## 1 Introduction

This paper investigates qualitative and quantitative effects of government spending for unemployment, based on an estimated medium-scale new Keynesian model.

Figure 1 shows unemployment rate from 1980Q2 to 2012Q4 in Japan. From the 1980s to the beginning of the 1990s, the unemployment rate stabilized at a low level (the lowest is 2.1%). After the burst of the so-called bubble economy, however, the unemployment rate increased to more than 5% (5.4% at peak), even though Japan was following expansionary fiscal policy as well as monetary easing policy.

After the so-called financial crisis of 2007-2008, the increase of unemployment rate in the U.S. induces a number of studies to (i) investigate whether an increase of government spending improves unemployment or not, and (ii) examine how large fiscal stimuli influences unemployment, extending a standard DSGE model (e.g. Smets and Wouters, 2007).

Surprisingly, the answer to the first question is still ambiguous, since there is opposite empirical evidence on the effectiveness of fiscal stimuli for unemployment. Monacelli et al. (2010) exhibits empirical evidence that fiscal stimuli improve unemployment when applying a structural VAR analysis, and constructs a reproducible DSGE model with matching friction in a fashion of Mortensen and Pissarides (1994). See also Mayer et al. (2010), Campolmi et al. (2011), and Kuo and Miyamoto (2014). Bruckner and Pappa (2012) show the opposite evidence that fiscal expansions worsen unemployment from a structural VAR analysis, and construct a new Keynesian model with matching friction that can explain the evidence. See also Yuan and Li (2000). So, our questions are quite simple: Can fiscal stimulus improve unemployment? If so, how large an increase in government spending improves unemployment?

We can roughly classify the ways to introduce unemployment into a medium-scale DSGE model in the following two ways: One is to embed a matching friction in the labor market into a DSGE model. Besides the studies cited above, Christiano et al. (2013, hereafter, CTW) construct a small open economy model not only with matching friction but also with financial friction. The other is to make differentiated skilled workers have some market power and to introduce heterogeneity on labor disutilities. Gali (2011) shows how to implement involuntary unemployment to a medium-scale DSGE model as simply as possible, extending the sticky wage model proposed by Erceg et al. (2000). Then, Gali et al. (2012, hereafter GSW) examine the effect of the government spending for unemployment in the U.S. economy, estimating a medium scale new Keynesian DSGE model. See also Casares et al. (2014).

Meanwhile, how one introduces the “effectiveness” of government spending also matters. Standard stories are as follows: $ ^{*1} $ Fiscal expansions create additional labor demand. But forward-looking households will decrease consumption because of the anticipation of future tax increase (negative wealth effect). The decrease of consumption lowers the labor demand and also brings an incentive for households to work more (an increase of labor supply). When wage adjustment is sluggish due to nominal rigidities, if the increase of labor demand domi-