Silviase/jgov_v1.4_full_ann huggingface dataset:
et al. (2008) and Sugo and Ueda (2008), I largely follow these studies in choosing prior distributions and in fixing several parameters that are difficult to identify. Specifically, I set the capital share $ \alpha = 0.3 $ , the discount rate $ \beta = 0.99 $ , the depreciation rate $ \delta = 0.06 $ , and the wage markup $ \lambda_{w} = 0.5 $ . As for the steady state values, I take sample period averages except for the capital-output ratio and debt-to-output ratio, which are set $ \bar{K}/\bar{Y} = 2.2 $ and $ \bar{B}/\bar{P}\bar{Y} = 0.6 $ , following Iiboshi et al. (2008) and Broda and Weinstein (2004) respectively. I set the steady state consumption-to-output ratio $ \bar{C}/\bar{Y} = 0.56 $ and assume $ \bar{C}^{R}/\bar{Y} = \bar{C}^{NR}/\bar{Y} = \bar{C}/\bar{Y} $ . The steady state values for government spending-to-output ratio, and consumption, labor and capital income tax rates are set $ \bar{G}/\bar{Y} = 0.16 $ , $ \bar{\tau}^{c} = 0.08 $ , $ \bar{\tau}^{d} = 0.32 $ , and $ \bar{\tau}^{k} = 0.61 $ , respectively. Note that I utilize the discarded data series mentioned above for the calculation of $ \bar{\tau}^{k} $ . Other steady state values, $ \bar{L}/\bar{Y} $ , $ \bar{w} $ , $ \bar{r}^{k} $ , and $ \overline{mc} $ are all set to be consistent with the steady state conditions implied by the model.

### 3.2 Estimation Results

In conducting Bayesian MCMC estimation, I use the DYNARE software for MATLAB. The draws from the posterior distribution have been obtained by taking two parallel chains of 1,000,000 replications for Metropolis-Hastings algorithm. Tables 1-2 report prior distributions, posterior means, and 90% credible intervals (or Bayesian confidence intervals) of the parameters. Prior and posterior distributions are also shown in Figures 1-5. Most parameters are well identified, but some are not. It should be noted that parameters related to investment show poor identifiability. For that reason, I choose to calibrate the parameter for the elasticity of investment on the price of capital adjustment cost $ \varsigma\equiv1/\bar{S}^{\prime\prime} $ to the posterior mean estimate of Sugo and Ueda (2008). Nonetheless, the persistence parameter of the shock to investment cost function could not be identified.

Tables 3-4 compare the estimated mean parameter values with those of previous DSGE studies: Smets and Wouters (2003) (SW), Coenen and Straub (2005) (CS), and FMS for the euro area, Levin et al. (2006) (LOWW) for the United States, and Iiboshi et al. (2008) (INW) and Sugo and Ueda (2008) (SU) for Japan. Studies listed here except FMS are all variants of the Smets and Wouters (2003) model. Although FMS employ adjustment cost functions for sticky price and wage mechanism, FMS's other features, such as real rigidities, shocks, and functional forms share much in common with these studies listed here.

Overall, the values of posterior mean estimates are not so different from those reported in previous studies. From the viewpoint of fiscal policy effectiveness, structural parameters for non-Ricardian share,
price and wage stickiness, habit persistency, and labor supply elasticity are of particular interest. Although there has been no other study that estimates non-Ricardian share in a DSGE framework for the Japanese economy, the estimated mean value of non-Ricardian share 0.25 is very much consistent with the Kalman filter estimates of Hatano (2004). Compared with other DSGE-based estimates for the euro area and the U.S. on the other hand, the value is somewhat smaller $ ^{13} $ . The Calvo parameter for wage stickiness is considerably higher, while that for price is considerably lower than the estimates of INW and SU. However, they are largely in line with the results of Koga and Nishizaki (2005). They estimate Japanese Calvo parameters for wage and price are in the range of 0.7-0.75 and 0.5-0.55 respectively $ ^{14} $ , based on the method of Galí and Gertler (1999). Parameter values for habit persistency and labor supply elasticity are in between INW and SU. All in all, posterior means of structural parameters do not suggest large fiscal multipliers in this economy.

