Federal Reserve of St. Louis website. We use growth rates rather than log-levels in the VAR because the logarithms of real GDP and output components exhibit non-stationarity. Johansen cointegration tests suggest the absence of cointegrating relationship between government spending and taxes, and between output and output components (consumption, government spending, taxes, investment, and consumption). However, we obtained roughly similar results when we allowed spending and taxes to be cointegrated, and when we allowed output components to be cointegrated with output. 3.3 Specication Issues The lag length for the VAR model is chosen based on AIC (for the linear VAR model estimated using maximum likelihood). Both AIC and SIC select four lags. Unlike Mittnik and Semmler (2009), who allow the number of lags to dier across regimes, we assume that the number of lags is the same in each regime. Also, we only consider a model with two regimes. While it is certainly possible to extend the model given by Equation 1 to accommodate more than two regimes, it would make the computation using numerical methods very burdensome because of the large number of parameters that need to be estimated. In terms of the solving for the SVAR given the reduced-form VAR parameters, we consider short-run restrictions with government spending ordered rst and taxes ordered second in all models; i.e. government spending is assumed to respond to economic conditions only with a lag, but economic conditions are allowed to respond immediately to government spending. Changing the order of spending and taxes does not aect our results signicantly. Economic theory implies several possible choices for the threshold variable. Ricardian equivalence suggests that when the decit is high, the eects of government spending are negative because agents expect future increase in taxes. The DSGE models in the literature suggest that the eects of government spend- 7

8 ing depend on the interest rates, and Keynesian models suggest that the dynamics may depend on the state of the economy. Because we do not want to x the threshold variable a priori, we consider a large set of possible threshold variables and select the preferred threshold variable via maximum likelihood. The threshold variables that we consider are 1. output: lagged output growth, long output dierences, moving averages of output dierences 2 2. lagged CBO output gap 3. lagged capacity utilization: levels, and demeaned levels, rst dierences, and rst dierences of the demeaned series 4. lagged unemployment: level, dierence, demeaned level, dierences in the demeaned series 5. decits and debt to GDP ratio 6. interest rates and changes in interest rates Both capacity utilization and the unemployment rate appear to have some changes in their long-run mean levels, which would make those series unsuitable for use in a stationary VAR model. Standard tests rejected the null of no structural break in mean for both capacity utilization and the unemployment rate. Meanwhile, there is some debate about whether the unemployment rate has a unit root or whether there were just exogenous structural breaks in its mean. For unemployment, therefore, we consider the level, rst dierences, the mean-adjusted levels, and the dierences of the mean-adjusted levels as possible threshold variables. 3.4 Inference Because the threshold VAR model is highly parameterized, we estimate the threshold, the coecients, the threshold variable, and the delay parameter using Bayesian methods; in particular, we use a multi-block Metropolis-Hastings algorithm, described in detail in the appendix. The advantages of using a Bayesian approach in this framework are twofold. First, it allows us to capture the uncertainty about the parameter values when constructing the impulse response functions. Second, comparing the linear to the nonlinear model and examining the presence of nonlinear eects is straightforward in the Bayesian framework. A critical question is whether the eects of government spending really do dier across regimes dened by economic slack. In a frequentist setting, to test for the presence of nonlinear eects, we would want to test the null hypothesis H 0 : Φ 2 0 = Φ 2 1 = 0 that the coecients are equal against subsamples against 2 Since we were already estimating a large number of parameters, the weights for the moving averages were xed exogenously.we considered an arithmetic mean of the past 4 dierences, and q l,t d = 1 l l d+1 j=d threshold_var t j for l = 1, d = 4. 8

9 the alternative that at least one of the elements of the matrices Φ 2 0, Φ 2 1 is not 0. This testing problem is tainted by the diculty that the threshold γ is not identied under the null. However, if the errors are iid, a test with near-optimal power against alternatives distant from the null hypothesis is the sup LR test: where LR = sup{lr n (γ)} (2) γ Γ LR n (γ) = 2{ln L 1 (γ) ln L 0 } (3) is the likelihood ratio statistics against H 1 when γ is known,with ln L 0 and ln L 1 (γ) denoting the estimated values of the likelihood function under the null and under the alternative hypothesis for each γ. Because γ is not identied under the null, the asymptotic distribution of the test statistics is nonstandard. Hansen (1996, 1997) shows that the asymptotic distribution can be approximated by a bootstrap procedure. It should be noted, however, that the fact we assume