GMM estimation with noncausal instruments under rational expectations

Lof, Matthijs (2011): GMM estimation with noncausal instruments under rational expectations.

Abstract

There is hope for the generalized method of moments (GMM). Lanne and Saikkonen (2011) show that the GMM estimator is inconsistent, when the instruments are lags of noncausal variables. This paper argues that this inconsistency depends on distributional assumptions, that do not always hold. In particular under rational expectations, the GMM estimator is found to be consistent. This result is derived in a linear context and illustrated by simulation of a nonlinear asset pricing model.

• Item Type: MPRA Paper
• Language: English
• Keywords: generalized method of moments, noncausal autoregression, rational expectations
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes

References

Hansen, B. E. and K. D. West: 2002, ‘Generalized Method of Moments and Macroeconomics’. Journal of Business & Economic Statistics 20(4), 460–69.

Hansen, L. P.: 1982, ‘Large Sample Properties of Generalized Method of Moments Estimators’. Econometrica 50(4), 1029–54.

Hansen, L. P. and K. J. Singleton: 1982, ‘Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models’. Econometrica 50(5), 1269–86.

Lanne, M., J. Luoto, and P. Saikkonen: 2012, ‘Optimal Forecasting of Noncausal Autoregressive Time Series’. International Journal of Forecasting (forthcoming).

Lanne, M. and P. Saikkonen: 2009, ‘Noncausal vector autoregression’. Research Discussion Papers 18/2009, Bank of Finland.

Lanne, M. and P. Saikkonen: 2011a, ‘GMM Estimation with Noncausal Instruments’. Oxford Bulletin of Economics and Statistics 73(5), 581–592.

Lanne, M. and P. Saikkonen: 2011b, ‘Noncausal Autoregressions for Economic Time Series’. Journal of Time Series Econometrics 3(3), Article 2.

Lucas, R. E. J.: 1978, ‘Asset Prices in an Exchange Economy’. Econometrica 46(6), 1429–45.

Ludvigson, S. C.: 2011, ‘Advances in Consumption-Based Asset Pricing: Empirical Tests’. Working Paper 16810, National Bureau of Economic Research.

Tauchen, G.: 1986, ‘Finite state markov-chain approximations to univariate and vector autoregressions’. Economics Letters 20(2), 177–181.

Tauchen, G. and R. Hussey: 1991, ‘Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models’. Econometrica 59(2), 371–96.

Wright, J. H.: 2003, ‘Detecting Lack of Identification in GMM’. Econometric Theory 19(02), 322–330.

Yogo, M.: 2004, ‘Estimating the Elasticity of Intertemporal Substitution when Instruments are Weak’. The Review of Economics and Statistics 86(3), 797–810.