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Smooth coefficient estimation of a seemingly unrelated regression

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  • Henderson, Daniel J.
  • Kumbhakar, Subal C.
  • Li, Qi
  • Parmeter, Christopher F.

Abstract

This paper proposes estimation and inference for the semiparametric smooth coefficient seemingly unrelated regression model. We discuss the imposition of cross-equation restrictions which are required by economic theory as well as methods for data driven bandwidth selection. A test of correct functional form for the entire system of equations is also constructed. Asymptotic and finite sample results are given. We illustrate our estimator by applying it to a cost system for US commercial banks. Our results show that most of the banks are operating under increasing returns to scale, but that returns to scale decrease with bank size.

Suggested Citation

  • Henderson, Daniel J. & Kumbhakar, Subal C. & Li, Qi & Parmeter, Christopher F., 2015. "Smooth coefficient estimation of a seemingly unrelated regression," Journal of Econometrics, Elsevier, vol. 189(1), pages 148-162.
    • Handle: RePEc:eee:econom:v:189:y:2015:i:1:p:148-162
    DOI: 10.1016/j.jeconom.2015.07.002
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    as
    1. Cai, Zongwu & Li, Qi, 2008. "Nonparametric Estimation Of Varying Coefficient Dynamic Panel Data Models," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1321-1342, October.
    2. Berger, Allen N. & Mester, Loretta J., 2003. "Explaining the dramatic changes in performance of US banks: technological change, deregulation, and dynamic changes in competition," Journal of Financial Intermediation, Elsevier, vol. 12(1), pages 57-95, January.
    3. QI Li & Desheng Ouyang & Jeffrey S. Racine, 2013. "Categorical semiparametric varying‐coefficient models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(4), pages 551-579, June.
    4. Hughes, Joseph P. & Mester, Loretta J., 2013. "Who said large banks don’t experience scale economies? Evidence from a risk-return-driven cost function," Journal of Financial Intermediation, Elsevier, vol. 22(4), pages 559-585.
    5. Asaftei, Gabriel & Parmeter, Christopher F., 2010. "Market power, EU integration and privatization: The case of Romania," Journal of Comparative Economics, Elsevier, vol. 38(3), pages 340-356, September.
    6. Andreas Savvides & Theofanis P. Mamuneas & Thanasis Stengos, 2006. "Economic development and the return to human capital: a smooth coefficient semiparametric approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 111-132.
    7. Li, Qi, et al, 2002. "Semiparametric Smooth Coefficient Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 412-422, July.
    8. Henderson, Daniel J. & Kumbhakar, Subal C. & Parmeter, Christopher F., 2012. "A simple method to visualize results in nonlinear regression models," Economics Letters, Elsevier, vol. 117(3), pages 578-581.
    9. Jun, Sung Jae, 2009. "Local structural quantile effects in a model with a nonseparable control variable," Journal of Econometrics, Elsevier, vol. 151(1), pages 82-97, July.
    10. Li, Qi & Racine, Jeffrey S., 2010. "Smooth Varying-Coefficient Estimation And Inference For Qualitative And Quantitative Data," Econometric Theory, Cambridge University Press, vol. 26(6), pages 1607-1637, December.
    11. Peter Hall & Qi Li & Jeffrey S. Racine, 2007. "Nonparametric Estimation of Regression Functions in the Presence of Irrelevant Regressors," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 784-789, November.
    12. Feng, Guohua & Serletis, Apostolos, 2010. "Efficiency, technical change, and returns to scale in large US banks: Panel data evidence from an output distance function satisfying theoretical regularity," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 127-138, January.
    13. Taylor, William E, 1976. "Prior Information on the Coefficients When the Disturbance Covariance Matrix is Unknown," Econometrica, Econometric Society, vol. 44(4), pages 725-739, July.
    14. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
