Endogenous growth, depreciation rates and technological progress

Modifying Shell's (1966) model, I analyze the effects of including a scale factor and a decay rate on the accumulation of knowledge equation and on the steady states of an endogenous growth model. I investigate the variability of the capital depreciation rate, which is set up as a function of the technological progress, and describe the effects on the steady state of changes in parameters controlled by policymakers I depict how technological progress affects the capital depreciation rate via obsolescence. I analyze empirically how the capital depreciation rate implicit on the national accounts of different countries is a variable parameter more than a fixed one, and develop an approximate measurement of it. I discuss how capital depreciation is related to the net-to-gross investment ratio (NGIR), and how both variables are related to the level of industrialization of an economy and to technological progress. I perform this analysis in two steps. First, I use cross-section data to contrast characteristics between industrialized and developing countries, in terms of depreciation, NGIR, and per capita output. Second, I use time-series data of an industrialized country to analyze how technological progress affects and per capita output affects capital depreciation and NGIR. For the time-series analysis, I estimate technological progress (a Solow residual), and develop an error-correction model to analyze the long-run behavior of the NGIR, the real per capita GDP, and the total factor productivity. In the cross sectional analysis I find that higher depreciation rates and lower NGIR are associated to higher per capita output. In the time-series analysis I confirm the results from the cross-section analysis, and I find a positive relationship between the stock of knowledge index and the real GDP per capita, and a negative relationship between the stock of knowledge and the NGIR. As conclusion, I present some policy recommendations.