Will Abenomics Expand Employment?–Interpreting Abenomics Through DSGE Modeling

Abstract

Using data from the first quarter of 1990 until the second quarter of 2013, we performed Bayesian estimation of DSGE model, which was developed from 10 endogenous variables. When we introduced productivity shock, monetary easing shock and preference shock to the estimated DSGE model, we obtained results that were mostly consistent with economic theory. We then analyzed these results to observe what kind of effect the shock of the inflation target, a primal policy of Abenomics, has on the major economic variables, such as employment and the like. To do this, we defined the inflation target’s shock as a shock that leads to the inflation rate deviating in the minus direction from the steady state of expected inflation rate, and calculated the impulse response function. As a result of this analysis, we found that inflation target shock leads to expanded production volume, and higher wage rates and inflation rates. Employment, our subject of focus, also improved. Excluding some parts, these results were also consistent with the trend of the real economy that followed after the start of Abenomics. We also learned that the inflation target’s effect was far more sustainable than monetary easing’s effect.

13.7 Appendix

Structure of log-linear approximation model

Here, we clearly show the relationship between the model developed in this paper and the DSGE model used for the simulation. The following equations (13.C.1) through (13.C.10) are, respectively, goods market equilibrium equations of (13.3), (13.9), (13.30), log-linear approximated terms or actual terms of (13.B.3), (13.B.1), (13.12), (13.21), (13.31), (13.A.4), (13.B.1) and (13.B.3). Through this process, ${\omega }$ appears, but this is erased using (13.11).

$$\begin{aligned} \tilde{\pi }_{t}=\mathrm {E}_{\mathrm {t}}\tilde{\pi }_{t+1}\mathrm {+}\frac{{\rho }^{\mathrm {2}}}{{1-\rho }}\left( \hat{w}_{\mathrm {t}}{-\alpha }\hat{K}_{\mathrm {t}}{+\alpha }\hat{N}_{\mathrm {t}} \right) \end{aligned}$$

(13.C.1)

$$\begin{aligned} \hat{Y}_{\mathrm {t}}=\hat{K}_{\mathrm {t}}\mathrm {+}\left( {1-\alpha } \right) \hat{N}_{\mathrm {t}} \end{aligned}$$

(13.C.2)

$$\begin{aligned} \hat{K}_{\mathrm {t+1}}={\delta }\hat{I}_{\mathrm {t}}\mathrm {+}\left( {1-\delta } \right) \hat{K}_{\mathrm {t}} \end{aligned}$$

(13.C.3)

$$\begin{aligned} \hat{Y}_{\mathrm {t+1}}=\frac{\mathrm {C}}{\mathrm {Y}}\hat{C}_{\mathrm {t}}\mathrm {+}\frac{\mathrm {I}}{\mathrm {Y}}\hat{I}_{\mathrm {t}} \end{aligned}$$

(13.C.4)

$$\begin{aligned} \mathrm {E}_{\mathrm {t}}\hat{q}_{\mathrm {t+1}}=\frac{\mathrm {1}}{{1-\delta }}\left( \frac{\mathrm {1+i}}{{1+\pi }}\left( \hat{q}_{\mathrm {t}}\mathrm {+}\mathrm {E}_{\mathrm {t}}\mathrm {(}\tilde{i}_{\mathrm {t+1}}\mathrm {-}\tilde{\pi }_{\mathrm {t+1}} \right) \mathrm {-}\frac{r}{q}\hat{r}_{\mathrm {t}} \right) \end{aligned}$$

(13.C.5)

$$\begin{aligned} \hat{c}_{\mathrm {t}}=\mathrm {E}_{\mathrm {t}}\hat{c}_{\mathrm {t+1}}\mathrm {-}\frac{\mathrm {1}}{\theta }\mathrm {E}_{\mathrm {t}}\tilde{i}_{\mathrm {t+1}}\mathrm {+}\frac{\mathrm {1}}{{\theta }}\mathrm {E}_{\mathrm {t}}\tilde{\pi }_{\mathrm {t+1}} \end{aligned}$$

(13.C.6)

$$\begin{aligned} \tilde{i}_{t}=\chi \tilde{i}_{t-1}+\left( 1-\chi \right) \left\{ \phi _{1}E_{t}\tilde{\pi }_{t+1}+\phi _{2}\hat{Y}_{t}\right\} \end{aligned}$$

(13.C.7)

$$\begin{aligned} \hat{w}_{\mathrm {t}}=\frac{{\sigma }}{\mathrm {1-N}}\tilde{N}_{\mathrm {t}}\mathrm {+}\left( {1-\sigma } \right) \hat{w}_{\mathrm {t-1}} \end{aligned}$$

(13.C.8)

$$\begin{aligned} \hat{r}_{\mathrm {t}}=\left( \hat{w}_{\mathrm {t}}{-\alpha }\hat{K}_{\mathrm {t}}{+\alpha }\hat{N}_{\mathrm {t}}\right) \mathrm {+}\left( {\alpha -1} \right) \hat{K}_{\mathrm {t}}\mathrm {-}\left( {\alpha -1}\right) \hat{N}_{\mathrm {t}} \end{aligned}$$

(13.C.9)

$$\begin{aligned} \hat{I}_{\mathrm {t}}=\frac{\mathrm {1+i}}{{2+i+\pi }}\hat{I}_{\mathrm {t-1}}\mathrm {+}\frac{{1+\pi }}{{2+i+\pi }}\mathrm {E}_{\mathrm {t}}\hat{I}_{\mathrm {t+1}}\mathrm {+}\frac{\mathrm {1+i}}{\left( {2+i+\pi } \right) \text {S''}\left( \mathrm {1}\right) }\hat{q}_{\mathrm {t}} \end{aligned}$$

(13.C.10)

Note, however, that the estimation was further set as follows:

$$ \frac{C}{Y}=\mathrm {Steady\, state\, consumption\, calculation\, ratio=0.8} $$

$$ \frac{I}{Y}=\mathrm {Steady\, state\, investment\, calculation\, ratio=0.2} $$

$$ \frac{1+i}{{1+\pi }}=\frac{\mathrm {1}}{\beta }=\frac{1}{0.995} $$

$$ \frac{r}{q}\hat{r}_{\mathrm {t}}=\frac{1}{q}r\hat{r}_{\mathrm {t}}=\frac{1}{1}\tilde{r}_{t}=\tilde{r}_{t} $$

$$ \frac{{\sigma }}{1-N}=\frac{{\sigma }}{\mathrm {1-0.95}} $$

$$ \hat{r}_{\mathrm {t}}=\frac{\tilde{r}_{t}}{r}=\frac{\tilde{r}_{t}}{r}=\frac{\tilde{r}_{t}}{\left\{ \frac{1}{\beta }-\left( 1-\delta \right) \right\} q}=\frac{\tilde{r}_{t}}{\left\{ \frac{1}{0.995}-\left( 1-\delta \right) \right\} 1} $$

$$ \frac{1+i}{{2+i+\pi }}=\frac{\mathrm {1}}{1+\beta } $$

$$ \frac{{1+\pi }}{{2+i+\pi }}=\frac{\beta }{1+\beta } $$