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This paper constructs a medium-scale dynamic stochastic general equilibrium (hereafter DSGE) model by modifying the formulation of capital utilization following Greenwood et al. (1988), and estimates the model using Japanese data, including that on actual capital utilization. There are similar empirical studies which estimate the medium-scale DSGE model developed by Christiano et al. (2005). Smets and Wouters (2003) is the first attempt to estimate a Christiano et al.'s model using Bayesian techniques. They apply the model to the Euro economy, and argue that the estimated parameters are more or less consistent with microeconometric findings and that their medium-scale DSGE model explains the actual economy almost as well as VAR. Their results were later confirmed by Onatski and Williams (2004). Levin et al. (2005) estimate a similar model for the US economy. As for applications to the Japanese economy, Iiboshi et al. (2006) have already estimated the model using Japanese data. Although these studies seem to succeed in explaining the actual economy very well, we find that there are still unresolved problems relating to capital utilization rates which previous studies did not focus on. In Smets and Wouters (2003) and others, this variable is treated as unobservable, and inferred using the Kalman filter. Fig. 1 shows the inferred movement of capital utilization rates obtained using Japanese data (shaded areas represent recessions). Since there are available statistics on capital utilization rates, although these are limited to manufacturing firms in Japan, a comparison is instructive. We find that the two utilization rates are very different in terms of their movements and their amplitude. Full-size image (23 K) Fig. 1. Actual and inferred capital utilization rates. Figure options Since we have data on capital utilization rates, it is quite natural to make use of this when estimating the model. This then generates another problem. The Christiano et al. (2005) model states that capital rental costs should positively affect capital utilization rates. This is because their model assumes that it is beneficial for capital lenders to increase capital utilization rates when capital rental costs are high. However, as is shown in Fig. 2, these two variables are in fact negatively correlated. Such a negative correlation is perfectly intuitive, and can be explained as follows. While capital rental costs are positively determined by the marginal product of effective capital, the latter depends negatively on the capital utilization rate, so a negative correlation will be observed. Full-size image (9 K) Fig. 2. Utilization rates and rental costs. Figure options The main contribution of this paper is to incorporate this negative correlation between capital utilization and rental rates for capital into a medium-scale DSGE model. To this end, we follow Greenwood et al. (1988). We assume that the adjustment costs of capital utilization take the form not of additional expenditure on goods but of an accelerating speed of capital depreciation. This assumption makes utilization rates depend not only upon rental costs positively but also upon the value of capital negatively. On the one hand, higher rental costs lead to greater capital utilization because households can receive higher revenues by increasing capital utilization and by renting more effective capital to firms. On the other hand, a higher value of capital discourages capital utilization because, by making future capital more valuable, it deters households from utilizing their capital in order not to accelerate its speed of depreciation. By applying this assumption to our DSGE model, we succeed in incorporating the negative correlation between rental costs and utilization rates. We improve the goodness of fit; our model explains the behavior of utilization rates in most parts of the sample periods. We find that an investment adjustment cost shock is as important as a productivity shock that affects business cycles such as output fluctuations. Furthermore, we confirm that our model yields the inertial behavior of inflation in response to monetary policy shocks, as observed in previous econometric studies (e.g. Kim, 1999 and Shioji, 2000). This result contrasts with the argument offered by Christiano et al. (2005). To explain the hump-shaped and persistent inflation behavior in response to a contractionary monetary policy shock, Christiano et al. (2005) advocate treating capital utilization costs not as capital depreciation but as additional spending on goods. This paper makes it clear that although Christiano et al.'s (2005) assertion is qualitatively true, the difference in the assumption about capital utilization has no quantitative impact when we consider the overall impulse response of utilization rates and inflation to a monetary policy shock. The rest of the paper is organized as follows. Section 2 presents the benchmark model following Christiano et al. (2005). In Section 3, we present estimation results: estimated parameters and the movement of capital utilization rates. We also investigate business cycles in Japan. Section 4 compares our model with those of Christiano et al. (2005), Smets and Wouters (2003), and Levin et al. (2005) from the viewpoint of the effect of monetary policy shocks. Section 5 concludes the paper.

