What do price equations say about future inflation?

This paper uses an econometric approach to examine the inflation consequences of the American Rescue Plan Act of 2021. Price equations are estimated and used to forecast future inflation. The main results are: (1) The data suggest that price equations should be specified in level form rather than in first or second difference form. (2) There is some slight evidence of nonlinear demand effects on prices. (3) There is no evidence that demand effects have gotten smaller over time. 4) The stimulus from the act combined with large wealth effects from past household saving, rising stock prices, and rising housing prices is large and is forecast to drive the unemployment rate down to below 3.5 percent by the middle of 2022. 5) Given this stimulus, the inflation rate is forecast to rise to slightly under 5 percent by the middle of 2022 and then comes down slowly. 6) There is considerable uncertainty in the point forecasts, especially two years out. The probability that inflation will be larger than 6 percent next year is estimated to be 31.6 percent. 7) If the Fed were behaving as historically estimated, it would raise the interest rate to about 3 percent by the end of 2021 and 3.5 percent by the end of 2022 according to the forecast. This would lower inflation, although slowly. By the middle of 2022 inflation would be about 1 percentage point lower. The unemployment rate would be 0.5 percentage points higher.