Mixed-frequency data, investment shocks and business cycles in China
【Abstract】This paper shows that the retail sales of consumer goods (RSCG) and fixed-asset investment (FAI) usually used in the estimation of Chinese dynamic stochastic general equilibrium (DSGE) models contain misleading information, and suggests replacing them with annual household consumption and fixed capital formation in gross domestic product (GDP) using the expenditure approach. Due to a lack of quarterly data, the usual practice in the estimation of Chinese DSGE models is aggregating monthly RSCG and FAI data to obtain quarterly data on consumption and investment. However, there are important differences between these series and the corresponding model variables by definition. The inconsistency between model variables and observed data may lead to incorrect results in parameter estimation. Chang et al. (2016) interpolate annual household consumption expenditure and fixed capital formation in expenditure GDP using RSCG and FAI as interpolaters to obtain usable quarterly data. However, the seasonal information of the interpolated series retained from RSCG and FAI may be misleading. This paper instead proposes the usage of mixed-frequency data in a DSGE model estimation, that is, replacing the quarterly data of RSCG and FAI with the annual data of household consumption expenditure and fixed capital formation, and combining annual data with quarterly data. The solution to the DSGE model can be cast in state-space form and estimated via the Kalman filter. The low frequency series are considered high frequency series with missing observations. Thus, the Kalman filter implemented in Dynare can deal with missing values easily. Apart from consumption and investment, the time series used for the model estimation include GDP, GDP deflator and money aggregates (M2) .Based on the Bayesian technique, this paper estimates a DSGE model using mixed- and single-frequency (quarterly) data, respectively. Comparing the estimation results, there are significant discrepancies between the mixed- and single-frequency estimates. In particular, compared with single-frequency estimates, the investment adjustment costs parameter of the mixed-frequency estimates is larger, while the standard deviation of permanent technology shocks is lower, indicating a smaller role for permanent technology shocks in driving business cycles. To assess the relative performance of alternative datasets, this paper considers the out-of-sample forecasting performance of the DSGE model. The predicted variables include GDP and inflation. The model is re-estimated every quarter and forecast forward for eight periods. The RMSE indicators are calculated from the predictive value and actual data. Based on the RMSE for GDP, the model estimated with mixed-frequency data outperforms that of quarterly data. For inflation, the model estimated with mixed-frequency data performs better in the long term but worse in the short term. This paper estimates the CEE/SW model using data sampled at different frequencies. The variance decomposition shows that the main factors explaining China’s output volatility are investment shocks, followed by monetary shocks, persistent technology shocks and external demand shocks. These four factors can explain more than 80% of the volatility of GDP, while the investment shocks alone can account for more than 30% of GDP variability. The contribution of investment shocks comes mainly from investment-specific technology shocks, measured by the relative price of investment. This result differs from that of Justiniano et al. (2010, 2011), who find that shocks to marginal investment efficiency are the key drivers of business cycle fluctuations in U.S. output. However, like their analysis, the theoretical analysis presented here shows that investment shocks may be interpreted as a proxy for the overall health of the financial system.
【Keywords】 DSGE model; Bayesian method; mixed-frequency data; investment shocks;
. ① For convenience of description, in the following, the retail sales of social consumer goods is also referred to as “social consumption data,” and the fixed asset investment amount is also referred to as “fixed investment data.”
. ② Compared with the consumption in the model, the retail sales of social consumer goods do not include services, and include some durable consumer goods and small commodities that are not consumer goods such as hardware and electric materials. Compared with the investment in the model, fixed asset investment includes land acquisition fees, but does not include residents’ purchase of durable consumer goods, intangible assets investment and fixed investment of less than CNY 500,000. A detailed discussion can be found in Xu (2010).
. ① The specific method is as follows. The quarterly investment data are formed by the annual fixed capital formation combined with the quarterly fixed asset investment data (added by the monthly data and seasonally adjusted). The quarterly consumption data are interpolated from the annual consumption expenditure based on the retail sales of social consumer goods.
