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We are grateful to the Banque de France for providing the time series on the duration of the workweek of capital, to Bob Ford and Marcello Estevão for stimulating comments, to Tam Bayoumi for his thoughtful discussion of an earlier version of the paper in an European I Department seminar, and to Jim Hamilton for a technical clarification. All errors and omissions remain the authors’ sole responsibility.
In the earlier studies, no adjustment was made for the utilization of the capital stock. Later, some (e.g., Jorgenson, 1966, and Solow, 1967) used the unemployment rate as a measure of the underutilization of capital. Griliches (1970) used the power utilization rate as a measure. Lucas (1970) modeled explicitly the supply of work effort to account for the absence of countercyclical real wage movements in the data, noting that as both hours worked and shift work are procyclical, they may be important in explaining cyclical fluctuations in the use of the capital stock.
A regressor’s measurement error makes ordinary-least-squares (OLS) estimates biased and inconsistent. The degree of the bias is directly related to the variance of the measurement error. See also Annex 1.
See Färe et al. (1994) for a detailed survey on production frontiers work, and Temple (1999) for a related survey on the empirical research on growth As discussed below, the measure of capital services used here also contains a unit root and is not cointegrated with labor hours and output. This suggests that the rejection of cointegration usually found in the literature may not hinge upon a regressor measurement error.
Since 1989 the Banque de France has conducted a survey specifically designed to assess capital operating time (Banque de France 2000) while Cette (1990) has constructed this indicator for 1957-1989.
In 1989, about 43 percent (4.5 percent) of workers worked in (continuous) shifts while in 2000 about 48 percent (nearly 9 percent) worked in (continuous) shifts.
Working in the opposite direction, the contractual workweek was reduced by law starting in 1998. The average workweek decreased from over 38 hours in 1998 to 36.5 hours in 2000.
The mean is weighted by the number of workers involved in shift work.
The unit root test is the augmented Dickey-Fuller test proposed by Elliott, Rothenberg, and Stock (1996).
An AR(2) process for TFP growth resulted in an order-two coefficient insignificantly different from zero.
This finding led Mankiw et al (1992) to consider a variant of the Solow model in which human capital as well as physical capital is accumulated.
Bernanke and Gürkaynak (2001) test a Solow growth model with human capital using the Summers-Heston database, and find in a cross-country framework that although the coefficient on human capital takes on reasonable values (between 0.3 and 0.4), the coefficient on physical capital becomes unreasonably low, and sometimes even insignificantly different from zero. While providing support for several of Mankiw et al’s key conclusions, Hamilton and Monteagudo (1998) find that investment in human capital has no ability to account for changes in growth rates over time.
The extent of the bias is large if we take the variance of the error in measurement as reflected by the difference in growth rates of the net capital stock unadjusted and adjusted. The variance is 2.8 with full adjustment of the capital stock, and 1.8 with an adjustment factor for the capital stock of only 10 percent of the workweek of capital.
The estimated regression is: unadjusted Solow residualt = 0.004 workweek of capitalt + rest, with a t-statistic for the slope of 7.71. The residual maximum gap with respect to the white noise alternative is 0.13 with a rejection limit of 0.31 for the null of white noise.
Values above 44 percent are statistically significant for this sample.
The unrestricted model estimated with the stock of capital adjusted for capacity utilization produced a labor coefficient of 0.67 and a capital coefficient of 0.26. The sum of coefficients was not statistically different from one. The level of the residuals was white noise, but the squared residuals displayed serial correlation.