Inference on sets in finance

Chernozhukov, Victor; Kocatulum, Emre; Menzel, Konrad

doi:10.3982/qe387

Cited by 20 publications

(19 citation statements)

References 51 publications

(73 reference statements)

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“…5 Here, we follow the set inference approach described in Chernozhukov, Kocatulum, and Menzel (2015), which builds on Chernozhukov, Hong, and Tamer (2007). In addition, our results justify the use of subsamplingbased methods as in Chernozhukov, Hong, and Tamer (2007) and Romano and Shaikh (2010).…”

Section: Inference On Most and Least Affected Subpopulationsmentioning

confidence: 63%

“…In addition, our results justify the use of subsamplingbased methods as in Chernozhukov, Hong, and Tamer (2007) and Romano and Shaikh (2010). 6 Note that we can also similarly construct an inner confidence region, which is the complement of the outer confidence region of X \ M −u ; see Chernozhukov, Kocatulum, and Menzel (2015) for relevant discussion. and x → Σ(x u) is a uniformly consistent estimator of x → Σ(x u), the variance function of the process G ∞ (x) − Z ∞ (u) defined in Section 4.…”

Section: Inference On Most and Least Affected Subpopulationsmentioning

confidence: 99%

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The Sorted Effects Method: Discovering Heterogeneous Effects Beyond Their Averages

Chernozhukov¹,

Fernández‐Val²,

Luo³

2018

Econometrica

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The partial (ceteris paribus) effects of interest in nonlinear and interactive linear models are heterogeneous as they can vary dramatically with the underlying observed or unobserved covariates. Despite the apparent importance of heterogeneity, a common practice in modern empirical work is to largely ignore it by reporting average partial effects (or, at best, average effects for some groups). While average effects provide very convenient scalar summaries of typical effects, by definition they fail to reflect the entire variety of the heterogeneous effects. In order to discover these effects much more fully, we propose to estimate and report sorted effects—a collection of estimated partial effects sorted in increasing order and indexed by percentiles. By construction, the sorted effect curves completely represent and help visualize the range of the heterogeneous effects in one plot. They are as convenient and easy to report in practice as the conventional average partial effects. They also serve as a basis for classification analysis, where we divide the observational units into most or least affected groups and summarize their characteristics. We provide a quantification of uncertainty (standard errors and confidence bands) for the estimated sorted effects and related classification analysis, and provide confidence sets for the most and least affected groups. The derived statistical results rely on establishing key, new mathematical results on Hadamard differentiability of a multivariate sorting operator and a related classification operator, which are of independent interest. We apply the sorted effects method and classification analysis to demonstrate several striking patterns in the gender wage gap. We find that this gap is particularly strong for married women, ranging from −60normal% to 0normal% between the 2normal% and 98normal% percentiles, as a function of observed and unobserved characteristics; while the gap for never married women ranges from −40normal% to +20normal%. The most adversely affected women tend to be married, do not have college degrees, work in sales, and have high levels of potential experience.

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Section: Inference On Most and Least Affected Subpopulationsmentioning

confidence: 63%

Section: Inference On Most and Least Affected Subpopulationsmentioning

confidence: 99%

The Sorted Effects Method: Discovering Heterogeneous Effects Beyond Their Averages

Chernozhukov¹,

Fernández‐Val²,

Luo³

2018

Econometrica

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“…There are important applications where this condition holds. Chernozhukov, Kocatulum, and Menzel (2015) provide results related to Molchanov (1998), as well as important extensions for the construction of confidence sets, and show that these can be applied to carry out statistical inference on the Hansen-Jagannathan sets of admissible stochastic discount factors (Hansen and Jagannathan, 1991), the Markowitz-Fama mean-variance sets for asset portfolio returns (Markowitz, 1952), and the set of structural elasticities in Chetty 2012…”

Section: Consistent Estimationmentioning

confidence: 99%

“…Kaido and Santos (2014) extend the applicability of the support function approach to other moment inequality models and establish important efficiency results. Chernozhukov, Kocatulum, and Menzel (2015) show that an Hausdorff distance-based test statistic can be weighted to enforce either exact or first-order equivariance to transformations of parameters.…”

