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Despite its critical importance, the famous X-model elaborated by Ziel and Steinert (2016) has neither bin been widely studied nor further developed. And yet, the possibilities to improve the model are as numerous as the fields it can be applied to. The present paper takes advantage of a technique proposed by Coulon et al. (2014) to enhance the X-model. Instead of using the wholesale supply and demand curves as inputs for the model, we rely on the transformed versions of these curves with a perfectly inelastic demand. As a result, computational requirements of our X-model reduce and its forecasting power increases substantially. Moreover, our X-model becomes more robust towards outliers present in the initial auction curves data.

X-model: further development and possible modifications

2019-07-22 12:59:08

Sergei Kulakov

http://arxiv.org/abs/1907.09206v1, http://arxiv.org/pdf/1907.09206v1

econ.EM

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In their IZA Discussion Paper 10247, Johansson and Lee claim that the main result (Proposition 3) in Abbring and Van den Berg (2003b) does not hold. We show that their claim is incorrect. At a certain point within their line of reasoning, they make a rather basic error while transforming one random variable into another random variable, and this leads them to draw incorrect conclusions. As a result, their paper can be discarded.

Rebuttal of "On Nonparametric Identification of Treatment Effects in Duration Models"

2019-07-20 12:18:44

Jaap H. Abbring, Gerard J. van den Berg

http://arxiv.org/abs/1907.09886v1, http://arxiv.org/pdf/1907.09886v1

econ.EM

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This study examines statistical performance of tests for time-varying properties under misspecified conditional mean and variance. When we test for time-varying properties of the conditional mean in the case in which data have no time-varying mean but have time-varying variance, asymptotic tests have size distortions. This is improved by the use of a bootstrap method. Similarly, when we test for time-varying properties of the conditional variance in the case in which data have time-varying mean but no time-varying variance, asymptotic tests have large size distortions. This is not improved even by the use of bootstrap methods. We show that tests for time-varying properties of the conditional mean by the bootstrap are robust regardless of the time-varying variance model, whereas tests for time-varying properties of the conditional variance do not perform well in the presence of misspecified time-varying mean.

Testing for time-varying properties under misspecified conditional mean and variance

2019-07-28 19:47:10

Daiki Maki, Yasushi Ota

http://arxiv.org/abs/1907.12107v2, http://arxiv.org/pdf/1907.12107v2

econ.EM

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This study compares statistical properties of ARCH tests that are robust to the presence of the misspecified conditional mean. The approaches employed in this study are based on two nonparametric regressions for the conditional mean. First is the ARCH test using Nadayara-Watson kernel regression. Second is the ARCH test using the polynomial approximation regression. The two approaches do not require specification of the conditional mean and can adapt to various nonlinear models, which are unknown a priori. Accordingly, they are robust to misspecified conditional mean models. Simulation results show that ARCH tests based on the polynomial approximation regression approach have better statistical properties than ARCH tests using Nadayara-Watson kernel regression approach for various nonlinear models.

Robust tests for ARCH in the presence of the misspecified conditional mean: A comparison of nonparametric approches

2019-07-30 09:19:18

Daiki Maki, Yasushi Ota

http://arxiv.org/abs/1907.12752v2, http://arxiv.org/pdf/1907.12752v2

econ.EM

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This paper provides a necessary and sufficient instruments condition assuring two-step generalized method of moments (GMM) based on the forward orthogonal deviations transformation is numerically equivalent to two-step GMM based on the first-difference transformation. The condition also tells us when system GMM, based on differencing, can be computed using forward orthogonal deviations. Additionally, it tells us when forward orthogonal deviations and differencing do not lead to the same GMM estimator. When estimators based on these two transformations differ, Monte Carlo simulations indicate that estimators based on forward orthogonal deviations have better finite sample properties than estimators based on differencing.

A Comparison of First-Difference and Forward Orthogonal Deviations GMM

2019-07-30 16:19:35

Robert F. Phillips

http://arxiv.org/abs/1907.12880v1, http://arxiv.org/pdf/1907.12880v1

econ.EM

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This paper introduces a version of the interdependent value model of Milgrom and Weber (1982), where the signals are given by an index gathering signal shifters observed by the econometrician and private ones specific to each bidders. The model primitives are shown to be nonparametrically identified from first-price auction bids under a testable mild rank condition. Identification holds for all possible signal values. This allows to consider a wide range of counterfactuals where this is important, as expected revenue in second-price auction. An estimation procedure is briefly discussed.

Nonparametric identification of an interdependent value model with buyer covariates from first-price auction bids

2019-10-23 19:12:17

Nathalie Gimenes, Emmanuel Guerre

http://arxiv.org/abs/1910.10646v1, http://arxiv.org/pdf/1910.10646v1

econ.EM

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Given the unconfoundedness assumption, we propose new nonparametric estimators for the reduced dimensional conditional average treatment effect (CATE) function. In the first stage, the nuisance functions necessary for identifying CATE are estimated by machine learning methods, allowing the number of covariates to be comparable to or larger than the sample size. The second stage consists of a low-dimensional local linear regression, reducing CATE to a function of the covariate(s) of interest. We consider two variants of the estimator depending on whether the nuisance functions are estimated over the full sample or over a hold-out sample. Building on Belloni at al. (2017) and Chernozhukov et al. (2018), we derive functional limit theory for the estimators and provide an easy-to-implement procedure for uniform inference based on the multiplier bootstrap. The empirical application revisits the effect of maternal smoking on a baby's birth weight as a function of the mother's age.

Estimation of Conditional Average Treatment Effects with High-Dimensional Data

2019-08-07 02:40:47

Qingliang Fan, Yu-Chin Hsu, Robert P. Lieli, Yichong Zhang

http://arxiv.org/abs/1908.02399v5, http://arxiv.org/pdf/1908.02399v5

econ.EM

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We consider nonparametric identification of independent private value first-price auction models, in which the analyst only observes winning bids. Our benchmark model assumes an exogenous number of bidders N. We show that, if the bidders observe N, the resulting discontinuities in the winning bid density can be used to identify the distribution of N. The private value distribution can be nonparametrically identified in a second step. This extends, under testable identification conditions, to the case where N is a number of potential buyers, who bid with some unknown probability. Identification also holds in presence of additive unobserved heterogeneity drawn from some parametric distributions. A last class of extensions deals with cartels which can change size across auctions due to varying bidder cartel membership. Identification still holds if the econometrician observes winner identities and winning bids, provided a (unknown) bidder is always a cartel member. The cartel participation probabilities of other bidders can also be identified. An application to USFS timber auction data illustrates the usefulness of discontinuities to analyze bidder participation.

Nonparametric Identification of First-Price Auction with Unobserved Competition: A Density Discontinuity Framework

2019-08-15 13:06:05

Emmanuel Guerre, Yao Luo

http://arxiv.org/abs/1908.05476v2, http://arxiv.org/pdf/1908.05476v2

econ.EM

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Establishing that a demand mapping is injective is core first step for a variety of methodologies. When a version of the law of demand holds, global injectivity can be checked by seeing whether the demand mapping is constant over any line segments. When we add the assumption of differentiability, we obtain necessary and sufficient conditions for injectivity that generalize classical \cite{gale1965jacobian} conditions for quasi-definite Jacobians.

Injectivity and the Law of Demand

2019-08-15 22:13:43

Roy Allen

http://arxiv.org/abs/1908.05714v1, http://arxiv.org/pdf/1908.05714v1

econ.EM

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Policy evaluation is central to economic data analysis, but economists mostly work with observational data in view of limited opportunities to carry out controlled experiments. In the potential outcome framework, the panel data approach (Hsiao, Ching and Wan, 2012) constructs the counterfactual by exploiting the correlation between cross-sectional units in panel data. The choice of cross-sectional control units, a key step in its implementation, is nevertheless unresolved in data-rich environment when many possible controls are at the researcher's disposal. We propose the forward selection method to choose control units, and establish validity of the post-selection inference. Our asymptotic framework allows the number of possible controls to grow much faster than the time dimension. The easy-to-implement algorithms and their theoretical guarantee extend the panel data approach to big data settings.

Forward-Selected Panel Data Approach for Program Evaluation

2019-08-16 12:00:57

Zhentao Shi, Jingyi Huang

http://arxiv.org/abs/1908.05894v3, http://arxiv.org/pdf/1908.05894v3

econ.EM

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A family of models of individual discrete choice are constructed by means of statistical averaging of choices made by a subject in a reinforcement learning process, where the subject has short, k-term memory span. The choice probabilities in these models combine in a non-trivial, non-linear way the initial learning bias and the experience gained through learning. The properties of such models are discussed and, in particular, it is shown that probabilities deviate from Luce's Choice Axiom, even if the initial bias adheres to it. Moreover, we shown that the latter property is recovered as the memory span becomes large. Two applications in utility theory are considered. In the first, we use the discrete choice model to generate binary preference relation on simple lotteries. We show that the preferences violate transitivity and independence axioms of expected utility theory. Furthermore, we establish the dependence of the preferences on frames, with risk aversion for gains, and risk seeking for losses. Based on these findings we propose next a parametric model of choice based on the probability maximization principle, as a model for deviations from expected utility principle. To illustrate the approach we apply it to the classical problem of demand for insurance.

A model of discrete choice based on reinforcement learning under short-term memory

2019-08-16 22:15:33

Misha Perepelitsa

http://arxiv.org/abs/1908.06133v1, http://arxiv.org/pdf/1908.06133v1

econ.EM

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We propose a new finite sample corrected variance estimator for the linear generalized method of moments (GMM) including the one-step, two-step, and iterated estimators. Our formula additionally corrects for the over-identification bias in variance estimation on top of the commonly used finite sample correction of Windmeijer (2005) which corrects for the bias from estimating the efficient weight matrix, so is doubly corrected. An important feature of the proposed double correction is that it automatically provides robustness to misspecification of the moment condition. In contrast, the conventional variance estimator and the Windmeijer correction are inconsistent under misspecification. That is, the proposed double correction formula provides a convenient way to obtain improved inference under correct specification and robustness against misspecification at the same time.

A Doubly Corrected Robust Variance Estimator for Linear GMM

2019-08-21 15:41:08

Jungbin Hwang, Byunghoon Kang, Seojeong Lee

http://arxiv.org/abs/1908.07821v2, http://arxiv.org/pdf/1908.07821v2

econ.EM

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This paper deals with the time-varying high dimensional covariance matrix estimation. We propose two covariance matrix estimators corresponding with a time-varying approximate factor model and a time-varying approximate characteristic-based factor model, respectively. The models allow the factor loadings, factor covariance matrix, and error covariance matrix to change smoothly over time. We study the rate of convergence of each estimator. Our simulation and empirical study indicate that time-varying covariance matrix estimators generally perform better than time-invariant covariance matrix estimators. Also, if characteristics are available that genuinely explain true loadings, the characteristics can be used to estimate loadings more precisely in finite samples; their helpfulness increases when loadings rapidly change.

Estimating a Large Covariance Matrix in Time-varying Factor Models

2019-10-26 03:08:24

Jaeheon Jung

http://arxiv.org/abs/1910.11965v1, http://arxiv.org/pdf/1910.11965v1

econ.EM

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This paper considers the practically important case of nonparametrically estimating heterogeneous average treatment effects that vary with a limited number of discrete and continuous covariates in a selection-on-observables framework where the number of possible confounders is very large. We propose a two-step estimator for which the first step is estimated by machine learning. We show that this estimator has desirable statistical properties like consistency, asymptotic normality and rate double robustness. In particular, we derive the coupled convergence conditions between the nonparametric and the machine learning steps. We also show that estimating population average treatment effects by averaging the estimated heterogeneous effects is semi-parametrically efficient. The new estimator is an empirical example of the effects of mothers' smoking during pregnancy on the resulting birth weight.

