We develop a linear GMM estimator of the discrete-time mixed proportional hazard (MPH) model of duration with an arbitrary distribution of unobserved heterogeneity. We allow for competing risks, observable characteristics, and censoring. We prove our estimator is consistent and apply it to the duration of price spells. We find substantial unobserved heterogeneity with economically meaningful implications for the response of output to a monetary policy shock in a model with time-dependent pricing rules and for the degree of state dependence in a model of price plans.

Monetary policy; Interest rates; Inflation (Finance)

The empirical evidence on rational inattention lags the theoretical developments: micro evidence on one of the most immediate consequences of observation costs––the infrequent observation of state variables––is not available in standard datasets. We contribute to filling the gap using new household surveys. To match these data we modify existing models, shifting the focus from nondurable to durable consumption. The model features both observation and transaction costs and implies a mixture of time-dependent and state-dependent rules. Numerical simulations explain the frequencies of trading and observation of the median investor with small observation costs and larger transaction costs.

We prove that the ratio of kurtosis to the frequency of price changes is a sufficient statistic for the real effects of monetary shocks, measured by the cumulated output response following the shock. The sufficient statistic result holds in a large class of models which includes Taylor (1980); Calvo (1983); Reis (2006 ); Golosov and Lucas (2007 ); Nakamura and Steinsson (2010); Midrigan (2011); and Alvarez and Lippi (2014). Several models in this class are able to account for the positive excess kurtosis of the size distribution of price changes that appears in the data. We review empirical measures of kurtosis and frequency and conclude that a model that successfully matches the microevidence on kurtosis and frequency produces real effects that are about four times larger than in the Golosov-Lucas model, and about 30 percent below those of the Calvo model. We discuss the robustness of our results to changes in the setup, including small inflation and leptokurtic cost shocks. (JEL, E23, E31)

If Exchange Rates are Random Walks, Then Almost Everything We Say About Monetary Policy is Wrong by Fernando Alvarez, Andrew Atkeson and Patrick J. Kehoe. Published in volume 97, issue 2, pages 339-345 of American Economic Review, May 2007