Silviase/jgov_v1.4_full_ann huggingface dataset:
presence of multiple distortionary taxation, it is possible to affect the results by changing the allocation of government finance across the taxes. Notice that both consumption and labor income taxes have dampening effects on labor, since the labor supply schedule is related to the utility-maximizing choice between consumption and labor on an after-tax basis. Hence, tax rule combinations such as specifications 2 and 3 limit initial increases in labor after a government spending shock more than specifications 1 and 4, which in turn partly offset the investment and output rises. Thus, initial declines in Ricardian consumption are larger in specifications 2 and 3 than in specifications 1 and 4. In later periods, however, specifications 1 and 4 show larger declines in investment and subsequently in Ricardian consumption, reflecting a capital income tax increase. This interpretation accords well with the model's impulse responses to tax shocks. As we have seen in Figures 8-10, consumption and labor income tax shocks both raise real wages and decrease labor hours, whereas the capital income tax shock decreases real wages and increases labor hours in the very initial period. The result here is largely in line with Jones (2002), which finds that labor income taxation decreases labor hours and output more than capital income taxation does.

Figure 16 illustrates the labor-dampening effects of consumption and labor income taxes. As expected, labor hour increases are prevented to a larger extent in specification 2 (dotted line) and specification 3 (dashed line), rather than in specification 1 (solid line) and specification 4 (dash-dotted line). These patterns correspond to those of investment and Ricardian consumption as shown in Figures 14-15. The resulting output responses to a government spending shock is depicted in Figure 17. It shows that initial output increase becomes greater if the government finance is allocated lightly on labor-dampening taxes, such as consumption and labor income taxes. One might wonder why labor hour increases are smaller in specifications 2 and 3 than in specification 1, which assumes the same value for $ \phi_{tcb} $ and $ \phi_{tdb} $ as specification 2 and specification 3, respectively. The reason is that the increases in consumption and labor income taxation under specification 1 are actually less than those under specifications 2 and 3, since government finance is nearly evenly allocated across three tax instruments under specification 1.

As discussed above, the increase in labor supply is definitely the main channel of fiscal policy transmission. However, it is not clear whether the change of its elasticity increases fiscal multipliers or not in the presence of distortionary taxation. Although Baxter and King (1993) find that it is possible to have a fiscal multiplier greater than one if the labor supply is highly elastic, the analysis essentially focuses on the case of lump-sum taxation $ ^{24} $ . In contrast, Kamps (2004) shows that an increase in government $ {}^{24} $ The distortionary tax rates are held fixed and debt is not considered in the analysis. See also Aiyagari et al. (1992).
investment financed by distortionary taxes reduces labor more in later periods as the elasticity of labor becomes larger in a neoclassical model with productive public capital. As already noted by Ludvigson (1996), distortionary tax finance has two different effects on labor in the opposite direction. The disincentive effects of distortionary taxes reduce the labor supply, while the negative wealth effect increases it. Since both effects are amplified as the elasticity becomes higher, its net influence on fiscal multipliers depends on their respective magnitude. It is interesting to consider an “indivisible labor” case (in which infinite elasticity $ \sigma_{l}=0 $ is assumed) for baseline specification (referred to as infinitely elastic labor supply case). Figure 18 reports the consumption and investment responses of the infinitely elastic labor supply case after a government spending shock (dotted line, and dash-dotted line, respectively) compared with those of baseline (solid line, and dashed line, respectively). The multipliers in initial periods are actually smaller in the infinitely elastic labor supply case.

Finally, I provide a brief assessment on the relative importance of non-Ricardian share and tax rule combination in determining fiscal policy effectiveness by conducting some sensitivity analyses. Table 7 reports fiscal multipliers under specification 4 with non-Ricardian shares $ \omega = 0.0, 0.1, 0.2, 0.3 $ , and those under specifications 1-3 with $ \omega = 0.3 $ . Interestingly, the model under specification 4 generates a positive (although small) response of consumption in the first period even in the case in which all households are Ricardian ( $ \omega = 0.0 $ ). Moreover, specification 4 with $ \omega = 0.1 $ exhibits larger output multipliers than specifications 1-3 with $ \omega = 0.3 $ until the fourth period. These results lead to the conclusion that a choice of tax rule combination can alter the consequences of fiscal policy anticipated by the given non-Ricardian share.