Nonparametric estimation of causal heterogeneity under high-dimensional confounding

2019-08-23 15:18:37

Michael Zimmert, Michael Lechner

http://arxiv.org/abs/1908.08779v1, http://arxiv.org/pdf/1908.08779v1

econ.EM

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The literature on stochastic programming typically restricts attention to problems that fulfill constraint qualifications. The literature on estimation and inference under partial identification frequently restricts the geometry of identified sets with diverse high-level assumptions. These superficially appear to be different approaches to closely related problems. We extensively analyze their relation. Among other things, we show that for partial identification through pure moment inequalities, numerous assumptions from the literature essentially coincide with the Mangasarian-Fromowitz constraint qualification. This clarifies the relation between well-known contributions, including within econometrics, and elucidates stringency, as well as ease of verification, of some high-level assumptions in seminal papers.

Constraint Qualifications in Partial Identification

2019-08-24 10:34:43

Hiroaki Kaido, Francesca Molinari, Jörg Stoye

http://dx.doi.org/10.1017/S0266466621000207, http://arxiv.org/abs/1908.09103v4, http://arxiv.org/pdf/1908.09103v4

econ.EM

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We develop a new extreme value theory for repeated cross-sectional and panel data to construct asymptotically valid confidence intervals (CIs) for conditional extremal quantiles from a fixed number $k$ of nearest-neighbor tail observations. As a by-product, we also construct CIs for extremal quantiles of coefficients in linear random coefficient models. For any fixed $k$, the CIs are uniformly valid without parametric assumptions over a set of nonparametric data generating processes associated with various tail indices. Simulation studies show that our CIs exhibit superior small-sample coverage and length properties than alternative nonparametric methods based on asymptotic normality. Applying the proposed method to Natality Vital Statistics, we study factors of extremely low birth weights. We find that signs of major effects are the same as those found in preceding studies based on parametric models, but with different magnitudes.

Fixed-k Inference for Conditional Extremal Quantiles

2019-09-01 01:39:33

Yuya Sasaki, Yulong Wang

http://arxiv.org/abs/1909.00294v3, http://arxiv.org/pdf/1909.00294v3

econ.EM

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We study the incidental parameter problem for the ``three-way'' Poisson {Pseudo-Maximum Likelihood} (``PPML'') estimator recently recommended for identifying the effects of trade policies and in other panel data gravity settings. Despite the number and variety of fixed effects involved, we confirm PPML is consistent for fixed $T$ and we show it is in fact the only estimator among a wide range of PML gravity estimators that is generally consistent in this context when $T$ is fixed. At the same time, asymptotic confidence intervals in fixed-$T$ panels are not correctly centered at the true point estimates, and cluster-robust variance estimates used to construct standard errors are generally biased as well. We characterize each of these biases analytically and show both numerically and empirically that they are salient even for real-data settings with a large number of countries. We also offer practical remedies that can be used to obtain more reliable inferences of the effects of trade policies and other time-varying gravity variables, which we make available via an accompanying Stata package called ppml_fe_bias.

Bias and Consistency in Three-way Gravity Models

2019-09-03 20:54:06

Martin Weidner, Thomas Zylkin

http://arxiv.org/abs/1909.01327v6, http://arxiv.org/pdf/1909.01327v6

econ.EM

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We analyze the challenges for inference in difference-in-differences (DID) when there is spatial correlation. We present novel theoretical insights and empirical evidence on the settings in which ignoring spatial correlation should lead to more or less distortions in DID applications. We show that details such as the time frame used in the estimation, the choice of the treated and control groups, and the choice of the estimator, are key determinants of distortions due to spatial correlation. We also analyze the feasibility and trade-offs involved in a series of alternatives to take spatial correlation into account. Given that, we provide relevant recommendations for applied researchers on how to mitigate and assess the possibility of inference distortions due to spatial correlation.

Inference in Difference-in-Differences: How Much Should We Trust in Independent Clusters?

2019-09-04 16:19:25

Bruno Ferman

http://arxiv.org/abs/1909.01782v7, http://arxiv.org/pdf/1909.01782v7

econ.EM

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This paper explores the estimation of a panel data model with cross-sectional interaction that is flexible both in its approach to specifying the network of connections between cross-sectional units, and in controlling for unobserved heterogeneity. It is assumed that there are different sources of information available on a network, which can be represented in the form of multiple weights matrices. These matrices may reflect observed links, different measures of connectivity, groupings or other network structures, and the number of matrices may be increasing with sample size. A penalised quasi-maximum likelihood estimator is proposed which aims to alleviate the risk of network misspecification by shrinking the coefficients of irrelevant weights matrices to exactly zero. Moreover, controlling for unobserved factors in estimation provides a safeguard against the misspecification that might arise from unobserved heterogeneity. The asymptotic properties of the estimator are derived in a framework where the true value of each parameter remains fixed as the total number of parameters increases. A Monte Carlo simulation is used to assess finite sample performance, and in an empirical application the method is applied to study the prevalence of network spillovers in determining growth rates across countries.

Shrinkage Estimation of Network Spillovers with Factor Structured Errors

2019-09-06 14:28:41

Ayden Higgins, Federico Martellosio

http://arxiv.org/abs/1909.02823v4, http://arxiv.org/pdf/1909.02823v4

econ.EM

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We consider the problem of inference in Difference-in-Differences (DID) when there are few treated units and errors are spatially correlated. We first show that, when there is a single treated unit, some existing inference methods designed for settings with few treated and many control units remain asymptotically valid when errors are weakly dependent. However, these methods may be invalid with more than one treated unit. We propose alternatives that are asymptotically valid in this setting, even when the relevant distance metric across units is unavailable.

Inference in Difference-in-Differences with Few Treated Units and Spatial Correlation

2020-06-30 20:58:43

Luis Alvarez, Bruno Ferman

http://arxiv.org/abs/2006.16997v7, http://arxiv.org/pdf/2006.16997v7

econ.EM

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The Economy Watcher Survey, which is a market survey published by the Japanese government, contains \emph{assessments of current and future economic conditions} by people from various fields. Although this survey provides insights regarding economic policy for policymakers, a clear definition of the word "future" in future economic conditions is not provided. Hence, the assessments respondents provide in the survey are simply based on their interpretations of the meaning of "future." This motivated us to reveal the different interpretations of the future in their judgments of future economic conditions by applying weakly supervised learning and text mining. In our research, we separate the assessments of future economic conditions into economic conditions of the near and distant future using learning from positive and unlabeled data (PU learning). Because the dataset includes data from several periods, we devised new architecture to enable neural networks to conduct PU learning based on the idea of multi-task learning to efficiently learn a classifier. Our empirical analysis confirmed that the proposed method could separate the future economic conditions, and we interpreted the classification results to obtain intuitions for policymaking.

Identifying Different Definitions of Future in the Assessment of Future Economic Conditions: Application of PU Learning and Text Mining

2019-09-08 02:13:46

Masahiro Kato

http://arxiv.org/abs/1909.03348v3, http://arxiv.org/pdf/1909.03348v3

econ.EM

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This paper investigates double/debiased machine learning (DML) under multiway clustered sampling environments. We propose a novel multiway cross fitting algorithm and a multiway DML estimator based on this algorithm. We also develop a multiway cluster robust standard error formula. Simulations indicate that the proposed procedure has favorable finite sample performance. Applying the proposed method to market share data for demand analysis, we obtain larger two-way cluster robust standard errors than non-robust ones.

Multiway Cluster Robust Double/Debiased Machine Learning

2019-09-08 19:03:37

Harold D. Chiang, Kengo Kato, Yukun Ma, Yuya Sasaki

http://arxiv.org/abs/1909.03489v3, http://arxiv.org/pdf/1909.03489v3

econ.EM

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A desire to understand the decision of the UK to leave the European Union, Brexit, in the referendum of June 2016 has continued to occupy academics, the media and politicians. Using topological data analysis ball mapper we extract information from multi-dimensional datasets gathered on Brexit voting and regional socio-economic characteristics. While we find broad patterns consistent with extant empirical work, we also evidence that support for Leave drew from a far more homogenous demographic than Remain. Obtaining votes from this concise set was more straightforward for Leave campaigners than was Remain's task of mobilising a diverse group to oppose Brexit.

An Economic Topology of the Brexit vote

2019-09-08 19:05:40

Pawel Dlotko, Lucy Minford, Simon Rudkin, Wanling Qiu

http://arxiv.org/abs/1909.03490v2, http://arxiv.org/pdf/1909.03490v2

econ.EM

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We recast the synthetic controls for evaluating policies as a counterfactual prediction problem and replace its linear regression with a nonparametric model inspired by machine learning. The proposed method enables us to achieve accurate counterfactual predictions and we provide theoretical guarantees. We apply our method to a highly debated policy: the relocation of the US embassy to Jerusalem. In Israel and Palestine, we find that the average number of weekly conflicts has increased by roughly 103\% over 48 weeks since the relocation was announced on December 6, 2017. By using conformal inference and placebo tests, we justify our model and find the increase to be statistically significant.

Tree-based Synthetic Control Methods: Consequences of moving the US Embassy

2019-09-09 19:15:03

Nicolaj Søndergaard Mühlbach, Mikkel Slot Nielsen

http://arxiv.org/abs/1909.03968v3, http://arxiv.org/pdf/1909.03968v3

econ.EM

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We analyze the properties of matching estimators when there are few treated, but many control observations. We show that, under standard assumptions, the nearest neighbor matching estimator for the average treatment effect on the treated is asymptotically unbiased in this framework. However, when the number of treated observations is fixed, the estimator is not consistent, and it is generally not asymptotically normal. Since standard inference methods are inadequate, we propose alternative inference methods, based on the theory of randomization tests under approximate symmetry, that are asymptotically valid in this framework. We show that these tests are valid under relatively strong assumptions when the number of treated observations is fixed, and under weaker assumptions when the number of treated observations increases, but at a lower rate relative to the number of control observations.

Matching Estimators with Few Treated and Many Control Observations

2019-09-11 17:49:03

Bruno Ferman

http://arxiv.org/abs/1909.05093v4, http://arxiv.org/pdf/1909.05093v4

econ.EM

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The paper proposes a quantile-regression inference framework for first-price auctions with symmetric risk-neutral bidders under the independent private-value paradigm. It is first shown that a private-value quantile regression generates a quantile regression for the bids. The private-value quantile regression can be easily estimated from the bid quantile regression and its derivative with respect to the quantile level. This also allows to test for various specification or exogeneity null hypothesis using the observed bids in a simple way. A new local polynomial technique is proposed to estimate the latter over the whole quantile level interval. Plug-in estimation of functionals is also considered, as needed for the expected revenue or the case of CRRA risk-averse bidders, which is amenable to our framework. A quantile-regression analysis to USFS timber is found more appropriate than the homogenized-bid methodology and illustrates the contribution of each explanatory variables to the private-value distribution. Linear interactive sieve extensions are proposed and studied in the Appendices.

Quantile regression methods for first-price auctions

2019-09-12 13:05:37

Nathalie Gimenes, Emmanuel Guerre

http://arxiv.org/abs/1909.05542v2, http://arxiv.org/pdf/1909.05542v2

econ.EM

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This paper develops a consistent series-based specification test for semiparametric panel data models with fixed effects. The test statistic resembles the Lagrange Multiplier (LM) test statistic in parametric models and is based on a quadratic form in the restricted model residuals. The use of series methods facilitates both estimation of the null model and computation of the test statistic. The asymptotic distribution of the test statistic is standard normal, so that appropriate critical values can easily be computed. The projection property of series estimators allows me to develop a degrees of freedom correction. This correction makes it possible to account for the estimation variance and obtain refined asymptotic results. It also substantially improves the finite sample performance of the test.

