zbMATH — the first resource for mathematics

Estimation of conditional moment restrictions without assuming parameter identifiability in the implied unconditional moments. (English) Zbl 1441.62744
Summary: A well-known difficulty in estimating conditional moment restrictions is that the parameters of interest need not be globally identified by the implied unconditional moments. In this paper, we propose an approach to constructing a continuum of unconditional moments that can ensure parameter identifiability. These unconditional moments depend on the “instruments” generated from a “generically comprehensively revealing” function, and they are further projected along the exponential Fourier series. The objective function is based on the resulting Fourier coefficients, from which an estimator can be easily computed. A novel feature of our method is that the full continuum of unconditional moments is incorporated into each Fourier coefficient. We show that, when the number of Fourier coefficients in the objective function grows at a proper rate, the proposed estimator is consistent and asymptotically normally distributed. An efficient estimator is also readily obtained via the conventional two-step GMM method. Our simulations confirm that the proposed estimator compares favorably with that of M. A. Domínguez and I. N. Lobato [Econometrica 72, No. 5, 1601–1615 (2004; Zbl 1141.91635)] in terms of bias, standard error, and mean squared error.

62P20 Applications of statistics to economics
Full Text: DOI
[1] Ai, C.; Chen, X., Efficient estimation of models with conditional moment restrictions containing unknown functions, Econometrica, 71, (2003), 1795-1843 · Zbl 1154.62323
[2] Bierens, H.J., Consistent model specification test, Journal of econometrics, 20, 105-134, (1982) · Zbl 0549.62076
[3] Bierens, H.J., A consistent conditional moment test of functional form, Econometrica, 58, 1443-1458, (1990) · Zbl 0737.62058
[4] Bierens, H.J., Topics in advanced econometrics, (1994), Cambridge University Press New York · Zbl 0806.62093
[5] Carrasco, M.; Florens, J.-P., Generalization of GMM to a continuum of moment conditions, Econometric theory, 16, 797-834, (2000) · Zbl 0968.62028
[6] Chao, J.C.; Swanson, N.R., Consistent estimation with large number of weak instruments, Econometrica, 73, 1673-1692, (2005) · Zbl 1151.62366
[7] Chamberlain, G., Asymptotic efficiency in estimation with conditional moment restrictions, Journal of econometrics, 34, 305-334, (1987) · Zbl 0618.62040
[8] Chen, X.; White, H., Laws of large numbers for Hilbert space-valued mixingales with applications, Econometric theory, 12, 284-304, (1996)
[9] Chen, X.; White, H., Central limit and functional central limit theorems for Hilbert-valued dependent heterogeneous arrays with applications, Econometric theory, 14, 260-284, (1998)
[10] Domínguez, M.A.; Lobato, I.N., Consistent estimation of models defined by conditional moment restrictions, Econometrica, 72, 1601-1615, (2004) · Zbl 1141.91635
[11] Donald, S.G.; Imbens, G.W.; Newey, W.K., Empirical likelihood estimation and consistent tests with conditional moment restrictions, Journal of econometrics, 117, 55-93, (2003) · Zbl 1022.62046
[12] Gallant, A.R.; White, H., A unified theory of estimation and inference for nonlinear dynamic models, (1988), Basil Blackwell Oxford, UK
[13] Hansen, L.P., Large sample properties of generalized method of moments estimators, Econometrica, 50, 1029-1054, (1982) · Zbl 0502.62098
[14] Hansen, L.P.; Heaton, J.; Yaron, A., Finite-sample properties of some alternative GMM estimators, Journal of business and economic statistics, 14, 262-280, (1996)
[15] Hansen, L.P.; Singleton, K.J., Generalized instrumental variable estimation of nonlinear rational expectations models, Econometrica, 50, 1269-1286, (1982) · Zbl 0497.62098
[16] Hansen, B.E.; West, K.D., Generalized method of moments and macroeconomics, Journal of business and economic statistics, 20, 460-469, (2002)
[17] Kitamura, Y., Empirical likelihood methods with weakly dependent processes, Annals of statistics, 25, 2084-2102, (1997) · Zbl 0881.62095
[18] Kitamura, Y.; Tripathi, G.; Ahn, H., Empirical likelihood-based inference in conditional moment restriction models, Econometrica, 72, 1167-1714, (2004) · Zbl 1142.62331
[19] Newey, W.K., Efficient instrumental variables estimation of nonlinear models, Econometrica, 58, 809-837, (1990) · Zbl 0728.62107
[20] Newey, W.K., Efficient estimation of models with conditional moment restrictions, (), 419-454
[21] Newey, W.K.; McFadden, D., Large sample estimation and hypothesis test, (), 2111-2245
[22] Qin, J.; Lawless, J., Empirical likelihood and generalized estimating equations, Annals of statistics, 22, 300-325, (1994) · Zbl 0799.62049
[23] Stinchcombe, M.B.; White, H., Consistent specification testing with nuisance parameters present only under the alternative, Econometric theory, 14, 295-325, (1998)
[24] Stuart, R.D., An introduction to Fourier analysis, (1961), Halsted Press New York · Zbl 0168.38102
[25] White, H., An additional hidden unit test for neglected nonlinearity, (), 451-455
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.