the variance-covariance matrix of the residuals has a structural break in 1984Q1 makes it unclear how well Hansen's procedure will perform in our cas. The Bayesian approach circumvents such problems by providing a direct method for comparing models via posterior odds ratios. In particular, we estimate the threshold VAR model using the MH algorithm and then we compare its marginal likelihood to that for a restricted linear version of the VAR model, specied as follows: Y t = Φ Φ0 1(L)Y t 1 + ε t (4) To estimate the eects of shocks to spending and taxes, we calculate impulse response functions for output and output components. For the nonlinear model, we construct two sets of impulse responses. In one case, the economy is assumed to remain in a given state forever to come up with state-dependent responses. In the other case, the economy is allowed to evolve because the threshold variable itself responds to shocks in government spending and taxes. When the economy is assumed to remain in one state forever (or for a given time horizon), the system is linear within a state, so the impulse-response functions can be obtained by using the estimated VAR coecients for the given regime. Because the system is linear within regimes, there are no sign or size asymmetries, and the IRF does not depend on the initial state. When we allow the system to evolve and switch between regimes, the impulse response function depends on the initial state and possibly on the size and the sign of the shock. Following Koop, Pesaran and Potter (1996), we consider generalized impulse response functions (GIRFs) to obtain the responses when the threshold variable is allowed to respond endogenously. A GIRF is dene as the change in conditional expectation of Y t+k as a result of an exogenous shock ε t : 9

10 E[Y t+k Ψ t 1, ε t ] E[Y t+k Ψ t 1 ] (5) where Ψ t 1 is the information set at time t-1. Calculating the GIRFs requires specifying the nature of the shock ε t and the initial conditions Ψ t 1, and then the conditional expectations E[Y t+k Ψ t 1, ε t ] and E[Y t+k Ψ t 1 ] are computed by simulating the model. In practice, the GIRFs are computed as follows (a detailed version of the algorithm is presented in the appendix). First, shocks for periods 0 to q are simulated using the estimated variance-covariance matrix for the threshold SVAR model and, for given initial values of the variables, fed through the estimated model to produce a simulated data series. The result is a forecast of the variables conditional on initial values and a particular sequence of shocks. Next, the same procedure is repeated with the same initial values and residuals, except that the shock to government spending or taxes in period 0 is xed at 1% of GDP (for that particular starting value of GDP). The shocks are fed though the model and a forecast is produced just as above. The dierence between this forecast and the baseline model is the impulse-response function for a particular sequence of shocks and initial values. This computation is repeated for ve hundred draws of the residuals and averaged to produce impulse-response function conditional only on a particular history. These impulse response functions are then averaged over a particular subset of initial values. A potential problem with the standard approach to calculating GIRFs is that by assuming that the residuals are iid, they do not take into account possible heteroskedasticity. Because threshold models imply that the responses to depend on a particular history, we rst simulate the responses for the evolving model, averaging over all rapid expansions and averaging over all normal states and recessions. Then we compare those results to those obtained when we simulate the GIRF for the New Economy" rapid expansion in the late 1990s and for the Great Recession". To capture the uncertainty about the parameter values, the credibility intervals for the impulse response functions are obtained by simulating the GIRFs for all iterations of the MH algorithm. Because the model given by equation 1 has more than 140 parameters, estimates obtained using maximum likelihood are very likely to have large standard errors, making them unreliable for conducting inference and for constructing impulse response functions. To address weak identication, we consider Bayesian estimation. An advantage of the Bayesian approach is that the output from the MH algorithm provides us with a direct way to compare the threshold VAR model to the linear VAR model using posterior odds ratios. The estimation is conducted by means of a multiple-block Metropolis-Hastings within Gibbs algorithm with a random-walk chain proposal for the Metropolis- Hastings Step. To provide an accurate approximation of the target posterior distribution of the parameters, we follow the standard approach in the applied literature and we use a tailored multivariate Student t distribution as the proposal distribution. 10