A Consistent LM Type Specification Test for Semiparametric Panel Data Models

2019-09-12 16:42:16

Ivan Korolev

http://arxiv.org/abs/1909.05649v1, http://arxiv.org/pdf/1909.05649v1

econ.EM

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One simple, and often very effective, way to attenuate the impact of nuisance parameters on maximum likelihood estimation of a parameter of interest is to recenter the profile score for that parameter. We apply this general principle to the quasi-maximum likelihood estimator (QMLE) of the autoregressive parameter $\lambda$ in a spatial autoregression. The resulting estimator for $\lambda$ has better finite sample properties compared to the QMLE for $\lambda$, especially in the presence of a large number of covariates. It can also solve the incidental parameter problem that arises, for example, in social interaction models with network fixed effects, or in spatial panel models with individual or time fixed effects. However, spatial autoregressions present specific challenges for this type of adjustment, because recentering the profile score may cause the adjusted estimate to be outside the usual parameter space for $\lambda$. Conditions for this to happen are given, and implications are discussed. For inference, we propose confidence intervals based on a Lugannani--Rice approximation to the distribution of the adjusted QMLE of $\lambda$. Based on our simulations, the coverage properties of these intervals are excellent even in models with a large number of covariates.

Adjusted QMLE for the spatial autoregressive parameter

2019-09-18 02:23:50

Federico Martellosio, Grant Hillier

http://arxiv.org/abs/1909.08141v1, http://arxiv.org/pdf/1909.08141v1

econ.EM

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This paper investigates and extends the computationally attractive nonparametric random coefficients estimator of Fox, Kim, Ryan, and Bajari (2011). We show that their estimator is a special case of the nonnegative LASSO, explaining its sparse nature observed in many applications. Recognizing this link, we extend the estimator, transforming it to a special case of the nonnegative elastic net. The extension improves the estimator's recovery of the true support and allows for more accurate estimates of the random coefficients' distribution. Our estimator is a generalization of the original estimator and therefore, is guaranteed to have a model fit at least as good as the original one. A theoretical analysis of both estimators' properties shows that, under conditions, our generalized estimator approximates the true distribution more accurately. Two Monte Carlo experiments and an application to a travel mode data set illustrate the improved performance of the generalized estimator.

Nonparametric Estimation of the Random Coefficients Model: An Elastic Net Approach

2019-09-18 16:22:28

Florian Heiss, Stephan Hetzenecker, Maximilian Osterhaus

http://arxiv.org/abs/1909.08434v2, http://arxiv.org/pdf/1909.08434v2

econ.EM

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In this paper, a statistical model for panel data with unobservable grouped factor structures which are correlated with the regressors and the group membership can be unknown. The factor loadings are assumed to be in different subspaces and the subspace clustering for factor loadings are considered. A method called least squares subspace clustering estimate (LSSC) is proposed to estimate the model parameters by minimizing the least-square criterion and to perform the subspace clustering simultaneously. The consistency of the proposed subspace clustering is proved and the asymptotic properties of the estimation procedure are studied under certain conditions. A Monte Carlo simulation study is used to illustrate the advantages of the proposed method. Further considerations for the situations that the number of subspaces for factors, the dimension of factors and the dimension of subspaces are unknown are also discussed. For illustrative purposes, the proposed method is applied to study the linkage between income and democracy across countries while subspace patterns of unobserved factors and factor loadings are allowed.

Subspace Clustering for Panel Data with Interactive Effects

2019-09-22 04:51:11

Jiangtao Duan, Wei Gao, Hao Qu, Hon Keung Tony

http://arxiv.org/abs/1909.09928v2, http://arxiv.org/pdf/1909.09928v2

econ.EM

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We show that moment inequalities in a wide variety of economic applications have a particular linear conditional structure. We use this structure to construct uniformly valid confidence sets that remain computationally tractable even in settings with nuisance parameters. We first introduce least favorable critical values which deliver non-conservative tests if all moments are binding. Next, we introduce a novel conditional inference approach which ensures a strong form of insensitivity to slack moments. Our recommended approach is a hybrid technique which combines desirable aspects of the least favorable and conditional methods. The hybrid approach performs well in simulations calibrated to Wollmann (2018), with favorable power and computational time comparisons relative to existing alternatives.

Inference for Linear Conditional Moment Inequalities

2019-09-22 21:24:09

Isaiah Andrews, Jonathan Roth, Ariel Pakes

http://arxiv.org/abs/1909.10062v5, http://arxiv.org/pdf/1909.10062v5

econ.EM

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There are many environments in econometrics which require nonseparable modeling of a structural disturbance. In a nonseparable model with endogenous regressors, key conditions are validity of instrumental variables and monotonicity of the model in a scalar unobservable variable. Under these conditions the nonseparable model is equivalent to an instrumental quantile regression model. A failure of the key conditions, however, makes instrumental quantile regression potentially inconsistent. This paper develops a methodology for testing the hypothesis whether the instrumental quantile regression model is correctly specified. Our test statistic is asymptotically normally distributed under correct specification and consistent against any alternative model. In addition, test statistics to justify the model simplification are established. Finite sample properties are examined in a Monte Carlo study and an empirical illustration is provided.

Specification Testing in Nonparametric Instrumental Quantile Regression

2019-09-23 05:41:14

Christoph Breunig

http://dx.doi.org/10.1017/S0266466619000288, http://arxiv.org/abs/1909.10129v1, http://arxiv.org/pdf/1909.10129v1

econ.EM

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This paper proposes several tests of restricted specification in nonparametric instrumental regression. Based on series estimators, test statistics are established that allow for tests of the general model against a parametric or nonparametric specification as well as a test of exogeneity of the vector of regressors. The tests' asymptotic distributions under correct specification are derived and their consistency against any alternative model is shown. Under a sequence of local alternative hypotheses, the asymptotic distributions of the tests is derived. Moreover, uniform consistency is established over a class of alternatives whose distance to the null hypothesis shrinks appropriately as the sample size increases. A Monte Carlo study examines finite sample performance of the test statistics.

Goodness-of-Fit Tests based on Series Estimators in Nonparametric Instrumental Regression

2019-09-23 05:55:22

Christoph Breunig

http://dx.doi.org/10.1016/j.jeconom.2014.09.006, http://arxiv.org/abs/1909.10133v1, http://arxiv.org/pdf/1909.10133v1

econ.EM

em

Nonparametric series regression often involves specification search over the tuning parameter, i.e., evaluating estimates and confidence intervals with a different number of series terms. This paper develops pointwise and uniform inferences for conditional mean functions in nonparametric series estimations that are uniform in the number of series terms. As a result, this paper constructs confidence intervals and confidence bands with possibly data-dependent series terms that have valid asymptotic coverage probabilities. This paper also considers a partially linear model setup and develops inference methods for the parametric part uniform in the number of series terms. The finite sample performance of the proposed methods is investigated in various simulation setups as well as in an illustrative example, i.e., the nonparametric estimation of the wage elasticity of the expected labor supply from Blomquist and Newey (2002).

Inference in Nonparametric Series Estimation with Specification Searches for the Number of Series Terms

2019-09-26 17:45:13

Byunghoon Kang

http://arxiv.org/abs/1909.12162v2, http://arxiv.org/pdf/1909.12162v2

econ.EM

em

In this study, we investigate estimation and inference on a low-dimensional causal parameter in the presence of high-dimensional controls in an instrumental variable quantile regression. Our proposed econometric procedure builds on the Neyman-type orthogonal moment conditions of a previous study Chernozhukov, Hansen and Wuthrich (2018) and is thus relatively insensitive to the estimation of the nuisance parameters. The Monte Carlo experiments show that the estimator copes well with high-dimensional controls. We also apply the procedure to empirically reinvestigate the quantile treatment effect of 401(k) participation on accumulated wealth.

Debiased/Double Machine Learning for Instrumental Variable Quantile Regressions

2019-09-27 13:11:18

Jau-er Chen, Chien-Hsun Huang, Jia-Jyun Tien

http://arxiv.org/abs/1909.12592v3, http://arxiv.org/pdf/1909.12592v3

econ.EM

em

Price indexes in time and space is a most relevant topic in statistical analysis from both the methodological and the application side. In this paper a price index providing a novel and effective solution to price indexes over several periods and among several countries, that is in both a multi-period and a multilateral framework, is devised. The reference basket of the devised index is the union of the intersections of the baskets of all periods/countries in pairs. As such, it provides a broader coverage than usual indexes. Index closed-form expressions and updating formulas are provided and properties investigated. Last, applications with real and simulated data provide evidence of the performance of the index at stake.

An econometric analysis of the Italian cultural supply

2019-09-30 22:58:41

Consuelo Nava, Maria Grazia Zoia

http://arxiv.org/abs/1910.00073v3, http://arxiv.org/pdf/1910.00073v3

econ.EM

em

We study the informational content of factor structures in discrete triangular systems. Factor structures have been employed in a variety of settings in cross sectional and panel data models, and in this paper we formally quantify their identifying power in a bivariate system often employed in the treatment effects literature. Our main findings are that imposing a factor structure yields point identification of parameters of interest, such as the coefficient associated with the endogenous regressor in the outcome equation, under weaker assumptions than usually required in these models. In particular, we show that a "non-standard" exclusion restriction that requires an explanatory variable in the outcome equation to be excluded from the treatment equation is no longer necessary for identification, even in cases where all of the regressors from the outcome equation are discrete. We also establish identification of the coefficient of the endogenous regressor in models with more general factor structures, in situations where one has access to at least two continuous measurements of the common factor.

Informational Content of Factor Structures in Simultaneous Binary Response Models

2019-10-03 09:29:40

Shakeeb Khan, Arnaud Maurel, Yichong Zhang

http://arxiv.org/abs/1910.01318v3, http://arxiv.org/pdf/1910.01318v3

econ.EM

em

This paper analyzes identifiability properties of structural vector autoregressive moving average (SVARMA) models driven by independent and non-Gaussian shocks. It is well known, that SVARMA models driven by Gaussian errors are not identified without imposing further identifying restrictions on the parameters. Even in reduced form and assuming stability and invertibility, vector autoregressive moving average models are in general not identified without requiring certain parameter matrices to be non-singular. Independence and non-Gaussianity of the shocks is used to show that they are identified up to permutations and scalings. In this way, typically imposed identifying restrictions are made testable. Furthermore, we introduce a maximum-likelihood estimator of the non-Gaussian SVARMA model which is consistent and asymptotically normally distributed.

Identification and Estimation of SVARMA models with Independent and Non-Gaussian Inputs

2019-10-09 19:06:46

Bernd Funovits

http://arxiv.org/abs/1910.04087v1, http://arxiv.org/pdf/1910.04087v1

econ.EM

em

We generalize well-known results on structural identifiability of vector autoregressive models (VAR) to the case where the innovation covariance matrix has reduced rank. Structural singular VAR models appear, for example, as solutions of rational expectation models where the number of shocks is usually smaller than the number of endogenous variables, and as an essential building block in dynamic factor models. We show that order conditions for identifiability are misleading in the singular case and provide a rank condition for identifiability of the noise parameters. Since the Yule-Walker equations may have multiple solutions, we analyze the effect of restrictions on the system parameters on over- and underidentification in detail and provide easily verifiable conditions.