## 5 Concluding Remarks

In this paper, I have made essentially two contributions: I have presented an estimated medium-scale DSGE model of the Japanese economy detailed in fiscal policy, and I have shown that tax rule combination plays a decisive role in determining fiscal policy effectiveness, which has been largely omitted in the literature. To this end, I introduced multiple distortionary tax rules and estimated them utilizing quarterly government expenditure and tax data on the Japanese economy. My main findings are as

Linnemann (2004) obtains a similar result using a DSGE model with labor income taxation, arguing that it is possible to have the crowding-in effect on consumption as long as the labor supply is sufficiently elastic. However, the result rests on its assumption of unemployment benefits, which makes government spending automatically countercyclical.
follows. First, non-Ricardian share in Japan is somewhat smaller than those in the euro area and the United States. Second, the estimated model successfully delivers the crowding-in effect on consumption regardless of its low share of non-Ricardian households. Third, fiscal policy becomes more effective if its finance is allocated lightly on labor-dampening taxes. This applies to Japan for the period 1980:Q1 to 1998:Q4. Fourth, a choice of tax rule combination can actually dominate the non-Ricardian share in its effect on fiscal multipliers. Furthermore, there may be cases that the model can generate the crowding-in effect in an economy where all households are Ricardian, depending on its choice of tax rule combination. I believe that this paper adds a new dimension to the recent debate about fiscal multipliers in New Keynesian models (e.g., see Cogan et al. (2009)).

Differently from monetary policy, there seems to be little consensus in the literature with respect to modeling fiscal policy rules. Most previous studies often abstract distortionary taxes and debt from models, or occasionally treat them as time-invariant. However, as we have confirmed, formulation of tax rules affects the magnitude of fiscal multipliers considerably. Given this, it should be stressed that proper modeling of the government's financing behavior is fairly important to assess the quantitative effects of fiscal policy. More broadly, the same applies to the modeling of the spending side. Allowing for a productive role for public capital is one possible extension (e.g., see Kamps (2004) and Linnemann and Schabert (2006)). This paper is the first step toward estimating the government behavior based on quarterly fiscal data. In future research on estimating a DSGE model of the Japanese economy, the fiscal policy rule specification may need to be further reexamined to see whether it best describes actual government behavior. Empirical evaluation of the model, such as a comparison with VAR models, is an important task I left out. It will be also necessary to explore proper procedures to obtain an appropriate capital income tax series for estimation. Another avenue worth pursuing is to consider the possibility that policy rules may change over time, since there is some indication in my result that policy parameters are sensitive to the estimation period. If that is the case, estimation techniques for models with time-varying parameters (e.g., see Fernández-Villaverde and Rubio-Ramírez (2008)) or models with Markov-switching rules (e.g., see Davig and Leeper (2007)) would be necessary. These techniques are also useful in dealing with the zero-interest-rate period of Japan (See Yano (2009)) $ ^{25} $ .
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## Appendix

## A Data sources

The model is estimated using quarterly data of the Japanese economy over the period from 1980:Q1 to 1998:Q4. All data except for interest rate (Bank of Japan), labor force (Ministry of Internal Affairs and Communications), and labor input (Ministry of Health, Labor and Welfare) are taken from the National Accounts of Japan (93SNA, Reference year: 1995) $ ^{26} $ . The effective tax rate series are constructed following Mendoza et al. (1994) on purely quarterly basis, and are seasonally adjusted by the author. The sources and the formula used are as follows.

Letting $ \tau^{h} $ denote households' average tax rate on total income, effective average tax rates for $ \tau^{c} $ , $ \tau^{d} $ , $ \tau^{k} $ are calculated as:

$$ \tau^{c}=\left[\frac{TI}{C-TI}\right]\times100 $$

$$ \tau^{h}=\left[\frac{TDI}{OSPUE+PEI+W}\right] $$

$$ \tau^{d}=\left[\frac{\tau^{h}W+ESC}{W+TSC}\right]\times100 $$

$$ \tau^{k}=\left[\frac{\tau^{d}(OSPUE+PEI)+(TD-TDI)+TP}{OS}\right]\times100 $$

where:

• TI : Taxes on products, General government, Allocation of primary income account, Income and Outlay Accounts classified by Institutional Sectors.

