Monetary Policy and the U.S. Housing Market Pt 2

3.2. Different horizons In the estimation the selection of the horizon for which the restrictions hold is adhoc. Other authors using the same identification procedure have selected different horizons for the sign restrictions. For instance, Scholl and Uhlig (2006) used a 12 month horizon to study the impact of monetary policy on exchange rates, while Uhlig (2005) used horizons of 3, 6, 12 and 24 months to study the impact of monetary policy on output. For completeness, we must check the results using different horizons. Figure 6 plots the response of housing starts (top) and residential investment (bottom), when the restrictions are imposed for 3, 9, 12 and 24 periods. Figure 6 indicates that as we expand the horizon under which the restrictions hold (i.e. longer horizon), the response of the housing market activity variable to a contractionary monetary policy shock lasts for a longer period. This is especially the case for residential investment. For instance, when the horizon is 3 periods the response of residential investment is not significant, while when the horizon is 9 periods the response is significant. In this case (horizon = 9), the initial drop in housing starts is close to 1%, while residential investment drops by about .5%. Moreover, when the horizon is 24 periods housing starts also drop by about 1%, while the drop in residential investment exceeds .5%. << Figure 6 >> Several studies have previously reported a negative response of residential investment to monetary policy shocks. For instance, Erceg and Levin (2006) showed that the initial response to a contractionary monetary policy shock of an index of consumer durables and residential investment is negative (they estimated the drop to be close to .7 percent). Iacoviello and Neri (2007) using a small-scale dynamic stochastic general equilibrium model estimated a drop in residential investment in response to a monetary policy shock that exceeded 3 percent. McCarthy and Peach (2002) estimated the initial drop of residential investment after a monetary policy shock to be close to 3 percent in both the pre-deregulation and post-deregulation periods. Our results suggest that the response is smaller (about .5 percent), but this does not necessarily imply a non-relevant response of the housing market to monetary policy shocks. Residential investment accounts for about 4 to 6 percent of GDP, which implies that a reduction of .5% in residential investment has important economic consequences. 4. Results using the Choleski decomposition One of the main critiques of the Choleski decomposition is that it is not unique, which means that results for impulse response functions will depend on the ordering of the variables. A possible solution is to try different orderings and compare the impulse response functions for each ordering. But this will only be valid if it is known that the true model is recursive (rare in economics), and only the ordering is unknown (Fackler, 1990). In order to impose a recursive structure, we must select the ordering of the variables. Furthermore, we have to choose one variable whose innovations will be interpreted as monetary policy shocks. Following Bernanke and Blinder (1992), shocks to monetary policy are defined as a one-unit standard deviation shock to the federal funds rate. We use two alternative orderings in the estimation. The first ordering is: real GDP, housing variable, house prices, GDP price deflator, the commodity price index, the federal funds rate, nonborrowed reserves and total reserves. In this case, nonborrowed reserves and total reserves respond contemporaneously to monetary policy shocks, while the other variables respond to innovations in monetary policy with one lag. In the second ordering we place the measure of housing market activity (housing starts or residential investment) after the federal funds rate. While for reasons of space we do not report the responses of all variables to a monetary policy shock under the recursive structure, a few words regarding the response of the federal funds rate are in order. The initial raise in the federal funds rate is above 60 basis points, the impact remains close to 50 basis points after one year. This response is bigger than the response obtained under the sign restrictions and it is also closer to the response obtained by Erceg and Levin (2006). The responses of housing starts and residential investment under the recursive structure are presented in Figure 7. In both cases, the response is negative and significant. The response is significant for almost 30 months for housing starts and for about 40 months for residential investment. In the estimations with the sign restrictions, only the response of residential investment when the restrictions horizon is 24 periods is significant for more than 30 months. In all other cases under the sign restrictions, the response lasts for a shorter period than the case with the Choleski decomposition. It is also important to notice the difference in the size of the impact. Using the sign restrictions the initial drop in housing starts after the contractionary monetary policy shock is about 1%. The impact is much bigger in the case of the Choleski decomposition. With the Choleski, the initial impact is close to 3%. The impact is also bigger for residential investment. In the estimation with sign restrictions the estimated impact on residential investment is about .5%, while with the Choleski decomposition the estimated impact is close to 2%. <

