×

Semiparametric trending panel data models with cross-sectional dependence. (English) Zbl 1443.62247

Summary: A semiparametric fixed effects model is introduced to describe the nonlinear trending phenomenon in panel data analysis and it allows for the cross-sectional dependence in both the regressors and the residuals. A pooled semiparametric profile likelihood dummy variable approach based on the first-stage local linear fitting is developed to estimate both the parameter vector and the nonlinear time trend function. As both the time series length \(T\) and the cross-sectional size \(N\) tend to infinity, the resulting estimator of the parameter vector is asymptotically normal with a root-(\(NT\)) convergence rate. Meanwhile, the asymptotic distribution for the nonparametric estimator of the trend function is also established with a root-(\(NTh\)) convergence rate. Two simulated examples are provided to illustrate the finite sample performance of the proposed method. In addition, the proposed model and estimation method are applied to a CPI data set as well as an input-output data set.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G08 Nonparametric regression and quantile regression
62P20 Applications of statistics to economics
PDFBibTeX XMLCite
Full Text: DOI Link Link

References:

[1] Atak, A.; Linton, O.; Xiao, Z., A semiparametric panel model for unbalanced data with application to climate change in the United Kingdom, Journal of Econometrics, 164, 92-115 (2011) · Zbl 1441.62593
[2] Bosq, D., (Nonparametric Statistics for Stochastic Processes: Estimation and Prediction. Nonparametric Statistics for Stochastic Processes: Estimation and Prediction, Lecture Notes in Statistics, vol. 110 (1998), Springer-Verlag) · Zbl 0902.62099
[3] Cai, Z., Trending time-varying coefficient time series models with serially correlated errors, Journal of Econometrics, 136, 163-188 (2007) · Zbl 1418.62306
[4] Chen, J., Gao, J., Li, D., 2012. A new diagnostic test for cross-section uncorrelatedness in nonparametric panel data models. Econometric Theory, Available on CJO 2012 http://dx.doi.org/10.1017/S0266466612000072; Chen, J., Gao, J., Li, D., 2012. A new diagnostic test for cross-section uncorrelatedness in nonparametric panel data models. Econometric Theory, Available on CJO 2012 http://dx.doi.org/10.1017/S0266466612000072 · Zbl 1369.62089
[5] Duffy, J.; Papageorgiou, C., A cross-country empirical investigation of the aggregate production function apecification, Journal of Economic Growth, 5, 87-120 (2000) · Zbl 0967.91028
[6] Fan, J.; Gijbels, I., Local Polynomial Modelling and Its Applications (1996), Chapman and Hall: Chapman and Hall London · Zbl 0873.62037
[7] Fan, J.; Huang, T., Profile likelihood inferences on semiparametric varying-coefficient partially linear models, Bernoulli, 11, 1031-1057 (2005) · Zbl 1098.62077
[8] Fan, J.; Yao, Q., Nonlinear Time Series: Nonparametric and Parametric Methods (2003), Springer: Springer New York · Zbl 1014.62103
[9] Freedman, D. A., On tail probabilities for martingales, Annals of Probability, 3, 100-118 (1975) · Zbl 0313.60037
[10] Gao, J., Nonlinear Time Series: Semiparametric and Nonparametric Methods (2007), Chapman & Hall/CRC: Chapman & Hall/CRC London · Zbl 1179.62118
[11] Gao, J.; Hawthorne, K., Semiparametric estimation and testing of the trend of temperature series, Econometrics Journal, 9, 332-355 (2006) · Zbl 1145.91381
[12] Hall, P.; Heyde, C. C., Martingale Limit Theory and Its Applications (1980), Academic Press: Academic Press New York · Zbl 0462.60045
[13] Hsiao, C., Analysis of Panel Data (2003), Cambridge University Press: Cambridge University Press Cambridge
[14] Li, D.; Chen, J.; Gao, J., Non-parametric time-varying coefficient panel data models with fixed effects, Econometrics Journal, 14, 387-408 (2011) · Zbl 1284.62222
[15] Li, D.; Chen, J.; Lin, Z., Statistical inference in partially time-varying coefficient models, Journal of Statistical Planning and Inference, 141, 995-1013 (2011) · Zbl 1200.62108
[16] Lin, Z.; Lu, C., Limit Theorems of Mixing Dependent Random Variables (1996), Science Press: Science Press New York, Kluwer Academic Publisher, Dordrecht
[17] Pesaran, M. H., Estimation and inference in large heterogenous panels with multifactor error, Econometrica, 74, 967-1012 (2006) · Zbl 1152.91718
[18] Phillips, P. C.B., Trending time series and macroeconomic activity: some present and future challengers, Journal of Econometrics, 100, 21-27 (2001) · Zbl 0961.62112
[19] Phillips, P. C.B., The mysteries of trend, Macroeconomic Review, IX, 82-89 (2010)
[20] Phillips, P. C.B.; Moon, H., Linear regression limit theory for nonstationary panel data, Econometrica, 67, 1057-1111 (1999) · Zbl 1056.62532
[21] Poirier, D. J., Intermediate Statistics and Econometrics: A Comparative Approach (1995), MIT Press: MIT Press Boston
[22] Robinson, P. M., Nonparametric estimation of time-varying parameters, (Hackl, P., Statistical Analysis and Forecasting of Economic Structural Change (1989), Springer: Springer Berlin), 164-253
[23] Robinson, P. M., Nonparametric trending regression with cross-sectional dependence, Journal of Econometrics, 169, 4-14 (2012) · Zbl 1443.62105
[24] Shao, Q.; Yu, H., Weak convergence for weighted empirical processes of dependent sequences, Annals of Probability, 24, 2098-2127 (1996) · Zbl 0874.60006
[25] Su, L.; Jin, S., Sieve estimation of panel data models with cross section dependence, Journal of Econometrics, 169, 34-47 (2012) · Zbl 1443.62508
[26] Su, L.; Ullah, A., Profile likelihood estimation of partially linear panel data models with fixed effects, Economic Letters, 92, 75-81 (2006) · Zbl 1255.62385
[27] Sun, Y.; Carroll, R. J.; Li, D., Semiparametric estimation of fixed effects panel data varying coefficient models, Advances in Econometrics, 25, 101-129 (2009) · Zbl 1190.62075
[28] You, J.; Zhou, X.; Zhou, Y., Series estimation in partially linear in-slide regression models, Scandinavian Journal of Statistics, 38, 89-107 (2011) · Zbl 1246.62113
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.