This paper constructs a medium-scale dynamic stochastic general equilibrium (hereafter DSGE) model by modifying the formulation of capital utilization following Greenwood et al. (1988), and estimates the model using Japanese data, including that on actual capital utilization. There are similar empirical studies which estimate the medium-scale DSGE model developed by Christiano et al. (2005). Smets and Wouters (2003) is the first attempt to estimate a Christiano et al.'s model using Bayesian techniques. They apply the model to the Euro economy, and argue that the estimated parameters are more or less consistent with microeconometric findings and that their medium-scale DSGE model explains the actual economy almost as well as VAR. Their results were later confirmed by Onatski and Williams (2004). Levin et al. (2005) estimate a similar model for the US economy. As for applications to the Japanese economy, Iiboshi et al. (2006) have already estimated the model using Japanese data. Although these studies seem to succeed in explaining the actual economy very well, we find that there are still unresolved problems relating to capital utilization rates which previous studies did not focus on. In Smets and Wouters (2003) and others, this variable is treated as unobservable, and inferred using the Kalman filter. Fig. 1 shows the inferred movement of capital utilization rates obtained using Japanese data (shaded areas represent recessions). Since there are available statistics on capital utilization rates, although these are limited to manufacturing firms in Japan, a comparison is instructive. We find that the two utilization rates are very different in terms of their movements and their amplitude. Full-size image (23 K) Fig. 1. Actual and inferred capital utilization rates. Figure options Since we have data on capital utilization rates, it is quite natural to make use of this when estimating the model. This then generates another problem. The Christiano et al. (2005) model states that capital rental costs should positively affect capital utilization rates. This is because their model assumes that it is beneficial for capital lenders to increase capital utilization rates when capital rental costs are high. However, as is shown in Fig. 2, these two variables are in fact negatively correlated. Such a negative correlation is perfectly intuitive, and can be explained as follows. While capital rental costs are positively determined by the marginal product of effective capital, the latter depends negatively on the capital utilization rate, so a negative correlation will be observed. Full-size image (9 K) Fig. 2. Utilization rates and rental costs. Figure options The main contribution of this paper is to incorporate this negative correlation between capital utilization and rental rates for capital into a medium-scale DSGE model. To this end, we follow Greenwood et al. (1988). We assume that the adjustment costs of capital utilization take the form not of additional expenditure on goods but of an accelerating speed of capital depreciation. This assumption makes utilization rates depend not only upon rental costs positively but also upon the value of capital negatively. On the one hand, higher rental costs lead to greater capital utilization because households can receive higher revenues by increasing capital utilization and by renting more effective capital to firms. On the other hand, a higher value of capital discourages capital utilization because, by making future capital more valuable, it deters households from utilizing their capital in order not to accelerate its speed of depreciation. By applying this assumption to our DSGE model, we succeed in incorporating the negative correlation between rental costs and utilization rates. We improve the goodness of fit; our model explains the behavior of utilization rates in most parts of the sample periods. We find that an investment adjustment cost shock is as important as a productivity shock that affects business cycles such as output fluctuations. Furthermore, we confirm that our model yields the inertial behavior of inflation in response to monetary policy shocks, as observed in previous econometric studies (e.g. Kim, 1999 and Shioji, 2000). This result contrasts with the argument offered by Christiano et al. (2005). To explain the hump-shaped and persistent inflation behavior in response to a contractionary monetary policy shock, Christiano et al. (2005) advocate treating capital utilization costs not as capital depreciation but as additional spending on goods. This paper makes it clear that although Christiano et al.'s (2005) assertion is qualitatively true, the difference in the assumption about capital utilization has no quantitative impact when we consider the overall impulse response of utilization rates and inflation to a monetary policy shock. The rest of the paper is organized as follows. Section 2 presents the benchmark model following Christiano et al. (2005). In Section 3, we present estimation results: estimated parameters and the movement of capital utilization rates. We also investigate business cycles in Japan. Section 4 compares our model with those of Christiano et al. (2005), Smets and Wouters (2003), and Levin et al. (2005) from the viewpoint of the effect of monetary policy shocks. Section 5 concludes the paper.

This paper formulates a medium-scale DSGE model and applies it to the Japanese economy. It employs estimation using Bayesian techniques, and obtains plausible results for structural and policy parameters, impulse responses, variance decomposition, and the movement of capital utilization rates. If we apply the same methods as Smets and Wouters (2003) and Levin et al. (2005), which are based on Christiano et al. (2005) model, we encounter problems—in particular the inconsistency between the movement of implied and actual capital utilization rates. This paper has thus made two main modifications. Firstly, we use actual capital utilization rate data for estimation. Secondly, we modify the Christiano et al. (2005) model with respect to capital utilization rates following Greenwood et al. (1988). In short, we assume that the cost of capital utilization is not to cause additional expenditure on goods but to accelerate capital depreciation. This enables us to incorporate a negative correlation between the capital utilization rate and the rental cost of capital and to make the movement of estimated capital utilization rates fall almost in line with the observed data. A remaining task, however, is to improve the goodness of fit of the estimation.26 As was mentioned in Section 3.4, estimated capital utilization rates do not quite coincide with those observed. As a possible reason for this, we suspect that, in our model, the adjustment of wages and labor is far slower than that of capital. This makes rental costs, or the relative productivity of capital over labor, highly dependent upon effective capital. This may make rental costs seem negatively correlated with utilization rates. One way of dealing with this would be to incorporate the movement of wages and labor into the model, such as by introducing a model of effective labor. If wages and labor were more volatile and procyclical, then productivity growth would become less pro-cyclical. This could be achieved, for example, by incorporating labor hoarding or overhead labor.27 Another and more promising remedy is to incorporate unemployment. Widely-accepted DSGE models are based on the model of full-employment, and ignore the existence of involuntary labor slack. This is truly an important factor which we should not overlook. Some economists have attempted the difficult task of combining unemployment with Real Business Cycle or New-Keynesian models.28 Incorporating real side costs as opposed to monetary frictions will certainly open up our understanding of the macroeconomy and help us to construct better models.