Identifiability of Structural Singular Vector Autoregressive Models

2019-10-09 19:18:57

Bernd Funovits, Alexander Braumann

http://dx.doi.org/10.1111/jtsa.12576, http://arxiv.org/abs/1910.04096v2, http://arxiv.org/pdf/1910.04096v2

econ.EM

em

This paper studies inter-trade durations in the NASDAQ limit order market and finds that inter-trade durations in ultra-high frequency have two modes. One mode is to the order of approximately 10^{-4} seconds, and the other is to the order of 1 second. This phenomenon and other empirical evidence suggest that there are two regimes associated with the dynamics of inter-trade durations, and the regime switchings are driven by the changes of high-frequency traders (HFTs) between providing and taking liquidity. To find how the two modes depend on information in the limit order book (LOB), we propose a two-state multifactor regime-switching (MF-RSD) model for inter-trade durations, in which the probabilities transition matrices are time-varying and depend on some lagged LOB factors. The MF-RSD model has good in-sample fitness and the superior out-of-sample performance, compared with some benchmark duration models. Our findings of the effects of LOB factors on the inter-trade durations help to understand more about the high-frequency market microstructure.

A multifactor regime-switching model for inter-trade durations in the limit order market

2019-12-02 16:30:42

Zhicheng Li, Haipeng Xing, Xinyun Chen

http://arxiv.org/abs/1912.00764v1, http://arxiv.org/pdf/1912.00764v1

econ.EM

em

This paper proposes averaging estimation methods to improve the finite-sample efficiency of the instrumental variables quantile regression (IVQR) estimation. First, I apply Cheng, Liao, Shi's (2019) averaging GMM framework to the IVQR model. I propose using the usual quantile regression moments for averaging to take advantage of cases when endogeneity is not too strong. I also propose using two-stage least squares slope moments to take advantage of cases when heterogeneity is not too strong. The empirical optimal weight formula of Cheng et al. (2019) helps optimize the bias-variance tradeoff, ensuring uniformly better (asymptotic) risk of the averaging estimator over the standard IVQR estimator under certain conditions. My implementation involves many computational considerations and builds on recent developments in the quantile literature. Second, I propose a bootstrap method that directly averages among IVQR, quantile regression, and two-stage least squares estimators. More specifically, I find the optimal weights in the bootstrap world and then apply the bootstrap-optimal weights to the original sample. The bootstrap method is simpler to compute and generally performs better in simulations, but it lacks the formal uniform dominance results of Cheng et al. (2019). Simulation results demonstrate that in the multiple-regressors/instruments case, both the GMM averaging and bootstrap estimators have uniformly smaller risk than the IVQR estimator across data-generating processes (DGPs) with all kinds of combinations of different endogeneity levels and heterogeneity levels. In DGPs with a single endogenous regressor and instrument, where averaging estimation is known to have least opportunity for improvement, the proposed averaging estimators outperform the IVQR estimator in some cases but not others.

Averaging estimation for instrumental variables quantile regression

2019-10-09 23:48:58

Xin Liu

http://arxiv.org/abs/1910.04245v1, http://arxiv.org/pdf/1910.04245v1

econ.EM

em

This paper proposes an imputation procedure that uses the factors estimated from a tall block along with the re-rotated loadings estimated from a wide block to impute missing values in a panel of data. Assuming that a strong factor structure holds for the full panel of data and its sub-blocks, it is shown that the common component can be consistently estimated at four different rates of convergence without requiring regularization or iteration. An asymptotic analysis of the estimation error is obtained. An application of our analysis is estimation of counterfactuals when potential outcomes have a factor structure. We study the estimation of average and individual treatment effects on the treated and establish a normal distribution theory that can be useful for hypothesis testing.

Matrix Completion, Counterfactuals, and Factor Analysis of Missing Data

2019-10-15 15:18:35

Jushan Bai, Serena Ng

http://arxiv.org/abs/1910.06677v5, http://arxiv.org/pdf/1910.06677v5

econ.EM

em

This paper develops a new standard-error estimator for linear panel data models. The proposed estimator is robust to heteroskedasticity, serial correlation, and cross-sectional correlation of unknown forms. The serial correlation is controlled by the Newey-West method. To control for cross-sectional correlations, we propose to use the thresholding method, without assuming the clusters to be known. We establish the consistency of the proposed estimator. Monte Carlo simulations show the method works well. An empirical application is considered.

Standard Errors for Panel Data Models with Unknown Clusters

2019-10-16 18:21:36

Jushan Bai, Sung Hoon Choi, Yuan Liao

http://arxiv.org/abs/1910.07406v2, http://arxiv.org/pdf/1910.07406v2

econ.EM

em

This article provides a selective review on the recent literature on econometric models of network formation. The survey starts with a brief exposition on basic concepts and tools for the statistical description of networks. I then offer a review of dyadic models, focussing on statistical models on pairs of nodes and describe several developments of interest to the econometrics literature. The article also presents a discussion of non-dyadic models where link formation might be influenced by the presence or absence of additional links, which themselves are subject to similar influences. This is related to the statistical literature on conditionally specified models and the econometrics of game theoretical models. I close with a (non-exhaustive) discussion of potential areas for further development.

Econometric Models of Network Formation

2019-10-17 12:18:59

Aureo de Paula

http://arxiv.org/abs/1910.07781v2, http://arxiv.org/pdf/1910.07781v2

econ.EM

em

Long memory in the sense of slowly decaying autocorrelations is a stylized fact in many time series from economics and finance. The fractionally integrated process is the workhorse model for the analysis of these time series. Nevertheless, there is mixed evidence in the literature concerning its usefulness for forecasting and how forecasting based on it should be implemented. Employing pseudo-out-of-sample forecasting on inflation and realized volatility time series and simulations we show that methods based on fractional integration clearly are superior to alternative methods not accounting for long memory, including autoregressions and exponential smoothing. Our proposal of choosing a fixed fractional integration parameter of $d=0.5$ a priori yields the best results overall, capturing long memory behavior, but overcoming the deficiencies of methods using an estimated parameter. Regarding the implementation of forecasting methods based on fractional integration, we use simulations to compare local and global semiparametric and parametric estimators of the long memory parameter from the Whittle family and provide asymptotic theory backed up by simulations to compare different mean estimators. Both of these analyses lead to new results, which are also of interest outside the realm of forecasting.

Forecasting under Long Memory and Nonstationarity

2019-10-18 02:57:34

Uwe Hassler, Marc-Oliver Pohle

http://dx.doi.org/10.1093/jjfinec/nbab017, http://arxiv.org/abs/1910.08202v1, http://arxiv.org/pdf/1910.08202v1

econ.EM

em

This paper develops the inferential theory for latent factor models estimated from large dimensional panel data with missing observations. We propose an easy-to-use all-purpose estimator for a latent factor model by applying principal component analysis to an adjusted covariance matrix estimated from partially observed panel data. We derive the asymptotic distribution for the estimated factors, loadings and the imputed values under an approximate factor model and general missing patterns. The key application is to estimate counterfactual outcomes in causal inference from panel data. The unobserved control group is modeled as missing values, which are inferred from the latent factor model. The inferential theory for the imputed values allows us to test for individual treatment effects at any time under general adoption patterns where the units can be affected by unobserved factors.

Large Dimensional Latent Factor Modeling with Missing Observations and Applications to Causal Inference

2019-10-18 08:38:04

Ruoxuan Xiong, Markus Pelger

http://arxiv.org/abs/1910.08273v6, http://arxiv.org/pdf/1910.08273v6

econ.EM

em

We discuss the issue of estimating large-scale vector autoregressive (VAR) models with stochastic volatility in real-time situations where data are sampled at different frequencies. In the case of a large VAR with stochastic volatility, the mixed-frequency data warrant an additional step in the already computationally challenging Markov Chain Monte Carlo algorithm used to sample from the posterior distribution of the parameters. We suggest the use of a factor stochastic volatility model to capture a time-varying error covariance structure. Because the factor stochastic volatility model renders the equations of the VAR conditionally independent, settling for this particular stochastic volatility model comes with major computational benefits. First, we are able to improve upon the mixed-frequency simulation smoothing step by leveraging a univariate and adaptive filtering algorithm. Second, the regression parameters can be sampled equation-by-equation in parallel. These computational features of the model alleviate the computational burden and make it possible to move the mixed-frequency VAR to the high-dimensional regime. We illustrate the model by an application to US data using our mixed-frequency VAR with 20, 34 and 119 variables.

Estimating Large Mixed-Frequency Bayesian VAR Models

2019-12-04 22:59:03

Sebastian Ankargren, Paulina Jonéus

http://arxiv.org/abs/1912.02231v1, http://arxiv.org/pdf/1912.02231v1

econ.EM

em

We introduce a synthetic control methodology to study policies with staggered adoption. Many policies, such as the board gender quota, are replicated by other policy setters at different time frames. Our method estimates the dynamic average treatment effects on the treated using variation introduced by the staggered adoption of policies. Our method gives asymptotically unbiased estimators of many interesting quantities and delivers asymptotically valid inference. By using the proposed method and national labor data in Europe, we find evidence that quota regulation on board diversity leads to a decrease in part-time employment, and an increase in full-time employment for female professionals.

Synthetic Control Inference for Staggered Adoption: Estimating the Dynamic Effects of Board Gender Diversity Policies

2019-12-13 07:29:19

Jianfei Cao, Shirley Lu

http://arxiv.org/abs/1912.06320v1, http://arxiv.org/pdf/1912.06320v1

econ.EM

em

Haavelmo (1944) proposed a probabilistic structure for econometric modeling, aiming to make econometrics useful for decision making. His fundamental contribution has become thoroughly embedded in subsequent econometric research, yet it could not answer all the deep issues that the author raised. Notably, Haavelmo struggled to formalize the implications for decision making of the fact that models can at most approximate actuality. In the same period, Wald (1939, 1945) initiated his own seminal development of statistical decision theory. Haavelmo favorably cited Wald, but econometrics did not embrace statistical decision theory. Instead, it focused on study of identification, estimation, and statistical inference. This paper proposes statistical decision theory as a framework for evaluation of the performance of models in decision making. I particularly consider the common practice of as-if optimization: specification of a model, point estimation of its parameters, and use of the point estimate to make a decision that would be optimal if the estimate were accurate. A central theme is that one should evaluate as-if optimization or any other model-based decision rule by its performance across the state space, listing all states of nature that one believes feasible, not across the model space. I apply the theme to prediction and treatment choice. Statistical decision theory is conceptually simple, but application is often challenging. Advancement of computation is the primary task to continue building the foundations sketched by Haavelmo and Wald.

Econometrics For Decision Making: Building Foundations Sketched By Haavelmo And Wald

2019-12-17 21:47:30

Charles F. Manski

http://arxiv.org/abs/1912.08726v4, http://arxiv.org/pdf/1912.08726v4

econ.EM

em

We analyze different types of simulations that applied researchers may use to assess their inference methods. We show that different types of simulations vary in many dimensions when considered as inference assessments. Moreover, we show that natural ways of running simulations may lead to misleading conclusions, and we propose alternatives. We then provide evidence that even some simple assessments can detect problems in many different settings. Alternative assessments that potentially better approximate the true data generating process may detect problems that simpler assessments would not detect. However, they are not uniformly dominant in this dimension, and may imply some costs.

Assessing Inference Methods

2019-12-18 21:09:57

Bruno Ferman

http://arxiv.org/abs/1912.08772v13, http://arxiv.org/pdf/1912.08772v13

econ.EM

em

Learning about cause and effect is arguably the main goal in applied econometrics. In practice, the validity of these causal inferences is contingent on a number of critical assumptions regarding the type of data that has been collected and the substantive knowledge that is available. For instance, unobserved confounding factors threaten the internal validity of estimates, data availability is often limited to non-random, selection-biased samples, causal effects need to be learned from surrogate experiments with imperfect compliance, and causal knowledge has to be extrapolated across structurally heterogeneous populations. A powerful causal inference framework is required to tackle these challenges, which plague most data analysis to varying degrees. Building on the structural approach to causality introduced by Haavelmo (1943) and the graph-theoretic framework proposed by Pearl (1995), the artificial intelligence (AI) literature has developed a wide array of techniques for causal learning that allow to leverage information from various imperfect, heterogeneous, and biased data sources (Bareinboim and Pearl, 2016). In this paper, we discuss recent advances in this literature that have the potential to contribute to econometric methodology along three dimensions. First, they provide a unified and comprehensive framework for causal inference, in which the aforementioned problems can be addressed in full generality. Second, due to their origin in AI, they come together with sound, efficient, and complete algorithmic criteria for automatization of the corresponding identification task. And third, because of the nonparametric description of structural models that graph-theoretic approaches build on, they combine the strengths of both structural econometrics as well as the potential outcomes framework, and thus offer an effective middle ground between these two literature streams.

