Identification of nonseparable models using instruments with small support. (English) Zbl 1410.62210
Summary: I consider nonparametric identification of nonseparable instrumental variables models with continuous endogenous variables. If both the outcome and first stage equations are strictly increasing in a scalar unobservable, then many kinds of continuous, discrete, and even binary instruments can be used to point-identify the levels of the outcome equation. This contrasts sharply with related work by G. W. Imbens and W. K. Newey [Econometrica 77, No. 5, 1481–1512 (2009; Zbl 1182.62215)] that requires continuous instruments with large support. One implication is that assumptions about the dimension of heterogeneity can provide nonparametric point-identification of the distribution of treatment response for a continuous treatment in a randomized controlled experiment with partial compliance.
Keywords:
nonseparable models; endogeneity; unobserved heterogeneity; quantile treatment effects; nonparametric identification; instrumental variablesCitations:
Zbl 1182.62215References:
| [1] | Abadie, A., J.Angrist, and G.Imbens (2002): “Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings,” Econometrica, 70, 91-117. 10.1111/1468‐0262.00270 · Zbl 1104.62331 |
| [2] | Altonji, J. G., and R. L.Matzkin (2005): “Cross Section and Panel Data Estimators for Nonseparable Models With Endogenous Regressors,” Econometrica, 73, 1053-1102. 10.1111/j.1468‐0262.2005.00609.x · Zbl 1152.62405 |
| [3] | Athey, S., and G. W.Imbens (2006): “Identification and Inference in Nonlinear Difference‐in‐Differences Models,” Econometrica, 74, 431-497. 10.1111/j.1468‐0262.2006.00668.x · Zbl 1145.62316 |
| [4] | Bitler, M. P., J. B.Gelbach, and H. W.Hoynes (2006): “What Mean Impacts Miss: Distributional Effects of Welfare Reform Experiments,” American Economic Review, 96, 988-1012. 10.1257/aer.96.4.988 |
| [5] | Chernozhukov, V., and C.Hansen (2005): “An IV Model of Quantile Treatment Effects,” Econometrica, 73, 245-261. 10.1111/j.1468‐0262.2005.00570.x · Zbl 1152.91706 |
| [6] | Chesher, A. (2003): “Identification in Nonseparable Models,” Econometrica, 71, 1405-1441. 10.1111/1468‐0262.00454 · Zbl 1154.62413 |
| [7] | Chesher, A. (2007): “Instrumental Values,” Journal of Econometrics, 139, 15-34. 10.1016/j.jeconom.2006.06.003 · Zbl 1418.62429 |
| [8] | D’Haultfœuille, X., and P.Février (2015): “Identification of Nonseparable Triangular Models With Discrete Instruments,” Econometrica, 83 (3), 1199-1210. · Zbl 1410.62060 |
| [9] | Djebbari, H., and J.Smith (2008): “Heterogeneous Impacts in PROGRESA,” Journal of Econometrics, 145, 64-80. 10.1016/j.jeconom.2008.05.012 · Zbl 1418.62443 |
| [10] | Doksum, K. (1974): “Empirical Probability Plots and Statistical Inference for Nonlinear Models in the Two‐Sample Case,” The Annals of Statistics, 2, 267-277. 10.1214/aos/1176342662 · Zbl 0277.62034 |
| [11] | Firpo, S. (2007): “Efficient Semiparametric Estimation of Quantile Treatment Effects,” Econometrica, 75, 259-276. 10.1111/j.1468‐0262.2007.00738.x · Zbl 1201.62043 |
| [12] | Florens, J. P., J. J.Heckman, C.Meghir, and E.Vytlacil (2008): “Identification of Treatment Effects Using Control Functions in Models With Continuous, Endogenous Treatment and Heterogeneous Effects,” Econometrica, 76, 1191-1206. 10.3982/ECTA5317 · Zbl 1152.91746 |
| [13] | Heckman, J. J. (2001): “Micro Data, Heterogeneity, and the Evaluation of Public Policy: Nobel Lecture,” Journal of Political Economy, 109, 673-748. 10.1086/322086 |
| [14] | Heckman, J. J., J.Smith, and N.Clements (1997): “Making the Most Out of Programme Evaluations and Social Experiments: Accounting for Heterogeneity in Programme Impacts,” Review of Economic Studies, 64, 487-535. 10.2307/2971729 · Zbl 0887.90040 |
| [15] | Hoderlein, S., and E.Mammen (2007): “Identification of Marginal Effects in Nonseparable Models Without Monotonicity,” Econometrica, 75, 1513-1518. 10.1111/j.1468‐0262.2007.00801.x · Zbl 1133.91052 |
| [16] | Hoderlein, S., and E.Mammen (2009): “Identification and Estimation of Local Average Derivatives in Non‐Separable Models Without Monotonicity,” Econometrics Journal, 12, 1-25. 10.1111/j.1368‐423X.2008.00273.x · Zbl 1190.62199 |
| [17] | Imbens, G. (2007): “Nonadditive Models With Endogenous Regressors,” in Advances in Economics and Econometrics: Theory and Applications, Ninth World Congress, Vol. 3, ed. by R.Blundell (ed.), W.Newey (ed.), and T.Persson (ed.). New York: Cambridge University Press. |
| [18] | Imbens, G. W., and W. K.Newey (2009): “Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity,” Econometrica, 77, 1481-1512. 10.3982/ECTA7108 · Zbl 1182.62215 |
| [19] | Krueger, A. B. (1999): “Experimental Estimates of Education Production Functions,” Quarterly Journal of Economics, 114, 497-532. 10.1162/003355399556052 |
| [20] | Matzkin, R. L. (2003): “Nonparametric Estimation of Nonadditive Random Functions,” Econometrica, 71, 1339-1375. 10.1111/1468‐0262.00452 · Zbl 1154.62327 |
| [21] | Torgovitsky, A. (2013): “Minimum Distance From Independence Estimation of Nonseparable Instrumental Variables Models,” Working Paper. · Zbl 1452.62255 |
| [22] | Torgovitsky, A. (2015): “Supplement to ‘Identification of Nonseparable Models Using Instruments With Small Support’,” Econometrica Supplemental Material, 83, http://dx.doi.org/10.3982/ECTA9984. · Zbl 1410.62210 · doi:10.3982/ECTA9984 |
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.
