Abstract
Disaggregated data are characterized by a high degree of diversity. Nonparametric models are often flexible enough to capture it but they are hardly interpretable. A semiparametric specification that models heterogeneity directly creates the preconditions to identify causal links. Certainly, the presence of endogenous variables can destroy the ability of the model to distinguish correlation from causality. Triangular varying coefficient models that consider the returns as nonrandom functions, and at the same time exogeneize the problematic regressors are able to add to the flexibility of a semiparametric specification the causal interpretability. Moreover, they make the necessary assumptions much more credible than they typically are in the standard linear models.
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Notes
- 1.
We thank an anonymous referee and the participants of the ISNPS 2014 meeting in Cadiz for helpful comments and discussion.
- 2.
Reverse engineering, also called back engineering, is the process of extracting knowledge or design information from anything man-made, and reproducing it. In economics, the reverse engineering process consists of extracting the structure of individual preferences from observed outcomes and then reproduce the outcomes using the conjectured informations.
- 3.
However, the most typical, though in economics rarely mentioned, endogeneity problem, i.e., the functional misspecification, can be largely diminished by the VCM.
References
Engle, R.F., Hendry, D.F., Richard, J.-F.: Exogeneity. Econometrica 51(2), 277–304 (1983)
Pudney, S.: Modelling Individual Choice: The Econometrics of Corners, Kinks, and Holes. Blackwell, Oxford (1989)
Eilers, P., Marx, B.: Flexible smoothing with B-splines and penalties. Stat. Sci. 11(2), 89–121 (1996)
White, H.L.: A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48(4), 817–838 (1980)
Hastie, T., Tibshirani, R.: Varying-coefficient models. J. Roy. Stat. Soc. Ser. B (Methodological) 55(4), 757–796 (1993)
Schultz, T.P.: Human capital, schooling and health returns. Econ. Hum. Biol. 1(2), 207–221 (2003)
Card, D.: Estimating the return to schooling: progress on some persistent econometric problems. Econometrica 69, 1127–1160 (2001)
Tesler, L.: Iterative estimation of a set of linear regression equations. J. Am. Stat. Assoc. 59, 845–862 (1964)
Kim, K., Petrin, A.: A New Control Function Approach for Non-Parametric Regressions with Endogenous Variables. NBER Working Paper, No. 16679 (2013)
Benini, G., Sperlich, S.: Modeling Heterogeneity by Structural Varying Coefficient Models Paper presented at the 2015 IAAE Annual Conference (2016)
Fan, J., Zhang, W.: Statistical methods with varying coefficient models. Stat. Interface 1(1), 179–195 (2008)
Linton, O., Nielsen, J.P.: A kernel method of estimating structured nonparametric regression based on marginal integration. Biometrika 82(2), 93–100 (1995)
Roca-Pardinas, J., Sperlich, S.A.: Feasible estimation in generalized structured models. Stat. Comput. 20, 367–379 (2010)
Sperlich, S.: A note on nonparametric estimation with predicted variables. Econ. J. 12, 382–395 (2009)
Park, B.U., Mammen, E., Lee, Y.K., Lee, E.R.: Varying coefficient regression models: a review and new developments. Int. Stat. Rev. 1–29 (2013)
R Core Team: R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria (2014). http://www.R-project.org/
Sperlich, S., Theler, R.: Modeling heterogeneity: a praise for varying-coefficient models in causal analysis. Comput. Stat. 30, 693–718 (2015)
Imbens, G. W., Angrist, J. D.: Identification and Estimation of Local Average Treatment Effects. Econometrica. 62(2), 467–475 (1994)
Angrist, J. D., Imbens, G. W.: Two-Stage Least Squares Estimation of Average Causal Effects in Models with Variable Treatment Intensity. J. Am. Stat. Assoc. 90(430), 431–442 (1995)
Murnane, R., Willett, J., Levy, F.: The growing importance of cognitive skills in wage determination. Rev. Econ. Stat. xxxvii(2), pp. 251–266 (1995)
Angrist, J.D., Krueger, A.B.: Does compulsory school attendance affect schooling and earnings? Q. J. Econ. 106(4), 979–1014 (1991)
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Benini, G., Sperlich, S., Theler, R. (2016). Varying Coefficient Models Revisited: An Econometric View. In: Cao, R., González Manteiga, W., Romo, J. (eds) Nonparametric Statistics. Springer Proceedings in Mathematics & Statistics, vol 175. Springer, Cham. https://doi.org/10.1007/978-3-319-41582-6_5
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