Causal Inference and Data Fusion in Econometrics

2019-12-19 13:24:04

Paul Hünermund, Elias Bareinboim

http://arxiv.org/abs/1912.09104v4, http://arxiv.org/pdf/1912.09104v4

econ.EM

em

We study the use of Temporal-Difference learning for estimating the structural parameters in dynamic discrete choice models. Our algorithms are based on the conditional choice probability approach but use functional approximations to estimate various terms in the pseudo-likelihood function. We suggest two approaches: The first - linear semi-gradient - provides approximations to the recursive terms using basis functions. The second - Approximate Value Iteration - builds a sequence of approximations to the recursive terms by solving non-parametric estimation problems. Our approaches are fast and naturally allow for continuous and/or high-dimensional state spaces. Furthermore, they do not require specification of transition densities. In dynamic games, they avoid integrating over other players' actions, further heightening the computational advantage. Our proposals can be paired with popular existing methods such as pseudo-maximum-likelihood, and we propose locally robust corrections for the latter to achieve parametric rates of convergence. Monte Carlo simulations confirm the properties of our algorithms in practice.

Temporal-Difference estimation of dynamic discrete choice models

2019-12-19 22:21:49

Karun Adusumilli, Dita Eckardt

http://arxiv.org/abs/1912.09509v2, http://arxiv.org/pdf/1912.09509v2

econ.EM

em

Researchers increasingly wish to estimate time-varying parameter (TVP) regressions which involve a large number of explanatory variables. Including prior information to mitigate over-parameterization concerns has led to many using Bayesian methods. However, Bayesian Markov Chain Monte Carlo (MCMC) methods can be very computationally demanding. In this paper, we develop computationally efficient Bayesian methods for estimating TVP models using an integrated rotated Gaussian approximation (IRGA). This exploits the fact that whereas constant coefficients on regressors are often important, most of the TVPs are often unimportant. Since Gaussian distributions are invariant to rotations we can split the the posterior into two parts: one involving the constant coefficients, the other involving the TVPs. Approximate methods are used on the latter and, conditional on these, the former are estimated with precision using MCMC methods. In empirical exercises involving artificial data and a large macroeconomic data set, we show the accuracy and computational benefits of IRGA methods.

Bayesian Inference in High-Dimensional Time-varying Parameter Models using Integrated Rotated Gaussian Approximations

2020-02-24 17:07:50

Florian Huber, Gary Koop, Michael Pfarrhofer

http://arxiv.org/abs/2002.10274v1, http://arxiv.org/pdf/2002.10274v1

econ.EM

em

Dynamic treatment regimes are treatment allocations tailored to heterogeneous individuals. The optimal dynamic treatment regime is a regime that maximizes counterfactual welfare. We introduce a framework in which we can partially learn the optimal dynamic regime from observational data, relaxing the sequential randomization assumption commonly employed in the literature but instead using (binary) instrumental variables. We propose the notion of sharp partial ordering of counterfactual welfares with respect to dynamic regimes and establish mapping from data to partial ordering via a set of linear programs. We then characterize the identified set of the optimal regime as the set of maximal elements associated with the partial ordering. We relate the notion of partial ordering with a more conventional notion of partial identification using topological sorts. Practically, topological sorts can be served as a policy benchmark for a policymaker. We apply our method to understand returns to schooling and post-school training as a sequence of treatments by combining data from multiple sources. The framework of this paper can be used beyond the current context, e.g., in establishing rankings of multiple treatments or policies across different counterfactual scenarios.

Optimal Dynamic Treatment Regimes and Partial Welfare Ordering

2019-12-20 21:43:01

Sukjin Han

http://arxiv.org/abs/1912.10014v4, http://arxiv.org/pdf/1912.10014v4

econ.EM

em

This paper presents a novel deep learning-based travel behaviour choice model.Our proposed Residual Logit (ResLogit) model formulation seamlessly integrates a Deep Neural Network (DNN) architecture into a multinomial logit model. Recently, DNN models such as the Multi-layer Perceptron (MLP) and the Recurrent Neural Network (RNN) have shown remarkable success in modelling complex and noisy behavioural data. However, econometric studies have argued that machine learning techniques are a `black-box' and difficult to interpret for use in the choice analysis.We develop a data-driven choice model that extends the systematic utility function to incorporate non-linear cross-effects using a series of residual layers and using skipped connections to handle model identifiability in estimating a large number of parameters.The model structure accounts for cross-effects and choice heterogeneity arising from substitution, interactions with non-chosen alternatives and other effects in a non-linear manner.We describe the formulation, model estimation, interpretability and examine the relative performance and econometric implications of our proposed model.We present an illustrative example of the model on a classic red/blue bus choice scenario example. For a real-world application, we use a travel mode choice dataset to analyze the model characteristics compared to traditional neural networks and Logit formulations.Our findings show that our ResLogit approach significantly outperforms MLP models while providing similar interpretability as a Multinomial Logit model.

ResLogit: A residual neural network logit model for data-driven choice modelling

2019-12-20 22:02:58

Melvin Wong, Bilal Farooq

http://arxiv.org/abs/1912.10058v2, http://arxiv.org/pdf/1912.10058v2

econ.EM

em

We propose a new sequential Efficient Pseudo-Likelihood (k-EPL) estimator for dynamic discrete choice games of incomplete information. k-EPL considers the joint behavior of multiple players simultaneously, as opposed to individual responses to other agents' equilibrium play. This, in addition to reframing the problem from conditional choice probability (CCP) space to value function space, yields a computationally tractable, stable, and efficient estimator. We show that each iteration in the k-EPL sequence is consistent and asymptotically efficient, so the first-order asymptotic properties do not vary across iterations. Furthermore, we show the sequence achieves higher-order equivalence to the finite-sample maximum likelihood estimator with iteration and that the sequence of estimators converges almost surely to the maximum likelihood estimator at a nearly-superlinear rate when the data are generated by any regular Markov perfect equilibrium, including equilibria that lead to inconsistency of other sequential estimators. When utility is linear in parameters, k-EPL iterations are computationally simple, only requiring that the researcher solve linear systems of equations to generate pseudo-regressors which are used in a static logit/probit regression. Monte Carlo simulations demonstrate the theoretical results and show k-EPL's good performance in finite samples in both small- and large-scale games, even when the game admits spurious equilibria in addition to one that generated the data. We apply the estimator to study the role of competition in the U.S. wholesale club industry.

Efficient and Convergent Sequential Pseudo-Likelihood Estimation of Dynamic Discrete Games

2019-12-22 20:34:23

Adam Dearing, Jason R. Blevins

http://arxiv.org/abs/1912.10488v5, http://arxiv.org/pdf/1912.10488v5

econ.EM

em

We propose an optimal-transport-based matching method to nonparametrically estimate linear models with independent latent variables. The method consists in generating pseudo-observations from the latent variables, so that the Euclidean distance between the model's predictions and their matched counterparts in the data is minimized. We show that our nonparametric estimator is consistent, and we document that it performs well in simulated data. We apply this method to study the cyclicality of permanent and transitory income shocks in the Panel Study of Income Dynamics. We find that the dispersion of income shocks is approximately acyclical, whereas the skewness of permanent shocks is procyclical. By comparison, we find that the dispersion and skewness of shocks to hourly wages vary little with the business cycle.

Recovering Latent Variables by Matching

2019-12-30 23:49:27

Manuel Arellano, Stephane Bonhomme

http://arxiv.org/abs/1912.13081v1, http://arxiv.org/pdf/1912.13081v1

econ.EM

em

Markov switching models are a popular family of models that introduces time-variation in the parameters in the form of their state- or regime-specific values. Importantly, this time-variation is governed by a discrete-valued latent stochastic process with limited memory. More specifically, the current value of the state indicator is determined only by the value of the state indicator from the previous period, thus the Markov property, and the transition matrix. The latter characterizes the properties of the Markov process by determining with what probability each of the states can be visited next period, given the state in the current period. This setup decides on the two main advantages of the Markov switching models. Namely, the estimation of the probability of state occurrences in each of the sample periods by using filtering and smoothing methods and the estimation of the state-specific parameters. These two features open the possibility for improved interpretations of the parameters associated with specific regimes combined with the corresponding regime probabilities, as well as for improved forecasting performance based on persistent regimes and parameters characterizing them.

Markov Switching

2020-02-10 11:29:23

Yong Song, Tomasz Woźniak

http://dx.doi.org/10.1093/acrefore/9780190625979.013.174, http://arxiv.org/abs/2002.03598v1, http://arxiv.org/pdf/2002.03598v1

econ.EM

em

Given the extreme dependence of agriculture on weather conditions, this paper analyses the effect of climatic variations on this economic sector, by considering both a huge dataset and a flexible spatio-temporal model specification. In particular, we study the response of N-fertilizer application to abnormal weather conditions, while accounting for other relevant control variables. The dataset consists of gridded data spanning over 21 years (1993-2013), while the methodological strategy makes use of a spatial dynamic panel data (SDPD) model that accounts for both space and time fixed effects, besides dealing with both space and time dependences. Time-invariant short and long term effects, as well as time-varying marginal effects are also properly defined, revealing interesting results on the impact of both GDP and weather conditions on fertilizer utilizations. The analysis considers four macro-regions -- Europe, South America, South-East Asia and Africa -- to allow for comparisons among different socio-economic societies. In addition to finding both spatial (in the form of knowledge spillover effects) and temporal dependences as well as a good support for the existence of an environmental Kuznets curve for fertilizer application, the paper shows peculiar responses of N-fertilization to deviations from normal weather conditions of moisture for each selected region, calling for ad hoc policy interventions.

The Effect of Weather Conditions on Fertilizer Applications: A Spatial Dynamic Panel Data Analysis

2020-02-10 19:31:15

Anna Gloria Billè, Marco Rogna

http://arxiv.org/abs/2002.03922v2, http://arxiv.org/pdf/2002.03922v2

econ.EM

em

This article deals with parameterisation, identifiability, and maximum likelihood (ML) estimation of possibly non-invertible structural vector autoregressive moving average (SVARMA) models driven by independent and non-Gaussian shocks. In contrast to previous literature, the novel representation of the MA polynomial matrix using the Wiener-Hopf factorisation (WHF) focuses on the multivariate nature of the model, generates insights into its structure, and uses this structure for devising optimisation algorithms. In particular, it allows to parameterise the location of determinantal zeros inside and outside the unit circle, and it allows for MA zeros at zero, which can be interpreted as informational delays. This is highly relevant for data-driven evaluation of Dynamic Stochastic General Equilibrium (DSGE) models. Typically imposed identifying restrictions on the shock transmission matrix as well as on the determinantal root location are made testable. Furthermore, we provide low level conditions for asymptotic normality of the ML estimator and analytic expressions for the score and the information matrix. As application, we estimate the Blanchard and Quah model and show that our method provides further insights regarding non-invertibility using a standard macroeconometric model. These and further analyses are implemented in a well documented R-package.

