استهلاک سرمایه مسکن، تعمیر و نگهداری، و تورم قیمت خانه : برآورد از مدل تکرار فروش

The rate at which physical capital depreciates is fundamental to investment in the economy. Nevertheless, although housing capital accounts for one-third of the total capital stock, the rate at which housing capital depreciates has only rarely been directly estimated, in part because prior studies do not control for maintenance. For that same reason, widely publicized measures of house price appreciation overstate the capital gain from homeownership. Using data from the American Housing Survey we examine these issues. Over the 1983 to 2001 period, results indicate that gross of maintenance, housing depreciates at roughly 2.5 percent per year, while net of maintenance, housing depreciates at approximately 2 percent per year. Moreover, although the typical home appreciated at an annual real rate of roughly 0.75 percent, after allowing for depreciation and maintenance, the average homeowner experienced little capital gain.

This paper examines two closely related issues. First, the rate at which housing capital depreciates is fundamental to investment in the economy. As shown in Table 1, estimates from the US Bureau of Economic Analysis (BEA) indicate that housing accounts for roughly half of all private fixed assets and one-third of the total capital stock.1 Nevertheless, the rate at which hous-ing depreciates has only rarely been estimated, in part because prior studies do not control for maintenance. As a result, major federal data agencies such as the Bureau of Economic Analysis have been forced to use measures of housing capital depreciation rates that are based more on approximations than hard evidence in the data. Given the important role that such measures play in calculations of the stock and flow of capital in the economy, obtaining more reliable estimates of the rate at which housing depreciates is of considerable importance. Second, although the belief that homeownership is an excellent investment is deeply entrenched in popular culture, the capital gain enjoyed by homeowners is likely less robust than often portrayed. That is because widely publicized repeat sales measures of house price appreciation do not control for the contribution of maintenance to house price appreciation (Case and Shiller [4], Case and Quigley [3]).2 Although such indexes are appropriate for valuing portfolios of homes, we show that they overstate the capital gain from homeownership. Understanding the role of depreciation and maintenance is especially important in the current social and political environment. Recent popular accounts, for example, credit house price appreciation with propping up the economy, while new government policy initiatives seek to boost homeownership, especially among low income and minority households.3 To illustrate, Fig. 1 displays the growth of house prices in both real and nominal terms as reported by the National Freddie Mac Conventional Mortgage Home Price Index (also known as the Freddie Mac repeat sales index). Evident in Fig. 1, the growth in house prices has been particularly dramatic since the mid-1990s. Since that time, the Freddie Index has risen more rapidly than inflation at the same time that prices on financial assets have declined sharply. In response to these price patterns,the popular press has routinely touted housing as an outstanding investment. In March 2002, The Economist [22] ran a cover story entitled “The Houses That Saved TheWorld” in which it argued that rising house prices had sheltered the world economy from deep recession by supporting con-sumer sentiment and spending.4 The perception that housing is an excellent investment has also contributed to recent federal policies designed to promote homeownership.5 While house price appreciation may well have buoyed the economy in recent years and generated capital gains for homeowners, analysis of these issues has failed to consider the role of depreciation and maintenance. Considering the role of depreciation and maintenance, however, is difficult for several reasons. The first challenge is to obtain data on home maintenance. In our case, we address that need by using the American Housing Survey, the only major survey that provides detailed information on home maintenance. But in addition, maintenance may be endogenous to house value: it is likely that owners of expensive homes will spend more on home maintenance than owners of inexpensive homes. As such, one cannot simply put maintenance into a standard ordinary least squares hedonic regression of house value. Our solution to this problem is to expand the traditional repeat sales model of house price appreciation in two important ways. In the standard specification (e.g. Case and Shiller [4]), the percentage change in house price between sale dates is regressed on a set of annual dummies associated with the dates of sale. Attributes of the home and their shadow prices are assumed to be unchanged between sale dates and, therefore, drop out of the model.We build directly on that feature. Specifically, a home’s attributes tend to be correlated with maintenance, but otherwise have no natural role in the standard repeat sales specification. Accordingly, the attributes of a home make excellent instruments for maintenance in a modified repeat sales regression that includes the influence of maintenance efforts between sale dates.To complete our model, we also control for age-related depreciation as this enables us to estimate the independent effects of depreciation and maintenance on house price appreciation. Controlling for depreciation, however, also is not straight forward. That is because the change in age of the home between sale dates is perfectly collinear with the dummy variables that identify the dates of sale. To address this issue, we specify a non-linear rate of age-related depreciation in the model. We estimate our models using a panel of single family home sales from the American Housing Survey that cover the 1983 to 2001 period. Two principal specifications are considered: the standard model that we argue is appropriate for estimating the change in value for an existing portfolio of homes, and our expanded model that controls for both depreciation and maintenance using both ordinary least squares (OLS) and a three-stage least squares (3SLS) approach. For the 1983 to 2001 period, the standard model implies roughly a 0.75 percent real annual rate of appreciation. Upon controlling for maintenance and depreciation, the annual real rate of house price inflation is 2.68 percent.6 Thus, while highly publicized repeat sales measures such as the Freddie Mac and OFHEO (Office of Federal Housing Enterprise Oversight) indexes are appro-priate for estimating the change in value for a portfolio of homes, users of these indexes should be aware that they substantially underestimate house price inflation. Additional findings indicate that in the absence of maintenance, housing depreciates at a real annual rate of roughly 3.0 percent for the typical (median) home, referred to hereafter as the gross-of-maintenance rate of depreciation. At this rate, after fifty years the original housing capital would have fallen more than 75 percent in value. Of course, homeowners maintain their homes and this serves to slow the rate of decay. We find that for the typical homeowner, maintenance adds roughly 1 percent real per year to the value of the home, lowering the “net-ofmaintenance” rate of depreciation to roughly 2 percent. At that rate, after fifty years the typical home would have fallen more than 60 percent in value relative to a newly constructed unit. That rate of depreciation would support longstanding theoretical arguments and recent evidence from Rosenthal [18] that older homes tend to filter down to families of lower economic status. At the same time, the sizable contribution of maintenance to house price appreciation underscores the importance of ensuring that homeowners—and especially low-income homeowners—have sufficient means to maintain their homes. Finally, we also estimate the real annual capital gain enjoyed by homeowners. For the median homeowner, this rate was a negative 0.25 percent over the 1983 to 2001 period. Thus, policy makers and homeowners alike should be aware that the majority of homeowners experienced little capital gain net of maintenance expenditures over the 1983 and 2001. We proceed as follows. The following section describes our methodology for building both maintenance and aging of the home into the repeat sales model. Next, we describe our data and summary measures. The remaining sections present our results and conclusions.

