'Small Data': Efficient Inference with Occasionally Observed States

58 Pages Posted: 22 Jul 2020 Last revised: 10 Jan 2022

See all articles by Andreas Lanz

Andreas Lanz

HEC Paris - Marketing

Philipp Müller

University of Zurich - Department of Business Administration

Gregor Reich

Tsumcor Research AG

Ole Wilms

University of Hamburg; Tilburg University - Tilburg University School of Economics and Management

Date Written: January 6, 2021

Abstract

We study the estimation of dynamic economic models for which some of the state variables are observed only occasionally by the econometrician—a common problem in many fields, ranging from industrial organization to marketing to finance. If such occasional state observations are serially correlated, the likelihood function of the model becomes a potentially high-dimensional integral over a nonstandard domain. We propose a method that generalizes the recursive likelihood function integration procedure (RLI; Reich, 2018) to numerically approximate this integral, and demonstrate its statistical efficiency in several well-understood examples from finance and industrial organization. In extensive Monte Carlo studies, we compare the performance of our approach to a recently suggested method of simulated moments. In all our demonstrations, we consistently and efficiently identify all model parameters, and we find that the additional variance of our estimator when going from full to occasional state observations is small for the parameters of interest.

JEL Classification: C13,C63,C49

Suggested Citation

Lanz, Andreas and Müller, Philipp and Reich, Gregor and Wilms, Ole, 'Small Data': Efficient Inference with Occasionally Observed States (January 6, 2021). HEC Paris Research Paper No. MKG-2020-1380, Available at SSRN: https://ssrn.com/abstract=3638618 or http://dx.doi.org/10.2139/ssrn.3638618

Andreas Lanz

HEC Paris - Marketing ( email )

Paris
France

Philipp Müller (Contact Author)

University of Zurich - Department of Business Administration ( email )

Rämistrasse 71
Zurich, CH-8006
Switzerland

Gregor Reich

Tsumcor Research AG ( email )

Switzerland

Ole Wilms

University of Hamburg ( email )

Allende-Platz 1
Hamburg, 20146
Germany

HOME PAGE: http://www.olewilms.com

Tilburg University - Tilburg University School of Economics and Management ( email )

PO Box 90153
Tilburg, 5000 LE Ti
Netherlands

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