Section: Confidence Setsmentioning

confidence: 99%

Econometrics with Partial Identification

Molinari¹

2019

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Econometrics has traditionally revolved around point identification. Much effort has been devoted to finding the weakest set of assumptions that, together with the available data, deliver point identification of population parameters, finite or infinite dimensional that these might be. And point identification has been viewed as a necessary prerequisite for meaningful statistical inference. The research program on partial identification has begun to slowly shift this focus in the early 1990s, gaining momentum over time and developing into a widely researched area of econometrics. Partial identification has forcefully established that much can be learned from the available data and assumptions imposed because of their credibility rather than their ability to yield point identification. Within this paradigm, one obtains a set of values for the parameters of interest which are observationally equivalent given the available data and maintained assumptions. I refer to this set as the parameters' sharp identification region. Econometrics with partial identification is concerned with: (1) obtaining a tractable characterization of the parameters' sharp identification region; (2) providing methods to estimate it; (3) conducting test of hypotheses and making confidence statements about the partially identified parameters. Each of these goals poses challenges that differ from those faced in econometrics with point identification. This chapter discusses these challenges and some of their solution. It reviews advances in partial identification analysis both as applied to learning (functionals of) probability distributions that are well-defined in the absence of models, as well as to learning parameters that are well-defined only in the context of particular models. The chapter highlights a simple organizing principle: the source of the identification problem can often be traced to a collection of random variables that are consistent with the available data and maintained assumptions. This collection may be part of the observed data or be a model implication. In either case, it can be formalized as a random set. Random set theory is then used as a mathematical framework to unify a number of special results and produce a general methodology to conduct econometrics with partial identification.

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“…where T 0 is a subset of T , is a continuous and uniformly positive weighting function, and ν is a probability measure over T whose support is T . 12 Allowing for a weighting function is important because, as shown in Chernozhukov, Kocatulum, and Menzel (2015), it enforces either exact or first-order equivariance of the statistics to transformations of parameters, yielding more powerful inference. More generally we can consider any continuous function f such that f (Z) (a) has a continuous distribution function when Z is a tight Gaussian process with non-degenerate covariance function and (b) f (ζ n + c) − f (ζ n ) = o(1) for any c = o(1) and any ζ n = O(1).…”

Section: Chandrasekhar Chernozhukov Molinari and Schrimpfmentioning

confidence: 99%

Best Linear Approximations to Set Identified Functions: With an Application to the Gender Wage Gap

Chandrasekhar

Chernozhukov

Molinari

et al. 2019

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte.Abstract. This paper provides inference methods for best linear approximations to functions which are known to lie within a band. It extends the partial identification literature by allowing the upper and lower functions defining the band to carry an index, and to be unknown but parametrically or non-parametrically estimable functions. The identification region of the parameters of the best linear approximation is characterized via its support function, and limit theory is developed for the latter. We prove that the support function can be approximated by a Gaussian process and establish validity of the Bayesian bootstrap for inference. Because the bounds may carry an index, the approach covers many canonical examples in the partial identification literature arising in the presence of interval valued outcome and/or regressor data: not only mean regression, but also quantile and distribution regression, including sample selection problems, as well as mean, quantile, and distribution treatment effects. In addition, the framework can account for the availability of instruments. An application is carried out, studying female labor force participation using data from Mulligan and Rubinstein (2008) and insights from Blundell, Gosling, Ichimura, and Meghir (2007). Our results yield robust evidence of a gender wage gap, both in the 1970s and 1990s, at quantiles of the wage distribution up to the 0.4, while allowing for completely unrestricted selection into the labor force. Under the assumption that the median wage offer of the employed is larger than that of individuals that do not work, the evidence of a gender wage gap extends to quantiles up to the 0.7. When the assumption is further strengthened to require stochastic dominance, the evidence of a gender wage gap extends to all quantiles, and there is some evidence at the 0.8 and higher quantiles that the gender wage gap decreased between the 1970s and 1990s. JEL Classification Codes: C13, C31.

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Inference on sets in finance

Cited by 20 publications

References 51 publications

The Sorted Effects Method: Discovering Heterogeneous Effects Beyond Their Averages

The Sorted Effects Method: Discovering Heterogeneous Effects Beyond Their Averages

Econometrics with Partial Identification

Best Linear Approximations to Set Identified Functions: With an Application to the Gender Wage Gap

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