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## Understanding Instrumental Variables in Models with Essential Heterogeneity (2006)

Venue: | The Review of Economics and Statistics |

Citations: | 157 - 21 self |

### Citations

3415 | Sample Selection Bias as a Specification Error", - Heckman - 1979 |

2778 | The central role of the propensity score in observational studies for causal effects
- Rosenbaum, Rubin
- 1983
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Citation Context ...plays a central role in selection models as a determinant of control functions (see Heckman and Robb, 1985, 1986) as noted in Section 1. It plays a more subsidiary role in matching models (see, e.g., =-=Rosenbaum and Rubin, 1983-=-; Heckman and Navarro, 2004). For the IV weight to be correctly constructed and interpreted, we need to know the correct model for P (Z), i.e. we need to know exactly which Z determine P (Z) . This fe... |

2592 | Large Sample Properties of Generalized Methods of Moments Estimators
- Hansen
- 1982
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Citation Context ...” denotetheOLS estimator, the large sample bias is plim (�α1 − α1) = Cov(D,U) Var(D) for standard sampling schemes. 2sdifferent instrumental variables estimators efficiently (see, e.g., Sargan, 1958; =-=Hansen, 1982-=-). Nevertheless, all valid instrumental variables estimators converge to α1. Tests of the validity of one instrument given the assumed validity of at least one other instrument, due to Durbin (1954); ... |

1418 | Specification Tests in Econometrics - Hausman - 1978 |

1087 | Identification and Estimation of Local Average Treatment Effects,” - Imbens, Angrist - 1994 |

1066 |
Advanced Econometrics
- Amemiya
- 1985
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Citation Context ...nent of the vector of instruments is uncorrelated with U but correlated with D, i.e., and Cov (Zj,U)=0, j =1,...,J (1.2a) Cov (Zj,D) 6= 0, j =1,...,J (1.2b) then under standard conditions (see, e.g., =-=Amemiya, 1985-=-), IV identifies α1: plim ¡ bα1,IVj ¢ = Cov (Y,Zj) Cov (D, Zj) = α1, j =1,...,J, (1.3) where “b” denotes the estimator and the subscript defines the particular instrument. The elements of Z shift D, k... |

938 | Local Polynomial Modelling and its Applications - Fan, Gijbels - 1996 |

929 | The common structure of statistical models of truncation, sample selection and limited dependent variables and a simple estimator for such models - Heckman - 1976 |

813 | The Economics and Econometrics of Active Labor Market Programs”. in: Ashenfelter O - Heckman, LaLonde, et al. - 1999 |

714 | Characterizing Selection Bias Using Experimental Data’. - Heckman, Ichimura, et al. - 1998 |

629 | Nonparametric estimation of average treatment effects under exogeneity: a review,” - Imbens - 2004 |

613 |
Alternative Methods for Evaluating the Impact of Interventions,”
- Heckman, Robb
- 1985
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Citation Context .... Under our assumptions, it is a monotonic function of the mean utility of treatment, µ D (Z). The propensity score plays a central role in selection models as a determinant of control functions (see =-=Heckman and Robb, 1985-=-, 1986) as noted in Section 1. It plays a more subsidiary role in matching models (see, e.g., Rosenbaum and Rubin, 1983; Heckman and Navarro, 2004). For the IV weight to be correctly constructed and i... |

540 | Principles of Econometrics - Theil - 1971 |

534 | Relaxing Price Competition Through Product Differentiation - Shaked, Sutton - 1982 |

425 | Matching as an Econometric Evaluation Estimator,” - Heckman, Ichimura, et al. - 1998 |

394 |
The Estimation of Economic Relationships Using Instrumental Variables’,
- Sargan
- 1958
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Citation Context ...3). Letting “�” denotetheOLS estimator, the large sample bias is plim (�α1 − α1) = Cov(D,U) Var(D) for standard sampling schemes. 2sdifferent instrumental variables estimators efficiently (see, e.g., =-=Sargan, 1958-=-; Hansen, 1982). Nevertheless, all valid instrumental variables estimators converge to α1. Tests of the validity of one instrument given the assumed validity of at least one other instrument, due to D... |