Turning to the policy parameters, the estimated response of monetary policy to inflation is weak while that to output gap is strong compared with those of INW. This may reflect the difference in the sample periods. The estimation period of INW is 1970:Q1 to 1998:Q4, while that is 1980:Q1 to 1998:Q4 in this paper. In fact, a recent study by Ichiue et al. (2008) employs the same formulation of monetary policy and reports a set of estimated mean parameter values $ \rho_{r}=0.85 $ , $ \phi_{r\pi}=1.49 $ , and $ \phi_{ry}=0.16 $ for a sample period 1981:Q1 to 1995:Q4 $ ^{15} $ , which are close to my estimates. Regarding fiscal policy, it is indicated that government spending was neither countercyclical nor procyclical during the estimation period. Although posterior mean estimates of tax rule parameters that govern their responses to debt-to-output ratio are all positive, those of consumption and labor income tax rules are not reliably different from zero. The results suggest that capital income taxation played a central role in stabilizing the government debt in Japan during the estimation period. This is not hardly surprising, considering that the debt-to-output ratio and corporate income tax rate show largely correlated movements throughout the 1980s in Japan. Both have increased in the first half of 80s and have decreased in the second half $ ^{16} $ , while the individual
income tax burden has increased in the 80s and has decreased in the 90s, and the indirect tax burden has largely been stable over the period. One more thing to be noted is that the estimated persistence parameters are all substantially smaller than those of FMS. This may be attributable to the difference in data sources used for the tax rate calculation, since only quarterly series are used in this paper, while FMS use some annual series and transform them into quarterly.

## 4 Assessing the Role of Tax Policy Rules

In this section, I first illustrate basic properties of the estimated model after a government spending shock. I then proceed to examine attributes of fiscal policy effectiveness with particular emphasis on exploring the role of tax feedback rules. To facilitate the assessment, I specify alternative tax rule combinations and conduct some simulations employing them in the estimated model. In the following analysis, all the parameters are calibrated to the estimated means of the posterior distributions for the parameters unless otherwise noted.

### 4.1 Responses to a Government Spending Shock

#### 4.1.1 Impulse responses

Figures 6-7 depict selected dynamic responses to a government spending shock equal to one standard error under the estimated parameterization. All dynamic responses are shown as percentage deviations from steady state. Along with previous DSGE studies on fiscal policy effectiveness, I mainly focus on the initial responses to a government spending shock. As seen in the upper middle panel of Figure 6, the model successfully delivers the crowding-in effect on consumption. This is somewhat surprising since none of the estimated values of key structural parameters for fiscal policy effectiveness, such as non-Ricardian share, price and wage stickiness, habit persistency, and labor supply elasticity show significance to generate the crowding-in effect. In particular, the estimated share of non-Ricardian households in Japan seems to be too small to predict the crowding-in effect according to previous studies (e.g., see Coenen and Straub (2005) $ ^{17} $ ).

Investment, which typically responds negatively to a government spending shock in a New Keynesian ___ raised in 1981 and 1984, and reduced in 1987, 1989, and 1990.
DSGE setting, also shows positive responses in initial periods. The initial responses probably reflect a relatively moderate increase in interest rates and a strong increase in labor. Recall that an increase in labor supply induced by the negative wealth effect on leisure shifts up the marginal product schedule for capital and hence increases investment in neoclassical models, while a sharp rise in interest rates drags down investment in DSGE models (e.g., see Baxter and King (1993) and Linnemann and Schabert (2003)).

As can be seen in the lower left panel of Figure 6, real wages decline after a government spending shock. This contrasts sharply with the results of Galí et al. (2007), in which a positive consumption response is obtained through a large wage increase. The high wage stickiness and distortionary taxation of the model may explain this. In general, real wage response after a government spending shock is rather complicated both theoretically and empirically. It has been known that real wages decline after a government spending shock to meet the labor supply increase in basic neoclassical models. Recent studies on DSGE models find that both price stickiness and inclusion of non-Ricardian households induce a real wage increase after a government spending shock, whereas wage stickiness and distortionary taxation reduce the wage increase $ ^{18} $ . The eventual reaction of the real wage is the sum of these effects. Turning to empirical studies, the response of real wage is also ambiguous as Fatás and Mihov (2001) and Blanchard and Perotti (2002) support a limited positive response while Burnside et al. (2004) support a negative response.

An increase in government spending is to be financed either through debt or through taxes, and the debt repayment needs to be financed by a split among consumption, labor and capital income taxes eventually. The upper left panel of Figure 7 confirms that fiscal solvency is guaranteed in the estimated model, although it is indicated that the debt stabilization takes a rather long time. The other three panels of Figure 7 show that three taxes all contribute to the stabilization $ ^{19} $ and that a capital income tax plays a central role.

