Silviase/jgov_v1.4_full_ann huggingface dataset:
respectively. It should be noted that the Taylor coefficient on inflation, $ \phi_{\Pi} $ , is transformed into $ \phi_{\Pi,0}(>0) $ which satisfies $ \phi_{\Pi}=1+\phi_{\Pi,0} $ to ensure the Taylor principle (equivalently, to avoid the indeterminacy problem).

Posterior distributions of structural parameters are estimated via Markov chain Monte Carlo (MCMC) method. We sample four separate chains for 52,000 replicates each, discarding the first 2,000 replicates. Thus, posterior means of parameters are calculated by 200,000 replicates.

## 4 Estimation Results

This section presents estimation results. First of all, we report posterior means of structural parameters. Then, we show impulse response functions (hereafter, IRFs), focusing on four structural shocks. Finally, we provide historical decompositions on output, inflation and unemployment.

### 4.1 Estimated Parameters

Table 5 reports posterior distributions of structural parameters. We can confirm convergence on all of the estimated parameters from the CI (convergence inference) proposed by Gelman and Rubin (1992). $ ^{*7} $ The average acceptance rate across four chains is about 39%.

First of all, we take notice of estimated parameters on EC and PPC. The posterior mean of $ \nu_{g} $ is estimated to a negative value $ (-0.023) $ , which implies that government consumption is a compliment to private consumption. The magnitude, however, is so small and EC is still ambiguous since the 90% credible interval includes zero. $ ^{*8} $ The posterior means of $ \alpha_{g} $ and $ \alpha $ are 0.155 and 0.386, respectively. This result implies the marginal productivity of public capital $ (\alpha \times \alpha_{g}) $ is calculated as about $ 0.06.^{*9} $

We now turn to the estimation results of parameters on fiscal policy rules. On parameters of the spending reversal rules, $ \phi_{g,c} $ and $ \phi_{g,i} $ are estimated as 0.289 and 0.496, respectively. On persistency parameters, $ \rho_{g,c} $ and $ \rho_{g,i} $ are 0.970 and 0.958, respectively. It should be pointed out that one government spending is partly canceled out by the reduction of the other spending due to debt accumulation. However, the canceling out effect is negligibly small, since estimation results imply that 1% increase of deficit reduces only by 0.0087% on government consumption and by 0.0197% on government investment.

Regarding monetary policy rule, the Taylor coefficient on inflation, $ \phi_{\Pi} $ , is 1.532 (from $ \phi_{\Pi,0}=0.532 $ ) and the Taylor coefficient on output, $ \phi_{y} $ , is 0.035. The interest rate smoothing parameter, $ \rho_{R} $ , is estimated by 0.507.

Finally, parameters on nominal rigidities, $ \xi_{p} $ and $ \xi_{w} $ , are estimated as 0.560 and 0.489, respectively. These results indicate average durations to remain the same price and wage are about 2.27 quarters on price and about 1.95 quarters on wage.
### 4.2 IRFs

Figures 4-1 (a)-(d) depict IRFs for government investment shock, government consumption shock, monetary policy shock, and neutral technology shock. All of IRFs are responses against a 1% shock and calculated by using posterior means of parameters.

#### 4.2.1 IRFs for government investment shock

First of all, we take notice of the IRFs for a 1% increase of government investment depicted in Figure 3 (a). The blue line corresponds to the case with PPC, i.e. when $ \alpha_{g}=0.155 $ , and the red line corresponds to the case without PPC, i.e. when $ \alpha_{g}=0 $ . A positive government investment shock with PPC leads to a relatively lower inflation rate since public capital accumulation gradually reduces real marginal cost. According to our result, the inflation rate on the blue line falls below the red line after eight quarters. Relatively lower inflation loosens monetary tightening policy (after 12 quarters), which delivers relatively higher consumption and investment (after 15 quarters). After all, a positive government investment shock persistently enhances output in the case with PPC.

However, there are no differences between two cases on effects of government investment for unemployment: In both cases, 1% stimulus arising from government investment brings an improvement of unemployment by 0.06%. Relatively lower inflation through the increase of productivity causes real wage to be relatively higher in the case with PPC than in the case without PPC. The higher real wage, however, partly hurts employment: The increase in labor demand from higher output is cancelled out by the decrease in employment from higher real wage.