368 |
Life Cycle Schooling and Dynamic Selection Bias: Models and Evidence for Five Cohorts of
- Cameron, Heckman
- 1998
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Citation Context ... grade s − 1 to proceed to grade s. The ordered choice model has been widely used to fit data on schooling transitions and its nonparametric identifiability has been studied (Harmon and Walker, 1999; =-=Cameron and Heckman, 1998-=-; Carneiro et al., 2003; Heckman and Navarro, 2004). It can be viewed as a duration model for dynamic treatment effects with associated outcomes. (See Heckman and Navarro (2004)) 36sOur analyses paral... |

344 | Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems,”
- Card
- 2001
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Citation Context ...ed that in a model with heterogeneous responses, IV identifies a weighted mean treatment effect of persons who switch treatment (or policy) status in response to a change in an instrument (see, e.g., =-=Card, 2001-=-; Delong et al., 2003; Kling, 2001). In general, IV estimates the mean response of persons who switch status in response to the variation induced by an instrument and this is a net effect arising from... |

314 | Asymptotic Theory for Econometricians - White - 2001 |

275 | Empirical Strategies in Labor Economics”, - Angrist, Krueger - 1999 |

274 | Two-Stage Least Squares Estimates of Average Causal Effects in Models with Variable Treatment Intensity”, - Angrist, Imbens - 1995 |

270 | Generalized econometric models with selectivity. - Lee - 1983 |

258 | Instrumental Variables. A Study of Implicit Behavioral Assumptions Used in Making Program Evaluations.” - Heckman - 1997 |

225 |
Varieties of selection bias‘,
- Heckman
- 1990
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Citation Context ... noted the distribution of P (Z) and the relationship between J (Z) and P (Z) determines the weight on MTE. Under conditions (A-1)—(A-5), along with rank and limit conditions (Heckman and Robb, 1986; =-=Heckman, 1990-=-; Heckman and Vytlacil, 2005a) one can identify µ 1 (X) ,µ 0 (X) ,K1 (P (Z) ,X) , and K0 (P (Z) ,X) . Misspecification of P (Z) (either its functional form or its arguments) and hence of K1 (P (Z) ,X)... |

196 | Convergence Rates and Asymptotic Normality for Series Estimators,” - Newey - 1997 |

192 | Semiparametric estimation of censored selection models,” - Ahn, Powell - 1993 |

188 | Competition and Collusion in the American Automobile Industry: the 1955 Price War - Bresnahan - 1987 |

185 |
Local Instrumental Variables and Latent Variable Models for Identifying and Bounding Treatment Effects,”
- Heckman, Vytlacil
- 1999
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Citation Context ... to identify the margin of UD selected by instruments, something currently not available in the literature. The MTE can be identified by taking derivatives of E (Y | Z = z) with respect to P (z) (see =-=Heckman and Vytlacil, 1999-=-). 20 The idea is as follows. For the model of essential heterogeneity, under assumptions (A1)-(A5), 19 Assumption (A-2) implies that Pr (Dz =1)=Pr(D =1| Z = z) , and Pr (Dz 0 =1)=Pr(D =1| Z = z0 ) . ... |

183 | Mobility and the Return to Education: Testing a Roy Model with Multiple Markets - Dahl |

181 | Shadow Prices, Market Wages, and Labor Supply’, - Heckman - 1974 |

177 | Monotone Instrumental Variables: With an Application to the Returns to Schooling,” - Manski, Pepper - 2000 |

175 | The statistical implications of a system of simultaneous equations. - Haavelmo - 1943 |

175 | Microdata, heterogeneity and the evaluation of public policy. - Heckman - 2001 |

168 |
Estimating Distributions of Treatment Effects with an Application to the Returns to Schooling and
- Carneiro, Hansen, et al.
- 2003
(Show Context)
Citation Context ...grade s. The ordered choice model has been widely used to fit data on schooling transitions and its nonparametric identifiability has been studied (Harmon and Walker, 1999; Cameron and Heckman, 1998; =-=Carneiro et al., 2003-=-; Heckman and Navarro, 2004). It can be viewed as a duration model for dynamic treatment effects with associated outcomes. (See Heckman and Navarro (2004)) 36sOur analyses parallels and generalizes th... |

167 | Using Matching, Instrumental Variables, and Control Functions to Estimate Economic Choice Models,” The Review of Economics and
- Heckman, Navarro-Lozano
- 2004
(Show Context)
Citation Context ...ection models as a determinant of control functions (see Heckman and Robb, 1985, 1986) as noted in Section 1. It plays a more subsidiary role in matching models (see, e.g., Rosenbaum and Rubin, 1983; =-=Heckman and Navarro, 2004-=-). For the IV weight to be correctly constructed and interpreted, we need to know the correct model for P (Z), i.e. we need to know exactly which Z determine P (Z) . This feature is not required in th... |

