1、 外文翻译 原文 Exploring Metropolitan Housing Price Volatility Material Source: Springer Science Business Media, LLC 2006 Author: Norman Miller however, several fundamental questions regarding the volatility of housing market prices remain unanswered. The questions include why a housing market seems more
2、volatile in some periods than in others; why some markets are more volatile than others; and whether and how housing market volatility affects the economy. To answer these questions, we use a six-equation VAR model to study the dynamic interactions between the housing price volatility and a few impo
3、rtant economic and demographic variables, including the home value appreciation rate, the per capita personal income growth rate, the population growth rate, the change in the unemployment rate, and the per capita gross metropolitan product (GMP) growth rate. Data and Volatility Estimation This pape
4、r uses a large panel data set which comprehensively describes the single family housing markets of the United States at the MSA level. The data comprise the following time series for 277 MSAs from the third quarter of 1990 to the second quarter of 2002: per capita GMP, transaction-based price indice
5、s for single family homes, per capita personal income, population, and unemployment rates. The home price indices are provided by the Office of Federal Housing Enterprise Oversight (OFEHO); the personal income data are provided by the Bureau of Economic Analysis; the population data are provided by
6、Bureau of Census; and the unemployment and GMP data are provided by the Bureau of Labor Statistics. Table1 summarizes the autocorrelations of the per capita GMP growth rate, home price appreciation rate, per capita personal income growth rate, population growth rate, and unemployment rate, as well a
7、s the correlations among them. The table suggests positive first order autocorrelations for all variables except the per capita personal income growth rate. The table also shows that per capita GMP growth rate, population growth rate, and unemployment rate have high autocorrelations (0.412, 0.922, a
8、nd 0.920, respectively), while the autocorrelation for home price appreciation rate is merely 0.003. We plot the average and standard deviation of the series in Fig. 1. We use the following notations throughout this paper. For metropolis i in period t, we denote the home price index level by HPi,t ,
9、 the per capita personal income by PIi,t , the total population by POi,t, the unemployment rate by URi,t ,the per capita gross metropolitan product by GMPi,t.We use lower cases to represent the logged gross returns, for example hpi,t=log(HPi,t/HPi,t-1). In the first step of our analysis, we estimate
10、 time series of housing price volatility for the MSAs. We first estimate a model in which market participants form rational expectations of future home value appreciation rates using all available information. We assume that, in equilibrium, all participants adopt their optimal strategies, and ratio
11、nally forecast the future appreciation rate given their knowledge of each others optimal strategies and all other currently available information. We assume that the realized appreciation rate of the representative house of metropolis i in time period t equals the sum of the expected appreciation ra
12、te and an unpredictable shock. hpi,t=Ehpi,t|It-1+ i,t ( 1 ) The literature provides strong evidence of heterogeneity in housing markets. To accommodate the heterogeneity of housing markets, we estimate the rational expectation model for each MSA, respectively. We assume that investors use an ARMA mo
13、del with quarterly dummies to form their expectation of the log of the future home value appreciation rate. The maximum order of lags is 8 and AIC is used to determine the optimal lag and the optimal order of moving average errors. Since the heterogeneity of housing markets is allowed, the optimal s
14、pecification of the ARMA model varies across MSAs. Note that the ARMA specification is essentially consistent with the conventional approach to estimate volatility of stock returns, which projects stock returns on lagged returns and seasonal dummies and then fits the residuals to GARCH models. Table
15、 1 Data summary GDP HP PI PO UR VLTY Panel A. Autocorrelations Lag 1 0.412 0.003 -0.061 0.922 0.920 0.363 Lag 2 0.217 0.139 0.256 0.779 0.817 0.239 Lag 3 0.046 0.165 -0.128 0.608 0.710 0.112 Lag 4 -0.107 0.122 0.006 0.442 0.608 0.054 Panel B. Correlations GMP 1.0000 -0.002 0.302 0.040 -0.060 0.050 H
16、P 1.0000 0.014 0.118 -0.144 -0.032 PI 1.0000 0.024 -0.055 0.046 PO 1.0000 0.220 -0.036 UR 1.0000 0.044 VLTY 1.0000 We use series of the unpredictable appreciation component i,t from the MSA specific ARMA models to estimate volatility series. We denote by vltyi,t the volatility of the housing value a