The tax responses to a government spending increase in turn affect the households' decisions and accordingly the time paths of economic variables. Therefore it is also important to see the effects of a tax increase to understand the consequences after a government spending shock. Figures 8-10 portray $ {}^{18} $ See Linnemann and Schabert (2003), Bilbiie and Straub (2004), Colciago (2007), Galí et al. (2007), and Furlanetto (2007).
the dynamic responses to tax increases of which each equals to one standard error. As can be seen in the figures, response patterns to consumption and labor income tax shocks are largely the same. By contrast, initial responses of real wages and labor hours to a capital income tax shock exhibit particular differences with those to consumption and labor income tax shocks. It also should be noted that investment shows a large decline following a capital income tax shock.

#### 4.1.2 Fiscal multipliers

To evaluate the quantitative effects of a government spending shock, I go on to examine the traditional fiscal multipliers. Table 5 compares fiscal multipliers $ ^{20} $ of the model with those of other DSGE models of which multipliers are available; FMS, the ECB's NAWM (cf. Straub and Tchakarov (2007) $ ^{21} $ ), and the QUEST III of the European Commission (cf. Ratto et al. (2009)). Since this is the first attempt to estimate a medium-scale DSGE model of the Japanese economy with a detailed role of fiscal policy, the multipliers of the Japanese government's traditional large-scale econometric model (the ESRI model, hereafter) are also reported as reference $ ^{22} $ .

Table 5 shows that the output multiplier in the first period is larger than those of other DSGE models for the euro area, reflecting the strong increase in investment and successfully crowded-in consumption. Furthermore, the yearly averages of the multipliers are not so different from those of the ESRI model, regardless of DSGE model structure. In later periods, however, the model exhibits large decreases in consumption, investment, and, hence, in output. One possible attribute of the large swings is the allocative effect examined by Trostel (1993). If government spending is debt-financed initially, the debt repayment needs to be financed by taxes in later periods and a large decline occurs subsequently. The timing of taxation is determined by the tax rule coefficients of the model. As we have seen in the previous subsection, debt stabilization takes a rather long time, and the estimated tax rule combination resorts its main financing source to a capital income tax. Naturally, the decline in later periods is significant.
in investment. Another possible explanation is that the negative effects of taxation is large because the model considers only distortionary taxes. Burnside et al. (2004) study dynamic responses to a government spending shock in a neoclassical model without debt under two different tax schemes, in which all taxes are either lump-sum or distortionary. Their calibration exercise shows that labor hour increases are less persistent and that investment declines in later periods are larger under a distortionary tax scheme. Recall that distortionary taxation reduces the households' incentives to work and invest, and creates a larger negative effect on output after a government spending shock compared with lump-sum taxation.

### 4.2 Policy Experiments

#### 4.2.1 Properties of the estimated tax rules

To examine the role of tax rules in fiscal policy effectiveness, I consider the sensitivity of fiscal multipliers to changes in tax policy parameters. I begin by comparing the simulation results under the estimated tax policy parameters with those under parameters that replicate tax rules estimated in FMS. Fixing the persistence parameters, I adjust the policy parameters $ \phi_{tcb} $ , $ \phi_{tdb} $ , and $ \phi_{tkb} $ of each tax rule so that the coefficients on debt-to-output ratio become equal to those of FMS estimates for the euro area $ ^{23} $ . The adjusted policy parameters and the coefficients are reported in Table 6 with those of my estimates and of FMS's original estimates. The coefficients suggest that debt in Japan is mainly financed through capital income taxation while its finance in the euro area is allocated nearly evenly across three taxes.

Figure 11 illustrates the dynamic responses of output to a government spending shock equal to a one percent of steady state output under the estimated tax rules (referred to as baseline specification, solid line) and those under the adjusted tax rules (referred to as FMS specification, dotted line). The dynamic responses are depicted as percentage deviations from steady state, and hence correspond to the fiscal multipliers examined in the previous subsection. The multipliers of baseline specification are larger in initial periods than those of FMS specification, while showing more declines in later periods. Figure 12 reveals that the greater multipliers of baseline specification in initial periods can be attributable both to dynamic responses of consumption and to those of investment, which are also depicted as percentage deviations from steady state. A closer look at the patterns of output, consumption, and investment responses indicates that investment serves as a major driving force for the stronger output response of
baseline specification. Furthermore, investment seems to start recovering first and consumption seems to follow. Indeed, consumption of Ricardian households, which are by definition asset holders, supports this view, showing a similar pattern to investment as can be seen in Figure 13. The smaller decline in investment under FMS specification in later periods is probably due to its relatively weak responsiveness of a capital income tax to a debt-to-output ratio compared with baseline specification.

