Estimation and Confidence Regions for Parameter Sets in Econometric Models

Chernozhukov, Victor; Hong, Han; Tamer, Elie

doi:10.1111/j.1468-0262.2007.00794.x

Cited by 625 publications

(708 citation statements)

References 62 publications

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“…For making inference for the structural parameter θ or its identified set (the set of θs satisfying (1)), level-sets of criterion functions are commonly used (Chernozhukov et al, 2007;Andrews & Soares, 2010). Following the literature, we consider set estimators and confidence regions of the form:…”

Section: Simulated Moments and Motivating Examplesmentioning

confidence: 99%

“…uniformly in θ as n → ∞ for any fixed R. 4 We state the Hausdorff consistency of level-set estimators as a proposition under a set of assumptions similar to those in Chernozhukov et al (2007). For this, let d H (A, B) ≡ max{sup a∈A inf b∈B a− b , sup b∈B inf a∈A a − b } denote the Hausdorff distance between two sets A, B.…”

Section: Simulated Moments and Motivating Examplesmentioning

confidence: 99%

“…The imposed conditions are analogous to Condition M.1 in Chernozhukov et al (2007) (see Section 3.2 in their paper for details). A key modification is that we assume that {m R (·, θ), θ ∈ Θ{ is P -Donsker instead of {m(·, θ), θ ∈ Θ} being P -Donsker.…”

Section: A1 Hausdorff Consistencymentioning

confidence: 99%

“…Simulated moment functions are consistent (and asymptotically unbiased) for their population counterparts E[m(X, ·)] for a finite number of draws. This ensures that level-set estimators of identified sets (Chernozhukov et al, 2007) are also consistent in the Hausdorff distance.…”

Section: Introductionmentioning

confidence: 99%

“…This irregularity is introduced by the following mechanism. Rather than finding optimal parameters through some kind of extremum estimator, moment inequality estimators typically build the estimated identified set or confidence region through level set computations, such as in Chernozhukov, Hong & Tamer (2007) and Andrews & Barwick (2012).…”

Section: Introductionmentioning

confidence: 99%

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Moment inequalities in the context of simulated and predicted variables

Kaido¹,

Li²,

Rysman³

2018

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This paper explores the effects of simulated moments on the performance of inference methods based on moment inequalities. Commonly used confidence sets for parameters are level sets of criterion functions whose boundary points may depend on sample moments in an irregular manner. Due to this feature, simulation errors can affect the performance of inference in non-standard ways. In particular, a (first-order) bias due to the simulation errors may remain in the estimated boundary of the confidence set. We demonstrate, through Monte Carlo experiments, that simulation errors can significantly reduce the coverage probabilities of confidence sets in small samples. The size distortion is particularly severe when the number of inequality restrictions is large. These results highlight the danger of ignoring the sampling variations due to the simulation errors in moment inequality models. Similar issues arise when using predicted variables in moment inequalities models. We propose a method for properly correcting for these variations based on regularizing the intersection of moments in parameter space, and we show that our proposed method performs well theoretically and in practice.

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Section: Simulated Moments and Motivating Examplesmentioning

confidence: 99%

Section: Simulated Moments and Motivating Examplesmentioning

confidence: 99%

Section: A1 Hausdorff Consistencymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Moment inequalities in the context of simulated and predicted variables

Kaido¹,

Li²,

Rysman³

2018

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Charles F. Manski, Identification for Prediction and Decision (Harvard University Press 2007)

Stoye¹

2009

J of Applied Econometrics

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Few econometricians have recently impacted the way we think about our field as much as Charles Manski. The main channel by which he has accomplished this is through study of partial identification, or bounds. For a simple example, consider the distribution of employment status in a population of interest. Say that 90% of this population report their status when prompted; of these, 80% are employed and 10% are unemployed. But 10% of the population refuse to answer questions on employment. Then the population probability of employment is not identified-no survey of any size will reveal it. However, these numbers imply that between 10% and 20% of the population are unemployed. A large sample will reveal these bounds with arbitrary precision. Also, they can be tightened by imposing identifying assumptions. If one is willing to assume that nonresponders entirely resemble the responders other than by not responding, then one can conclude that the unemployment rate is 11%. Less restrictive assumptions will lead to less sharp conclusions, illustrating what Manski calls the 'Law of Decreasing Credibility. ' In a nutshell, the idea of bounds is that this type of reasoning can be fruitfully applied to a huge range of problems. This insight did not exactly change the game overnight. Some readers may be surprised to learn that Manski's first explicit 'bounds' paper was published precisely two decades ago (Manski, 1989). Ten years later, partial identification was still a niche enterprise. Today, things look much different: The theoretical literature on partial identification has assumed such a pace that this reviewer is behind on readings despite attending two specialized meetings in 2008 alone. Bounds are incorporated throughout a recent textbook on causal inference (Morgan and Winship, 2007) that was not even written by economists. Perhaps most tellingly, it is not unusual these days to hear the phrase 'point identified' in place of 'identified'-in talks that do not even feature any bounds.Identification for Prediction and Decision (Harvard University Press 2007; IPD henceforth) is Manski's new monograph, and there is no denying that much of it is about bounds. Yet a monograph on bounds already exists (Manski, 2003). How does IPD differ? First, it has a much wider scope. Manski's recent projects (including bounds, the measurement of expectations, and treatment choice) are held together by a specific worldview that would be somewhat trivialized by reducing it to bounds. His agenda in IPD is to present the coherent whole, from bounds via

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Non-parametric bounds on quantiles under monotonicity assumptions: with an application to the Italian education returns

Giustinelli

2010

J. Appl. Econ.

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SUMMARYWithin the inferential context of predicting a distribution of potential outcomes P[y t ] under a uniform treatment assignment t 2 T, this paper deals with partial identification of the˛-quantile of the distribution of interest Q˛[y t ] under relatively weak and credible monotonicity-type assumptions on the individual response functions and the population selection process. On the theoretical side, the paper adds to the existing results on non-parametric bounds on quantiles with no prior information and under monotone treatment response (MTR) by introducing and studying the identifying properties of˛-quantile monotone treatment selection (˛-QMTS),-quantile monotone instrumental variables (˛-QMIV) and their combinations. The main result parallels that for the mean; MTR and˛-QMTS aid identification in a complementary fashion, so that combining them greatly increases identification power. The theoretical results are illustrated through an empirical application on the Italian returns to educational qualifications. Bounds on several quantiles of ln(wage) under different qualifications and on quantile treatments effects (QTE) are estimated and compared with parametric quantile regression (˛-QR) and˛-IVQR estimates from the same sample. Remarkably, the˛-QMTS & MTR upper bounds on the˛-QTE of a college degree versus elementary education imply smaller year-by-year returns than the corresponding˛-IVQR point estimates.

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Estimation and Confidence Regions for Parameter Sets in Econometric Models

Cited by 625 publications

References 62 publications

Moment inequalities in the context of simulated and predicted variables

Moment inequalities in the context of simulated and predicted variables

Charles F. Manski, Identification for Prediction and Decision (Harvard University Press 2007)

Non-parametric bounds on quantiles under monotonicity assumptions: with an application to the Italian education returns

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