17、ppreciation, which is defined as the variance of the unpredictable component of home value appreciation rate. We estimate vltyi,t with a GARCH (1,1) model with leverage terms. Unfortunately, the estimation of the GARCH model converges in only 34 MSAs, probably due to the relatively short sample peri
18、od. The characteristics of the volatility for the 34 MSAs are summarized in the last plot of Fig. 1, which documents the mean and standard deviation of the 34 volatility series, as well as the last column in Table 1, which documents the average autocorrelations of the volatility series and the avera
19、ge correlations between the volatility and other variables. It can be misleading to draw any conclusions regarding the time-varying nature of the volatility based on only the 34 MSAs, for they constitute about only 12% of the entire sample.Furthermore, estimations may be more likely to converge if t
20、he volatility has specific patterns that help the BHHH algorithm. In this sense, the 34 MSAs could be self-selected and thus are biased samples. Therefore, we use a simpler and more intuitive model to investigate the possible ARCH/GARCH structure for all 277 MSAs. Consider the following regression 2
21、2, , ,1ni t i k i t k i tiuu (2) Exploring the Determinants and Impact of Volatility We use vector autoregressions to study the determinants and impacts of the housing price volatility. Our analysis relies on the 34 MSAs, in which the GARCH estimation converges and thus we have reliable estimated vo
22、latility series. Vector autoregressions are popularized by Simss (1980) and are widely used to describe vector time series. We set up the following VAR model, . , ,1 1 1, , ,1 1 1Cp p pk i t k k i t k k i t ki t i tk k kip p pi t i tik i t k k i t k k i t kk k kA X B X v ltyXUDv lty ud a X b X c v l
23、ty (3) in which Xi,t is a vector of gmpi,t , hpi,t, pii,t, poi,t, and uri,t, Di is a vector of MSA dummies, Dt is a vector of time dummies, ,i t i tXXis a vector of positive (negative) values of Xi, tor 0, Ak, Bk, and Ck are vectors of coefficients, and Ui,t is a vector of error terms that is orthog
24、onal to the space spanned by the explanatory variables. We estimate the system in equation 3 row by row with feasible GLS that allows heteroskedasticity across MSAs. We first use OLS to obtain preliminary coefficient estimators and error terms. In the OLS regression, within transformation is used to
25、 eliminate MSA dummies, and transformed time dummies are kept in the regression. We use the residuals of the OLS regressions to construct the weighting matrix that allows for the heteroskedasticity across MSAs, and then use weighted OLS to obtain the FGLS estimators. We use AIC to choose the optimal
26、 order of the system, p, with preliminary vector autoregressions. Table 2 reports the estimated coefficients of the regression with the home price volatility as the dependent variable. This regression is particularly important for it reveals information with respect to the determination of the volat
27、ility. Among the 55 coefficients of lagged endogenous variables, the coefficients of ,1itgmp , ,3itgmp , ,1ithp , ,3ithp , ,1ithp , ,3itpi , ,1itvlty and ,2itvlty are statistically significant. The R2 of the regression is 0.35, which appears to indicate that the housing price volatility is fairly we
28、ll explained by lagged variables. We test the Granger causality between the volatility and other variables with F-tests. F-statistics can be constructed with the sum of squared regression residuals from a constrained regression and the sum from an unconstrained regression. Table 3 reports the F-stat
29、istics for 11 different null hypotheses. It provides evidence with respect to the determinants and impacts of the home price volatility: the volatility is statistically significantly affected by the growth rate of per capita GMP and the home value appreciation rate, and it statistically significantl
30、y affects the growth rate of per capita personal income and future volatility. The F-tests do not reveal much information regarding the economic significance of the interactions between the home price volatility and other variables; therefore, we use impulse response functions to investigate the eco
31、nomic significance of the relations. To construct the impulse response functions, we follow the convention (e.g., Hamilton, 1994) and let all lagged variables and intercepts be 0, and introduce a transitory shock on a particular noise term but not others. Figure 2 reveals how the home price volatili
32、ty responds to a transitory 10% increase (positive shock) and a transitory 10% decrease (negative shock) in the per capita GMP growth rate. Both the increase and the decrease magnify the home price volatility. However, the effects of the positive and the negative shocks are not symmetric. First, the