Identifiability and Estimation of Possibly Non-Invertible SVARMA Models: A New Parametrisation

2020-02-11 15:35:14

Bernd Funovits

http://arxiv.org/abs/2002.04346v2, http://arxiv.org/pdf/2002.04346v2

econ.EM

em

This paper analyses the number of free parameters and solutions of the structural difference equation obtained from a linear multivariate rational expectations model. First, it is shown that the number of free parameters depends on the structure of the zeros at zero of a certain matrix polynomial of the structural difference equation and the number of inputs of the rational expectations model. Second, the implications of requiring that some components of the endogenous variables be predetermined are analysed. Third, a condition for existence and uniqueness of a causal stationary solution is given.

The Dimension of the Set of Causal Solutions of Linear Multivariate Rational Expectations Models

2020-02-11 16:33:04

Bernd Funovits

http://arxiv.org/abs/2002.04369v1, http://arxiv.org/pdf/2002.04369v1

econ.EM

em

We construct long-term prediction intervals for time-aggregated future values of univariate economic time series. We propose computational adjustments of the existing methods to improve coverage probability under a small sample constraint. A pseudo-out-of-sample evaluation shows that our methods perform at least as well as selected alternative methods based on model-implied Bayesian approaches and bootstrapping. Our most successful method yields prediction intervals for eight macroeconomic indicators over a horizon spanning several decades.

Long-term prediction intervals of economic time series

2020-02-13 11:11:18

Marek Chudy, Sayar Karmakar, Wei Biao Wu

http://arxiv.org/abs/2002.05384v1, http://arxiv.org/pdf/2002.05384v1

econ.EM

em

Conjugate priors allow for fast inference in large dimensional vector autoregressive (VAR) models but, at the same time, introduce the restriction that each equation features the same set of explanatory variables. This paper proposes a straightforward means of post-processing posterior estimates of a conjugate Bayesian VAR to effectively perform equation-specific covariate selection. Compared to existing techniques using shrinkage alone, our approach combines shrinkage and sparsity in both the VAR coefficients and the error variance-covariance matrices, greatly reducing estimation uncertainty in large dimensions while maintaining computational tractability. We illustrate our approach by means of two applications. The first application uses synthetic data to investigate the properties of the model across different data-generating processes, the second application analyzes the predictive gains from sparsification in a forecasting exercise for US data.

Combining Shrinkage and Sparsity in Conjugate Vector Autoregressive Models

2020-02-20 17:45:38

Niko Hauzenberger, Florian Huber, Luca Onorante

http://arxiv.org/abs/2002.08760v2, http://arxiv.org/pdf/2002.08760v2

econ.EM

em

This paper considers estimation and inference about tail features when the observations beyond some threshold are censored. We first show that ignoring such tail censoring could lead to substantial bias and size distortion, even if the censored probability is tiny. Second, we propose a new maximum likelihood estimator (MLE) based on the Pareto tail approximation and derive its asymptotic properties. Third, we provide a small sample modification to the MLE by resorting to Extreme Value theory. The MLE with this modification delivers excellent small sample performance, as shown by Monte Carlo simulations. We illustrate its empirical relevance by estimating (i) the tail index and the extreme quantiles of the US individual earnings with the Current Population Survey dataset and (ii) the tail index of the distribution of macroeconomic disasters and the coefficient of risk aversion using the dataset collected by Barro and Urs{\'u}a (2008). Our new empirical findings are substantially different from the existing literature.

Estimation and Inference about Tail Features with Tail Censored Data

2020-02-23 23:43:24

Yulong Wang, Zhijie Xiao

http://arxiv.org/abs/2002.09982v1, http://arxiv.org/pdf/2002.09982v1

econ.EM

em

Discrete Choice Experiments (DCE) have been widely used in health economics, environmental valuation, and other disciplines. However, there is a lack of resources disclosing the whole procedure of carrying out a DCE. This document aims to assist anyone wishing to use the power of DCEs to understand people's behavior by providing a comprehensive guide to the procedure. This guide contains all the code needed to design, implement, and analyze a DCE using only free software.

A step-by-step guide to design, implement, and analyze a discrete choice experiment

2020-09-23 19:13:10

Daniel Pérez-Troncoso

http://arxiv.org/abs/2009.11235v1, http://arxiv.org/pdf/2009.11235v1

econ.EM

em

This paper studies the identification, estimation, and hypothesis testing problem in complete and incomplete economic models with testable assumptions. Testable assumptions ($A$) give strong and interpretable empirical content to the models but they also carry the possibility that some distribution of observed outcomes may reject these assumptions. A natural way to avoid this is to find a set of relaxed assumptions ($\tilde{A}$) that cannot be rejected by any distribution of observed outcome and the identified set of the parameter of interest is not changed when the original assumption is not rejected. The main contribution of this paper is to characterize the properties of such a relaxed assumption $\tilde{A}$ using a generalized definition of refutability and confirmability. I also propose a general method to construct such $\tilde{A}$. A general estimation and inference procedure is proposed and can be applied to most incomplete economic models. I apply my methodology to the instrument monotonicity assumption in Local Average Treatment Effect (LATE) estimation and to the sector selection assumption in a binary outcome Roy model of employment sector choice. In the LATE application, I use my general method to construct a set of relaxed assumptions $\tilde{A}$ that can never be rejected, and the identified set of LATE is the same as imposing $A$ when $A$ is not rejected. LATE is point identified under my extension $\tilde{A}$ in the LATE application. In the binary outcome Roy model, I use my method of incomplete models to relax Roy's sector selection assumption and characterize the identified set of the binary potential outcome as a polyhedron.

Estimating Economic Models with Testable Assumptions: Theory and Applications

2020-02-24 20:58:41

Moyu Liao

http://arxiv.org/abs/2002.10415v3, http://arxiv.org/pdf/2002.10415v3

econ.EM

em

We examine the impact of annual hours worked on annual earnings by decomposing changes in the real annual earnings distribution into composition, structural and hours effects. We do so via a nonseparable simultaneous model of hours, wages and earnings. Using the Current Population Survey for the survey years 1976--2019, we find that changes in the female distribution of annual hours of work are important in explaining movements in inequality in female annual earnings. This captures the substantial changes in their employment behavior over this period. Movements in the male hours distribution only affect the lower part of their earnings distribution and reflect the sensitivity of these workers' annual hours of work to cyclical factors.

Hours Worked and the U.S. Distribution of Real Annual Earnings 1976-2019

2020-02-26 01:55:07

Iván Fernández-Val, Franco Peracchi, Aico van Vuuren, Francis Vella

http://arxiv.org/abs/2002.11211v3, http://arxiv.org/pdf/2002.11211v3

econ.EM

em

This paper combines causal mediation analysis with double machine learning to control for observed confounders in a data-driven way under a selection-on-observables assumption in a high-dimensional setting. We consider the average indirect effect of a binary treatment operating through an intermediate variable (or mediator) on the causal path between the treatment and the outcome, as well as the unmediated direct effect. Estimation is based on efficient score functions, which possess a multiple robustness property w.r.t. misspecifications of the outcome, mediator, and treatment models. This property is key for selecting these models by double machine learning, which is combined with data splitting to prevent overfitting in the estimation of the effects of interest. We demonstrate that the direct and indirect effect estimators are asymptotically normal and root-n consistent under specific regularity conditions and investigate the finite sample properties of the suggested methods in a simulation study when considering lasso as machine learner. We also provide an empirical application to the U.S. National Longitudinal Survey of Youth, assessing the indirect effect of health insurance coverage on general health operating via routine checkups as mediator, as well as the direct effect. We find a moderate short term effect of health insurance coverage on general health which is, however, not mediated by routine checkups.

Causal mediation analysis with double machine learning

2020-02-28 16:39:49

Helmut Farbmacher, Martin Huber, Lukáš Lafférs, Henrika Langen, Martin Spindler

http://arxiv.org/abs/2002.12710v6, http://arxiv.org/pdf/2002.12710v6

econ.EM

em

Alternative data sets are widely used for macroeconomic nowcasting together with machine learning--based tools. The latter are often applied without a complete picture of their theoretical nowcasting properties. Against this background, this paper proposes a theoretically grounded nowcasting methodology that allows researchers to incorporate alternative Google Search Data (GSD) among the predictors and that combines targeted preselection, Ridge regularization, and Generalized Cross Validation. Breaking with most existing literature, which focuses on asymptotic in-sample theoretical properties, we establish the theoretical out-of-sample properties of our methodology and support them by Monte-Carlo simulations. We apply our methodology to GSD to nowcast GDP growth rate of several countries during various economic periods. Our empirical findings support the idea that GSD tend to increase nowcasting accuracy, even after controlling for official variables, but that the gain differs between periods of recessions and of macroeconomic stability.

When are Google data useful to nowcast GDP? An approach via pre-selection and shrinkage

2020-07-01 09:58:00

Laurent Ferrara, Anna Simoni

http://dx.doi.org/10.1080/07350015.2022.2116025, http://arxiv.org/abs/2007.00273v3, http://arxiv.org/pdf/2007.00273v3

econ.EM

em

In this paper, we estimate and leverage latent constant group structure to generate the point, set, and density forecasts for short dynamic panel data. We implement a nonparametric Bayesian approach to simultaneously identify coefficients and group membership in the random effects which are heterogeneous across groups but fixed within a group. This method allows us to flexibly incorporate subjective prior knowledge on the group structure that potentially improves the predictive accuracy. In Monte Carlo experiments, we demonstrate that our Bayesian grouped random effects (BGRE) estimators produce accurate estimates and score predictive gains over standard panel data estimators. With a data-driven group structure, the BGRE estimators exhibit comparable accuracy of clustering with the Kmeans algorithm and outperform a two-step Bayesian grouped estimator whose group structure relies on Kmeans. In the empirical analysis, we apply our method to forecast the investment rate across a broad range of firms and illustrate that the estimated latent group structure improves forecasts relative to standard panel data estimators.

Forecasting with Bayesian Grouped Random Effects in Panel Data

2020-07-05 22:48:27

Boyuan Zhang

http://arxiv.org/abs/2007.02435v8, http://arxiv.org/pdf/2007.02435v8

econ.EM

em

We develop a Stata command xthenreg to implement the first-differenced GMM estimation of the dynamic panel threshold model, which Seo and Shin (2016, Journal of Econometrics 195: 169-186) have proposed. Furthermore, We derive the asymptotic variance formula for a kink constrained GMM estimator of the dynamic threshold model and include an estimation algorithm. We also propose a fast bootstrap algorithm to implement the bootstrap for the linearity test. The use of the command is illustrated through a Monte Carlo simulation and an economic application.

Estimation of Dynamic Panel Threshold Model using Stata

2019-02-27 06:19:33

Myung Hwan Seo, Sueyoul Kim, Young-Joo Kim

http://dx.doi.org/10.1177/1536867X19874243, http://arxiv.org/abs/1902.10318v1, http://arxiv.org/pdf/1902.10318v1

econ.EM

em

This paper presents a novel estimator of orthogonal GARCH models, which combines (eigenvalue and -vector) targeting estimation with stepwise (univariate) estimation. We denote this the spectral targeting estimator. This two-step estimator is consistent under finite second order moments, while asymptotic normality holds under finite fourth order moments. The estimator is especially well suited for modelling larger portfolios: we compare the empirical performance of the spectral targeting estimator to that of the quasi maximum likelihood estimator for five portfolios of 25 assets. The spectral targeting estimator dominates in terms of computational complexity, being up to 57 times faster in estimation, while both estimators produce similar out-of-sample forecasts, indicating that the spectral targeting estimator is well suited for high-dimensional empirical applications.