11 In terms of priors, we consider a truncated normal distribution for Φ to ensure stationarity. Ω is inverse-wishart, λ is Gamma, and γ is uniform over [q l, q h ] where q l and q h are the highest and the lowest observed values of threshold variable. Conditional on the other parameters, the posterior distribution for Φ is normal, so it can be drawn using a Gibbs step. Similarly, the posterior distribution for Ω conditional on the other parameters is inverse-wishart, and the posterior for λ is Gamma, so we draw from the conditional posteriors using a Gibbs step. The conditional distribution for γ is nonstandard, and draws from the conditional posterior are obtained using a Metropolis-Hastings step. Following the standard literature, the proposal density is Student t with 15 degrees of freedom. To obtain the mode for the proposal distribution for the rst draw, we use concentrated maximum likelihood and grid search over the middle 70% of the switching variable in order to obtain the posterior mode of the parameter γ. Because ε t is assumed to be Gaussian, the ML estimators can be obtained by using least squares estimation. For this maximization γ is restricted to a bounded set Γ = [γ, γ] that covered the middle 70% of the threshold variable. The estimator θ = [Φ γ d] is obtained using the following procedure: Conditional on γ and the threshold variable, the model is linear in Φ and Ω. Estimating the linear model by splitting the sample into two subsamples yields the conditional estimators Φ and Ω. The estimated threshold value (conditional on the threshold variable and the delay lag) can be identied uniquely as γ = arg max γ Γ n llik n (γ q, d) (6) where Γ is approximated by a grid search on Γ n = Γ {q 1, q 2,..., q n }. To ensure identication, the bottom and top 15% quantiles of the threshold variable are trimmed. We use the estimated value γ for constructing the proposal for the rst draw of the MH algorithm. The grid search makes it infeasible to obtain the variance of the estimate of γ. To address this issue, we use the approach proposed by Lo and Morley (2011). In particular, we obtain a measure of the curvature of the posterior with respect to γ by inverting the likelihood ratio statistics for the threshold parameters, based on the assumption that the parameter estimate is normally distributed and the LR statistics is χ 2 (1). We use the 95% CI for the likelihood ratio statistics to obtain a corresponding standard error for γ.this approach is only an approximation, and it not asymptotically accurate for obtaining standard errors of the ML estimate for γ, but it is much faster than bootstrapping and inverting the LR test in order to obtain the scale for the rst draw of the MH algorithm. Since this approximation aects only the rst draw, it will not aect the estimates of the parameters if the burn-in is large enough, and it provides a much faster way of obtaining an approximation of the scale and the mode for the proposal density. To ensure that our results are robust to the choice of priors, we also repeat the estimation using dierent hyperparameters and functional forms for the 11

12 priors, including non-conjugate priors where all parameters are drawn via an MH step. We use a large burn-in sample of 20,000 draws and make inference based on an additional 50,000 MH iterations. The technical details of the MH algorithm can be found in the appendix. 4 Empirical Results We nd evidence for nonlinearity for all of the measures of slack under consideration. The preferred threshold variable for the baseline model, selected by the ML procedure, is the rst lag of the adjusted capacity utilization series and the estimated threshold was 2.1. The series and the estimated threshold are plotted in Figure 2 in the appendix. The high-utilization regime dates estimated with capacity utilization as the threshold variable largely coincide with the high-utilization regime dates found when using output gap as a measure of slack. Furthermore, the rst lag of adjusted capacity utilization is also the best threshold variable in all the models that included output components, with the estimated threshold from the baseline model included in the 95% condence intervals for all of the extended models. In order to compare the linear to the nonlinear model, we calculate the marginal likelihood for each model and we compared the linear to the nonlinear model using Chib and Jeliazkov's (2001) algorithm, placing equal prior probabilities of 0.5 on the linear and the nonlinear specications. The results strongly favor the nonlinear specication. When estimating the eects of government spending and tax cuts on output components and on interest rates, we substitute output with an alternative variable of interest in the baseline VAR. We also considered the eects of spending and tax cuts on output components by adding a fth variable to the baseline model. The point estimates for the threshold and the median impulse responses are very similar for both specications, but the 95% condence bands are very wide in the specication with ve variables because there are too few observations per regime to precisely estimate a threshold VAR with ve variables. The results presented below are obtained using the four-variable versions of the model. As with the baseline model, we estimate the threshold and compare the nonlinear specication to the linear specication for each individual output component, for interest rates, and for the unemployment rate. Table 1 reports the the estimated threshold levels, the posterior odds ratios, and the bootstrapped p-value for the LR test for all models. There is evidence of nonlinearity in all of the models that include output components and the unemployment rate, and the periods belonging to the low- and the high-utilization regimes are almost the same as those we obtained from the baseline model that includes output. There is also some evidence of nonlinearity in the models that included real interest rates, but the nonlinearity only aects the behavior of G and T. The response of interest rates constructed using ination was not signicantly dierent from 0 in the linear or in the nonlinear model. It should also be noted that the estimated 12

