Friday, December 10, 2010

The Marginal Products of Residential and Nonresidential Capital through 2010 Q2

We will soon be updating our paper.

The level of the non-residential series changed a bit when we changed our treatment of indirect business taxes. Here's the (slightly) revised introduction:

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, help identify causes and consequences of the recent housing “bubble,” and help quantify the economic burdens of business taxes. The purpose of this paper 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, holding constant the total supply of all other factors. The additional $1 of capital is assumed to 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.” (Real investment did fall through the first year and a half of this recession.) The credit crunch theory says that the marginal product of capital would rise over this period as a consequence of the increased cost of capital faced by those with new capital projects. Alternatively, a financial crisis or something else could reduce labor usage more directly, and, given the complementarity of labor and non-residential capital in production, a fall in non-residential investment would merely result from 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. In a Robinson Crusoe economy, the consumer would save for the future by reducing current consumption and using the proceeds to build capital assets. She would then use the marginal product and capital gains from those assets to add to consumption in the future. Because the saving decision is made in the present while the principal and interest are spent in an uncertain future, the incentive to save depends on, among other things, the expected marginal product and expected capital gains. The current marginal product itself helps predict the incentive to save only to the extent that it is closely related to the expected sum of future marginal product and capital gains. For this reason, we present measures of the marginal product that might be more indicative of those expected gains, and (consistent with national accounting practices: see Fraumeni, 1997) measures of depreciation that reflect expected depreciation and obsolescence, rather than actual depreciation and obsolescence.

It is helpful to examine the marginal product of residential capital separately from the marginal product of non-residential capital for at least two reasons. For one, the aggregate demand for labor is expected to have a closer relationship with the stock of non-residential capital than the stock of houses, because workers use non-residential capital in doing their jobs. Additionally, some important capital market distortions – such as business taxes and the “housing bubble” – are expected to have opposite effects on the stocks of residential and non-residential capital, and thereby opposite effects on their marginal products.

Section II presents our methods for calculating annual marginal products, and discusses the findings for 1930-2009. The marginal product of capital is very different in the residential and non-residential sectors, both in terms of levels and fluctuations. Section III examines the importance of taxes in explaining the gap between marginal products in the two sectors. The methods and results for quarterly postwar marginal products through 2009-IV are presented in Section IV. In order to isolate some of the possible determinants of measured marginal products, Section V compares them with average products. Section VI concludes, and Appendices record the time series values discussed in the body of the paper.


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