
on Econometrics 
By:  Haitian Xie 
Abstract:  This paper examines the identification and estimation of the structural function in fuzzy regression discontinuity (RD) designs with a continuous treatment variable. Under a dual monotonicity condition, we show that the nonlinear and nonseparable structural function can be nonparametrically identified at the RD cutoff. The dual monotonicity condition requires that the structural function and the treatment choice be strictly increasing in the unobserved causal factor. This condition is satisfied by standard parametric models used in practice. The identification result contrasts with the local average treatment effect literature, where only a certain weighted average of the structural function is identified. We propose a threestep semiparametric estimation procedure and derive the asymptotic distribution of the estimator. The semiparametric estimator achieves the same convergence rate as in the case of a binary treatment variable. As an application of the method, we estimate the causal effect of sleep time on health status by the discontinuity in natural light timing at timezone boundaries. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.08168&r= 
By:  Jonas Metzger 
Abstract:  We develop an asymptotic theory of adversarial estimators (`Aestimators'). Like maximumlikelihoodtype estimators (`Mestimators'), both the estimator and estimand are defined as the critical points of a sample and population average respectively. Aestimators generalize Mestimators, as their objective is maximized by one set of parameters and minimized by another. The continuousupdating Generalized Method of Moments estimator, popular in econometrics and causal inference, is among the earliest members of this class which distinctly falls outside the Mestimation framework. Since the recent success of Generative Adversarial Networks, Aestimators received considerable attention in both machine learning and causal inference contexts, where a flexible adversary can remove the need for researchers to manually specify which features of a problem are important. We present general results characterizing the convergence rates of Aestimators under both pointwise and partial identification, and derive the asymptotic rootn normality for plugin estimates of smooth functionals of their parameters. All unknown parameters may contain functions which are approximated via sieves. While the results apply generally, we provide easily verifiable, lowlevel conditions for the case where the sieves correspond to (deep) neural networks. Our theory also yields the asymptotic normality of general functionals of neural network Mestimators (as a special case), overcoming technical issues previously identified by the literature. We examine a variety of Aestimators proposed across econometrics and machine learning and use our theory to derive novel statistical results for each of them. Embedding distinct Aestimators into the same framework, we notice interesting connections among them, providing intuition and formal justification for their recent success in practical applications. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.10495&r= 
By:  Liyang Sun; Jesse M. Shapiro 
Abstract:  Linear panel models featuring unit and time fixed effects appear in many areas of empirical economics. An active literature studies the interpretation of the ordinary least squares estimator of the model, commonly called the twoway fixed effects (TWFE) estimator, in the presence of unmodeled coefficient heterogeneity. We illustrate some implications for the case where the research design takes advantage of variation across units (say, US states) in exposure to some treatment (say, a policy change). In this case, the TWFE can fail to estimate the average (or even a weighted average) of the units' coefficients. Under some conditions, there exists no estimator that is guaranteed to estimate even a weighted average. Building on the literature, we note that when there is a unit totally unaffected by treatment, it is possible to estimate an average effect by replacing the TWFE with an average of differenceindifferences estimators. 
JEL:  C23 C87 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:29976&r= 
By:  Matias D. Cattaneo; Rajita Chandak; Michael Jansson; Xinwei Ma 
Abstract:  We begin by introducing a class of conditional density estimators based on local polynomial techniques. The estimators are automatically boundary adaptive and easy to implement. We then study the (pointwise and) uniform statistical properties of the estimators, offering nonasymptotic characterizations of both probability concentration and distributional approximation. In particular, we establish optimal uniform convergence rate in probability and valid Gaussian distributional approximations for the tstatistic process indexed over the data support. We also discuss implementation issues such as consistent estimation of the covariance function of the Gaussian approximation, optimal integrated mean squared error bandwidth selection, and valid robust biascorrected inference. We illustrate the applicability of our results by constructing valid confidence bands and hypothesis tests for both parametric specification and shape constraints, explicitly characterizing their nonasymptotic approximation probability errors. A companion R software package implementing our main results is provided. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.10359&r= 
By:  Eustasio del Barrio; Alberto GonzálezSanz; Marc Hallin 
Abstract:  Based on the novel concept of multivariate centeroutward quantiles introduced recently in Chernozhukov et al. (2017) and Hallin et al. (2021), we are considering the problem of nonparametric multipleoutput quantile regression. Our approach defines nested conditional centeroutward quantile regression contours and regions with given conditional probability content irrespective of the underlying distribution; their graphs constitute nested centeroutward quantile regression tubes. Empirical counterparts of these concepts are constructed, yielding interpretable empirical regions andcontours which are shown to consistently reconstruct their population versions in the PompeiuHausdorff topology. Our method is entirely nonparametric and performs well in simulations including heteroskedasticity and nonlinear trends; its power as a dataanalytic tool is illustrated on some real datasets. 