> There is also a difference in the fraction of the variance in housing that monetary policy shocks explain when sign restrictions and the Choleski decomposition are used. Using the Choleski decomposition, results from variance decompositions suggest that monetary policy shocks account for 11 to 14 % of the variations in housing starts. On the other hand, the sign restrictions approach indicates that monetary policy shocks account for only 4 to 5 % of the variations in housing, a fraction that is not significant. 5. Summary and conclusion This article has examined the relationship between monetary policy and the U.S. housing market using an identification procedure similar to the one suggested by Uhlig (2005). The identification scheme imposes sign restrictions on the response of some of the variables for a number of periods after a monetary policy shock. We assume that shocks to monetary policy do not lead to increases in the GDP deflator, house prices, a commodity price index, non-borrowed reserves and real GDP, or decreases in the federal funds rate for a certain period. No restrictions are placed on the response of the housing market activity variable (housing starts or residential investment). The response of the housing variable is left “agnostically” open by the identification procedure. Overall, the results suggest that contractionary monetary policy shocks have a negative impact on housing starts and residential investment. The response is, in general, similar across U.S. regions. However, the impact of monetary policy on housing seems to be stronger in the Midwest. When the horizon for which the restrictions are imposed is expanded (to 9, 12 or 24 periods), the impact of a monetary policy shock lasts for a longer period (especially for residential investment). A comparison with the results obtained using the conventional Choleski decomposition reveals important differences. In the estimation with sign restrictions the response of the housing activity variable to a monetary policy shock is smaller and lasts for a shorter period than in the case with the Choleski decomposition. Moreover, there are cases under the sign restrictions for which we fail to find a significant response of the housing variable to the monetary policy shock. Once we become “agnostics” about the impact of monetary policy on the housing market, the results suggest that the impact is much less certain. Appendix What follows is a brief summary of Uhlig’s (2005) pure-sign-restriction methodology. Please refer to the original source for further details. We want to define a monetary policy impulse vector as one in which the sign restrictions hold. That is, a monetary policy impulse vector is an impulse vector, so that the responses of prices, real GDP and nonborrowed reserves are non-positive and the response of the federal funds rate is non-negative at all horizons k = 0,.., K . Because of identification issues, Uhlig recommends that we supplement the identification assumption by imposing a prior. The prior is proportional to a Normal-Wishart (see Uhlig (1994) for details). Empirically, the procedure is as follows: 1) Take n1 draws from the VAR posterior and n2 draws from an independent uniform prior (see Uhlig (2005) for details). 2) Construct the impulse vector. 3) For each draw, calculate the impulse responses at horizon k = 0,.., K . 4) Check if the impulse response functions satisfy the sign restrictions. 5) If all the impulse response functions satisfy the sign restrictions keep the draw. If any of the impulse response functions do not satisfy the sign restrictions discard the draw. Stop after obtaining n3 impulse response functions with the desired sign. The error bands are calculated using the draws kept. In the estimation we used n1 = n2 = 2,000, n3 = 1,000 and K = 3, 6, 9, 12 and 24. Figure 1 – Housing starts (thousand units, annualized) and recessions as determined by the NBER (shaded areas). Source: U.S. Census Bureau. 1400 1200 1000 800 600 400 200 0 1965 1970 1975 1980 1985 1990 1995 2000 2005 Figure 2 - Housing starts (thousand units, annualized) divided by regions. South (dashed), West (solid, light), Midwest (solid) and Northeast (solid, bold). Source: U.S. Census Bureau. .5 .0 -.5 4 0.0 0.0 0 -0.5 -0.5 -1.0 -4 10 20 30 40 10 20 30 40 Real GDP Housing Starts 4 .5 0 -1.0 10 20 30 40 10 20 30 40 House Prices Price Deflator 1 1 0 0 -1 -1 -2 -2 .0 -.5 -4 10 20 30 40 10 20 30 40 Commodity Price Federal Funds Rate 10 20 30 40 10 20 30 40 Nonborrowed Reserves Total Reserves Figure 3 – Response to a contractionary monetary policy shock one standard deviation in size. Restrictions are in place for 6 periods. Housing stars are included in the estimation. .5 .0 -.5 4 0.0 0.0 0 -0.5 -0.5 -1.0 -4 10 20 30 40 Real GDP 4 Residential Investment .5 0 -1.0 10 20 30 40 10 20 30 40 10 20 30 40 House Prices Price Deflator 1 1 0 0 -1 -1 .0 -.5 -4 10 20 30 40 Commodity Price -2 10 20 30 40 Federal Funds Rate -2 10 20 30 40 Nonborrowed Reserves 10 20 30 40 Total Reserves Figure 4 – Response to a contractionary monetary policy shock one standard deviation in size. Restrictions are in place for 6 periods. Residential investment is included in the estimation. 4 4 4 4 0 0 0 0 -4 -4 -4 10 20 30 40 -4 10 20 30 40 10 20 30 40 Northeast Midwest 10 20 30 40 West South Figure 5 – Response of housing starts by U.S. region to a contractionary monetary policy shock one standard deviation in size. Restrictions are in place for 6 Periods. Housing Starts 4 4 4 4 0 0 0 0 -4 -4 -4 -4 10 20 30 40 10 20 30 40 10 20 30 40 10 20 30 40 Horizon = 3 Horizon = 9 Horizon = 12 Horizon = 24 Residential Investment 2 2 2 2 0 0 0 0 -2 -2 -2 10 20 30 40 Horizon = 3 10 20 30 40 Horizon = 9 -2 10 20 30 40 Horizon = 12 10 20 30 40 Horizon = 24 Figure 6 – Response of housing starts and residential investment to a contractionary monetary policy shock one standard deviation in size, using different horizons for the restrictions. First ordering Second ordering 4 4 4 4 0 0 0 0 -4 -4 10 20 30 40 Housing Starts -4 -4 10 20 30 40 Residential Investment 10 20 30 40 Housing Starts 10 20 30 40 Residential Investment Figure 7 – Response of housing starts and residential investment to a contractionary monetary policy shock using the Choleski decomposition. The monetary policy shock corresponds to one standard deviation in the federal funds rate. Correlations Residential Investment (2 Leads) Residential Investment (1 Lead) Residential Investment Residential Investment (1 Lag) Residential Investment (2 Lags) Mean Standard Deviation N Housing Starts Residential Investment 28.7 30.1 24.3 14.5 4.8 1559.9 337.2 492 58.6 86.0 100.0 86.0 58.6 316.6 105.6 492 Table 1 – Descriptive statistics of housings starts (thousand units, annualized), and residential investment (billion of chained 2000 dollars). Correlations are estimated using growth rates.