33、 volatility peaks more quickly after the positive shock, and the peak value is about 1.16, which means the volatility is about 16% higher than its equilibrium level. The effects of the negative shock seem more substantial and long lasting. The volatility peaks about 4 quarters after the shock, and t
34、he peak value is about 1.59, which indicates that the volatility level is about 59% higher than the equilibrium level. The effects decay slowly after 9 quarters, the volatility is still about 10% higher than the equilibrium level. Figure 3 reveals how the home price volatility responds to a transito
35、ry 10% increase (positive shock) and a transitory 10% decrease (negative shock) in the home appreciation rate. This figure also demonstrates asymmetry of the effects of positive and negative shocks. The volatility peaks at about 20% higher than the equilibrium level a quarter after the positive shoc
36、k, while it peaks at 218% higher than the equilibrium level a quarter after the negative shock. The effects of the negative shock decays more slowly after 9 quarters, the volatility is still about 10% higher than the equilibrium level. Interestingly, the effects seem cyclical the volatility almost r
37、eturns to the normal level 3 and 4 quarters after the positive and negative shocks, respectively, before increases again and then decays slowly. Both Figs. 2 and 3 appear to indicate that the housing market adjusts much more quickly to positive shocks than to negative shocks. This may relate to the
38、kinked supply curve of housing supply. Housing supply can increase relatively quickly since new houses can be built in quarters, but decreases only slowly. Consequently, positive shocks may be absorbed by the market more quickly than negative shocks. On the impact of volatility, Fig. 4 documents the
39、 dynamic responses of the home price volatility to an exogenous increase (positive shock) and an exogenous decrease (negative shock) in the volatility itself. The figure indicates that the volatility shocks decay fairly quickly. In fact, the volatility is just about 3% above (below) the equilibrium
40、level a quarter after the positive (negative) shock. The response of the per capita personal income growth rate to volatility shocks is statistically significant, as shown by Table 3, but not economically significant. The per capita personal income growth rate changes little after volatility shocks,
41、 so we do not plot the corresponding impulse response function. In short, there is not much economic impact of volatility change. Conclusions This paper analyzes the time variation as well as determinants and impact of the housing price volatility using a large panel dataset at the MSA level. Here t
42、he volatility series are estimated with GARCH models using regression residuals from rational expectation models of home appreciation rates. A six-equation panel VAR system is then used to study the dynamic interactions between volatility, the home appreciation rate, the per capita personal income g
43、rowth rate, the population growth rate, the unemployment rate change, and the per capita GMP growth rate. Granger causality tests are conducted based on the panel VAR. Our analysis allows for time-varying expectation of home appreciation rates, and controls for MSA- specific and time-specific variab
44、les. Our analysis provides a few important results. First, the possibility of an ARCH/ GARCH structure is confirmed for about 17% of the MSAs by X2 tests based on regressions of squared regression residuals from rational expectation models of home appreciation rates with respect to its lags. Further
45、more, F-tests based on the panel VAR regression also indicate that the volatility Granger-causes future volatility. Second, we find the per capita GMP growth rate and the home value appreciation rate Granger-causes the volatility. The volatility is magnified by both increases and decreases in the pe
46、r capita GMP growth rate and the home value appreciation rate. The effects are significant not only statistically but also in the economic sense. Impulse response functions show that the volatility can increase by 59 and 118% after a transitory 10% decrease in the per capita GMP growth rate and the
47、home value appreciation rate, respectively. Finally, we find the volatility Granger-causes the per capita personal income growth rate and future volatility. However, the impact of the volatility on the personal income growth rate is not economically significant. 译文 探索大城市房价波动 资料来源 ： 斯普林格 电子期刊网 作者： Norman Miller & Liang Peng 摘要： 本文 选取 美国 从 1990 年 1 月至 2002 年 2 月包含了 277 个测量系统的 一个大季度数据集 ， 运用 GARCH 模型和面板 VAR 模型来分析独栋住宅 价值增值的波动的时间变化和经济与波动之间的相互作用 。我们发现时变波动对17%的 测量系统（ MSAs） 作出解释 。利用 GARCH 模型判断系列波动，我们发现波动 是由住宅 增值速度和 GMP 增长率 引起的 。另一方面 ， 波动影响 了 个
