2.4. PRELIMINARY SETTINGS AND DATA 59
where εpt is the price markup shock. Let Xπ,t and eπ,t denote inflation data and ME attached to the inflation data, respectively. Then, the measurement equation on inflation can be written as the following expression.
Xπ,t = ˆπt+eπ,t
We can see that both markup shock εpt and ME eπ,t are hanging in the same way for the inflation dataXπ,t(the coefficients of both disturbance terms are unity). The wage markup shock also has the similar problem. Consequently, wage and price markup shocks, εwt and εpt, are difficult to identify from MEs. So we exclude those two markup shocks when estimating the model with ME. Thus, unlike SW (2003, 2007) and CEE (2005), state variables fluctuations such as wage and inflation are caused by variations in MEs or structural shocks except for markup shocks.13
Our motivation, as emphasized in Section 1, is to consider how much introducing ME affects estimated state variables (especially, wage and inflation) and estimated structural parameters (espe-cially, nominal rigidities). Hence, we will estimate and compare the two cases: “case w/o ME” and
“case with ME”. In “case w/o ME”, the DSGE model without ME is estimated which corresponds to normal estimation method as in SW (2003, 2007). On the other hand, in “case with ME”, we estimate the DSGE model introducing the ME. Again, it should be noted that “the case with ME”
excludes the two markup shocks and “case w/o ME” includes markup shocks as structural shocks.
2.4.2 Calibrated Parameters and Prior Settings
We assume that the seven structural shocks, sources of the business cycle, are independent of each other. Also, the two structural shocks of equity premium shock εqt and monetary policy shock εmt are assumed to be i.i.d. shocks. The remaining five structural shocks are assumed to have inertia and follow the AR(1) process: Preference shockεct, TFP shockεzt, investment adjustment cost shock εinvt , labor supply shockεLt, and government expenditure shockεt. As shown in Table 2.1, the prior for persistence parameter ρ of the AR shock process is specified as the Beta distribution so as to satisfy the stationary condition ρ ∈ (0,1), with mean of 0.85, standard error of 0.10, which is a relatively strong prior distribution. Also, since the variance of i.i.d. shockεtis a positive value, the prior is specified as inverse Gamma distribution. The parameters regions in which the solution is not uniquely determined are excluded from the prior distribution.
As with SW (2003, 2007), Levin et al. (2005) and Onatski and Williams (2010), some structural parameters need to be calibrated in advance. We will calibrate parameters according to the previous studies on Japan, the U.S. and Europe.
First, the subjective discount factor β is set to 0.99, which means that the steady state of real interest rate is assumed to be 4% at annual rate. The capital depreciation rate τ is 0.025 per quarter, assuming 10% when converting on an annual basis. From the above setting, the steady state of real rental rate of capital can also be calculated as ¯rk = β1 −(1−τ). The capital income share α is 0.30, which implies the steady state of labor income share is 70%. The steady state of government expenditure-output ratio gy is 0.10, and the steady of capital-output ratio ky is set to 1.50. In addition, because of identification problem, we set the wage markup rate parameter λw to 0.05 according to Onatski and Williams (2010).
Table 2.1 shows the preliminary settings on the remaining structural parameters. The prior mean is set mainly in accordance with SW (2003), and the standard deviation is set so that the
13Note that Justiniano and Primiceri (2008) and Fueki et al. (2010) also replace markup shocks with MEs. However, it differs in that they adopt the MH algorithm but we adopt the hybrid MCMC method with the simulation smoother.
2.4. PRELIMINARY SETTINGS AND DATA 61 parameter value covers a reasonable range. For example, the prior means for price and wage Calvo parameters ξp and ξw roughly follow the estimation result of Gali, et al. (2001) that the average contract period of price and wage is one year so set to 0.75. On the other hand, its standard deviation is set to 0.15 so that the contract period can vary from three quarters to two years.
Similarly, the prior mean for the IES (σc) is set to unity. The prior mean of elasticity on capital utilization adjustment costψis set to 0.2, and we set the standard deviation, in which the elasticity can fluctuate up to 0.1, the value reported by King and Rebelo (1999). The prior mean of fixed cost share φis 1.45, which is set to the value close to CEE (2005). On the inverse Frisch elasticity (σL), the prior mean is set to 2, but the standard deviation is set up so as to cover a wide range of low values reported in microeconomic evidence up to high values reported in estimation results of DSGE models. Finally, with regard to the prior mean of Taylor coefficients, to guarantee the uniqueness of the solution, parameter µπ related to inflation is 1.70, and we set 0.8 as the prior mean of the interest rate smoothing parameter ρm and 0.125 as the coefficient µy on the output gap.
2.4.3 Data
We use Japanese macroeconomic quarterly data and the estimation period, following Sugo and Ueda (2008), is 1981:Q1 to 1995:Q4 (15 years), excluding the period of the second oil shock and zero interest rate policy. The reason for limiting to this period is based on the fact that the monetary policy rule is linear in the standard DSGE model.
We employ the following data which corresponds to seven observation variablesXt: (1) output yt is real GDP per capita (per unit is one million yen, base year is 1990, seasonally adjusted), (2) consumption ct is real consumption per capita (unit and others are the same as GDP) calculated as the nominal private final consumption expenditure divided by the GDP deflator and the labor force population, (3) investment invt is real investment per capita (unit and others are the same as GDP) calculated as nominal private capital investment divided by GDP deflator and by labor force, (4) laborlt is a calculated series so that the product of the working hour index and the total employment is divided by the labor force, (5) real wagewt is a calculated real wage index obtained from dividing nominal wage index by GDP deflator, (6) inflationπtis an annualized growth rate of GDP deflator, and (7) nominal interest rateRtis annualized uncollateralized call rate. On the other hand, capital stock Kt and capital shadow price qt are regarded as unobservable state variables as in SW (2003).
We detrend five real series of output yt, consumption ct, investment invt, labor lt, real wage wt by taking natural log and removing trend components using Hodrick-Prescott filter. Then, by multiplying the series by 100, we derive the percent deviation from steady states. The two series with percent displayed values of nominal interest rate Rt and inflation πt are detrended by the Prescott filter. It should be noted that there is one drawback by employing the Hodrick-Prescott filter: Detrending the data inconsistent with the balanced growth model. Del Negro et al. (2007) assumed that output, consumption, investment, real wage, capital have a common stochastic trend accompanying technological progress growth rate and simultaneously estimated not only structural parameters but also the technological progress growth rate consistent with the balanced growth theory. When trends are removed by the Hodrick-Prescott filter independently for output, consumption, and investment, trend components are not necessarily common, which could seem not to be desired detrending method since it is inconsistent with the balanced growth theory.
However, when estimating the model using Japan’s data, Watanabe and Iiboshi (2007) and Iiboshi (2011) reported that trend changes, that is, structural breaks occurred in the early 1990s. Thus,
we should not apply the method of removing trend components by Del Negro et al. (2007) or SW (2007). Instead, we extract the cycle component of each data by removing the time-varying trend component by the Hodrick-Prescott filter without handling the trend break. Finally, all data was demeaned to make the means zeros. The solid line in Figure 2.1 displays the data Xt used in our estimation.