پرتفوی بهینه باید خاص منطقه باشد ؟مدل چند منطقه ای با سیاست های پولی و قیمت دارایی جنبش مشترک

A multi-region, dynamic stochastic general equilibrium (MRDSGE) model is built to show that differences in the price elasticity of housing supply can be related to stylized facts on regional differences in (1) house price level, (2) house price volatility, (3) monetary policy propagation mechanism and (4) household asset portfolio. In addition, regional house prices are found to move more closely with regional fundamentals than with the national GDP. The correlation between the national stock price and the regional housing price also vary significantly across regions, which suggests that optimal portfolio should be region specific.

Several striking stylized facts on regional economic differences are related to the real estate markets. First, even within the same country, tremendous differences in house prices are observed across regions. For instance, Hwang and Quigley (2006) show that for a sample of U.S. metropolitan areas (MSAs), during the period 1975–2000, the real prices of housing in three California housing markets had more than tripled, while the real housing prices in three other MSAs (Houston, Albany, and Oklahoma City) were stagnant. What accounts for such cross-sectional diversity becomes an important research topic. The empirical works of Glaeser et al., 2005a, Glaeser et al., 2005b and Hwang and Quigley, 2006, among others, suggest that it is the local government regulation, such as “growth control” that limits the increase of housing supply and leads to a higher housing price at the equilibrium. Wheaton and Simonton (2007) find that “real construction costs have fallen slightly over the last 35 years,” suggesting that house price increase is very unlikely to be driven by “cost-inflation.” Recently, Saiz (2010) estimates the price elasticity of housing supply (henceforth, supply elasticity) and finds that variations across different metropolitan areas are very significant. 2 For example, the supply elasticities in both Miami and Los Angeles–Long Beach are estimated to be below 0.7, the counterpart in Las Vegas is close to 1.4, while the supply elasticities in Kansas City and Oklahoma City are estimated to be well above 3.0. Saiz (2010) also finds that highly regulated metropolitan areas typically have low estimates of supply elasticities. Not only the dramatic differences in the level of house prices can be attributed to the differences in the supply elasticities, the differences in the volatility of house prices may also be explained by the differences in the supply elasticities. To show the relation between volatility of real house price and supply elasticity, we construct semi-annual real house price by dividing nominal housing price index from Case–Shiller (monthly data are averaged into semi-annual data) by semi-annual city level CPI data from the BLS. 3 We focus on semi-annual data because city-level CPIs are not available on a consistent basis for higher frequency. We choose the longest sample for which we can obtain the most data points, resulting in a sample from 1991 S1–2010 S1 (S here denotes semi-annual), yielding 39 data points for each of the 14 metropolitan areas we have data. The real house price is then logged and HP filtered with a smoothing parameter of 400 before standard deviation is calculated. The estimates of the supply elasticities are from Saiz (2010). Table 1 reports the data while Fig. 1 provides a scatter-plot of the data together with the OLS regression line (red line). The slope of the regression line is − 3.6, 4 which is significant at 5%. It shows that metropolitan areas with higher supply elasticities tend to have lower volatility of real house prices.The third stylized fact is that the monetary policy propagation mechanism varies across regions. For instance, Carlino and Defina, 1998, Carlino and Defina, 1999 and Carlino and Defina, 2006, among others, find significant heterogeneity in the income responses to monetary policy across different regions or states. In particular, they find (1) strong evidence that manufacturing-intensive states are more responsive to changes in monetary policy shocks than the more industrially diverse states, and (2) weaker evidence that states containing a relatively larger concentration of small firms tend to be more responsive to monetary policy shifts than states composed of smaller concentrations of small firms. They also conclude that the evidence for a broad credit channel is weak. Fratantoni and Schuh (2003) construct a large VAR model in which the regional economic variables (regional house price, regional output, etc.) have potentially time-varying impact on the aggregate variables. The aggregate variables will then affect different regional variables simultaneously through the change in the mortgage rate, among other variables. They show that regional housing markets display heterogeneous responses to monetary policy shocks. The fourth stylized fact is related to the apparently spatial-dependent household portfolio. For instance, Goetzmann et al. (2004) find that rural portfolios are more diversified than urban portfolios in their Swedish dataset. Moreover, the portfolio diversification of the agents in their sample seems to be characterized by factors associated with urban growth. Kohler and Smith (2005) find that in the Australian data, with a 100 persons/km2 increase in urbanization, the portfolio share of home will increase by 0.4 percentage points on average. While there may be different explanations for each of these stylized facts, this paper attempts to study these facts in a unifying framework by extending a standard dynamic stochastic general equilibrium (DSGE) model to a multi-regional setting. While the previous literature focuses on the fiscal policy competition or coordination among regions, 5 this paper is devoted to study the regional housing markets and their interactions with the monetary policy in a multi-regional setting. 6 A merit of DSGE model is that both the quantity variables (such as consumption and investment) and price variables (such as non-durable goods price, housing price and stock price) are all endogenously determined. All agents maximize their objective functions in the model. Thus, it is easier to understand the transmission mechanism of the monetary policy. To highlight the role of the housing market in the aggregate economy as well as the financial market, we assume that the two regions are ex-ante identical except that the housing adjustment costs differ across regions. Without loss of generality, the adjustment cost is assumed to be lower in the region 1. 7 The two regions will then be subject to region-specific shocks. In this model as in practice, history dependent contingent claims are not available. Fortunately, there is a national stock market which (1) “owns” the firms in both regions, and (2) welcomes investment of agents from different regions. 8 The housing market, however, is “regional.” In particular, we assume that the agents in each region can only purchase and derive utility from the housing stock in the same region. 9 For monetary policy to have any real effects, we introduce nominal rigidity in the goods market. Following Calvo (1983), the renewal of nominal price contracts are random (which will be explained in more details later). To facilitate the comparison with the literature, the government is restricted to follow the Taylor rule (Taylor, 1993). In words, it means that the monetary authority will respond to the fluctuations of the inflation rate and the GDP. Taylor (1993) and many subsequent writers find that the Taylor rule is a good (first-order) approximation of the monetary policy that has been practiced. To focus on the business cycle effect, the regions in the model are assumed to have the same (long run) economic growth rate, which is then normalized to zero. While it might seem to be a strong assumption in the first glance, it may nevertheless be consistent with some empirical research.10 To further simplify the analysis, we also assume that the agents will not move across regions.11 Clearly, this paper builds on a large literature on monetary policy. 12 This paper complements the literature by explicitly considering different regions in a DSGE model. This enables us to differentiate the assets into two classes: national assets called “stock” and “bonds,” and a regional one called “housing.” Thus, this paper also introduces a “regional aspect” into the standard general equilibrium asset pricing literature, such as Jermann, 1998, Jermann, 2002 and Jermann, 2006. As it will become clear, the behavior of the national housing price (index) can behave very differently from the regional counterpart. An important implication, which we will discuss further, is that the optimal portfolio of agents from different regions can be very different. After the first draft of this paper has been presented in conferences, we become aware of Ortalo-Magne and Prat (2007). They intend to provide a micro-foundation for the difference in the supply elasticity based on a political economy model. This paper instead attempts to relate stylized facts concerning the city-level house prices to the corresponding supply elasticities. In particular, this paper shows that the difference in the supply elasticity does not only contribute to the differences in the levels and volatilities of the house prices, it can also lead to difference in the agents portfolio as well as difference in the monetary policy propagation mechanism across regions. Thus, the two papers have very different focuses and should be viewed as complementary to each other. The organization of this paper is as follows. The next section presents the model. Section 3 discusses solution method and calibration issues. Numerical results are presented in Section 4. The last section concludes.

