Small and Large Price Changes and the Propagation of Monetary Shocks, By Alvarez, Le Bihan, and Lippi. Discussion

Transcription

1 Small and Large Price Changes and the Propagation of Monetary Shocks, By Alvarez, Le Bihan, and Lippi Discussion Alberto Cavallo MIT and NBER Central Bank of Chile, August

2 Main Findings For a large class of models, the cumulative output effect of a monetary shock is shock Distribution of size of changes Frequency Main advantage: no need to specify details of the model kurtosis/frequency is a sufficient statistic for output effects Empirical results: kurtosis of 4 for US, 5 for France distribution is between a normal and Laplace

3 The shape of the distribution of price changes Why use kurtosis? it measures the share of extreme values (small and large) relative to intermediate values peakedness + fat tails or lack of shoulders Source: Balandra and MacGillivray (98) Intuition selection in size and timing

4 Empirical Challenges for Kurtosis 1. Kurtosis is very sensitive to measurement error, which affects both extremes of the distribution Fat tails: typos, incorrect matching of products Small changes: weekly averages, coupon use, unit values, product substitutions With unit values or weekly averages Cavallo (2012) Scraped Data and Sticky Prices Cavallo & Rigobon (2012) The Distribution of the Size of Price Changes

5 Empirical Challenges for Kurtosis Many distributions are bimodal, with relatively little mass close to zero Cavallo & Rigobon (2012) we reject unimodality in 2/3 rds of the distributions Model is better suited to match unimodal distributions JAPAN_GAS CANADA_SUPERMARKET

6 Empirical Challenges for Kurtosis 2. Kurtosis is very sensitive to the effects of cross-sectional heterogeneity A solution: standardize price changes at sub-category level US_SUPERMARKET AUSTRIA_SUPERMARKET

7 Empirical Challenges for Kurtosis Problem: standardization changes the meaning of a small or large price change it is small or large relative to the mean of that category UK_ELECTRONICS Alternative: why not measure kurtosis at a sub-category level, and get a summary statistic (eg. mean) across all sub-categories?

8 Empirical Challenges for Kurtosis 3. Asymmetry, bimodality, and center away from zero Kurtosis is well defined for symmetric, unimodal distributions. Symmetric bimodal distributions tend to have lower kurtosis because there is more mass at the shoulders Kurtosis in asymmetric distributions? With multiple modes away from zero? With less standard distributions additional parameters may be needed to fully describe the shape of the distribution.

9 Kurtosis and the Size of Price Changes An alternative to measure the relative importance of small vs large changes Proportional Mass Score Cavallo & Rigobon (2012)

10 Results with BPP data in many countries 250 retailers in 40 countries Large brick-&-mortars that sell online 2008 to 2014 Measure frequency kurtosis kurtosis of standardized changes mean kurtosis across categories and

11 Stickiness and Kurtosis in 40 countries Removing Sales country Duration Months % increases kurt st_kurt mean_kurt M M (using mean_kurt) r_duration r_st_kurt r_m ARGENTINA AUSTRALIA AUSTRIA BELGIUM BRAZIL CANADA CHILE CHINA COLOMBIA FRANCE GERMANY GREECE HUNGARY INDIA INDONESIA IRAN IRELAND ISRAEL ITALY JAPAN KOREA NETHERLAND NEW ZEALAN NORWAY POLAND PORTUGAL RUSSIA SINGAPORE SOUTH AFRIC SPAIN SWEDEN THAILAND TURKEY UAE UK USA VENEZUELA Mean PRELIMINARY

12 Cumulative Output Effects (kur/freq) PRELIMINARY Note: Using mean_kurt

13 Time series of kur/frequency PRELIMINARY

14 Time series of kur/frequency PRELIMINARY

15 Chile: Major Retail Chains

16 Conclusions The paper highlights the importance of the shape distribution of the size of price changes to estimate output effects Allows us to abstract from details of the various competing models existing in the literature, and focus on something we can objectively measure Kurtosis may be a sufficient statistic to describe the shape of the distribution but empirically there are many challenges Measurement error Heterogeneity across categories Ratio kurtosis/frequency can be easily measured over time in a large number of countries opportunity to study reactions to observable shocks