## Time Series Estimation of the Effects of Natural Experiments (2006)

### Cached

### Download Links

Venue: | Journal of Econometrics |

Citations: | 7 - 6 self |

### BibTeX

@ARTICLE{White06timeseries,

author = {Halbert White},

title = {Time Series Estimation of the Effects of Natural Experiments},

journal = {Journal of Econometrics},

year = {2006}

}

### OpenURL

### Abstract

Abstract This paper builds on the labor econometrics and classical treatment effects literatures to provide a framework supporting causal concepts and methods for estimating effects of natural experiments operating over time in an explicitly dynamic time-series context. We examine conditions for the construction of covariates instrumental in identifying effects of interest that lead to new tests for unconfoundedness, a key condition for the identification of causal effects that we link to the concept of Granger non-causality. Our new tests for unconfoundedness are useful in both cross-section and dynamic time-series settings. Acknowledgments: The author is grateful for the comments and suggestions of the editor, two anony-

### Citations

7048 | Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference - Pearl - 1988 |

1411 |
Econometric analysis
- Greene
- 2002
(Show Context)
Citation Context ...1 ⎛ ⎜ ⎝ D′ Y Z ′ Y where D is the T × 1 vector with elements Dt, Z is the T × k matrix with rows Z ′ t and Y is the T × 1 vector with elements Yt. The traditional textbook interpretation of OLS (e.g. =-=Greene, 1993-=-, pp. 231-232) holds that ˆα estimates the ceteris paribus effect of the natural experiment, and ˆ β estimates the ceteris paribus effects of all the other included regressors. 8 ⎞ ⎟ ⎠ ,sOne area wher... |

1223 | Multilayer feedforward networks are universal approximators - Hornik, Stinchcombe, et al. - 1989 |

1012 |
The central role of the propensity score in observational studies for causal effects
- Rosenbaum, Rubin
- 1983
(Show Context)
Citation Context ... is therefore not well served by use of the dummy variable method. Modern labor econometrics has drawn on and considerably extended methods from the treatment 10seffects literature (e.g. Rubin, 1974; =-=Rosenbaum and Rubin, 1983-=-) to obtain less problematic estimators for causal effects of interest. Key contributions are those of Heckman, Ichimura, and Todd (1997, 1998), Hahn (1998), Hirano and Imbens (2001), and Hirano, Imbe... |

622 |
Investigating causal relations by econometric models and cross-spectral methods,” Econometrica
- Granger
- 1969
(Show Context)
Citation Context ...rest to Clive Granger are time series and causality. Despite the wide application of and considerable insight provided by Clive’s seminal investigations into what is now known as “Granger Causality” (=-=Granger, 1969-=-), notions of causality for economic time series are still not settled, in relative contrast to the situation in labor economics, for example. There, concepts and methods from the statistical treatmen... |

468 |
Estimating causal effects of treatments in randomized and non randomized studies
- Rubin
- 1974
(Show Context)
Citation Context ...on is the average effect of treatment on the treated: ∆ ∗ 1 ≡ � ∆(˜z, ¨z) d ˜ G1(¨z | ˜z) d ˜ H1(˜z) = E(Y 1 t |Dt = 1) − E(Y 0 t |Dt = 1), where Y 1 t ≡ c1( ˜ Zt, ¨ Zt), Y 0 t ≡ c0( ˜ Zt, ¨ Zt) (cf. =-=Rubin, 1974-=-). In the cartel or merger examples, ∆ ∗ 1 represents the average effect of the cartel or merger, averaging over underlying market conditions in that regime. For example, this is the difference betwee... |

413 |
Matching as an Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme
- Heckman, Ichimura, et al.
- 1997
(Show Context)
Citation Context ... ex-cartel regimes for reasons causally unrelated to the cartel. Methods for analyzing non-randomized experiments pioneered by Rubin (1974) and Rosenbaum and Rubin (1983) and in labor economics (e.g. =-=Heckman, Ichimura, and Todd, 1997-=-, 1998; Hahn, 1998; Hirano and Imbens, 2001; Hirano, Imbens, and Ridder, 2003) permit one to avoid confounding the effect of interest with shifts in the distribution of other causes. Assumption A.1 pe... |

209 |
A generalization of sampling without replacement from a finite universe
- Horvitz, Thompson
- 1952
(Show Context)
Citation Context ...y score as ˆωt ≡ ˆp(Xt)/(1− ˆp(Xt)). The role of the weights is not to achieve efficiency á la GLS, but rather to reweight the regime 0 covariate distribution to that of regime 1, similar to HIR (cf. =-=Horvitz and Thompson, 1952-=-). The HIR estimator corresponds to the special case in which Xψt ≡ 1. As HI note, ˆ ∆ HI 1 t=1 can be conveniently obtained as the WLS estimator ˆα of α in the regression Yt = Dtα + X ′ ψtβ + Dt( ˜ X... |