165 |
The Estimation of the Parameters of a Linear Regression System Obeying Two Separate Regimes,”
- Quandt
- 1958
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Citation Context ...an and Vytlacil (2005a,b). 8 A large class of latent index, threshold crossing models will have this representation. See Vytlacil (2004). 9 This is the standard switching regression model (see, e.g., =-=Quandt, 1958-=-, 1972). 10sY1 = µ 1 (X) +U1 and Y0 = µ 0 (X) +U0 so β, as used in equation (1.7), may be written as β =(Y1 − Y0) = µ 1 (X) − µ 0 (X)+U1 − U0 and U = U0. Another special case that links to standard mo... |

161 | The empirical content of the Roy model. - Heckman, Honore - 1990 |

149 | Errors in variables - Durbin - 1954 |

135 | Dynamic discrete choice and dynamic treatment effects,” - Heckman, Navarro - 2007 |

130 | Social background and school continuation decisions. - Mare - 1980 |

121 | Alternative Tests of Independence Between Stochastic Regressors and - Wu - 1973 |

117 |
Alternative methods for solving the problem of selection bias in evaluating the impact of treatments on outcomes,
- Heckman, Robb
- 1986
(Show Context)
Citation Context ... P (Z) but as previously noted the distribution of P (Z) and the relationship between J (Z) and P (Z) determines the weight on MTE. Under conditions (A-1)—(A-5), along with rank and limit conditions (=-=Heckman and Robb, 1986-=-; Heckman, 1990; Heckman and Vytlacil, 2005a) one can identify µ 1 (X) ,µ 0 (X) ,K1 (P (Z) ,X) , and K0 (P (Z) ,X) . Misspecification of P (Z) (either its functional form or its arguments) and hence o... |

113 | Estimation of semiparametric models.
- Powell
- 1994
(Show Context)
Citation Context ...sary to know P (Z) up to a monotonic transformation. 29 The distributions of U1,U0 and V do not need to be specified to estimate these models (see 29 See Heckman, Ichimura, Smith, and Todd (1998). 29s=-=Powell, 1994-=-). One criticism of selection models, featured by Imbens and Angrist (1994) is that without invoking functional form assumptions identification of µ 1(X) and µ 0(X) requires that P (Z) → 1 and P (Z) →... |

113 | Wage comparison: A selectivity bias. - Gronau - 1974 |

103 | A New Approach to Estimating Switching Regressions,” - Quandt - 1972 |

100 | A rank-invariant method of linear and polynomial regression analysis - Theil - 1950 |

96 | Separating uncertainty from heterogeneity in life cycle earnings.”Oxford - Cunha, Heckman, et al. - 2005 |

94 | The Estimation of Wage Gains and Welfare Gains in Selfselection Review of - Björklund, Moffitt - 1987 |

92 | Sequential location among firms with foresight - Prescott, Vischer - 1977 |

85 |
Interpreting Instrumental Variables Estimates of the Returns to
- Kling
- 2001
(Show Context)
Citation Context ...eous responses, IV identifies a weighted mean treatment effect of persons who switch treatment (or policy) status in response to a change in an instrument (see, e.g., Card, 2001; Delong et al., 2003; =-=Kling, 2001-=-). In general, IV estimates the mean response of persons who switch status in response to the variation induced by an instrument and this is a net effect arising from two way flows into and out of tre... |

83 | Independence, Monotonicity, and Latent Index Models: An Equivalence Result,” - Vytlacil - 2002 |

67 | Semiparametric Estimation of the Intercept of a Sample Selection Model,” Review of Economic Studies, - Andrews, Schafgans - 1998 |

55 | Estimating treatment effects for discrete outcomes when responses to treatment vary: An application to Norwegian vocational rehabilitation programs. - Aakvik, Heckman, et al. - 2005 |

53 | The interpretation of instrumental variables estimators in simultaneous equation models with an application to the demand for fish. The Review of Economic Studies, - Angrist, Graddy, et al. - 2000 |

42 | Sources of selection bias in evaluating social programs: an interpretation of conventional measures and evidence on the effectiveness of matching as a program evaluation method," - Heckman, Ichimura, et al. - 1996 |

