تعمیر و نگهداری سرمایه و استهلاک در طول چرخه کسب و کار

This paper develops and estimates a stochastic general equilibrium model with capital maintenance, which affects endogenously the depreciation rate of capital. The estimate of maintenance series is found to track survey-based measures for Canada quite closely and to generate the procyclical pattern of maintenance observed in the data. We use our model estimates to infer the time profile of equipment capital depreciation in Canadian and US manufacturing. The depreciation rate is estimated to be volatile and highly procyclical in both countries.

Casual empiricism suggests that expenditures on capital maintenance constitute an integral part of the capital accumulation process. Broadly, outlays on capital maintenance cover the “deliberate utilization of all resources that preserve the operative state of capital goods” ( Bitros, 1976). As pointed out by Feldstein and Foot (1971), surveys on planned investment in the US for the period 1949–1968 suggest that roughly one-half of ‘gross’ investment aimed at maintaining the operative state of capital goods (replacement and modernization) as opposed to ‘new’ investment (expansion). Capital maintenance is, thus, directly related to capital depreciation and many authors have studied the optimal maintenance level at the firm level with the depreciation rate modeled as an endogenous function of maintenance outlays. 1 McGrattan and Schmitz (1999) were the first to provide a detailed picture on the size of aggregate capital maintenance using evidence from the Canadian survey on Capital and Repair Expenditures, which is the only source of aggregate long-run data on capital expenditures in newly purchased assets (‘new’ investment) and maintenance available at the national level. According to this survey, total (private and public) maintenance and repair expenditures in Canada amounted on an average to around 6.3% of GDP for the period 1956–1993. This number is roughly equal to one-third of spending on ‘new’ investments and, when compared to other ‘engines of growth’, is somewhat lower than education spending (6.8% of GDP), but far above the average spending on R&D (1.4% of GDP) over the same period, suggesting that maintenance expenditures are ‘too big to ignore’. This paper develops and estimates a Dynamic Stochastic General Equilibrium (DSGE) model, in which capital maintenance together with capital utilization affect endogenously the capital depreciation rate. Our model is found to perform well in replicating key features of the data and allows us to derive the time profile of endogenous capital depreciation in a general equilibrium setup. Several studies have attempted to estimate the depreciation rate, mainly in US manufacturing, using various single or multi-equation econometric approaches (see Epstein and Denny, 1980; Hulten and Wykoff, 1981a and Hulten and Wykoff, 1981b; Nadiri and Prucha, 1996a and Nadiri and Prucha, 1996b; Jorgenson, 1996, Oliner, 1996 and Huang and Diewert, 2011). Most of these papers find that the depreciation rate is fairly stable and that a constant depreciation rate may be a valid approximation for calibration exercises. On the other hand, Tevlin and Whelan (2003) point out that the rapid depreciation of computing equipment that took place in the 1990s led to a rise of the estimated depreciation rate for aggregate equipment capital. This assessment is confirmed by Doms et al. (2004) and Geske et al. (2007). Our results complement the findings in those studies: the implied depreciation rate for equipment capital in Canadian and US manufacturing displayed substantial volatility and a highly procyclical pattern over the last 50 years. What generates the difference in our estimate relative to the previous ones is the behavior of capital maintenance. While investment spending can be typically obtained from fixed non-residential private investment on property, plant and equipment in national accounts, and capital outlays from panel data for two-digit or plant-level manufacturing firms (in the US Compustat Industrial database), capital maintenance is mainly undertaken by employees. Hence there are no recorded market transactions. Moreover, maintenance and repair services purchased by firms in the market are typically treated as transactions involving intermediate goods. Thus, although maintenance activities are included in measured real output, their magnitude cannot be recovered by standard sources, like national accounting systems. Given the scarcity of available estimates for maintenance, we use the ‘Capital and Repair Expenditures,’ survey, which covers the period 1956–2005, to obtain proxies for maintenance and ‘new’ investment of equipment capital in the Canadian manufacturing sector. According to this data, total expenditures in ‘new’ investment and maintenance was on an average 16.7% of manufacturing output, with the average share of maintenance over total investment amounting to 36.1% and accounting for 6% of output and 4.9% of the capital stock. Turning to the cyclical properties of the data, we observe that maintenance expenditures are procyclical. Fig. 1a and b plots spending on capital maintenance and the associated maintenance to capital ratio (henceforth, MK ratio), and manufacturing output. Both measures of maintenance are strongly procyclical in agreement with the evidence reported by McGrattan and Schmitz (1999). 