'Small Data': Efficient Inference with Occasionally Observed States

60 Pages Posted: 22 Jul 2020 Last revised: 24 Feb 2021

See all articles by Andreas Lanz

Andreas Lanz

HEC Paris - Marketing

Philipp Müller

University of Zurich - Department of Business Administration

Gregor Reich

Norwegian School of Economics (NHH) - Department of Strategy and Management

Ole Wilms

Tilburg University - Tilburg University School of Economics and Management

Date Written: June 29, 2020

Abstract

We study the estimation of dynamic economic models if some of the state variables are observed only occasionally by the econometrician—a common problem in many fields, ranging from industrial organization over 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 non-standard 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. Further, we compare the performance of our approach to a recently suggested method of simulated moments in extensive Monte Carlo studies. In all our demonstrations, we can 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: CO1

Suggested Citation

Lanz, Andreas and Müller, Philipp and Reich, Gregor and Wilms, Ole, 'Small Data': Efficient Inference with Occasionally Observed States (June 29, 2020). 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

Norwegian School of Economics (NHH) - Department of Strategy and Management ( email )

Breiviksveien 40
N-5045 Bergen
Norway

Ole Wilms

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

PO Box 90153
Tilburg, 5000 LE Ti
Netherlands

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