#### 4.2.2 IRFs for government consumption shock

Next, we consider the effect of government consumption. Figure 4-1 (b) reports IRFs for a 1% increase in government consumption. The blue line corresponds to the case with EC, i.e. $ \nu_{g} = -0.023 $ , and the red line corresponds to the case without EC, i.e. $ \nu_{g} = 0 $ . In the case with EC, an increase of government consumption directly boosts private consumption (the crowd-in effect), whereas the crowd-out effect also appears in both cases since the fiscal stimulus causes inflation, which leads to an increase in real interest rate through the monetary tightening policy. Our results indicate the latter effect completely dominates the former one. Since the magnitude of $ \nu_{g} $ is so small, almost all of the same responses are shown among both cases. As a result, we can see a 1% increase of government consumption reduces unemployment by 0.18% in both cases.

After all, we can see that fiscal stimuli improve unemployment, but almost all of contributions are explained by the creation of aggregate demand. The channels of non-wasteful government spending play little role in improvement of unemployment.
#### 4.2.3 IRFs for monetary policy shock

Figures 4-1 (a) and (b) indicate that both fiscal stimuli can be regarded as demand shocks since these shocks generate a cyclical comovement of output with inflation. The monetary authority is assumed to raise inevitably nominal interest rate against inflation caused by fiscal stimuli, which worsens unemployment through the crowd-out effect. So we turn to the effect of monetary policy. Figure 4-1 (c) shows IRFs for 1% monetary easing policy: IRFs are responses against unanticipated 1% reduction in short-term nominal interest rate. Unemployment is improved by 0.15% by the reduction of 100 basis points of nominal interest rate. This result might suggest that policy coordination matters in evaluating the effects of fiscal stimuli on unemployment. Again, it should be noted that zero interest rate periods are included during our estimation periods. Since the crowding out effect will become smaller under policy coordination between fiscal expansions and zero-interest-rate policy, we will discuss the robustness of our estimation results in section 4.4.

#### 4.2.4 IRFs for neutral technology shock

Finally, we examine the effect of productivity improvement. Figure 4-1 (d) reports IRFs for a 1% positive neutral technology shock. The response of unemployment for a productivity improvement is still ambiguous since totally opposite evidence is shown by the previous empirical studies: Gali (1999) and GSW show a positive response, whereas Christiano et al. (2004) report a negative one. The results of this paper indicate a positive response of unemployment against an increase of productivity (about 1.1% increase at peak) and unemployment returns to the steady state after five quarters, which is in line with the result of GSW. Real rigidities are key factors, as are nominal rigidities: An increase in productivity (a decrease of marginal cost) delivers a deflation and triggers a reduction of real interest rate through monetary easing policy, which stimulates aggregate demand from the intertemporal substitution effect. However, consumption and investment cannot respond immediately due to habit persistence and adjustment cost. These sluggish responses of aggregate demand require real wage adjustment to clear the labor market, but the real wage also cannot be adjusted quickly because of nominal rigidities. After all, the temporary excess supply caused by a positive productivity shock is resolved by the reduction in employment.

### 4.3 Historical Decomposition

#### 4.3.1 Output

Figure 4-2 (a) shows historical decomposition on output. The variations of output are mostly explained by four structural shocks: neutral technology shock, investment specific technology (hereafter, IST) shock, labor supply shock and preference shock.

It should be noted that there are three findings on the determinants of the variations on output: First, neutral technology shock is not a key factor explaining the recession during the so-called lost decade. Second, preference shock switches from positive to negative contri-
butions after the bursting of the bubble economy. Finally, IST shock is one of the key factors of depression after the 2000s including periods of financial crisis of 2007-2008.

The first finding is in contrast to Hayashi and Prescott (2002), who conclude that a decline in productivity plays an important role in the long-lasting recession. On the other hand, the above two findings are in line with Kawamoto (2005), in that there is a possibility that productivity continued growing even during the so-called lost decade and that the decline of labor utilization rate (a proxy of a demand component) is a key determinant of the recession. Regarding the third finding, the negative contribution of IST shock might be related to negative financial shocks. $ ^{*10} $

#### 4.3.2 Inflation

Figure 4-2 (b) depicts historical decomposition on inflation. We can recognize that serious deflation after the late 1990s is mainly attributed to negative contributions of IST shock, preference shock, and labor supply shock. After the beginning of the burst of the bubble economy, IST shock contributes negatively to inflation. Then, preference shock and labor supply shock follow the negative contributions of IST shock after 2000. It can be pointed out that the negative preference shock is a key factor on deflation during the financial crisis of 2008-2009.

#### 4.3.3 Unemployment

Figure 4-2 (c) shows the historical decomposition on unemployment. There are two main driving forces of unemployment variations: Neutral technology shock and labor supply shock. As mentioned above, a positive neutral technology shock makes employment decrease due to real and nominal rigidities. In addition, a negative labor supply shock indicates a decrease in the reservation wage, which causes an increase in aggregate labor supply. The combination of positive neutral technology shock with negative labor supply shock leads to serious unemployment, especially after 2000.