204 | The Direction of Time - Reichenbach |

188 | Tests of Equality Between Sets of Coefficients in Two Linear Regressions - Chow - 1960 |

186 |
Conditional independence in statistical theory
- Dawid
- 1979
(Show Context)
Citation Context ...sally impacted by treatment. (Note that Xt is conceptually distinct from ˜ Zt. We discuss the relation between Xt and ˜ Zt at length below.) Expressed in the notation of conditional independence (see =-=Dawid, 1979-=-), the unconfoundedness condition is (Y 0 t , Y 1 t ) ⊥ Dt | Xt. This condition is also known as “selection on observables” (see Barnow, Cain, and Goldberger, 1981). Below, we relate this condition to... |

186 | Natural and QuasiExperiments in Economics - Meyer - 1995 |

173 |
Matching as an econometric evaluation estimator. Review of Economic Studies 65
- Heckman, Ichimura, et al.
- 1998
(Show Context)
Citation Context ...government policy intervention, a merger, or the formation or disintegration of a cartel. We draw on the extensive literature of treatment effects (Rubin, 1974; Rosenbaum and Rubin, 1983; Hahn, 1998; =-=Heckman, Ichimura, and Todd, 1998-=-; Hirano, Imbens, and Ridder, 2003), but the fact that the treatment constituted by the natural experiment may precede the measurement of relevant covariates requires us to develop and operate within ... |

168 | Efficient estimation of average treatment effects using the estimated propensity score. Econometrica 71
- Hirano, Imbens, et al.
- 2003
(Show Context)
Citation Context ...nalyzing non-randomized experiments pioneered by Rubin (1974) and Rosenbaum and Rubin (1983) and in labor economics (e.g. Heckman, Ichimura, and Todd, 1997, 1998; Hahn, 1998; Hirano and Imbens, 2001; =-=Hirano, Imbens, and Ridder, 2003-=-) permit one to avoid confounding the effect of interest with shifts in the distribution of other causes. Assumption A.1 permits us to formally define the effects of interest here. The effect of the n... |

158 | Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks - Hornik, Stinchcombe, et al. - 1990 |

157 |
Matching as an econometric evaluation estimator
- Heckman, Ichimura, et al.
- 1998
(Show Context)
Citation Context ... of the natural experiment given (˜z, ¨z) is ∆(˜z, ¨z) ≡ c1(˜z, ¨z) − c0(˜z, ¨z), where we write ci(˜z, ¨z) ≡ c(i, ˜z, ¨z) for i = 0, 1. This is a standard definition of a treatment effect (see, e.g. =-=Heckman, Ichimura, and Todd, 1998-=-). This effect is unobservable, however, because c1(˜z, ¨z) and c0(˜z, ¨z) are not simultaneously observable: we can usually observe only one of these quantities. Nevertheless, averaging leads to effe... |

157 |
Asymptotic Theory for Econometricians
- White
- 1988
(Show Context)
Citation Context ...ese law of large number requirements are also mild and hold under a wide variety of differing primitive conditions on {Λt, ˜ Zt, ¨ Zt} suitable either for crosssection or time-series data (see, e.g., =-=White, 2001-=-, ch. 3). Assumptions A.2 and A.3 can be further relaxed, but we maintain them for simplicity. Our first result follows immediately from the continuity of ˆα and ˆ β as functions of the sample moments... |

131 | Connectionist Nonparametric Regression: Multilayer Feedforward Networks Can - White - 1990 |

113 |
Estimation, Inference and Specification Analysis
- White
- 1996
(Show Context)
Citation Context ...l can be driven to zero, and, provided this is not too fast, power still approaches one. These results are entirely standard. Local power properties are also entirely standard. (Specialize results of =-=White, 1994-=-, ch. 8). Now consider the consequences of rejecting or of failing to reject H0. If one rejects H0, then CIPP fails and the effects of interest cannot be consistently estimated using covariates Xt. Th... |

111 | Empirical Strategies in Labor Economics - Angrist, Krueger - 1999 |

104 | Gallant: A Unified Theory of Estimation and Inference for Nonlinear Dynamic Models - White - 1988 |

