Inflation and the Government Budget Constraint

In Sargent and Wallace (1973), we created a rational expectations model of the bivariate inflation-money creation process by solving the ‘inverse optimal predictor problem’ for Cagan’s (1956) adaptive expectations scheme. Our model was constructed by working backwards and finding a bivariate process for inflation and money creation that implied both that Cagan’s portfolio balance equation held and that adaptive expectations were rational.1 That model is ‘successful’ in several ways. First, the model explains the pattern of Granger causality in Cagan’s data, in which inflation Granger causes money creation, but not vice versa. Second, a version of the model predicts the pattern of correlations across countries between Cagan’s estimates of X and a (see Sargent and Wallace, 1973). Third, the model predicts that the residuals in the regression equation fit by Cagan will be random walks, which explains the very high serial correlation that Cagan actually encountered (see Sargent, 1977). Fourth, the model predicts a pattern of results obtained by Rodney Jacobs (1975) when he reversed the direction of regression in Cagan’s equation (see Sargent, 1976).