Figure 4-2 (d) displays government contributions for unemployment. We can see a negative comovement of government consumption shock with unemployment after the bursting of the bubble economy. Since the late 1990s and especially after the financial crisis of 2007-2008, the positive government consumption shock plays a significant role in the reduction of unemployment rate by more than 1.5%.

### 4.4 Robustness Check

The periods of zero-interest-rate policy are included during our estimation period. The policy will suppress the crowding out effect, which will enhance the effects of expansionary fiscal policies (see e.g. Christiano et al. 2011). Thus, the inclusion of periods of zero-interest-rate policy may support our main findings, i.e. fiscal stimuli improve unemployment. In this
## 5 Conclusion

Introducing unemployment and non-wasteful government spending into a medium-scale DSGE model, this paper examines the effect of government spending on unemployment in the Japanese economy. There are four findings: (i) 1% increase of government consumption reduces unemployment by 0.18%. (ii) 1% stimulus arising from government investment brings an improvement of unemployment by 0.06%. (iii) Since the late 1990s and especially after the financial crisis of 2007-2008, the positive government consumption shock plays a significant role in the reduction of unemployment rate by more than 1.5%. (iv) We also find the “crowd-in” channel where fiscal stimuli induce private consumption and investment to increase through the EC and PPC does not have much influence on unemployment variations.

There are remaining issues in this paper: First, as mentioned before, several papers suggest different methods to introduce non-wasteful government spending under alternative specifications of utility and production functions. Thus, we should check the robustness of our result to ensure that the channels of non-wasteful fiscal expansions do not play important roles for variations of unemployment. Second, we introduce not only non-wasteful government spending but also tax rules. If we attempt to simulate the effect of a tax increase, we should estimate parameters, taking news shocks into account. $ ^{*11} $ Third, we should reconsider the validity of modeling unemployment based on the market power of workers. While our model predicts higher market power of workers will raise the unemployment rate, Christiano (2011) points out that the hypothesis is rejected in Japan. Thus, it should be necessary to model the labor market more richly, for instance, by embedding search-matching friction where firms have some bargaining power.
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## A Appendix

### A.1 Model Description

This subsection describes the entire model: The dynamic optimization conditions on firms and households, fiscal and monetary policy rules and market clearing conditions.

#### A.1.1 Firms

We can classify firms into three types according to type of goods: Final goods firms, intermediate goods firms, and capital-producing firms. The final goods firms purchase intermediate goods, produce homogenous final goods by bundling differentiated intermediate goods, and sell the final goods to households and government. Intermediate goods firms purchase labor from households and capital from the capital-producing firms, produce the differentiated intermediate goods using labor and capital as factors of production, and sell the intermediate goods to the final goods firms. The capital-producing firms rent private capital from households, produce homogenous capital goods by combining private capital with public capital, and sell the homogenous capital goods to the intermediate goods firms.

## Final Goods Firms

Final goods firms bundle the differentiated intermediate goods $ Y_{j,t}, (j \in [0,1]) $ , and produce homogenous final goods. Given the final good price, $ P_{t} $ , and the intermediate good price, $ P_{j,t} $ , the final good firm solves the following profit maximization problem:

$$ \begin{aligned}&\max_{Y_{j,t}}P_{t}Y_{t}-\int_{0}^{1}P_{j,t}Y_{j,t}dj.\\&s.t.Y_{t}=\left[\int_{0}^{1}Y_{j,t}^{\frac{1}{\lambda}}dj\right]^{\lambda},where\lambda\geq1.\end{aligned} $$

From the first order condition (hereafter FOC), the demand function for an intermediate-good produced by the firm j is obtained as:

$$ Y_{j,t}=\left(\frac{P_{j,t}}{P_{t}}\right)^{\frac{\lambda}{1-\lambda}}Y_{t}. $$

Substituting the demand function above into the production function, the price of final goods can be expressed as:

$$ P_{t}=\left[\int_{0}^{1}(P_{j,t})^{\frac{1}{1-\lambda}}d j\right]^{1-\lambda}. $$

## I ntermediate Goods Firms

An intermediate good firm j produces a differentiated good $ Y_{j,t}\ (j \in [0,1]) $ , using capital $ \tilde{K}_{j,t} $ and labor input $ H_{j,t} $ :

$$ Y_{j,t}=\epsilon_{t}\tilde{K}_{j,t-1}^{\alpha}\left(z_{t}H_{j,t}\right)^{1-\alpha}-z_{t}^{+}\Theta $$

$ \epsilon_{t} $ stands the neutral technology shock. The scaling variable, $ z_{t}^{+} $ , is defined as

$$ z_{t}^{+}=\Psi_{t}^{\frac{\alpha}{1-\alpha}}z_{t}. $$