Economic and Statistical Measurement of Physical Capital with an Application to the Spanish Economy

Empirical studies in macroeconomics and economic growth literature are highly dependent on the measure of the physical capital stock. The variables that contribute to explain the major problems in these areas of research always appear related, whether directly or indirectly, to capital stock and depreciation. The standard measurements of capital and depreciation are statistical measures based on assumptions about the average service life of capital goods, which are accumulated according to the perpetual inventory method. In this paper we propose an alternative method based on the equations that solve the dynamic optimization problem of the neoclassical firm. This method enables us to endogenously calculate the variables rate of depreciation and capital stock, yielding an economic estimation based on indicators of profitability such as the distributed profits and the Tobin's q ratio. This represents a change of paradigm in measuring capital and depreciation, which we supply along with an application to the Spanish economy. The results show an economic depreciation rate (endogenous) that fluctuates around the statistical rate (exogenous), and two time profiles for the economic and statistical capital stocks that are markedly different. In the context of a growth accounting exercise we show how capital intensity and total factor productivity play different roles in explaining growth over the past fifty years, depending on whether we are using statistical or economic measures. Finally, we analyze the paradox of productivity and conclude that the absence of positive correlation between investment in information and communication technologies and the rate of growth of total factor productivity may be due to a combination of the delay effect associated with such investment and the under-estimation of the true economic depreciation.