An N-dimensional generalization of the Amiti–Weinstein estimator

ABSTRACT

Amiti and Weinstein proposed an estimation framework to disentangle credit demand and supply shocks using matched bank-firm loan data. Here, we show that their estimator can be generalized to capture shocks arising in an arbitrary number of dimensions. Our algorithm permits empirical researchers to analyse multi-dimensional data sets using the Amiti–Weinstein framework. This may be beneficial both for studies on micro-level outcomes as well as for the literature on assessing the macroeconomic impact of idiosyncratic shocks. In an empirical application to a firm-product-country export data set, we highlight the usefulness of the generalized Amiti–Weinstein estimator, and we demonstrate the importance of considering additional dimensions when gauging the effect of granular shocks on aggregate fluctuations.

KEYWORDS:

• Aggregate fluctuations
• idiosyncratic shocks
• firm-level data
• multi-product firms

JEL CLASSIFICATION:

• C55
• C63
• F14
• F40

Acknowledgements

The views expressed are those of the author and do not necessarily reflect those of the Deutsche Bundesbank. I would like to thank João Amador for insightful discussions and invaluable help with the data. Comments by Dirk Bursian, Matthias Hartmann and Beau Lowhon are also gratefully acknowledged.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ Granular shocks in this literature refer to idiosyncratic shocks to large economic agents such as banks and firms that may result in aggregate effects, for example, by their interactions with other firms. In particular, Gabaix (2011) shows that with a fat-tailed distribution of firms, independent shocks to firms do not average out such that idiosyncratic fluctuations have a nonnegligible aggregate effect.

² Examples in the investment and trade literature include holder-institution-security (Pérez and Huerga 2016) and exporter-product-destination-importer data sets (Kramarz, Martin, and Mejean 2016), respectively.

³ The Stata code is available at https://sites.google.com/site/arnenagengast/.

⁴ Naturally, alternative methods for solving underdetermined linear systems, such as QR solvers, can be used.

⁵ See the Appendix for details on the equation system for $N=3$ as well as the data set and descriptive statistics.