In U.S. business cycles, residential investment differs from consumption and business investment in two respects. First, residential investment leads US GDP, while business investment lags and consumption coincides with U.S. GDP. This lead-lag relationship is supported empirically by and widely studied in existing literature, e.g. in Green (1997) and Leamer (2007). Second, residential investment is more volatile than consumption and business investment. This chapter attempts to explain these two dynamic features of residential investment. This chapter defines the lead-lag relationship using the auto correlation of residential investment, consumption and business investment with GDP. For instance, residential investment leads GDP. What I mean by this is that residential investment has a higher correlation with future GDP than it has with previous and current GDP. Please refer to Appendix 4 for a detailed descriptions of the data and these second moments.
Understanding the dynamics of residential investment and its role in the business cycle is important. The United States’ aggregate housing value constitutes about half of the country’s aggregate private wealth, as documented by Greenwood and Hercowitz (1991). Therefore, the housing market is an important element affecting the behavior of consumption and investment. In addition, residential investment is a good predictor of economic recessions. In the past fifty years, eight of ten recessions (including the most recent one) were preceded by a severe reduction in residential investment, as discussed in Leamer (2007). Indeed, Leamer (2007) suggested that housing is the sector most important to economic recessions, and any attempt to control the business cycle needs to focus particularly on household investment.
In this chapter, two key assumptions help explain the dynamics of residential investment. First, collateralized consumer loans, such as mortgages, are less restricted in size and carry lower interest rates than unsecured consumer loans, such as credit card debt. This assumption is consistent with the reality of the U.S. financial market. In 2002, the 30-year mortgage rate in the U.S. was 6.40 percent, while the average interest rate on credit card loans was 16.6 percent. This suggests that, even if unsecured consumer loans are available to everyone, their high cost of borrowing will keep most consumers from using them as a major financing resource. This finding is consistent with the fact that most consumer debt in the United States is collateralized.
Second, agents receive a signal of TFP one period in advance, which provides more information than current TFP. There is an empirical literature that presents evidence supporting this assumption about information. For example, Beaudry and Portier (2006) show that changes in interest rates and equity prices are almost perfectly correlated with innovations in future TFP. Some recent studies incorporate this assumption in their business cycle models and match the U.S. data better than models without this assumption, which further validates the assumption. For instance, Backus, Routledge and Zin (2007) demonstrate that by adding a predictable component into TFP growth, the DSGE model can account for the fact that the interest rate leads GDP by two quarters. Jaimovich and Rebelo (2006) provide a new theory of recessions from the perspective of information shocks. Recessions can occur when current productivity fails to reach the level that has previously been signaled.
A simple example can illustrate the main mechanism at work in this chapter. An agent receives good news about future productivity shocks and wants to increase current purchases, including housing purchases, in order to intertemporally smooth her consumption. Because her current income does not increase, she has to dissave to finance her increased expenditures. She is able to borrow at a lower rate of interest for most of her housing purchases, which is not possible for purchases of other types of consumption. As a result, the agent will buy more housing relative to other goods. In other words, the accessibility of credit through mortgages makes residential investment respond more quickly to signals of future TFP shocks. This can account for why residential investment leads consumption and GDP. If the signal turns out to be accurate, the agent will achieve a higher income and become less financially constrained. At this time, she is able to increase her consumption of other goods, which explains why consumption tends to coincide with GDP. This is the income effect of a positive signal.
However, there is also a substitution effect in the general equilibrium model where interest rates are endogenously determined by the marginal return on business capital. Because future productivity is expected to increase, the agent can also expect to obtain a higher capital income if she chooses to invest more in business capital now and consume later. The result discussed above will therefore reverse if the substitution effect dominates the income effect. The substitution effect is the reason why the existing literature gets the counter factual result that business investment leads consumption, which leads residential investment in business cycles. This question is addressed in my model by considering income and wealth heterogeneity. The agent’s current consumption increases with her expected life-time income. For a wealthy individual, financial wealth constitutes the majority of her expected lifetime income, which decreases in the event of good news due to a higher expected discount rate. Thus, wealthy agents tend to reduce housing and invest more in business capital in response to positive news. In contrast, for a poor individual, labor income constitutes the majority of her expected lifetime income, which increases because of a higher expected wage. Poor individuals borrow more and buy more housing in response to positive signals. The savings from the wealthy will be used to finance increased mortgages taken by the poor. Because most of the consumption in this economy is carried out by the agents whose wealth is below the mean, this process leads to a reallocation of wealth from business investment to residential investment in the event of positive signals. Therefore, the model can generate the lead-lag relationship and the high volatility of residential investment. This mechanism is consistent with the differences in the compositions of family finances over various wealth levels in the United States. As shown in 2001 data, households between the 10th and 90th percentiles of the wealth distribution borrowed 72.7 percent of collateralized consumer loans. Households above the 90th percentile in terms of wealth held 72.8 percent of financial assets. This mechanism is also consistent with the existing literature on consumption and saving. For example, Storesletten, Telmer and Yaron (2004) document that consumption choices of less wealthy agents, such as the young, are more sensitive to changes in expected labor income.
The existing literature attempts to account for these two dynamic features of residential investment, but has done so with limited success. In standard DSGE models of homogeneous agents, when there is a positive technology shock, the representative agent tends to reduce residential investment and increase business investment because of the substitution effect explained above. Modified versions of these standard models have had some success, but they need very special assumptions. Davis and Heath-cote (2005), for instance, can obtain the result that both residential investment and business investment coincide with GDP. In their models, the increase of residential investment is due to the positive productivity shocks in construction sectors. Consumers buy more houses as a result of lower prices. However, this story of supply-driven cycles is inconsistent with the positive correlation between house prices and residential investment, which instead favors a demand-driven explanation. Gomme, Kydland and Rupert (2001) introduce a time-to-build component, making the assumption that business investment projects require one more period to start than does home investment. Their models generate similar results in terms of the lead-lag relationship as Davis and Heath-cote (2005). This key assumption might be true for the constructions of business structures, which take more time than residential construction. However, these models do not account for the fact that business investments in equipment and software can happen almost instantly.
Fisher (2007) assumes a complementary relationship between business capital and household capital in business productivity. Fisher (2007) makes improvements in accounting for the lead-lag relationship. His model is consistent with residential investment leading business investment, though the leadership of residential investment to GDP is still absent. Moreover, this key assumption that larger houses can improve labor efficiency is not that firmly convincing to me.
In contrast to these papers, my chapter stresses the demand effect. It emphasizes that, as a form of consumption, housing mostly relies on the aggregate effect of individuals with low and medium wealth. These individuals are more adversely affected by borrowing constraints. Hence, mortgages are important in that they enable poor agents to respond rapidly to expectation shocks in the form of increased housing purchases.
In section 2, I first solve the partial equilibrium model where interest rates are fixed. Following Jaimovich and Rebelo (2006), I introduce information as noisy signals about next period’s productivity. The signal has the probability p ? [0,1] of being correct. The agents form their expectations of future productivity based on the current TFP and the signal. I compute three different models. By comparing the numerical results from the three models, I find that the two assumptions of information and collateral constraints both crucial in generating the result that residential investment leads consumption and GDP.
In section 3, I discuss the general equilibrium model where interest rates are determined endogenously as the marginal return on business capital. Numerical results display the difference of policy functions among agents at different wealth levels. In the event of good signals, poor agents tend to borrow more and buy larger houses while rich agents tend to save more and buy less. I compute the correlation coefficients of residential investment, consumption and business investment with GDP from the simulated data. They are consistent with the broad patterns of lead-lag relationship and the higher volatility of residential investment that we observe in the data.