13 threshold values are very similar in all models. In the models that included output components, the estimated thresholds were very close to the estimated thresholds from the baseline model with aggregate output. Furthermore, the 95% CI for the estimated thresholds always include the estimated thresholds from the baseline model. 4.1 Responses of Output to a Government Spending Shock In the SVAR models, government spending is ordered rst. This imposes a timing restriction: output and output components can respond to G within a quarter, but government spending does not respond to Y within the same quarter. Changing the order government spending and taxes does not alter the results very much. When constructing the impulse response-functions to government spending, we assume that government spending increases by 1% of GDP, and when constructing the impulse-response functions to tax shocks, we assumed that taxes increase by 1% of GDP. Government spending and taxes are allowed to respond to their own shocks. Since the model is linear within regimes, the response to a tax cut equal to 1% of GDP is exactly equal in magnitude to the response to a tax increase equal to 1% of GDP. We obtain almost identical results using Blanchard and Perotti's (2002) identication scheme that imposes tax elasticities. To make the interpretation of the results more straightforward, we convert the responses to dollar-for-dollar responses in the levels of the variables. In order to convert the response of log level to log level to dollar-for-dollar responses, we use the ratio X t /G t where X is the variable of interest. In the given graphs, if the response of variable X t at quarter q is n, it means that the level of the variable in quarter q is n dollars higher compared to the level of the variable without a spending shock. The responses of output to spending shocks depended strongly on the initial state of the economy. The response in the linear model peaks at, which is only slightly lower than the maximal response obtained by Blanchard and Perotti. When the economy was assumed to stay in the lower regime, the response of output is always positive and large, but the exact magnitude varies depending on the timing of the spending shock. The median response when averaging over all histories peaked at after 4 quarters and then the eects of the spending shock die out. In comparison, the median when averaging over all high-utilization histories peaks at after 8 quarters, and then it remains stable. When averaging over recent histories that occurred after 1984, the results are slightly dierent. For example, during the rapid New Economy" boom the maximum response of output was, which is higher than the average for all high states. This may look surprising at rst sight, but the evolution of the capacity utilization series explains the larger multiplier since After 1984, capacity utilization spends less time in the high-regime states, and the economy reverts to the low-utilization regime faster. To ensure that these results were not due to removing the time-varying mean in capacity utilization, we compared our results with the results we obtained when using the output gap, lagged output 13

14 growth, or moving averages of output growth. The results were very similar regardless of the measure of slack we used. The median response of output during the Great Recession period peaks at 1.5, which is comparable to the response obtained when averaging over all low-utilization periods. It is important to note that the response of output is not only larger, but also much more persistent when the economy is initially in a low utilization state. When the economy starts in a high-utilization state, the eects of the shock die out (the total increase in the level of output becomes at) after about four quarters. When the economy starts from a low state, the response is still positive (the level is still increasing) two years after the shock. The combination of the asymmetric response of output to government spending shocks with the historical distribution of the estimated state of the economy across regimes leads to another key nding. The U.S. economy has spent most of its recent history in a state in which insucient aggregate demand is the binding constraint on the economy in the sense that a positive demand shock would cause a persistent increase in output at least equal to the size of the shock. Therefore, the normal" situation is the low-utilization regime. Boom periods when supply-side resource constraints bind appear to be the exception, not the rule. 4.2 Responses of Future Fiscal Policy to a Government Spending Shock The response of government spending to government spending shocks does not depend very strongly on the regime, although not allowing for the regimeswitching dynamics leads to very dierent results. In the linear model, G increases by 1 on impact (by construction), and it keeps increasing for 6 quarters. The total response in the level of spending is 2 after 