There is a growing empirical literature on the regional difference as well as regional comovement. Theoretical works are, however, relatively rare. This paper takes a preliminary step in extending a typical DSGE model to incorporate regional considerations. The model is calibrated to match the U.S. economy in several dimensions and numerical results are generated. First, our model is consistent with the stylized fact that with lower housing supply elasticity, both the level and volatility of the house price will be higher. We are also able to generate heterogeneous regional housing market responses to monetary shock though we find that heterogeneity in housing supply elasticities alone is not enough to explain heterogeneous responses of regional output to monetary policy shock. Thus, we reproduce the empirical findings for both Carlino and Defina, 1998, Carlino and Defina, 1999, Carlino and Defina, 2006 and Fratantoni and Schuh, 2003. In a sense, we also confirm the observation that the housing market seems to be more vulnerable to monetary shocks compared to output. Moreover, we find that differences between the national variable and its regional counterpart can be very significant. For instance, while the national housing price is highly correlated to the national GDP, the housing price in some region needs not be. While the national housing price is highly persistent, the regional counterparts need not be. In general, the correlation between the regional housing price and the regional output is stronger than the counterpart between the regional housing price and the national GDP. In terms of the asset prices, this model successfully reproduces the near-unit-root behavior of the stock price. While the housing prices in both national and regional levels are also positively and serially correlated, there are regional differences. This model predicts that regions with lower housing adjustment costs would tend to have lower serial correlations. This model also predicts that the regions with lower housing adjustment costs will display much lower correlations with the national stock price, suggesting that the optimal portfolio can be region-specific. While some of these results have been documented before, some are awaiting further empirical confirmations. We hope that future empirical works will verify the testable implications delivered in this paper. This paper can be, and should be extended in other ways. For instance, for simplicity, we have assumed that the regions are ex-ante identical except for the housing adjustment cost. In practice, regions can differ in many dimensions. For instance, growth management or other forms of new supply restrictions seem to occur more frequently in areas with fast-growing housing price and economic output. In addition, different regions tend to specialize in different sectors, and hence will have different volatility in income. For instance, some regions may be more export-dependent, and hence are exposed to exchange rate risk, while some tend to mainly serve customers within the same country. The output in some regions may be more tied to some natural resources (such as oil or metal) or agricultural products. Their income would be more volatile than those that are not. Future work should incorporate such asymmetries as well. The model has also assumed a representative agent in each region. In practice, heterogeneity among agents, such as in the form of income inequality, is important. The heterogeneity among agents may also call for very different policies in a political economy context. This will significantly enrich the current framework. Open economy considerations such as the foreign capital flow or regional trade exposure should also be explored.