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Specification test for panel data models with interactive fixed effects. (English) Zbl 1331.62485
Summary: In this paper, we propose a consistent nonparametric test for linearity in a large dimensional panel data model with interactive fixed effects. Both lagged dependent variables and conditional heteroskedasticity of unknown form are allowed in the model. We estimate the model under the null hypothesis of linearity to obtain the restricted residuals which are then used to construct the test statistic. We show that after being appropriately centered and standardized, the test statistic is asymptotically normally distributed under both the null hypothesis and a sequence of Pitman local alternatives by using the concept of conditional strong mixing that was recently introduced by B. L. S. Prakasa Rao [Ann. Inst. Stat. Math. 61, No. 2, 441–460 (2009; Zbl 1314.60054)]. To improve the finite sample performance, we propose a bootstrap procedure to obtain the bootstrap $$p$$-value. A small set of Monte Carlo simulations illustrates that our test performs well in finite samples. An application to an economic growth panel dataset indicates significant nonlinear relationships between economic growth, initial income level and capital accumulation.

##### MSC:
 62P20 Applications of statistics to economics 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62G10 Nonparametric hypothesis testing 62G20 Asymptotic properties of nonparametric inference 62E20 Asymptotic distribution theory in statistics 91B62 Economic growth models
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##### References:
 [1] Ahn, S. C.; Lee, Y. H.; Schmidt, P., GMM estimation of linear panel data models with time-varying individual effects, J. Econometrics, 101, 219-255, (2001) · Zbl 0966.62091 [2] Ahn, S. C.; Lee, Y. H.; Schmidt, P., Panel data models with multiple time-varying individual effects, J. Econometrics, 174, 1-14, (2013) · Zbl 1277.62202 [3] Andrews, D. W.K., Cross-section regression with common shocks, Econometrica, 73, 1551-1585, (2005) · Zbl 1153.91665 [4] Avarucci, M., Zafaroni, P., 2012. Generalized least squares estimation of panel with common shocks. Working paper, Imperial College London. [5] Bai, J., Panel data models with interactive fixed effects, Econometrica, 77, 1229-1279, (2009) · Zbl 1183.62196 [6] Bai, J.; Li, K., Statistical analysis of factor models of high dimension, Ann. Statist., 40, 436-465, (2012) · Zbl 1246.62144 [7] Bai, J.; Ng, S., Determining the number of factors in approximate factor models, Econometrica, 70, 191-221, (2002) · Zbl 1103.91399 [8] Bai, J.; Ng, S., Evaluating latent and observed factors in macroeconomics and finance, J. Econometrics, 131, 507-537, (2006) · Zbl 1337.62341 [9] Barro, R., Economic growth in a cross section of countries, Quart. J. Econom., 106, 407-443, (1991) [10] Bernstein, D. S., Matrix mathematics: theory, facts, and formulas with application to linear systems theory, (2005), Princeton University Press Princeton · Zbl 1075.15001 [11] Bierens, H. J., Consistent model specification tests, J. Econometrics, 20, 105-134, (1982) · Zbl 0549.62076 [12] Bierens, H. J., A consistent conditional moment test of functional form, Econometrica, 58, 1443-1458, (1990) · Zbl 0737.62058 [13] Bond, S.; Leblebicioglu, A.; Schiantarelli, F., Capital accumulation and growth: a new look at the empirical evidence, J. Appl. Econometrics, 25, 1073-1099, (2010) [14] Carneiro, P.; Hansen, K.; Heckman, J., Estimating distributions of counterfactuals with an application to the returns to schooling and measurement of the effect of uncertainty on schooling choice, Internat. Econom. Rev., 44, 361-422, (2003) [15] Chen, S.; Gao, J., An adaptive empirical likelihood test for parametric time series regression models, J. Econometrics, 141, 950-972, (2007) · Zbl 1418.62191 [16] Chudik, A., Pesaran, M.H., 2013. Common correlated effects estimation of heterogenous dynamic panel data models with weakly exogenous regressors. Working paper, Department of