Substitution Bias and Fixed-Weight Price Indices in Time-Dependent Pricing Models

This paper compares inflation in true price indices to inflation in fixed-weight price indices. We construct model-based inflation measures in time-dependent pricing models that are analogous to measures of inflation in the data, e.g., the Consumer Price Index. In the standard new Keynesian model, when inflation rises rapidly, the differences between inflation in those indices and true price indices are increasing in the degree of price stickiness and the elasticity of substitution across goods. For commonly used parameter values, those differences are large and persistent for increases in inflation of the size seen after 2020 in the U.S