2 Fig. 1. Maintenance, capital and output: Canada, 1956–2005. (a) Maintenance vs output. (b) Maintenance to capital ratio vs output. Figure options We set up an otherwise standard Real Business Cycle (RBC) model in which capital outlays comprise, apart from ‘new’ investment that adds directly to the capital stock, maintenance expenditures that affect the capital decay rate. We also employ a general specification for the depreciation function that embeds the effect of capital utilization on depreciation, as in Burnside and Eichenbaum (1996), and its interactions with capital maintenance. The structural parameters of the model are estimated with Bayesian techniques using aggregate Canadian manufacturing data for output, capacity utilization, total investment, consumption and hours worked as observables for the period 1956–2005. The model generates estimates for capital maintenance expenditures that mimic reasonably well the cyclical behavior of actual survey-based series for Canada. Given the success of the model for Canada we also obtain consistent estimates for capital maintenance in the US over the period 1958–2009, a period for which there has been no systematic data collection on this type of outlays.3 We then use these estimates to obtain the time profile of the depreciation rate of equipment capital in Canadian and US manufacturing over the business cycle. To the best of our knowledge very few DSGE macroeconomic models have attempted to endogenize maintenance outlays. Early contributions to this literature can be found in Licandro and Puch (2000) and Collard and Kollintzas (2000). In both studies maintenance moves countercyclically, which contradicts the stylized facts presented in Fig. 1a and b. Collard and Kollintzas (2000) consider two types of labor that can be used in production and maintenance, respectively. Since higher productivity causes labor in production activities to be more efficient, maintenance activities may fall after a total factor productivity (henceforth TFP) shock, but, at the same time, higher output efficiency releases labor towards maintenance activities. In equilibrium the first effect dominates and maintenance is countercyclical driving depreciation rates up during booms. In our specification the impact of technology shocks on maintenance depends solely on its interaction with capital utilization. Licandro and Puch (2000) argue that maintenance should be countercyclical because it is cheaper for firms to repair and maintain machines in recessions. They formalize this argument by assuming that the cross derivative of the depreciation function with respect to maintenance and utilization is positive. Our estimates instead suggest that the sign of this derivative is negative. Some papers have investigated issues that affect the trade offs discussed in this paper. For example, Whelan (2002) and Tevlin and Whelan (2003) study how investment and depreciation respond to technology shocks, a feature that is crucial to determine the magnitude of the depreciation rate, particularly in high-technology sectors like computing. Boucekkine and Ruiz-Tamarit (2003) and Saglam and Veliov (2008) have studied how depreciation reacts to different types of technology shocks. Boucekkine et al. (2009) distinguish between endogenous age-related depreciation, which depends on optimal capital utilization when new capital goods arrive, and endogenous capital scrapping. They find that the scrapping rate drops when neutral technical progress accelerates while age-related depreciation remains unaffected, whereas both age-related depreciation and scrapping rates increase with investment-specific technical progress. In our model, a TFP shock raises capital utilization, maintenance and depreciation, while an investment-specific shock reduces the price of investment, leading to higher capital utilization and depreciation. When maintenance is considered, the fall in the price of investment increases the relative price of maintenance and agents find it optimal to decrease maintenance expenditures, which further raises the depreciation rate. Boucekkine et al. (2010) examine the short-run responses of investment and maintenance and find that they move in the same direction following technology shocks, thus, suggesting that they act complementary to each other. The rest of the paper is organized as follows. Section 2 presents the model. Section 3 discusses the results from the Bayesian estimation and presents the model dynamics. Section 4 presents the estimates for the time profile of capital depreciation in Canada and the US. Finally, Section 5 concludes.