Friday, April 9, 2010

The Marginal Products of Residential and Non-residential Capital

Economic theory suggests that marginal product of capital series might help predict economic growth forward one or two years, even under abnormal conditions such as wartime or depression. In some situations, the marginal product of capital is an essential ingredient in cost-benefit analyses (Harberger 1968; Byatt, et al., 2006; Mityakov and Ruehl, 2009). Evidence on the marginal product of capital can also help test various explanations for business cycles, and help identify causes and consequences of the recent housing “bubble.” The purpose of this paper with Luke Threinen is to produce annual and quarterly estimates of the marginal product of capital (net of depreciation), one each for the residential and nonresidential sectors of the U.S. economy.

By definition, the marginal product of capital net of depreciation is the change in net domestic product (NDP) during the accounting period (e.g., one quarter) that would result from an increase in the beginning-of-period capital stock of $1 worth of capital. In particular, the additional $1 of capital would have the same composition as the rest of the capital stock. For example, if the economy’s capital consisted of 400 identical structures and 100 identical vehicles, each of which cost $2 to acquire, then the marginal product of capital would be the extra NDP attained by starting the quarter with 400.4 identical structures and 100.1 identical vehicles (that is, $0.80 worth of structures and $0.20 worth of vehicles).

Suppose that origins of the current recession could be traced back to limits on the supply of aggregate investment due to a “credit crunch.” In fact real investment fell through the first year and a half of this recession, but the credit crunch theory says that the marginal product of capital would rise as a consequence of the increased cost of capital faced by those with new capital projects. Alternatively, financial crisis or something else could reduce labor usage more directly, and, given the complementarity of labor and non-residential capital in production, non-residential investment would merely respond to low marginal products of capital, thereby putting the non-residential capital stock on a path that is consistent with a lesser amount of labor usage (Mulligan, 2010).

The marginal product of capital is also interesting as an aggregate leading indicator of business conditions, which is the motivation for its use in a number of studies (e.g., Feldstein and Summers (1977), Auerbach (1983)). This relationship alone may make it a predictor of subsequent economic growth.

Additionally, Fisherian consumption-saving theory suggests that the marginal product of capital, or variations of it, should predict consumption growth.

Over the last ten years, the marginal and average products of residential capital fell, and then increased, as housing construction was booming and busting. In this sense, the residential data suggests that the supply of residential capital shifted along a relatively stable demand for the services of that capital. As indicated by the marginal product of residential capital at the end of 2009, current housing supply seems restricted by comparison with the housing boom (when the residential MPK was low), but fairly normal by comparison with the 1990s when the residential MPK was similar to what is was at the end of 2009. These patterns are consistent with the findings of Davis, Lehnert, and Martin (2008) and others that housing rent-price ratios were low during the housing boom, and with the conclusions that the housing boom was fueled by optimistic expectations, or by easy credit.

The marginal product of non-residential capital was much higher during the housing boom than it was during the recession, when rates of investment in non-residential equipment and software were low. In this sense, the supply of non-residential capital seems less restricted during the recession than it was before. In other words, the recession’s investment rates may have been low because of a slack labor market, rather than the other way around. In any case, the testing of various theories of this recession, and the prior housing cycle, can be enhanced with marginal products data like those shown in this paper.

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