Sources of Output and Price Variability in a Macroeconometric Model

There has been much recent discussion about the ultimate sources of macroeconomic variability. Shiller (1987) surveys this work, where he points out that a number of authors attribute most of output or unemployment variability to only a few sources, sometimes only one. The sources vary from technology shocks for Kydland and Prescott (1982), to unanticipated changes in the money stock for Barro (1977), to "unusual structural shifts," such as changes in the demand for produced goods relative to services, for Lilien (1982), to oil price shocks for Hamilton (1983), to changes in desired consumption for Hall (1986). (See Shiller (1987) for more references.) Although it may be that there are only a few important sources of macroeconomic variability, this is far from obvious. Economies seem complicated, and it may be that there are many important sources. The purpose of this paper is to estimate the quantitative importance of various sources of variability using a macroeconometric model. Macroeconometric models provide an obvious vehicle for estimating the sources of variability of endogenous variables. There are two types of shocks that one needs to consider: shocks to the stochastic equations and shocks to the exogenous variables. Shocks to the stochastic equations are easy to handle. They are simply draws from the postulated distribution (usually normal) of the structural error terms, the distribution upon which the estimation of the model is based. Shocks to the exogenous variables are less straightforward to handle. Since by definition exogenous variables are not modeled, it is not unambiguous what one means by exogenous-variable shock. Another possibility is to postulate that exogenous-variable shocks are the errors that forecasting services make in their forecasts of the exogenous variables. The sources of output and price variability are examined in this paper using my United States model (Fair (1984)). The procedure that was followed, which is discussed in detail in the next section, is briefly as follows. Autoregressive equations were estimated for 23 exogenous variables in the model. These variables make up all the important exogenous variables in the model (in my view). These equations were then added to the model. There are 30 structural stochastic equations in the model, and so the expanded model includes 53 stochastic equations. The 53 x 53 covariance matrix of the error terms was then estimated. In estimating this matrix the error terms in the structural equations were assumed to be uncorrelated with the error terms in the exogenous-variable equations, which means that the matrix was taken to be block diagonal (with a 30 x 30 block and a 23 x 23 block). This procedure is consistent with the assumption upon which the estimation of the model is based, namely that the exogenous variables are not correlated with the error terms in the structural equations.