zbMATH — the first resource for mathematics

Nonparametric dynamic panel data models: kernel estimation and specification testing. (English) Zbl 1284.62268
Summary: Motivated by the first-differencing method for linear panel data models, we propose a class of iterative local polynomial estimators for nonparametric dynamic panel data models with or without exogenous regressors. The estimators utilize the additive structure of the first-differenced model – the fact that the two additive components have the same functional form, and the unknown function of interest is implicitly defined as a solution of a Fredholm integral equation of the second kind. We establish the uniform consistency and asymptotic normality of the estimators. We also propose a consistent test for the correct specification of linearity in typical dynamic panel data models based on the $$L_2$$ distance of our nonparametric estimates and the parametric estimates under the linear restriction. We derive the asymptotic distributions of the test statistic under the null hypothesis and a sequence of Pitman local alternatives, and prove its consistency against global alternatives. Simulations suggest that the proposed estimators and tests perform well for finite samples. We apply our new method to study the relationships among economic growth, the initial economic condition and capital accumulation, and find a significant nonlinear relation between economic growth and the initial economic condition.

MSC:
 62G08 Nonparametric regression and quantile regression 62G09 Nonparametric statistical resampling methods 62G20 Asymptotic properties of nonparametric inference 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62P20 Applications of statistics to economics
Full Text:
References:
 [1] Ahn, H., Semiparametric estimation of a single-index model with nonparametrically generated regressors, Econometric Theory, 13, 3-31, (1997) [2] Anderson, T. W.; Hsiao, C., Estimation of dynamic models with error components, Journal of the American Statistical Association, 76, 598-606, (1981) · Zbl 0491.62080 [3] Arellano, M., Testing for autocorrelation in dynamic random effects models, Reviews of Economic Studies, 57, 124-134, (1990) · Zbl 0694.62042 [4] Arellano, M., Panel data econometrics, (2003), Oxford University Press Oxford · Zbl 1057.62112 [5] Arellano, M.; Bond, S., Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations, Reviews of Economic Studies, 58, 277-297, (1991) · Zbl 0719.62116 [6] Baltagi, B. H., Specification tests in panel data model using artificial regressions, Annales D’Economie et de Statistique, 55-56, 277-297, (1999) [7] Baltagi, B. H., Econometric analysis of panel data, (2008), John Wiley & Sons Chichester, West Sussex [8] Baltagi, B. H.; Li, D., Series estimation of partially linear panel data models with fixed effects, Annals of Economic and Finance, 3, 103-116, (2002) [9] Baltagi, B. H.; Li, Q., On instrumental variable estimation of semiparametric dynamic panel data models, Economics Letters, 76, 1-9, (2002) · Zbl 1100.91566 [10] Barro, R., Economic growth in a cross section of countries, Quarterly Journal of Economics, 106, 407-443, (1991) [11] Blundell, R.; Chen, X.; Kristensen, D., Semi-nonparametric IV estimation of shape-invariant Engel curves, Econometrica, 75, 1613-1669, (2007) · Zbl 1133.91461 [12] Bond, S.; Leblebicioglu, A.; Schiantarelli, F., Capital accumulation and growth: a new look at the empirical evidence, Journal of Applied Econometrics, 25, 1073-1099, (2010) [13] Carrasco, M.; Florens, J.-P.; Renault, E., Linear inverse problems in structural econometrics estimation based on spectral decomposition and regularization, (Heckman, J. J.; Leamer, E., Handbook of Econometrics, Vol. 6, (2007), North Holland Amsterdam), 5633-5751 [14] Carroll, C., Weil, D., 1994. Saving and growth: a reinterpretation. In Carnegie-Rochester Conference Series on Public Policy, vol. 40, pp. 133-192. [15] Chen, X., Large sample sieve estimation of semi-nonparametric models, (Heckman, J. J.; Leamer, E., Handbook of Econometrics, Vol. 6, (2007), North Holland Amsterdam), 5549-5632 [16] Darolles, S.; Fan, Y.; Florens, J.; Renault, E., Nonparametric instrumental regression, Econometrica, 79, 1541-1565, (2011) · Zbl 1274.62277 [17] de Jong, P., A central limit theorem for generalized quadratic forms, Probability Theory and Related Fields, 75, 261-277, (1987) · Zbl 0596.60022 [18] Durlauf, S., Econometric analysis and the study of economic growth: a skeptical perspective, (Backhouse, R.; Salanti, A., Macroeconomics and the Real World, (2000), Oxford University Press Oxford), 249-262 [19] Fu, B.; Li, W. K.; Fung, W. K., Testing model adequacy for dynamic panel data with intercorrelation, Biometrika, 89, 591-601, (2002) · Zbl 1036.62073 [20] Hall, P., Central limit theorem for integrated square error properties of multivariate nonparametric density estimators, Journal of Multivariate Analysis, 14, 1-16, (1984) · Zbl 0528.62028 [21] Hansen, B. E., Uniform convergence rates for kernel estimation with dependent data, Econometric Theory, 24, 726-748, (2008) · Zbl 1284.62252 [22] Härdle, W.; Mammen, E., Comparing nonparametric versus parametric regression fits, Annals of Statistics, 21, 1926-1947, (1993) · Zbl 0795.62036 [23] Hausman, J., Specification tests in econometrics, Econometrica, 46, 1251-1271, (1978) · Zbl 0397.62043 [24] Hausman, J.; Taylor, W. E., Panel