Economic Measurement of Endogenous Capital and Depreciation: an Application to the Spanish Economy and its Regions
In the quantitative and applied economic literature it is frequent to find references to the statistical measurement of capital and depreciation. In this paper we present an alternative method of estimating the capital stock and the depreciation rate. The equations that solve the dynamic optimization problem of the neoclassical firm also enable us to endogenously calculate the rate of depreciation and capital stock variables, yielding an economic estimate of both. Our calculation method uses profitability indicators such as distributed profits and Tobin’s q ratio. Our results differ from those obtained by applying the permanent inventory method for Spanish economy and its regions during the period 1964-2011. The economic depreciation rate fluctuates around the statistical rate. Two time profiles for the economic and statistical capital are markedly different, as attested to by the disparity of their growth rates. The paper also shows that economic shocks turn aside the economic depreciation rate of the statistical rate with different intensity in the Spanish regions. This allows us to approximate the relative regional resilience based on the behaviour of depreciation and to establish three groups of regions according to their capacity of absorption and adaptation to the different shocks.