Maintenance and Repair: Too Big to Ignore

Most models of aggregate economic activity, like the standard neoclassical growth model, ignore the fact that equipment and structures are maintained and repaired. Once physical capital is purchased in these models, there are typically no more decisions made regarding its use. The theme of this article is that there is evidence to suggest that incorporating expenditures on the maintenance and repair of physical capital into models of aggregate economic activity will change the quantitative answers to some key questions that have been addressed with these models. This evidence is primarily from a little-used economywide survey in Canada. The survey shows that the activity of maintaining and repairing equipment and structures is an activity that is generally both large relative to investment and a substitute for investment to some extent—and to a large extent during some episodes. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. Most models of aggregate economic activity, like the standard neoclassical growth model, ignore the fact that equipment and structures are maintained and repaired. Once physical capital is purchased in these models, there are typically no more decisions made regarding its use. The theme of this article is that there is evidence to suggest that incorporating expenditures on the maintenance and repair of physical capital into models of aggregate economic activity will change the quantitative answers to some key questions that have been addressed with these models. This evidence is primarily from a little-used economywide survey in Canada. The survey shows that the activity of maintaining and repairing equipment and structures is an activity that is generally both large relative to investment and a substitute for investment to some extent—and to a large extent during some episodes. To illustrate our point that the answers to some key questions may change when spending on maintenance and repair is included in aggregate models, we present a simple representative firm model in which the maintenance and repair activity is a substitute for investment in providing gross capital services. In this model, we ask, What is the effect on the firm’s capital intensity of a cut in the capital income tax rate? We show that under reasonable conditions, the size of the increase in the firm’s capital intensity as a result of the tax cut depends on whether the model incorporates expenditures on the maintenance and repair of capital: including these expenditures in the model reduces the size of the increase in the firm’s capital stock. The reason the tax cut effect on the capital stock is smaller in the model with maintenance and repair is that the model reflects the fact that spending on maintenance and repair is treated differently in many tax codes than investment spending is. Usually, while investment expenditures are capitalized and depreciated over time, maintenance and repair expenditures can be deducted today from revenues in calculating pretax profits. Hence, changes in tax rates influence the firm’s spending decision. As tax rates are increased, maintenance and repair spending is substituted for investment. Because this substitute activity is available, the decrease in capital intensity following a tax increase is smaller than it otherwise would be. The same is true, of course, for the opposite direction: when tax rates are cut, the increase in capital intensity is smaller as well. To keep matters simple, we focus on this single question: What is the impact on a firm’s capital intensity of a cut in income tax rates? But it may well be that the answers to many other questions will change as spending on maintenance and repair is included in aggregate models. One key question is, What is the size of the welfare gain from cutting the capital income tax rate? This question has been studied by Lucas (1990) and Laitner (1995), but without attention to the maintenance and repair activity. The extent to which including maintenance and repair in aggregate models will change their quantitative answers to such questions will depend on the size of these expenditures compared to investment and the extent to which the maintenance and repair activity substitutes for investment. These are some of the data that will be needed to calibrate aggregate models with maintenance and repair. This brings us to the second part of the article, where we discuss the existing evidence on maintenance and repair. For many countries, like the United States, it is not possible to determine the size of maintenance and repair in the aggregate given current data collection procedures. However, this is not true for Canada: For over 40 years, the government agency Statistics Canada has conducted an annual survey of businesses, government organizations, and households which collects data on maintenance and repair expenditures and investment expenditures for all sectors of the economy. The Canadian survey shows that maintenance and repair expenditures in Canada are large. Over the period 1961–93, they averaged about 6 percent of the country’s gross domestic product (GDP). Over roughly the same period, spending on the maintenance and repair of equipment averaged about 50 percent of spending on new equipment. Spending on maintenance and repair of structures is not as large, averaging about 20 percent of spending on new structures. Spending to maintain and repair both equipment and structures averaged 30 percent of spending on all new physical capital. The Canadian survey also suggests that the activities of maintenance and repair and investment are to some degree close substitutes for each other. For example, during downturns in economic activity, maintenance and repair spending falls less sharply than investment spending does. During upswings, maintenance and repair spending rises less sharply than investment spending does. Overall, the standard deviation of maintenance and repair expenditures is about 60 percent of the standard deviation of investment expenditures. Within the manufacturing industry, the difference is even more dramatic: there the standard deviation of maintenance and repair expenditures is about 38 percent of the standard deviation of investment expenditures. This suggests that during downturns, new purchases are delayed and older equipment and structures are maintained to a greater extent. We also look at a particular Canadian industry, the iron ore industry, which in the 1980s faced much more than a typical downturn—its output fell about 50 percent in a year, and its future was extremely uncertain. In this industry, equipment investment spending fell to nearly zero during the period of crisis; yet the industry still spent significant amounts on the maintenance and repair of equipment. (Maintenance and repair expenditures on equipment fell about the same amount as output, that is, in half.) This evidence on the behavior of maintenance and repair spending over the business cycle and in times of crisis suggests a good deal of substitutability between the activities of maintenance and repair and investment. The organization of the article is as follows. In the next section, we present a standard representative firm model in which the maintenance and repair and investment activities are substitutes in augmenting next period’s gross capital services. There we examine the effect of an income tax cut on the firm’s capital intensity, asking how adding maintenance and repair to the model changes the model’s conclusions. In the following section, we discuss the available data on maintenance and repair. We focus on the Canadian data, though we also discuss the U.S. data, which are much less comprehensive. We close the article with some remarks about the value of the Canadian survey data. A Simple Model In this section, we discuss the simplest possible decision problem of a representative firm that can both invest in new capital and maintain and repair its old capital. We then introduce taxes and show how the two activities are often treated differently in the tax code. After these two steps, we show how a cut in income taxes will have a smaller impact on capital intensity in a model which incorporates maintenance and repair. A Firm’s Problem Consider the problem of a firm that can opt to maintain its capital stock in order to slow the rate at which the capital stock depreciates. (For now, we will ignore the repair function.) The firm uses capital K and labor L to produce a final good Y, Y = F(K,L). The capital stock evolves over time according to the following law of motion: (1) Kt+1 = [1 − δ(Mt/Kt)]Kt + Xt where time is indexed by t, X is purchases of new capital goods, M is purchases of maintenance services, and δ(M/K) is the rate at which the capital stock depreciates. In most analyses, δ(M/K) is assumed to be constant. Here we assume that δ is a decreasing function, so that as you increase the maintenance services per unit of the capital stock, you decrease the rate at which capital depreciates, as in Chart 1. In Chart 1, δ(0) = 1, so that if not maintained, the current stock of capital vanishes in one period, and the capital stock next period is equal to investment expenditures this period. Suppose that the firm sells its output at a unit price, hires labor at a wage w, buys new capital goods at a price p (measured in, say, dollars), and buys maintenance services at a price q (also measured in dollars). The firm’s problem is to maximize its discounted profit stream,