Keywords:  Multipleoutput regression, Centeroutward quantiles, Optimal transport 
Date:  2022–05 
URL:  http://d.repec.org/n?u=RePEc:eca:wpaper:2013/342212&r= 
By:  Alexander Mayer 
Abstract:  Weak consistency and asymptotic normality of the ordinary leastsquares estimator in a linear regression with adaptive learning is derived when the crucial, socalled, `gain' parameter is estimated in a first step by nonlinear least squares from an auxiliary model. The singular limiting distribution of the twostep estimator is normal and in general affected by the sampling uncertainty from the first step. However, this `generatedregressor' issue disappears for certain parameter combinations. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.05298&r= 
By:  Ben Deaner 
Abstract:  We apply results in Hu and Schennach (2008) to achieve nonparametric identification of causal effects using noisy proxies for unobserved confounders. We call this the `triple proxy' approach because it requires three proxies that are jointly independent conditional on unobservables. We consider three different choices for the third proxy: it may be an outcome, a vector of treatments, or a collection of auxiliary variables. We compare to an alternative identification strategy introduced by Miao et. al. (2018) in which causal effects are identified using two conditionally independent proxies. We refer to this as the `double proxy' approach. We show that the conditional independence assumptions in the double and triple proxy approaches are nonnested, which suggests that either of the two identification strategies may be appropriate depending on the particular setting. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.13815&r= 
By:  Victor Aguirregabiria 
Abstract:  This paper studies identification and estimation of a dynamic discrete choice model of demand for differentiated product using consumerlevel panel data with few purchase events per consumer (i.e., short panel). Consumers are forwardlooking and their preferences incorporate two sources of dynamics: last choice dependence due to habits and switching costs, and duration dependence due to inventory, depreciation, or learning. A key distinguishing feature of the model is that consumer unobserved heterogeneity has a Fixed Effects (FE) structure  that is, its probability distribution conditional on the initial values of endogenous state variables is unrestricted. I apply and extend recent results to establish the identification of all the structural parameters as long as the dataset includes four or more purchase events per household. The parameters can be estimated using a sufficient statistic  conditional maximum likelihood (CML) method. An attractive feature of CML in this model is that the sufficient statistic controls for the forwardlooking value of the consumer's decision problem such that the method does not require solving dynamic programming problems or calculating expected present values. 
Keywords:  Structural dynamic discrete choice models; Dynamic demand of differentiated products; Panel data; Fixed effects; Habits; Switching costs; Storable products; Durable products 
JEL:  C23 C25 C51 D12 
Date:  2022–05–08 
URL:  http://d.repec.org/n?u=RePEc:tor:tecipa:tecipa723&r= 
By:  Philipp Gersing; Leopold Soegner; Manfred Deistler 
Abstract:  The "REtrieval from MIxed Sampling" (REMIS) approach based on blocking developed in Anderson et al. (2016a) is concerned with retrieving an underlying high frequency model from mixed frequency observations. In this paper we investigate parameteridentifiability in the Johansen (1995) vector error correction model for mixed frequency data. We prove that from the second moments of the blocked process after taking differences at lag N (N is the slow sampling rate), the parameters of the high frequency system are generically identified. We treat the stock and the flow case as well as deterministic terms. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.05952&r= 
By:  Cinzia Daraio; Leopold Simar 
Abstract:  Nonparametric methods have been widely used for assessing the performance of organizations in the private and public sector. The most popular ones are based on envelopment estimators, like the FDH or DEA estimators, that estimate the attainable sets and its efficient boundary by enveloping the cloud of observed units in the appropriate inputoutput space. The statistical properties of these flexible estimators have been established. However these nonparametric techniques do not allow to make sensitivity analysis of the production outputs to some particular inputs, or to infer about marginal products and other coefficients of economic interest. On the contrary, parametric models for production frontiers allow richer and easier economic interpretation but at a cost of restrictive assumptions on the data generating process. In addition, the latter rely mostly on regression methods fitting the center of the cloud of observed points. In this paper we offer a way to avoid these drawbacks and provide approximations of these coefficients of economic interest by â€œsmoothingâ€ the popular nonparametric estimators of the frontiers. Our approach allows to handle fully multivariate cases. We describe the statistical properties for both the full and the partial (robust) frontiers. We consider parametric but also flexible approximations based on local linear tools providing local estimates of all the desired partial derivatives and we show how to deal with environmental factors. An illustration on real data from European Higher Education Institutions (HEI) shows the usefulness of the proposed approach. 
Keywords:  Nonparametric production frontiers; DEA; FDH; partial frontiers; directional distances; linear approximations; local linear approximations. 
Date:  2022–05–10 
URL:  http://d.repec.org/n?u=RePEc:ssa:lemwps:2022/14&r= 
By:  Juli\'an Mart\'inezIriarte; Pietro Emilio Spini 
Abstract:  This paper studies the implication of a fraction of the population not responding to the instrument when selecting into treatment. We show that, in general, the presence of nonresponders biases the Marginal Treatment Effect (MTE) curve and many of its functionals. Yet, we show that, when the propensity score is fully supported on the unit interval, it is still possible to restore identification of the MTE curve and its functionals with an appropriate reweighting. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2204.10445&r= 