GMM Estimation with Non‐causal Instruments*
| Published date | 01 October 2011 |
| Date | 01 October 2011 |
| DOI | http://doi.org/10.1111/j.1468-0084.2010.00631.x |
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©Blackwell Publishing Ltd and the Department of Economics, University of Oxford, 2011. Published by Blackwell Publishing Ltd,
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OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 73, 5 (2011) 0305-9049
doi: 10.1111/j.1468-0084.2010.00631.x
GMM Estimation with Non-causal InstrumentsÅ
Markku Lanne† and Pentti Saikkonen‡
†Department of Political and Economic Studies, University of Helsinki, PO Box 17
(Arkadiankatu 7), 00014 Helsinki, Finland (e-mail: markku.lanne@helsinki.fi)
‡Department of Mathematics and Statistics, University of Helsinki, PO Box 68
(Gustaf Hällströmin katu 2b), 00014 Helsinki, Finland
(e-mail: pentti.saikkonen@helsinki.fi)
Abstract
This note provides a warning against careless use of the generalized method of moments
(GMM) with time series data. Weshow that if time series follow non-causal autoregressive
processes, their lags are not valid instruments, and the GMM estimator is inconsistent.
Moreover, endogeneity of the instruments may not be revealed by the J-test of over-
identifying restrictions that may be inconsistent and has, in general, low finite-sample
power. Our explicit results pertain to a simple linear regression, but they can easily be
generalized. Our empirical results indicate that non-causality is quite common among
economic variables, making these problems highly relevant.
I. Introduction
The generalized method of moments (GMM) is widely used in different fields of eco-
nomics, including macroeconomics and finance. Among other things, its popularity pre-
sumably follows from the development of more and more complicated theoretical models
which would in practice be impossible to take to data by alternative methods, such as the
method of maximum likelihood (ML). Even if ML estimation was possible, the GMM
may be considered more robust in that it allows the researcher to concentrate on the central
implications of the theory without the need to specify an empirical model in detail. In their
survey, Hansen and West (2002) list the three most common uses of the GMM in eco-
nomics: estimation of a first-order condition or a decision rule from dynamic optimization
problem, examination of forecasting ability of survey data or of a financial variable, and
setups with efficiency gains from the use of many moments. The first two of these are
ubiquitous in the empirical analysis of asset pricing models, while all of them pertain to
macroeconomic applications.
For the GMM to be applicable, a sufficiently large number of instrumental variables are
needed that satisfy the relevance and exogeneity requirements. The former has received
ÅWe thank Joose Sauli for excellent research assistance and an autonomous referee and Anindya Banerjee (the
editor) for useful comments The usual disclaimer applies. Financial support from the Academy of Finland and the
OP-Pohjola Group Research Foundation is gratefully acknowledged.
JEL Classification numbers: C12, C22, C51.
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