Before turning to further analysis on tax rule combination, it is worth addressing briefly the role of the estimated monetary policy since it generally plays a decisive role in responses after a government shock by reducing both investment and Ricardian consumption (See Linnemann and Schabert (2003) and Cogan et al. (2009)). For that purpose, I consider a reference case in which more anti-inflationary monetary policy is employed by setting $ \phi_{r\pi}=1.7 $ (referred to as anti-inflationary monetary policy case), which seems to be a kind of consensus value for the euro area (cf. SW, CS, and FMS). Figure 13 shows that the initial decline of Ricardian consumption in the anti-inflationary monetary policy case (dash-dotted line) is bigger than that of baseline specification as expected, but it is smaller than that of FMS specification. Given that FMS specification allocates its financing source nearly evenly among three taxes, the results suggest that the rather greater fiscal multipliers of the estimated model owe much to its tax rule combination, which resorts its main financing source to capital income taxation.

I close this subsection by making some general remarks on the role of tax rules after a government spending shock. An increase in government spending needs to be financed through taxation in the end whether or not it is partially (or all) debt-financed for some time. The size of a coefficient on a debt-to-output ratio of a tax rule determines the timing of the taxation and accordingly affects the time paths of economic variables such as output, consumption, and investment after a government spending shock. Even more importantly, when analyzing an economy with multiple distortionary taxes, the relative size of the coefficient compared with those of other tax rules also affects the time paths, since different distortionary taxes differ in their disincentive effects on the households' decisions. Thus, both absolute and relative sizes of the coefficients are important to investigate the role of different tax rule combinations in fiscal policy effectiveness. To make this point clear, I consider a case in which responsiveness of each tax rule to a debt-to-output ratio is equally strong $ \left(\phi_{tcb} = \phi_{tdb} = \phi_{tkb} = 0.2\right) $ , referred to as specification 1 (SP1), keeping the values of the estimated persistence parameters. The coefficients of specification 1 indicate that consumption, labor and capital income are all taxed more heavily than in the case of baseline and FMS specification for a given debt-to-output ratio. However, Figure 13 shows that the initial decline
of Ricardian consumption after a government spending shock in specification 1 (dashed line) is smaller than that in FMS specification. It follows that the difference between fiscal multipliers under baseline and those under FMS specification cannot be explained only by absolute sizes of the coefficients. Therefore we will examine next how responses to a government spending shock differ by changing the relative degrees of responsiveness to the debt-to-output ratio across the tax rules.

#### 4.2.2 Illustrative simulations under alternative tax rule combinations

We now move to an exploration of the role of tax rule combination, with an emphasis on the relative size of coefficients on the responsiveness to the debt-to-output ratio. To this end, I consider three alternative specifications, which employ different parameter values that govern the responsiveness, referring to them as specification 2 (SP2), specification 3 (SP3), and specification 4 (SP4). Each resorts its main financing source to a consumption tax $ \left(\phi_{tcb}=0.2,\phi_{tdb}=\phi_{tkb}=0.01\right) $ , a labor income tax $ \left(\phi_{tdb}=0.2,\phi_{tcb}=\phi_{tkb}=0.01\right) $ , and a capital income tax $ \left(\phi_{tkb}=0.2,\phi_{tcb}=\phi_{tdb}=0.01\right) $ , respectively. The policy parameters and corresponding coefficients are reported again in Table 6. Figures 14-15 portray investment and Ricardian consumption responses to a government spending shock under these specifications with those under specification 1 (solid line). The responses under specification 4 (dash-dotted line), which resorts its main financing source to capital income taxation, show similar patterns to those under baseline specification as expected, while those under specification 2 (dotted line) and specification 3 (dashed line) show similar patterns to those under FMS specification. As in the case of baseline specification, investment rises initially after a government spending shock and shows a large decline in later periods under specification 4. Again, a similar pattern of Ricardian consumption is also observed.

What is the economic rationale behind these patterns? Recall that the initial output increase after a government spending shock in a general equilibrium model is brought about by a labor hour increase and following an investment rise. An increase in government spending needs to be financed by a corresponding increase in taxation; it is inevitable to have the negative wealth effect, which decreases consumption and the leisure of Ricardian households. The decrease in leisure is the flipside of the labor hour increase. The labor hour increase induces capital accumulation to rise since it has a positive impact on the marginal product of capital, making investment more attractive. These are the basic mechanisms discussed in Aiyagari et al. (1992) and Baxter and King (1993). Beyond this, the model we have studied here considers three distortionary taxes, and each affects the households' decisions in different ways. Therefore, in the