استهلاک درون زا، اندازه گیری اشتباه سرمایه کل و کاهش رشد بهره وری

When we allow capital depreciation to be endogenous, the acceleration of investment-specific technological progress can distort the measurement of the aggregate capital stock. Our quantitative exercise shows that this effect may cause a substantial bias in the measurement of total factor productivity and can account for a large portion of the observed productivity slowdown since the 1970s.

This paper demonstrates that, when we allow capital depreciation to be endogenous, the acceleration of investment-specific technological progress can distort the measurement of the aggregate capital stock. The mechanism is that faster investment-specific technological progress makes the replacement of capital more frequent,1 and this faster depreciation leads to a bias in the measurement of the capital stock. Rapid replacement of capital leads to an overestimation of the existing amount of capital since the capital depreciation rate is assumed to be constant in the conventional measurement.2 This mismeasurement is potentially very important. Caballero (1999) writes: Scrapping is an important aspect of the process of capital accumulation. Understanding it is essential for constructing informative measures of the quantity and quality of capital at each point in time. Nonetheless, the scrapping margin is seldom emphasized, I suspect, mostly because of the difficulties associated with obtaining reliable data. As a result, many time series comparisons of capital accumulation and productivity growth (especially across countries) are polluted by inadequate accounting of scrapping. Effective capital depreciation must surely be higher in countries undergoing rapid modernization process. (p. 847). Here, we formally evaluate this “scrapping margin”. Our approach is to use a formal model of the replacement decision to overcome the lack of economy-wide data on scrapping. Although Caballero’s emphasis is on cross-country comparison, we believe that this concern is warranted even when we analyze one country over time, especially when the economic environment is changing rapidly. Many economists reported an acceleration of investment-specific technological progress in the late 1970s. In a recent paper, Cummins and Violante (2002) argued that during this period, investment-specific technological progress accelerated from an annual rate of 3% to 5%. Our analysis shows that this acceleration can cause a large change in the rate of replacement. As a result, with the conventional measurement of capital (the perpetual inventory method with constant depreciation), the aggregate capital stock is overestimated. This bias has an important consequence in measuring total factor productivity (TFP). In the usual growth accounting exercise, the growth rate of TFP is measured as output growth minus the contribution of the growth in capital and labor. When the existing amount of capital stock is overestimated, the contribution of capital accumulation is overstated. Therefore, the growth rate of TFP is underestimated. The productivity slowdown in US economy since the 1970s has been the subject of many recent studies. In their paper analyzing recent US economic growth, Greenwood et al. (1997) observed that when investment-specific technological progress is taken into account, the level of the TFP in the US economy has been declining secularly since the late 1970s.3 From their Fig. 3 (p. 351), it can be seen that the TFP level (z) in 1990 is about 13% lower than in the late 1970s. This amounts to a 1% annual rate of decline. This large decline during the span of more than one decade is puzzling, since it is difficult to believe that the US economy has suffered from technological regress for so long. We show that the underestimation of TFP due to the mismeasurement of capital can resolve a substantial part of this puzzle. This paper is organized as follows. The next section reviews the empirical literature on investment-specific technological progress. Section 3 describes our model. In Section 4, we evaluate the effect of the change in the speed of investment-specific technological progress. In Section 5, we consider the implications of the model to the productivity slowdown. Section 6 concludes.

This paper demonstrates that investment-specific technological progress can have a substantial impact on the firm’s decision of capital replacement. When constant depreciation is assumed in the measurement of capital, the change in the rate of investment-specific technological progress causes substantial mismeasurement. This can account for Greenwood et al.’s (1997) observation that the growth rate of TFP has been negative for more than a decade. Our result is robust to the degree of specificity of capital (the change in θ). However, it turns out that the rate of wear and tear (the parameter δ) has an important effect on the degree of mismeasurement. An important future research topic is to empirically determine what fraction of capital depreciation is due to replacement and what fraction is due to wear and tear.