    15. BARTEN, Anton P., 1969. "Maximum likelihood estimation of a complete system of demand equations," LIDAM Reprints CORE 34, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. Barten, A. P., 1969. "Maximum likelihood estimation of a complete system of demand equations," European Economic Review, Elsevier, vol. 1(1), pages 7-73.
    17. Henderson, Daniel J. & Ullah, Aman, 2005. "A nonparametric random effects estimator," Economics Letters, Elsevier, vol. 88(3), pages 403-407, September.
    18. Cai, Zongwu & Fan, Jianqing & Yao, Qiwei, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
    19. Henderson, Daniel J. & Carroll, Raymond J. & Li, Qi, 2008. "Nonparametric estimation and testing of fixed effects panel data models," Journal of Econometrics, Elsevier, vol. 144(1), pages 257-275, May.
    20. Berger, Allen N. & Miller, Nathan H. & Petersen, Mitchell A. & Rajan, Raghuram G. & Stein, Jeremy C., 2005. "Does function follow organizational form? Evidence from the lending practices of large and small banks," Journal of Financial Economics, Elsevier, vol. 76(2), pages 237-269, May.
    21. Lavergne, Pascal & Vuong, Quang, 2000. "Nonparametric Significance Testing," Econometric Theory, Cambridge University Press, vol. 16(4), pages 576-601, August.
    22. Orbe, Susan & Ferreira, Eva & Rodriguez-Poo, Juan, 2003. "An algorithm to estimate time-varying parameter SURE models under different types of restriction," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 363-383, March.
    23. David C. Wheelock & Paul W. Wilson, 2012. "Do Large Banks Have Lower Costs? New Estimates of Returns to Scale for U.S. Banks," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 44(1), pages 171-199, February.
    24. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
    25. Orbe, Susan & Ferreira, Eva & Rodriguez-Poo, Juan, 2005. "Nonparametric estimation of time varying parameters under shape restrictions," Journal of Econometrics, Elsevier, vol. 126(1), pages 53-77, May.
    26. Ouyang, Desheng & Li, Qi & Racine, Jeffrey S., 2009. "Nonparametric Estimation Of Regression Functions With Discrete Regressors," Econometric Theory, Cambridge University Press, vol. 25(1), pages 1-42, February.
    27. Jun, Sung Jae & Pinkse, Joris, 2009. "Efficient Semiparametric Seemingly Unrelated Quantile Regression Estimation," Econometric Theory, Cambridge University Press, vol. 25(5), pages 1392-1414, October.
    28. Cai, Zongwu, 2007. "Trending time-varying coefficient time series models with serially correlated errors," Journal of Econometrics, Elsevier, vol. 136(1), pages 163-188, January.
    29. Guohua Feng & Apostolos Serletis, 2009. "Efficiency and productivity of the US banking industry, 1998-2005: evidence from the Fourier cost function satisfying global regularity conditions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(1), pages 105-138.
    30. Das, M., 2005. "Instrumental variables estimators of nonparametric models with discrete endogenous regressors," Journal of Econometrics, Elsevier, vol. 124(2), pages 335-361, February.
    31. Berger, Allen N, 2003. "The Economic Effects of Technological Progress: Evidence from the Banking Industry," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 35(2), pages 141-176, April.
    32. Rosa L. Matzkin, 2008. "Identification in Nonparametric Simultaneous Equations Models," Econometrica, Econometric Society, vol. 76(5), pages 945-978, September.
    33. Cai, Zongwu & Das, Mitali & Xiong, Huaiyu & Wu, Xizhi, 2006. "Functional coefficient instrumental variables models," Journal of Econometrics, Elsevier, vol. 133(1), pages 207-241, July.
    34. Christensen, Laurits R & Greene, William H, 1976. "Economies of Scale in U.S. Electric Power Generation," Journal of Political Economy, University of Chicago Press, vol. 84(4), pages 655-676, August.
    35. Cai, Zongwu & Li, Qi & Park, Joon Y., 2009. "Functional-coefficient models for nonstationary time series data," Journal of Econometrics, Elsevier, vol. 148(2), pages 101-113, February.