41 | Four Parameters of Interest in the Evaluation of Social Programmes’. - Heckman, Tobias, et al. - 2001 |

40 | Vytlacil (2007a), Econometric evaluation of social programs, part I: Causal models, structural models and econometric policy evaluation - Heckman, J |

34 | 2006), Counterfactual analysis of inequality and social mobility, Mobility and Inequality: Frontiers of Research in Sociology and Economics, edited by - Cunha, Heckman, et al. |

34 | Earnings equations and rates of return: The Mincer equation and beyond. - Heckman, Lochner, et al. - 2006 |

29 | Vytlacil (2007b), Econometric evaluation of social programs, part II: Using the marginal treatment effect to organize alternative economic estimators to evaluate social programs and to forecast their effects in new environments - Heckman, J |

27 | Removing the veil of ignorance in assessing the distributional impacts of social policies. Working paper, - Carneiro, Hansen, et al. - 2002 |

22 | 2000c), “The Relationship Between Treatment Parameters Within a Latent Variable Framework - Heckman, Vytlacil |

20 | An Introduction to Econometric Applications of Empirical Process Theory for Dependent Random Variables,”Econometric Reviews - ANDREWS - 1993 |

15 | Simultaneous Equation Models with Both Continuous and DisDiscrete Data crete Endogenous Variables with and without Structural Shift in the Equations." Pp - Heckman - 1976 |

15 | On using linear regressions in welfare economics - Yitzhaki - 1996 |

14 | Policy-relevant treatment effects,” - Heckman, Vytlacil - 2001 |

11 | Specification Tests in Econometrics - A - 1978 |

9 | Some contributions to the theory of order statistics - Bickel - 1967 |

9 | A Note on Additive Separability and Latent Index Models of Binary Choice: Representation Results, unpublished manuscript - Vytlacil - 2005 |

7 |
Sustaining American Economic Growth
- Delong, Katz, et al.
- 2003
(Show Context)
Citation Context ... model with heterogeneous responses, IV identifies a weighted mean treatment effect of persons who switch treatment (or policy) status in response to a change in an instrument (see, e.g., Card, 2001; =-=Delong et al., 2003-=-; Kling, 2001). In general, IV estimates the mean response of persons who switch status in response to the variation induced by an instrument and this is a net effect arising from two way flows into a... |

7 |
The Marginal and Average Return to Schooling in the UK". European Economic Review
- Harmon, Walker
- 1999
(Show Context)
Citation Context ...r developing the case of binary outcomes, we extend our analysis to an ordered choice model where there are multiple schooling levels. Creative applications of IV in the recent literature (see, e.g., =-=Harmon and Walker, 1999-=-) seek to identify causal effects at various margins. These margins can be defined within a single binary choice (e.g. college vs. high school) or across choices (e.g. dropout vs. high school vs. coll... |

7 | Vytlacil (2001a). Instrumental variables, selection models, and tight bounds on the average treatment effect - Heckman, J |

6 | On using linear regression in welfare economics. Working Paper 217 - Yitzhaki - 1989 |

5 | Vytlacil (2001b). Local instrumental variables - Heckman, J |

4 | 2001a. “Local Instrumental Variables - Heckman, Vytlacil |

4 | Vytlacil (2005a). Econometric evaluation of social programs - Heckman, J |

4 | Vytlacil (2001c - Heckman, J |

3 | Ordered discrete choice selection models: Equivalence, nonequivalence, and representation results - Vytlacil |

3 | Non/Semiparametric identification and estimation of a dynamic discrete-time discrete-choice models with unobserved heterogeneity. Unpublished working paper - X, Vytlacil - 1998 |

3 | Identification and square-root-n efficient estimation of semiparametric panel data models with binary dependent variables and a latent factor. Unpublished working paper - Chen, Heckman, et al. - 1999 |

3 | The identification and economic content of orderedchoicemodelswithstochasticcutoffs. International Economic Review. Under revision - Cunha, Heckman, et al. - 2007 |

3 | Simpleestimatorsfortreatment parameters in a latent variable framework - Heckman, Tobias |

3 | Interpreting iv estimates of the effect of schooling on earnings. Unpublished manuscript - Heckman, Urzua - 2006 |

3 | Identification of semiparametric discrete choice models. Discussion Paper 249 - S - 1989 |

1 | Structural equations,treatment effects and econometric policy evaluation - Heckman, Vytlacil |