Spectral Targeting Estimation of $λ$-GARCH models

2020-07-06 11:53:59

Simon Hetland

http://arxiv.org/abs/2007.02588v1, http://arxiv.org/pdf/2007.02588v1

econ.EM

em

We study the effects of counterfactual teacher-to-classroom assignments on average student achievement in elementary and middle schools in the US. We use the Measures of Effective Teaching (MET) experiment to semiparametrically identify the average reallocation effects (AREs) of such assignments. Our findings suggest that changes in within-district teacher assignments could have appreciable effects on student achievement. Unlike policies which require hiring additional teachers (e.g., class-size reduction measures), or those aimed at changing the stock of teachers (e.g., VAM-guided teacher tenure policies), alternative teacher-to-classroom assignments are resource neutral; they raise student achievement through a more efficient deployment of existing teachers.

Teacher-to-classroom assignment and student achievement

2020-07-06 14:20:59

Bryan S. Graham, Geert Ridder, Petra Thiemann, Gema Zamarro

http://arxiv.org/abs/2007.02653v2, http://arxiv.org/pdf/2007.02653v2

econ.EM

em

This paper studies optimal decision rules, including estimators and tests, for weakly identified GMM models. We derive the limit experiment for weakly identified GMM, and propose a theoretically-motivated class of priors which give rise to quasi-Bayes decision rules as a limiting case. Together with results in the previous literature, this establishes desirable properties for the quasi-Bayes approach regardless of model identification status, and we recommend quasi-Bayes for settings where identification is a concern. We further propose weighted average power-optimal identification-robust frequentist tests and confidence sets, and prove a Bernstein-von Mises-type result for the quasi-Bayes posterior under weak identification.

Optimal Decision Rules for Weak GMM

2020-07-08 14:48:10

Isaiah Andrews, Anna Mikusheva

http://arxiv.org/abs/2007.04050v7, http://arxiv.org/pdf/2007.04050v7

econ.EM

em

In this paper, we test the contribution of foreign management on firms' competitiveness. We use a novel dataset on the careers of 165,084 managers employed by 13,106 companies in the United Kingdom in the period 2009-2017. We find that domestic manufacturing firms become, on average, between 7% and 12% more productive after hiring the first foreign managers, whereas foreign-owned firms register no significant improvement. In particular, we test that previous industry-specific experience is the primary driver of productivity gains in domestic firms (15.6%), in a way that allows the latter to catch up with foreign-owned firms. Managers from the European Union are highly valuable, as they represent about half of the recruits in our data. Our identification strategy combines matching techniques, difference-in-difference, and pre-recruitment trends to challenge reverse causality. Results are robust to placebo tests and to different estimators of Total Factor Productivity. Eventually, we argue that upcoming limits to the mobility of foreign talents after the Brexit event can hamper the allocation of productive managerial resources.

Talents from Abroad. Foreign Managers and Productivity in the United Kingdom

2020-07-08 15:07:13

Dimitrios Exadaktylos, Massimo Riccaboni, Armando Rungi

http://arxiv.org/abs/2007.04055v1, http://arxiv.org/pdf/2007.04055v1

econ.EM

em

We study treatment-effect estimation using panel data. The treatment may be non-binary, non-absorbing, and the outcome may be affected by treatment lags. We make a parallel-trends assumption, and propose event-study estimators of the effect of being exposed to a weakly higher treatment dose for $\ell$ periods. We also propose normalized estimators, that estimate a weighted average of the effects of the current treatment and its lags. We also analyze commonly-used two-way-fixed-effects regressions. Unlike our estimators, they can be biased in the presence of heterogeneous treatment effects. A local-projection version of those regressions is biased even with homogeneous effects.

Difference-in-Differences Estimators of Intertemporal Treatment Effects

2020-07-08 20:01:22

Clément de Chaisemartin, Xavier D'Haultfoeuille

http://arxiv.org/abs/2007.04267v12, http://arxiv.org/pdf/2007.04267v12

econ.EM

em

This paper develops an empirical balancing approach for the estimation of treatment effects under two-sided noncompliance using a binary conditionally independent instrumental variable. The method weighs both treatment and outcome information with inverse probabilities to produce exact finite sample balance across instrument level groups. It is free of functional form assumptions on the outcome or the treatment selection step. By tailoring the loss function for the instrument propensity scores, the resulting treatment effect estimates exhibit both low bias and a reduced variance in finite samples compared to conventional inverse probability weighting methods. The estimator is automatically weight normalized and has similar bias properties compared to conventional two-stage least squares estimation under constant causal effects for the compliers. We provide conditions for asymptotic normality and semiparametric efficiency and demonstrate how to utilize additional information about the treatment selection step for bias reduction in finite samples. The method can be easily combined with regularization or other statistical learning approaches to deal with a high-dimensional number of observed confounding variables. Monte Carlo simulations suggest that the theoretical advantages translate well to finite samples. The method is illustrated in an empirical example.

Efficient Covariate Balancing for the Local Average Treatment Effect

2020-07-08 21:04:46

Phillip Heiler

http://arxiv.org/abs/2007.04346v1, http://arxiv.org/pdf/2007.04346v1

econ.EM

em

This paper considers estimation and inference for heterogeneous counterfactual effects with high-dimensional data. We propose a novel robust score for debiased estimation of the unconditional quantile regression (Firpo, Fortin, and Lemieux, 2009) as a measure of heterogeneous counterfactual marginal effects. We propose a multiplier bootstrap inference and develop asymptotic theories to guarantee the size control in large sample. Simulation studies support our theories. Applying the proposed method to Job Corps survey data, we find that a policy which counterfactually extends the duration of exposures to the Job Corps training program will be effective especially for the targeted subpopulations of lower potential wage earners.

Unconditional Quantile Regression with High Dimensional Data

2020-07-27 19:13:41

Yuya Sasaki, Takuya Ura, Yichong Zhang

http://arxiv.org/abs/2007.13659v4, http://arxiv.org/pdf/2007.13659v4

econ.EM

em

This paper analyzes a semiparametric model of network formation in the presence of unobserved agent-specific heterogeneity. The objective is to identify and estimate the preference parameters associated with homophily on observed attributes when the distributions of the unobserved factors are not parametrically specified. This paper offers two main contributions to the literature on network formation. First, it establishes a new point identification result for the vector of parameters that relies on the existence of a special repressor. The identification proof is constructive and characterizes a closed-form for the parameter of interest. Second, it introduces a simple two-step semiparametric estimator for the vector of parameters with a first-step kernel estimator. The estimator is computationally tractable and can be applied to both dense and sparse networks. Moreover, I show that the estimator is consistent and has a limiting normal distribution as the number of individuals in the network increases. Monte Carlo experiments demonstrate that the estimator performs well in finite samples and in networks with different levels of sparsity.

A Semiparametric Network Formation Model with Unobserved Linear Heterogeneity

2020-07-10 17:09:41

Luis E. Candelaria

http://arxiv.org/abs/2007.05403v2, http://arxiv.org/pdf/2007.05403v2

econ.EM

em

This paper characterises dynamic linkages arising from shocks with heterogeneous degrees of persistence. Using frequency domain techniques, we introduce measures that identify smoothly varying links of a transitory and persistent nature. Our approach allows us to test for statistical differences in such dynamic links. We document substantial differences in transitory and persistent linkages among US financial industry volatilities, argue that they track heterogeneously persistent sources of systemic risk, and thus may serve as a useful tool for market participants.

Persistence in Financial Connectedness and Systemic Risk

2020-07-14 18:45:33

Jozef Barunik, Michael Ellington

http://arxiv.org/abs/2007.07842v4, http://arxiv.org/pdf/2007.07842v4

econ.EM

em

This paper studies the latent index representation of the conditional LATE model, making explicit the role of covariates in treatment selection. We find that if the directions of the monotonicity condition are the same across all values of the conditioning covariate, which is often assumed in the literature, then the treatment choice equation has to satisfy a separability condition between the instrument and the covariate. This global representation result establishes testable restrictions imposed on the way covariates enter the treatment choice equation. We later extend the representation theorem to incorporate multiple ordered levels of treatment.

Global Representation of the Conditional LATE Model: A Separability Result

2020-07-16 07:30:59

Yu-Chang Chen, Haitian Xie

http://dx.doi.org/10.1111/obes.12476, http://arxiv.org/abs/2007.08106v3, http://arxiv.org/pdf/2007.08106v3

econ.EM

em

I devise a novel approach to evaluate the effectiveness of fiscal policy in the short run with multi-category treatment effects and inverse probability weighting based on the potential outcome framework. This study's main contribution to the literature is the proposed modified conditional independence assumption to improve the evaluation of fiscal policy. Using this approach, I analyze the effects of government spending on the US economy from 1992 to 2019. The empirical study indicates that large fiscal contraction generates a negative effect on the economic growth rate, and small and large fiscal expansions realize a positive effect. However, these effects are not significant in the traditional multiple regression approach. I conclude that this new approach significantly improves the evaluation of fiscal policy.

Government spending and multi-category treatment effects:The modified conditional independence assumption

2020-07-16 18:16:35

Koiti Yano

http://arxiv.org/abs/2007.08396v3, http://arxiv.org/pdf/2007.08396v3

econ.EM

em

We propose using a permutation test to detect discontinuities in an underlying economic model at a known cutoff point. Relative to the existing literature, we show that this test is well suited for event studies based on time-series data. The test statistic measures the distance between the empirical distribution functions of observed data in two local subsamples on the two sides of the cutoff. Critical values are computed via a standard permutation algorithm. Under a high-level condition that the observed data can be coupled by a collection of conditionally independent variables, we establish the asymptotic validity of the permutation test, allowing the sizes of the local subsamples to be either be fixed or grow to infinity. In the latter case, we also establish that the permutation test is consistent. We demonstrate that our high-level condition can be verified in a broad range of problems in the infill asymptotic time-series setting, which justifies using the permutation test to detect jumps in economic variables such as volatility, trading activity, and liquidity. These potential applications are illustrated in an empirical case study for selected FOMC announcements during the ongoing COVID-19 pandemic.

Permutation-based tests for discontinuities in event studies

2020-07-20 05:12:52

Federico A. Bugni, Jia Li, Qiyuan Li

http://arxiv.org/abs/2007.09837v4, http://arxiv.org/pdf/2007.09837v4

econ.EM

em

Mean, median, and mode are three essential measures of the centrality of probability distributions. In program evaluation, the average treatment effect (mean) and the quantile treatment effect (median) have been intensively studied in the past decades. The mode treatment effect, however, has long been neglected in program evaluation. This paper fills the gap by discussing both the estimation and inference of the mode treatment effect. I propose both traditional kernel and machine learning methods to estimate the mode treatment effect. I also derive the asymptotic properties of the proposed estimators and find that both estimators follow the asymptotic normality but with the rate of convergence slower than the regular rate $\sqrt{N}$, which is different from the rates of the classical average and quantile treatment effect estimators.

The Mode Treatment Effect

2020-07-22 21:05:56

Neng-Chieh Chang

http://arxiv.org/abs/2007.11606v1, http://arxiv.org/pdf/2007.11606v1

econ.EM

em

The multinomial probit model is a popular tool for analyzing choice behaviour as it allows for correlation between choice alternatives. Because current model specifications employ a full covariance matrix of the latent utilities for the choice alternatives, they are not scalable to a large number of choice alternatives. This paper proposes a factor structure on the covariance matrix, which makes the model scalable to large choice sets. The main challenge in estimating this structure is that the model parameters require identifying restrictions. We identify the parameters by a trace-restriction on the covariance matrix, which is imposed through a reparametrization of the factor structure. We specify interpretable prior distributions on the model parameters and develop an MCMC sampler for parameter estimation. The proposed approach significantly improves performance in large choice sets relative to existing multinomial probit specifications. Applications to purchase data show the economic importance of including a large number of choice alternatives in consumer choice analysis.

