Aggregating Phillips curves

Since it burst onto the scene of mainstream monetary economics, the New Neo-Classical Phillips Curve has been the focus of two important empirical debates. First, to what extent properly measured marginal costs affect inflation dynamics. Second, to what extent purely forward looking inflation can be reconciled with the data. In this paper, we show heterogeneity in the pricing behavior of firms, matters for both issues. If pricing is heterogeneous, any estimation that ignores the issue – whether based on GMM techniques, or on Maximum Likelihood Estimators – is flawed, to an extent that increases with the correlation between aggregate and disaggregate price dynamics. We show the direction of the bias depends on the estimator, and is not the same for marginal costs or for expected inflation. In particular, under plausible parameter values, (homogeneous) Maximum Likelihood estimators induce a negative bias on the effects of marginal costs, but a positive one on the importance of inflation dynamics. In contrast, (homogeneous) GMM estimators induce a negative bias on marginal costs, yet a negative one as well on inflation dynamics. These are derived analytically. We use sectoral quarterly French data on prices and marginal costs to confirm the magnitude and direction of these biases in the data as well. These data also motivate our parametrization. This provides a rationale for the discrepancy of results in the literature according to the estimation method. Specifically, our French data illustrate the importance of the issue within one specific economy. More generally, and perhaps most importantly, our analytics provide a toolkit with which to gauge the magnitude and direction of an aggregation bias on the basis of any disaggregated data.