Economics, University of Southern California. · Zbl 1337.62354 [17] Cunha, F.; Heckman, J.; Navarro, S., Separating uncertainty from heterogeneity in life cycle earnings, Oxford Econom. Papers, 57, 191-261, (2005) [18] de Jong, P., A central limit theorem for generalized quadratic form, Probab. Theory Related Fields, 75, 261-277, (1987) · Zbl 0596.60022 [19] Fan, Y.; Li, Q., Consistent model specification tests: omitted variables and semiparametric functional forms, Econometrica, 64, 865-890, (1996) · Zbl 0854.62038 [20] Feldstein, M.; Horioka, C., Domestic saving and international capital flows, Econ. J., 90, 314-329, (1980) [21] Freyberger, J., 2012. Nonparametric panel data models with interactive fixed effects. Working paper, Department of Economics, Northwestern University. [22] Gao, J.; Gijbels, I., Bandwidth selection in nonparametric kernel testing, J. Amer. Statist. Assoc., 103, 1584-1594, (2008) · Zbl 1286.62043 [23] Giannone, D.; Lenza, M., The feldstein-horioka fact, (Reichlin, L.; West, K., The NBER International Seminar on Macroeconomics, (2010), University of Chicago Press), 103-117 [24] Gagliardini, P., Gouriéroux, C., 2012. Efficiency in large dynamic panel models with common factor. Working paper, Swiss Finance Institute. [25] Greenaway-McGrevy, R. C.; Han, C.; Sul, D., Asymptotic distribution of factor augmented estimators for panel regression, J. Econometrics, 169, 48-53, (2012) · Zbl 1443.62452 [26] Hahn, J.; Kuersteiner, G., Bias reduction for dynamic nonlinear panel models with fixed effects, Econometric Theory, 27, 1152-1191, (2011) · Zbl 1442.62739 [27] Hansen, B. E., Testing for linearity, J. Econ. Surv., 13, 551-576, (1999) [28] Hansen, B. E., Testing for structural change in conditional models, J. Econometrics, 97, 93-115, (2000) · Zbl 1122.62326 [29] Hansen, B. E., Uniform convergence rates for kernel estimation with dependent data, Econometric Theory, 24, 726-748, (2008) · Zbl 1284.62252 [30] Härdle, W.; Mammen, E., Comparing nonparametric versus parametric regression fits, Ann. Statist., 21, 1926-1947, (1993) · Zbl 0795.62036 [31] Hausman, J. A., Specification testing in econometrics, Econometrica, 46, 1251-1271, (1978) · Zbl 0397.62043 [32] Hjellvik, V.; Yao, Q.; Tjøstheim, D., Linearity testing using local polynomial approximation, J. Statist. Plann. Inference, 68, 295-321, (1998) · Zbl 0942.62051 [33] Hjellvik, V.; Tjøstheim, D., Nonparametric tests of linearity for time series, Biometrika, 82, 351-368, (1995) · Zbl 0823.62044 [34] Hong, Y.; White, H., Consistent specification testing via nonparametric series regression, Econometrica, 63, 1133-1159, (1995) · Zbl 0941.62125 [35] Horowitz, J. L.; Spokoiny, V. G., An adaptive, rate-optimal test of a parametric mean-regression model against a nonparametric alternative, Econometrica, 69, 599-631, (2001) · Zbl 1017.62012 [36] Hsiao, C.; Li, Q.; Racine, J., A consistent model specification test with mixed discrete and continuous data, J. Econometrics, 140, 802-826, (2007) · Zbl 1247.62126 [37] Jin, S.; Su, L., A nonparametric poolability test for panel data models with cross section dependence, Econometric Rev., 32, 469-512, (2013) [38] Jones, C., Time series tests of endogenous growth models, Quart. J. Econom., 110, 495-525, (1995) · Zbl 0831.90028 [39] Kapetanios, G.; Pesaran, M. H., Alternative approaches to estimation and inference in large multifactor panels: small sample results with an application to modelling of asset returns, (Phillips, G. & E. Tzavalis, The Refinement of Econometric Estimation and Test Procedures: Finite Sample and Asymptotic Analysis, (2007), Cambridge University Press New York), 239-281, (Chapter 11) [40] Lee, Y., 2013. Nonparametric estimation of dynamic panel models with fixed effects. Econometric Theory, forthcoming, http://dx.doi.org/10.1017/S0266466614000188. [41] Lee, Y.