Research / BFI Working PaperNov 23, 2021

Empirical Investigation of a Sufficient Statistic for Monetary Shocks

Fernando Alvarez, Andrea Ferrara, Erwan Gautier, Hervé Le Bihan, Francesco Lippi

In a broad class of sticky price models the non-neutrality of nominal shocks is encoded by a simple sufficient statistic: the ratio of the kurtosis of the size-distribution of price changes over the frequency of price changes. We test this theoretical prediction using data for a large number of firms representative of the French economy. We use the micro data to measure the cross sectional moments, including kurtosis and frequency, for about 120 PPI industries and 220 CPI categories. We use a Factor Augmented VAR to measure the sectoral responses to a monetary shock, as summarized by the cumulative impulse response of sectoral prices (CIRP ), under three alternative identification schemes. The estimated CIRP correlates with the kurtosis and the frequency consistently with the prediction of the theory (i.e. they enter the relationship as a ratio). The analysis also shows that other moments not suggested by the theory, such as the mean, standard deviation and skewness of the size-distribution of price changes, are not correlated with the CIR. Several robustness checks are discussed.

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