data and unobservable individual effects, Econometrica, 49, 1377-1398, (1981) · Zbl 0464.90013 [25] Henderson, D. J.; Carroll, R. J.; Li, Q., Nonparametric estimation and testing of fixed effects panel data models, Journal of Econometrics, 144, 257-275, (2008) · Zbl 1418.62158 [26] Hoderlein, S., Su, L., White, H., 2011. Specification testing for nonparametric structural models with monotonicity in unobservables. Working Paper, Dept. of Economics, Boston College. [27] Hong, Y., Hypothesis testing in time series via the empirical characteristic function: a generalized spectral density approach, Journal of the American Statistical Association, 84, 1201-1220, (1999) · Zbl 1072.62632 [28] Hsiao, C., Analysis of panel data, (2003), Cambridge University Press Cambridge [29] Inoue, A.; Solon, G., A portmanteau test for serially correlated errors in fixed effects models, Econometric Theory, 22, 835-851, (2006) · Zbl 1100.62085 [30] Jones, C., Time series tests of endogenous growth models, Quarterly Journal of Economics, 110, 495-525, (1995) · Zbl 0831.90028 [31] Lee, A. J., $$U$$-statistics: theory and practice, (1990), Marcel Dekker New York · Zbl 0771.62001 [32] Lee, Y.-J., 2011. Testing a linear dynamic panel data model against nonlinear alternatives. Working Paper, Dept. of Economics, Indiana University. [33] Lee, Y., 2013. Nonparametric estimation of dynamic panel models with fixed effects. Working Paper, Dept. of Economics, Michigan University. [34] Li, D.; Lu, Z.; Linton, O., Local linear Fitting under near epoch dependence: uniform consistency with convergence rates, Econometric Theory, 28, 935-958, (2012) · Zbl 1369.62075 [35] Li, Q.; Stengos, T., A hausman specification test based on root $$n$$ consistent semiparametric estimators, Economics Letters, 40, 141-146, (1992) · Zbl 0773.62073 [36] Li, Q.; Stengos, T., Semiparametric estimation of partially linear panel data models, Journal of Econometrics, 71, 289-397, (1996) · Zbl 0842.62097 [37] Li, Q., Sun, Y., 2011. A consistent nonparametric test of parametric regression functional form in fixed effects panel data models. Working Paper, Dept. of Economics, Texas A&M University. [38] Linton, O.; Mammen, E., Estimating semiparametric ARCH(∞) model by kernel smoothing methods, Econometrica, 73, 771-836, (2005) · Zbl 1153.91798 [39] Linton, O.; Nielsen, J. P., A kernel method of estimating structured nonparametric regression based on marginal integration, Biometrika, 82, 93-101, (1995) · Zbl 0823.62036 [40] Lucas, R., On the mechanics of economic development, Journal of Monetary Economics, 22, 3-42, (1988) [41] Mammen, E.; Linton, O.; Nielsen, J., The existence and asymptotic properties of a backfitting projection algorithm under weak conditions, Annals of Statistics, 27, 1443-1490, (1999) · Zbl 0986.62028 [42] Mammen, E.; Støve, B.; Tjøstheim, D., Nonparametric additive models for panels of time series, Econometric Theory, 25, 442-481, (2009) · Zbl 1279.62189 [43] Mammen, E.; Yu, K., Nonparametric estimation of noisy integral equations of the second kind, Journal of the Korean Statistical Society, 38, 99-110, (2009) · Zbl 1293.62077 [44] Masry, E., Multivariate local polynomial regression for time series: uniform strong consistency rates, Journal of Time Series Analysis, 17, 571-599, (1996) · Zbl 0876.62075 [45] Metcalf, G. E., Specification testing in panel data with instrumental variables, Journal of Econometrics, 71, 291-307, (1996) · Zbl 0848.62062 [46] Nielsen, J. P.; Sperlich, S., Smooth backfitting in practice, Journal of the Royal Statistical Society, Series B, 67, 43-61, (2005) · Zbl 1060.62048 [47] Okui, R., Testing serial correlation in fixed effects regression models based on asymptotically unbiased autocorrelation estimators, Mathematics and Computers in Simulation, 79, 2897-2909, (2009) · Zbl 1171.62052 [48] Opsomer, J. D.; Ruppert, D., Fitting a bivariate additive model by local polynomial regression, Annals of Statistics, 25, 186-211, (1997) · Zbl 0869.62026 [49] Qian, J.; Wang, L., Estimating semiparametric panel data models by marginal integration, Journal of Econometrics, 167, 483-493, (2012) · Zbl 1441.62846 [50] Romer, P., Increasing returns and long-run growth, Journal of Political Economy, 94, 1002-1037, (1986) [51] Solow, R., A contribution to the theory of economic growth, Quarterly Journal of Economics, 70, 65-94, (1956) [52] Su, L.; Ullah, A., Profile likelihood estimation of partially linear panel data models with fixed effects, Economics Letters, 92, 75-81, (2006) · Zbl 1255.62385 [53] Su, L.; Ullah, A., More efficient estimation in nonparametric regression with nonparametric autocorrelated errors, Econometric Theory, 22, 98-126, (2006) · Zbl 1083.62037 [54] Su, L.; Ullah, A., Nonparametric and semiparametric panel econometric models: estimation and testing, (Ullah, A.; Giles, D. E.A., Handbook of Empirical Economics and Finance, (2011), Taylor & Francis Group New York), 455-497 [55] Sun, Y.; Carroll, R. J.; Li, D., Semiparametric estimation of fixed effects panel data varying coefficient models, Advances in Econometrics, 25, 101-130, (2009) · Zbl 1190.62075 [56] Xiao, Z.; Linton, O. B.; Carroll, R. J.; Mammen, E., More efficient local polynomial estimation in nonparametric regression with autocorrelated errors, Journal of American Statistical Association, 98, 980-992, (2003) · Zbl 1043.62075
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.