-J., Testing a linear dynamic panel data model against nonlinear alternatives, J. Econometrics, 178, 146-166, (2014) · Zbl 1293.62195 [42] Li, Q.; Wang, S., A simple consistent bootstrap test for a parametric regression function, J. Econometrics, 87, 145-165, (1998) · Zbl 0943.62031 [43] Lin, Z.; Li, Q.; Sun, Y., A consistent nonparametric test of parametric regression functional form in fixed-effects panel data models, J. Econometrics, 178, 167-179, (2014) · Zbl 1293.62196 [44] Liu, Z.; Stegnos, T., Non-linearities in cross-country growth regression: a semiparametric approach, J. Appl. Econometrics, 14, 527-538, (1999) [45] Lu, X., Su, L., 2013. Shrinkage estimation of dynamic panel data models with interactive fixed effects. Working paper, HKUST. [46] Lucas, R., On the mechanics of economic development, J. Monetary Econom., 22, 3-42, (1988) [47] Ludvigson, S. C.; Ng, S., Macro factors in bond risk premia, Rev. Financial Studies, 22, 5027-5067, (2009) [48] Ludvigson, S. C.; Ng, S., A factor analysis of bond risk premia, (Ullah, A.; Giles, D., Handbook of Empirical Economics and Finance, (2011), Chapman and Hall), 313-372 [49] Moon, H., Weidner, M., 2010. Dynamic linear panel regression models with interactive fixed effects. Working paper, Department of Economics, USC. · Zbl 1441.62816 [50] Moon, H., Weidner, M., 2013. Linear regression for panel with unknown number of factors as interactive fixed effects. Working paper, Department of Economics, University College London. · Zbl 1410.62126 [51] Onatski, A., Testing hypotheses about the number of factors in large factor models, Econometrica, 77, 1447-1479, (2009) · Zbl 1182.62180 [52] Pesaran, M. H., Estimation and inference in large heterogeneous panels with a multifactor error structure, Econometrica, 74, 967-1012, (2006) · Zbl 1152.91718 [53] Pesaran, M. H.; Tosetti, E., Large panels with common factors and spatial correlation, J. Econometrics, 161, 182-202, (2011) · Zbl 1441.62838 [54] Prakasa Rao, B. L.S., Conditional independence, conditional mixing and conditional association, Ann. Inst. Statist. Math., 61, 441-460, (2009) · Zbl 1314.60054 [55] Ramsey, J. B., Tests for specification errors in classical linear least squares regression analysis, J. Roy. Statist. Soc. Ser. B, 31, 350-371, (1969) · Zbl 0179.48902 [56] Romer, P., Increasing returns and long-run growth, J. Political Economy, 94, 1002-1037, (1986) [57] Ross, S., The arbitrage theory of capital asset pricing, J. Economic Theory, 13, 341-360, (1976) [58] Roussas, G. G., On conditional independence, mixing and association, Stoch. Anal. Appl., 26, 1274-1309, (2008) · Zbl 1160.60002 [59] Solow, R., A contribution to the theory of economic growth, Quart. J. Econom., 70, 65-94, (1956) [60] Song, M., 2013. Asymptotic theory for dynamic heterogeneous panels with cross-sectional dependence and its applications. Working paper, Columbia University. [61] Stinchcombe, M.; White, H., Consistent specification testing with nuisance parameters present only under alternative, Econometric Theory, 14, 295-324, (1998) [62] Su, L.; Chen, Q., Testing homogeneity in panel data models with interactive fixed effects, Econometric Theory, 29, 1079-1135, (2013) · Zbl 1290.62088 [63] Su, L.; Jin, S., Sieve estimation of panel data model with cross section dependence, J. Econometrics, 169, 34-47, (2012) · Zbl 1443.62508 [64] Su, L.; Lu, X., Nonparametric dynamic panel data models: kernel estimation and specification testing, J. Econometrics, 176, 112-133, (2013) · Zbl 1284.62268 [65] Su, L.; Ullah, A., A nonparametric goodness-of-fit-based test for conditional heteroskedasticity, Econometric Theory, 29, 187-212, (2013) · Zbl 1316.62058 [66] Su, L., Zhang, Y., 2013. Nonparametric dynamic panel data models with interactive fixed effects: sieve estimation and specification testing. Working paper, Singapore Management University. [67] Wooldridge, J. M., A test for functional form against nonparametric alternatives, Econometric Theory, 8, 452-475, (1992) [68] Yatchew, A. J., Nonparametric regression tests based on least squares, Econometric Theory, 8, 435-451, (1992) [69] Zheng, X., Consistent test of functional form via nonparametric estimation technique, J. Econometrics, 75, 263-289, (1996) · Zbl 0865.62030
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