6 quarters, which is similar to the total response (obtained by adding up the individual responses) obtained by Blanchard and Perotti (2002) and by Perotti (2007). The results we obtain from the asymmetric model indicate that failing to account for the regimeswitching dynamics leads to an overstatement of the persistence of spending shocks. The peak response when averaging over the high regime states was 1.3, and the peak response when averaging over the low regime state was 1.1. Furthermore, there was no strong evidence in favor of asymmetry of the response of spending to spending shocksthe median responses in both regimes were similar, and the credibility intervals overlapped, even when we looked at the 68% CIs. The responses of spending to spending across the two regimes show that the higher increase in output in the low state is not due to more persistent spending shocks in the low regime. It also shows that failing to account for the dierent responses in output and capacity utilization across regimes may lead to overestimating the persistence and magnitude of spending shocks. Tax revenues initially drop slightly after a positive government spending shock, then increase in both the high- and in the low-utilization regimes. When a spending shock occurs during the high-utilization regime, tax revenues drop by 0.1 on impact then rise to after 8 quarters and the response dies out 14

15 after 8 quarters. When the economy starts from a low-utilization regime, taxes drop on impact, then increase by 0.6 in the long run. It is important to note that those are the median responses, and while the median responses are dierent across regimes, the credibility intervals for the impulse responses overlap. Because the responses are similar in magnitude across regimes, and the bands overlap, the results do not suggest asymmetry in the responses of tax revenues to spending shocks. Again, as with government spending, the notable result is that the responses of taxes are uniformly smaller in both regimes than in the linear regime. Thus, ignoring the changing dynamics of the responses of output and capacity utilization leads would overestimate the response of tax revenues to government spending shocks. Note that the responses in the linear model are similar to those obtained by Blanchard and Perotti (2002): taxes initially decrease, then increase. The level response after 20 quarters is very similar to the level response obtained by Blanchard and Perotti (if we approximate the integral under the curve in Figure VIII in their paper to obtain the level responses). It is important to note that the increases are for tax revenues, not tax rates. Tax revenues are correlated with income, so part of the increase in revenues comes from increases in income and is essentially a self-nancing tax increase. Another part of the increase in revenues could come from the endogenous response of tax rates to a government spending shock. The use of tax revenues also makes it dicult to interpret the responses of output and output components to changes in taxes, because individuals and rms respond to marginal tax rates. Unfortunately, though, reliable data for marginal tax rates are only available at an annual frequency. 4.3 Responses of Consumption and Investment to a Government Spending Shock Gross consumption increases in both regimes, but the increase is larger when the economy is in the low-utilization regime. The response of consumption in the linear model peaks at after 4 quarters, and the long-run response after 5 years is. When the economy starts in a low regime, the response of consumption peaks at, but the response is much more persistent than the response obtained from the linear model. The long-run response levels o after 3 years at 0.75, with no signicant drop. Consumption is much less responsive to shocks in spending when the economy starts in a high-utilization regime. The peak response in this case is only 0.2. The responses of consumption of nondurables and services were very similar. During rapid expansions, the response peaks slightly below 0.18 after 10 quarters and then levels o, and during periods of slower growth, the response peaks at 0.9 after 10 quarters. A large part of the increase in output in the low regime is due to the increase in consumption Our results are consistent with the results obtained by Blanchard and Perotti (2002), Papa (2005), and Woodford (2010), because there is no evidence of consumption crowding out in either regime. Indeed, a rise in government 15

16 spending causes a positive and statistically signicant increase in consumption in both regimes. Accounting for anticipated government spending by including Ramey's military spending variable and ordering it rst in the linear or nonlinear versions of the SVAR did not change the median response or the signicance of the response in either case. Contrary to neoclassical predictions and to the results obtained by Blanchard and Perotti (2002), we nd that investment does not decrease signicantly in the long run in response to higher government spending. The median response of investment was weakly positive in both regimes, and there was no evidence of asymmetry across regimes. Again, not accounting for dierent dynamics between Y and the measure of slack leads to very dierent results. In the linear model, the median response of investment is indeed negative, as found by Blanchard and Perotti (2002), with a maximum drop of 0.7 after 4 quarters. However, the credibility intervals for the impulse response functions always included 0 if the CI was wider than 68%, and the results were robust to the choice of prior and to the measure of slack we used. Furthermore, even if the model is estimated via maximum likelihood and we construct asymptotic condence intervals, the response of investment is not signicantly dierent from zero. The results indicate that accounting for slack by explicitly including a measure of slack in the SVAR may explain the investment paradox" in Blanchard and Perotti (2002). 