    36. Li, Q. & Wang, Suojin, 1998. "A simple consistent bootstrap test for a parametric regression function," Journal of Econometrics, Elsevier, vol. 87(1), pages 145-165, August.
    37. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
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    3. Guohua Feng & Chuan Wang & Apostolos Serletis, 2018. "Shadow prices of $$\hbox {CO}_{2}$$ CO 2 emissions at US electric utilities: a random-coefficient, random-directional-vector directional output distance function approach," Empirical Economics, Springer, vol. 54(1), pages 231-258, February.
    4. Ali Mehrabani & Aman Ullah, 2020. "Improved Average Estimation in Seemingly Unrelated Regressions," Econometrics, MDPI, vol. 8(2), pages 1-22, April.
    5. Casas Villalba, Maria Isabel, 2020. "Adaptative predictability of stock market returns," DES - Working Papers. Statistics and Econometrics. WS 31648, Universidad Carlos III de Madrid. Departamento de Estadística.
    6. Chaohua Dong & Jiti Gao & Bin Peng, 2018. "Series estimation for single-index models under constraints," Monash Econometrics and Business Statistics Working Papers 5/18, Monash University, Department of Econometrics and Business Statistics.
    7. Isabel Casas & Eva Ferreira & Susan Orbe, 2021. "Time-Varying Coefficient Estimation in SURE Models. Application to Portfolio Management," Journal of Financial Econometrics, Oxford University Press, vol. 19(4), pages 707-745.
    8. Xu, Ke-Li, 2017. "Regression discontinuity with categorical outcomes," Journal of Econometrics, Elsevier, vol. 201(1), pages 1-18.
    9. Čížek, Pavel & Koo, Chao Hui, 2021. "Jump-preserving varying-coefficient models for nonlinear time series," Econometrics and Statistics, Elsevier, vol. 19(C), pages 58-96.
    10. Li, Hong & Shi, Yanlin, 2021. "A new unique information share measure with applications on cross-listed Chinese banks," Journal of Banking & Finance, Elsevier, vol. 128(C).
    11. Shun Matsuura & Hiroshi Kurata, 2020. "Covariance matrix estimation in a seemingly unrelated regression model under Stein’s loss," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 79-99, March.
    12. Guohua Feng & Jiti Gao & Xiaohui Zhang, 2018. "Estimation of technical change and price elasticities: a categorical time–varying coefficient approach," Journal of Productivity Analysis, Springer, vol. 50(3), pages 117-138, December.
    13. Zhe Li & Ping Wang & Tianlong Wu, 2021. "Do foreign institutional investors drive corporate social responsibility? Evidence from listed firms in China," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 48(1-2), pages 338-373, January.
    14. Subal C. Kumbhakar & Kai Sun & Rui Zhang, 2016. "Semiparametric Smooth Coefficient Estimation of a Production System," Pacific Economic Review, Wiley Blackwell, vol. 21(4), pages 464-482, October.
    15. Chaohua Dong & Jiti Gao & Bin Peng, 2016. "Another Look at Single-Index Models Based on Series Estimation," Monash Econometrics and Business Statistics Working Papers 19/16, Monash University, Department of Econometrics and Business Statistics.
    16. Isabel Casas & Xiuping Mao & Helena Veiga, 2018. "Reexamining financial and economic predictability with new estimators of realized variance and variance risk premium," CREATES Research Papers 2018-10, Department of Economics and Business Economics, Aarhus University.
    17. Mark Andor & Christopher Parmeter, 2017. "Pseudolikelihood estimation of the stochastic frontier model," Applied Economics, Taylor & Francis Journals, vol. 49(55), pages 5651-5661, November.
    18. Ye Chen & Jian Li & Qiyuan Li, 2023. "Seemingly Unrelated Regression Estimation for VAR Models with Explosive Roots," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(4), pages 910-937, August.

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    More about this item

    Keywords

    Semiparametric smooth coefficient model; System estimation; Bandwidth selection; Banking;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C39 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Other

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