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GMM Estimation with Non‐causal Instruments *
Author(s) -
Lanne Markku,
Saikkonen Pentti
Publication year - 2011
Publication title -
oxford bulletin of economics and statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.131
H-Index - 73
eISSN - 1468-0084
pISSN - 0305-9049
DOI - 10.1111/j.1468-0084.2010.00631.x
Subject(s) - endogeneity , econometrics , estimator , generalized method of moments , autoregressive model , instrumental variable , causality (physics) , series (stratigraphy) , simple (philosophy) , sample (material) , mathematics , economics , statistics , paleontology , philosophy , physics , chemistry , epistemology , chromatography , quantum mechanics , biology
This note provides a warning against careless use of the generalized method of moments (GMM) with time series data. We show 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 overidentifying 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.