4.4 Responses of Other Variables to a Government Spending Shock The responses of exports are similar across regimes. Exports weakly decrease (median level response of - in the low regime, in the high regime) and imports weakly increase (0.34 in the high regime vs 0.25 in the low regime). The credibility intervals overlap, indicating that there is no strong evidence in favor of asymmetric responses of imports and exports to government spending. The increase in imports and the decrease in exports roughly cancel each other, regardless of the priors or the measure of slack we consider. The shape of the response of exports is virtually identical, both in shape and in magnitude, to the response obtained by Blanchard and Perotti (2002). Even though the CIs include zero, the median increase in imports is still somewhat puzzling, until one takes into account the importance of initial conditions and looks at the response of imports averaged over dierent histories. The average response of imports to spending before 1984 (or even for the period ) is weakly negative. The average response after 1984 is positive, and the median response is even higher after Taking into account that the ratio of (G/IM) fell from the 1967Q1-1983Q4 average of 2.98 to 9 during the Great Recession, the median dollar-for-dollar responses are not surprising. The responses of capacity utilization is very dierent across regimes. When the economy starts in the low-utilization regime, the impact response is 0.22%, and the total eect on the level of capacity utilization after ve years is %. When the economy starts in the high-utilization regime, the impact response is 16

17 0.13% and the total eect on the level of capacity utilization after ve years is 0.56%. When the system is allowed to evolve, the eects on capacity utilization are similar to the eects obtained in the xed low-utilization regime, since the normal" state of the economy in our model is one of low utilization. The unemployment rate decreases in response to a spending shock, both in the linear model and in the nonlinear model. In the linear model, the unemployment rate decreases by 0.15 percentage points on impact and by 0.3 percentage points after ve years. While the long-run responses from the linear model and the response from the low-utilization regime are similar, the short-run response is much stronger in the low-utilization regime. In the low-utilization regime, the unemployment rate decreases by 0.16 percentage points on impact, and by 0.7 percentage points after six quarters. The eect of spending on the unemployment rate is much weaker and much less persistent when the economy is in the high-utilization regime. The impact response is 0, the maximum response is percentage points after four quarters, and the long-run eect after 5 years is -0.2 percentage points. It is important to note that spending decreases the unemployment rate in both regimes, but the eects are much larger when the economy starts from a low-utilization state. 4.5 Responses to a Tax Shock Output decreases in response to an increase in tax revenues. The maximal decrease in output is -1.1 after six quarters, which is comparable to the estimates obtained by Romer and Romer (2009). Tax revenues increase by 1 in response to their own shock, then the response dies out quickly because of the decline in output, and the net increase after ve years is 0.5. Government spending increases weakly in response to a tax increase, but the response is never signicant. As mentioned in the above, we are using tax revenues, so interpreting the results is to tax shocks is dicult, given that output and output components should respond to tax rates rather than to tax revenues. Because of this diculty, we do not examine if there are signicant asymmetries in the responses to tax shocks at this point, and we hope to explore this topic in future research. 4.6 Counterfactual Analysis One of the main criticisms of the ARRA is that output growth remained anemic two years after the scal stimulus and that the unemployment rate remained high. However, in order to fully evaluate whether the stimulus had any eect on the economy, one has to compare what output and unemployment would have been if there had been no scal stimulus. Taking into account that in the months before the stimulus package was implemented interest rates were already approaching the zero bound, and that employment was dropping precipitously, not implementing some form of scal stimulus could have led to output growth being even lower, and unemployment rising even higher than the peak In order to evaluate the eects of the stimulus, we perform counterfactual analysis for the period and compare the path of output and employment without 17