. ② After the quarterly adjustment of monthly fixed asset investment data, it can be found that there is a peak in December every year through analyzing its seasonal factor; it is difficult to imagine that such increase in investment will happen in the cold winter. The main reason is due to the availability of funds for investment grants. And the slow decline of this peak in recent years is largely due to human factors.
. ① State-adaptive securities purchased by families are designed to isolate the uncertainty caused by the ability to optimize wages in the current period.
. ① One of the more commonly used interest rate rules in the DSGE model is:(Fernández-Villaverde, 2010). Among them, interest rates react to growth rates rather than output gaps. Orphanides (2003) showed that this form of Taylor rule fits the data better.
. ② Here, the deviation of the output growth rate from the steady state is used instead of the output gap. On the one hand, because of China’s fast-growing economy, the growth rate is more concerned by the monetary authorities. On the other hand, there are large errors in the measurement of output gaps, and the results are often too random and severely affected by data revisions (Orphanides, 2002; Orphanides and Van Norden, 2002).
. ③ If ρπ = ρy = 1, then this rule is equivalent to the McCallum rule that does not consider the change in the velocity of money.
. ① Christiano and Davis (2006) demonstrated that a costly state verification mechanism can be internalized to the financial wedge Δkt. For example, in the financial accelerator model of Bernanke et al. (1999), capital production and investment processes are carried out in separate departments, asymmetric information between capital producers (borrowers) and financial intermediaries (lenders) generates a random external financing premium (the difference between financial assets and return on capital).
. ② Following Christiano et al. (2005), the monetary stock Mb in the monetary model M2 is used here. M2 is a broader monetary amount that is more able to generalize economic activity than M0 and M1. Moreover, from the actual data analysis, the relationship between M2 changes and CPI is more stable.
. ① For the first three quarters of each year, it is still valid. But c_yeart and i_yeart cannot be observed.
. ② Harvey and Pieres (1984) for the first time transformed the mixed-frequency ARMA model was transformed into a state space model for estimation. This method was later extended to the estimation of VAR and dynamic factor models (Zadrozny, 1988). A VAR model for estimating the mixed frequency based on the Bayesian method can be found in Schorfheide and Song (2012).
. ① From we can derive missing values in yt, where is a value based on Kalman filter smoothing. Details can be obtained from the author if needed.
. ① The mode and standard deviation are obtained in the Dynare software based on Laplace approximation. Further, the posterior mean value can be obtained by MCMC simulation, and the result is very close to the result of the mode in the table.
. ② Guerron-Quintana (2010) has similar results. The estimates of investment adjustment cost parameters are extremely sensitive to the choice of observed variables.
. ① When using quarterly retail sales of social consumer goods and fixed asset investment data for prediction, in order to ensure consistency with the information set predicted by the annual data, the retail sales of social consumer goods and fixed asset investment data used will be until the fourth quarter of the previous year. For example, based on the prediction for the third quarter of 2012, the model is estimated using quarterly GDP, price, and monetary data up to the third quarter of 2012, while quarterly retail sales of social consumer goods and fixed asset investment data for the fourth quarter of 2011 are used.
. ② Although quarterly retail sales of social consumer goods and fixed asset investment data contain some valuable information, based on current technology, it is not yet possible to combine this information in DSGE estimates.
. ③ Schmitt-Grohé and Uribe (2012) found that if investment goods price data are not used, the contribution of investment know-how technical shocks in economic fluctuation may be overestimated.
. ① Based on the compilation method of the price index of the National Bureau of Statistics, for the quarterly price index, the year-on-year growth rate of the cumulative value is a simple arithmetic average of the quarterly year-on-year growth rate. See Zhao (2005).
. ② The downward trend in the equipment price index relative to the GDP deflator is more pronounced than the total fixed asset investment price index. When the steady-state Ƴ value increases from 1.003 to 1.01, its corresponding annual investment production technology progress rate increases from 1.2% to about 4%.
. ① The model assumes that there is a financing and net worth problem for the investment goods producer, the input is it, and the output is it represents the probability of corporate bankruptcy, which is affected by the net value of the enterprise and the risk shock; μ represents the observed cost caused by asymmetric information.
. ② See Christiano and Davis (2006) and Chari et al. (2007) for rigorous proof.
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