99 |
Money, Income and Causality
- Sims
- 1972
(Show Context)
Citation Context ...sociated with recurring interventions, such as the monetary policy interventions studied by Romer and Romer (1989); and they relate their new tests to the classical Granger- and Sims-causality tests (=-=Sims, 1972-=-). Although Angrist and Kuersteiner provide tests for the presence of causal effects of interventions, they do so indirectly by making use of the “policy propensity score,” rather than by directly est... |

99 | Tests of Statistical Hypotheses Concerning Several Parameters When the Number of Observations is - Wald - 1943 |

95 | Comment: Graphical models, causality, and intervention - Pearl - 1993 |

88 | Large Sample Sieve Estimation of Semi-Nonparameteric Models,”in Handbook of Econometrics - Chen - 2007 |

85 | Causal Inference without Counterfactuals (with Discussion - Dawid - 2000 |

84 |
On the role of the propensity score in efficient semiparametric estimation of average treatment effects. Econometrica 66: 315–331
- Hahn
- 1998
(Show Context)
Citation Context ...nrelated to the cartel. Methods for analyzing non-randomized experiments pioneered by Rubin (1974) and Rosenbaum and Rubin (1983) and in labor economics (e.g. Heckman, Ichimura, and Todd, 1997, 1998; =-=Hahn, 1998-=-; Hirano and Imbens, 2001; Hirano, Imbens, and Ridder, 2003) permit one to avoid confounding the effect of interest with shifts in the distribution of other causes. Assumption A.1 permits us to formal... |

81 | Vouchers for Private Schooling in Colombia: Evidence from a Randomized Natural Experiment,” American Economic Review 92 - Angrist, Bettinger, et al. - 2002 |

67 | An Introduction to Wavelets and Other Filtering Methods in Finance and Economics - Gençay, Selçuk, et al. - 2001 |

66 | Learning the Derivatives of an Unknown Mapping with Multilayer Feedforward Networks - Gallant, ”On - 1992 |

65 | Influence diagrams for causal modelling and inference - Dawid |

64 | The economic consequences of unwed motherhood: Using twin births as a natural experiment - Bronars, Grogger - 1994 |

62 | Testing the quantity-quality fertility model: The use of twins as a natural experiment. Econometrica - R, Wolpin - 1980 |

56 | The Consquences of Adjustment for a Concomitant Variable That Has Been Affected by the Treatment - Rosenbaum - 1984 |

56 | White: ”Consistent Specification Testing with Nuisance Parameters Present Only Under the Alternative,” Econometric Theory - Stinchcombe |

51 | How do sex ratios affect marriage and labor markets? evidence from america's second generation. The Quarterly - Angrist - 2002 |

39 | Causal diagrams for empirical research", (with discussion - Pearl - 1995 |

37 | Workers’ compensation and injury duration: evidence from a natural experiment. The American economic review - Meyer, Viscusi, et al. - 1995 |

36 | Estimation of Causal Effects Using Propensity Score Weighting: An Application to Data - Hirano, Imbens - 2001 |

36 | Marginal structural models and causal inference in epidemiology - Robins, Hernán, et al. - 2000 |

33 |
Structural equation methods in the social sciences
- Goldberger
- 1972
(Show Context)
Citation Context .... This framework blends concepts explicit and implicit in the classical 3sCowles Foundation approach to econometric modeling originated by Tinbergen, Frisch, Koopmans, and Haavelmo, among others (see =-=Goldberger, 1972-=-, 1991) with concepts developed in recent work of Pearl (1988, 1993a, 1993b, 1995, 2000). It is closely related to the intervention directed acyclic graphs (DAGs) of Dawid (2002). The result is an exp... |

32 | Bounding Causal Effects Using Data from a Contaminated Natural Experiment: Analyzing the Effects of Teenage Childbearing - HOTZ, MULLINS, et al. - 1997 |

27 | Does monetary policy matter - Romer, Romer - 1989 |

26 | White: ”Improved Rates and Asymptotic Normality for Nonparametric Neural Network Estimators - Chen - 1999 |

26 | The control of confounding by intermediate variables - Robins - 1989 |

25 | Causality in Macroeconomics - Hoover - 2001 |

25 | Estimation of the causal effect of a time-varying exposure on the marginal mean of a repeated binary outcome - M, Greenland, et al. - 1999 |

20 | Rationing by waiting and the value of time: Results from a natural experiment - Deacon, Sonstelie - 1985 |

19 | Natural ‘Natural Experiments - Rosenzweig, Wolpin - 2000 |

18 | The Competitive Effects of Not-For-Profit Hospital Mergers: A Case Study - Vita, Sacher |