This paper addresses two closely related issues. First, we estimate the rate at which housing capital depreciates gross of maintenance. Although that rate is fundamental to investment in the economy, we are not aware of other micro-data based estimates in the literature, in part because prior studies fail to control for both maintenance and age-related depreciation. Second, we estimate the capital gain realized by homeowners taking depreciation and maintenance into account. We examine these issues by comparing estimates from a standard house price repeat sales Model to a modified specification that takes age-related depreciation and maintenance into account. Because structural attributes of the home difference out of the standardModel, these make excellent instruments for maintenance in a two-stage least squares specification of the modified Model in which maintenance is allowed to be endogenous. In addition, we allow for a non-linear rate of age-related depreciation to avoid perfect collinearity with the annual house price index. These Models are estimated using a panel of single family home sales constructed from the American Housing Survey for the years 1983 to 2001. Results indicate that for the typical single family home, quality adjusted house price inflation over the 1983 to 2001 period averaged roughly 2.68 percent real per year, well above the roughly 0.75 percent real annual rate at which a typical portfolio of homes appreciated. That difference arises because standard repeat sales methods of measuring “quality adjusted” house price appreciation fail to control for the combined effects of maintenance and age-related depreciation. Maintenance, in this context, adds roughly one-half to one percent real annual appreciation to the typical home in the US, while age-related depreciation subtracts roughly 2.5 to 3.0 percent per year. Net of maintenance, therefore, the typical single family home depreciates at roughly a0.75 percent real annual rate at which a typical portfolio of homes appreciated. That difference arises because standard repeat sales methods of measuring “quality adjusted” house price appreciation fail to control for the combined effects of maintenance and age-related depreciation. Maintenance, in this context, adds roughly one-half to one percent real annual appreciation to the typical home in the US, while age-related depreciation subtracts roughly 2.5 to 3.0 percent per year. Net of maintenance, therefore, the typical single family home depreciates at roughly a 1.9 percent rate per year. At that rate, after fifty years the home would have depreciated roughly sixty percent, broadly consistent with longstanding arguments that aging of the housing stock is the primary mechanism by which markets provide low-income housing. Deeply entrenched folklore has also long held that owning a home is one of the most effective investments a family can make. Our estimates indicate that after controlling for depreciation and maintenance, homeownership was basically a breakeven investment for the typical homeowner over the 1983 to 2001 period. This result is well below what advocates of homeownership might hope for.