A multivariate time series analysis of the United States aggregate production function

This study examines the effects of hours of work per unit of private sector capital, the relative price of energy, government capital per unit of private sector capital, and inflation on private sector output per unit of capital in the U.S. over the period 1952–90. A small vector autoregressive model that comprises the variables typically employed in single-equation estimates of the aggregate production function is used. Variance decompositions and cumulative impulse response functions indicate that hours of work per unit of private sector capital, the relative price of energy, and the inflation rate have significant effects on private sector output per unit of capital over the 1952–90 period. However, there is no evidence of a significant effect for government capital per unit of private capital. An historical decomposition that begins in 1973 with the emergence of a “productivity slump” and continues through 1990 indicates that shocks to hours of work per unit of capital, the relative price of oil, and inflation appear important in explaining output per unit of capital but shocks to government capital are not important.