• C : Private final consumption expenditure, Gross domestic product (Expenditure approach at current prices), Main Time Series.
• TDI : Current taxes on income, wealth, etc., Households (including private unincorporated enterprises), Secondary distribution of income account, Income and Outlay Accounts classified by Institutional Sectors.

• OSPUE : Operating surplus, Households (including private unincorporated enterprises), Allocation of primary income account, Income and Outlay Accounts classified by Institutional Sectors.

• PEI : Property income, Households (including private unincorporated enterprises), Allocation of primary income account, Income and Outlay Accounts classified by Institutional Sectors.

• W : Wages and salaries, Households (including private unincorporated enterprises), Allocation of primary income account, Income and Outlay Accounts classified by Institutional Sectors.

• ESC : Employers’ social contributions, Households (including private unincorporated enterprises), Allocation of primary income account, Income and Outlay Accounts classified by Institutional Sectors.

• TSC : Total social contributions, Households (including private unincorporated enterprises), Secondary distribution of income account, Income and Outlay Accounts classified by Institutional Sectors.

• TD : Current taxes on income, wealth, etc., General government, Secondary distribution of income account, Income and Outlay Accounts classified by Institutional Sectors.

• TP : Other taxes on production, General government, Allocation of primary income account, Income and Outlay Accounts classified by Institutional Sectors.

• OS : Operating surplus, Total economy, Allocation of primary income account, Income and Outlay Accounts classified by Institutional Sectors.
## B Log-linearized Model

### B.1 Ricardian Households

#### B.1.1 Consumption Euler Equation

From (3) and (4):

$$ \begin{aligned}\hat{C}_{t}^{R}&=\frac{h}{1+h}\hat{C}_{t-1}^{R}+\frac{1}{1+h}E_{t}\hat{C}_{t+1}^{R}-\frac{1-h}{(1+h)\sigma_{c}}\left(\hat{R}_{t}-E_{t}\hat{\pi}_{t+1}\right)\\&+\frac{1-h}{(1+h)\sigma_{c}}\left(\hat{\varepsilon}_{t}^{b}-E_{t}\hat{\varepsilon}_{t+1}^{b}\right)-\frac{1-h}{(1+h)\sigma_{c}}\left(\hat{\tau}_{t}^{c t i l}-E_{t}\hat{\tau}_{t+1}^{c t i l}\right),\end{aligned} $$

where

$$ \hat{\tau}_{t}^{c t i l}=\frac{\bar{\tau}^{c}}{1+\bar{\tau}^{c}}\hat{\tau}_{t}^{c}, $$

$$ \hat{\varepsilon}_{t}^{b}=\rho_{b}\hat{\varepsilon}_{t-1}^{b}+\eta_{t}^{b}. $$

#### B.1.2 Investment Euler Equation

From (5) and (4):

$$ \hat{I}_{t}=\frac{1}{1+\beta}\hat{I}_{t-1}+\frac{\beta}{1+\beta}E_{t}\hat{I}_{t+1}+\frac{\varsigma}{1+\beta}\hat{Q}_{t}-\frac{\beta E_{t}\hat{\varepsilon}_{t+1}^{i}-\hat{\varepsilon}_{t}^{i}}{1+\beta}, $$

where $ \varsigma\equiv1/S^{''}(1) $ and

$$ \hat{\varepsilon}_{t}^{i}=\rho_{i}\hat{\varepsilon}_{t-1}^{i}+\eta_{t}^{i}. $$

#### B.1.3 Q Equation

From (6) and (4):

$$ \begin{aligned}\hat{Q}_{t}&=-\left(\hat{R}_{t}-\hat{\pi}_{t+1}\right)+\frac{1-\delta}{1-\delta+\left(1-\bar{\tau}^{k}\right)\bar{r}^{k}}\hat{Q}_{t+1}\\&+\frac{\left(1-\bar{\tau}^{k}\right)\bar{r}^{k}}{1-\delta+\left(1-\bar{\tau}^{k}\right)\bar{r}^{k}}\hat{r}_{t+1}^{k}-\frac{\bar{\tau}^{k}\bar{r}^{k}}{1-\delta+\left(1-\bar{\tau}^{k}\right)\bar{r}^{k}}\hat{\tau}_{t+1}^{k}+\hat{\eta}_{t}^{q}.\end{aligned} $$