Scalable Bayesian estimation in the multinomial probit model

2020-07-27 02:38:14

Ruben Loaiza-Maya, Didier Nibbering

http://arxiv.org/abs/2007.13247v2, http://arxiv.org/pdf/2007.13247v2

econ.EM

em

Applied macroeconomists often compute confidence intervals for impulse responses using local projections, i.e., direct linear regressions of future outcomes on current covariates. This paper proves that local projection inference robustly handles two issues that commonly arise in applications: highly persistent data and the estimation of impulse responses at long horizons. We consider local projections that control for lags of the variables in the regression. We show that lag-augmented local projections with normal critical values are asymptotically valid uniformly over (i) both stationary and non-stationary data, and also over (ii) a wide range of response horizons. Moreover, lag augmentation obviates the need to correct standard errors for serial correlation in the regression residuals. Hence, local projection inference is arguably both simpler than previously thought and more robust than standard autoregressive inference, whose validity is known to depend sensitively on the persistence of the data and on the length of the horizon.

Local Projection Inference is Simpler and More Robust Than You Think

2020-07-28 01:03:23

José Luis Montiel Olea, Mikkel Plagborg-Møller

http://dx.doi.org/10.3982/ECTA18756, http://arxiv.org/abs/2007.13888v3, http://arxiv.org/pdf/2007.13888v3

econ.EM

em

Commonly used methods of production function and markup estimation assume that a firm's output quantity can be observed as data, but typical datasets contain only revenue, not output quantity. We examine the nonparametric identification of production function and markup from revenue data when a firm faces a general nonparametri demand function under imperfect competition. Under standard assumptions, we provide the constructive nonparametric identification of various firm-level objects: gross production function, total factor productivity, price markups over marginal costs, output prices, output quantities, a demand system, and a representative consumer's utility function.

Nonparametric Identification of Production Function, Total Factor Productivity, and Markup from Revenue Data

2020-10-31 02:34:40

Hiroyuki Kasahara, Yoichi Sugita

http://arxiv.org/abs/2011.00143v1, http://arxiv.org/pdf/2011.00143v1

econ.EM

em

Macroeconomists increasingly use external sources of exogenous variation for causal inference. However, unless such external instruments (proxies) capture the underlying shock without measurement error, existing methods are silent on the importance of that shock for macroeconomic fluctuations. We show that, in a general moving average model with external instruments, variance decompositions for the instrumented shock are interval-identified, with informative bounds. Various additional restrictions guarantee point identification of both variance and historical decompositions. Unlike SVAR analysis, our methods do not require invertibility. Applied to U.S. data, they give a tight upper bound on the importance of monetary shocks for inflation dynamics.

Instrumental Variable Identification of Dynamic Variance Decompositions

2020-11-03 02:32:44

Mikkel Plagborg-Møller, Christian K. Wolf

http://arxiv.org/abs/2011.01380v2, http://arxiv.org/pdf/2011.01380v2

econ.EM

em

Forecasters often use common information and hence make common mistakes. We propose a new approach, Factor Graphical Model (FGM), to forecast combinations that separates idiosyncratic forecast errors from the common errors. FGM exploits the factor structure of forecast errors and the sparsity of the precision matrix of the idiosyncratic errors. We prove the consistency of forecast combination weights and mean squared forecast error estimated using FGM, supporting the results with extensive simulations. Empirical applications to forecasting macroeconomic series shows that forecast combination using FGM outperforms combined forecasts using equal weights and graphical models without incorporating factor structure of forecast errors.

Learning from Forecast Errors: A New Approach to Forecast Combinations

2020-11-04 03:16:16

Tae-Hwy Lee, Ekaterina Seregina

http://arxiv.org/abs/2011.02077v2, http://arxiv.org/pdf/2011.02077v2

econ.EM

em

We use a decision-theoretic framework to study the problem of forecasting discrete outcomes when the forecaster is unable to discriminate among a set of plausible forecast distributions because of partial identification or concerns about model misspecification or structural breaks. We derive "robust" forecasts which minimize maximum risk or regret over the set of forecast distributions. We show that for a large class of models including semiparametric panel data models for dynamic discrete choice, the robust forecasts depend in a natural way on a small number of convex optimization problems which can be simplified using duality methods. Finally, we derive "efficient robust" forecasts to deal with the problem of first having to estimate the set of forecast distributions and develop a suitable asymptotic efficiency theory. Forecasts obtained by replacing nuisance parameters that characterize the set of forecast distributions with efficient first-stage estimators can be strictly dominated by our efficient robust forecasts.

Robust Forecasting

2020-11-06 04:17:22

Timothy Christensen, Hyungsik Roger Moon, Frank Schorfheide

http://arxiv.org/abs/2011.03153v4, http://arxiv.org/pdf/2011.03153v4

econ.EM

em

Following in the footsteps of the literature on empirical welfare maximization, this paper wants to contribute by stressing the policymaker perspective via a practical illustration of an optimal policy assignment problem. More specifically, by focusing on the class of threshold-based policies, we first set up the theoretical underpinnings of the policymaker selection problem, to then offer a practical solution to this problem via an empirical illustration using the popular LaLonde (1986) training program dataset. The paper proposes an implementation protocol for the optimal solution that is straightforward to apply and easy to program with standard statistical software.

Optimal Policy Learning: From Theory to Practice

2020-11-10 12:25:33

Giovanni Cerulli

http://arxiv.org/abs/2011.04993v1, http://arxiv.org/pdf/2011.04993v1

econ.EM

em

This paper studies identification of the effect of a mis-classified, binary, endogenous regressor when a discrete-valued instrumental variable is available. We begin by showing that the only existing point identification result for this model is incorrect. We go on to derive the sharp identified set under mean independence assumptions for the instrument and measurement error. The resulting bounds are novel and informative, but fail to point identify the effect of interest. This motivates us to consider alternative and slightly stronger assumptions: we show that adding second and third moment independence assumptions suffices to identify the model.

Identifying the effect of a mis-classified, binary, endogenous regressor

2020-11-14 14:35:13

Francis J. DiTraglia, Camilo Garcia-Jimeno

http://dx.doi.org/10.1016/j.jeconom.2019.01.007, http://arxiv.org/abs/2011.07272v1, http://arxiv.org/pdf/2011.07272v1

econ.EM

em

This study considers the treatment choice problem when outcome variables are binary. We focus on statistical treatment rules that plug in fitted values based on nonparametric kernel regression and show that optimizing two parameters enables the calculation of the maximum regret. Using this result, we propose a novel bandwidth selection method based on the minimax regret criterion. Finally, we perform a numerical analysis to compare the optimal bandwidth choices for the binary and normally distributed outcomes.

Bandwidth Selection for Treatment Choice with Binary Outcomes

2023-08-28 10:46:05

Takuya Ishihara

http://arxiv.org/abs/2308.14375v2, http://arxiv.org/pdf/2308.14375v2

econ.EM

em

To estimate causal effects from observational data, an applied researcher must impose beliefs. The instrumental variables exclusion restriction, for example, represents the belief that the instrument has no direct effect on the outcome of interest. Yet beliefs about instrument validity do not exist in isolation. Applied researchers often discuss the likely direction of selection and the potential for measurement error in their articles but lack formal tools for incorporating this information into their analyses. Failing to use all relevant information not only leaves money on the table; it runs the risk of leading to a contradiction in which one holds mutually incompatible beliefs about the problem at hand. To address these issues, we first characterize the joint restrictions relating instrument invalidity, treatment endogeneity, and non-differential measurement error in a workhorse linear model, showing how beliefs over these three dimensions are mutually constrained by each other and the data. Using this information, we propose a Bayesian framework to help researchers elicit their beliefs, incorporate them into estimation, and ensure their mutual coherence. We conclude by illustrating our framework in a number of examples drawn from the empirical microeconomics literature.

A Framework for Eliciting, Incorporating, and Disciplining Identification Beliefs in Linear Models

2020-11-14 14:43:44

Francis J. DiTraglia, Camilo Garcia-Jimeno

http://dx.doi.org/10.1080/07350015.2020.1753528, http://arxiv.org/abs/2011.07276v1, http://arxiv.org/pdf/2011.07276v1

econ.EM

em

In this paper we propose a semi-parametric Bayesian Generalized Least Squares estimator. In a generic setting where each error is a vector, the parametric Generalized Least Square estimator maintains the assumption that each error vector has the same distributional parameters. In reality, however, errors are likely to be heterogeneous regarding their distributions. To cope with such heterogeneity, a Dirichlet process prior is introduced for the distributional parameters of the errors, leading to the error distribution being a mixture of a variable number of normal distributions. Our method let the number of normal components be data driven. Semi-parametric Bayesian estimators for two specific cases are then presented: the Seemingly Unrelated Regression for equation systems and the Random Effects Model for panel data. We design a series of simulation experiments to explore the performance of our estimators. The results demonstrate that our estimators obtain smaller posterior standard deviations and mean squared errors than the Bayesian estimators using a parametric mixture of normal distributions or a normal distribution. We then apply our semi-parametric Bayesian estimators for equation systems and panel data models to empirical data.

A Semi-Parametric Bayesian Generalized Least Squares Estimator

2020-11-20 10:50:15

Ruochen Wu, Melvyn Weeks

http://arxiv.org/abs/2011.10252v2, http://arxiv.org/pdf/2011.10252v2

econ.EM

em

This paper proposes a new class of M-estimators that double weight for the twin problems of nonrandom treatment assignment and missing outcomes, both of which are common issues in the treatment effects literature. The proposed class is characterized by a `robustness' property, which makes it resilient to parametric misspecification in either a conditional model of interest (for example, mean or quantile function) or the two weighting functions. As leading applications, the paper discusses estimation of two specific causal parameters; average and quantile treatment effects (ATE, QTEs), which can be expressed as functions of the doubly weighted estimator, under misspecification of the framework's parametric components. With respect to the ATE, this paper shows that the proposed estimator is doubly robust even in the presence of missing outcomes. Finally, to demonstrate the estimator's viability in empirical settings, it is applied to Calonico and Smith (2017)'s reconstructed sample from the National Supported Work training program.

Doubly weighted M-estimation for nonrandom assignment and missing outcomes

2020-11-23 18:48:39

Akanksha Negi

http://arxiv.org/abs/2011.11485v1, http://arxiv.org/pdf/2011.11485v1

econ.EM

em

This paper develops a first-stage linear regression representation for the instrumental variables (IV) quantile regression (QR) model. The quantile first-stage is analogous to the least squares case, i.e., a linear projection of the endogenous variables on the instruments and other exogenous covariates, with the difference that the QR case is a weighted projection. The weights are given by the conditional density function of the innovation term in the QR structural model, conditional on the endogeneous and exogenous covariates, and the instruments as well, at a given quantile. We also show that the required Jacobian identification conditions for IVQR models are embedded in the quantile first-stage. We then suggest inference procedures to evaluate the adequacy of instruments by evaluating their statistical significance using the first-stage result. The test is developed in an over-identification context, since consistent estimation of the weights for implementation of the first-stage requires at least one valid instrument to be available. Monte Carlo experiments provide numerical evidence that the proposed tests work as expected in terms of empirical size and power in finite samples. An empirical application illustrates that checking for the statistical significance of the instruments at different quantiles is important. The proposed procedures may be specially useful in QR since the instruments may be relevant at some quantiles but not at others.

A first-stage representation for instrumental variables quantile regression

2021-02-02 01:26:54

Javier Alejo, Antonio F. Galvao, Gabriel Montes-Rojas

http://arxiv.org/abs/2102.01212v4, http://arxiv.org/pdf/2102.01212v4

econ.EM

em

How much do individuals contribute to team output? I propose an econometric framework to quantify individual contributions when only the output of their teams is observed. The identification strategy relies on following individuals who work in different teams over time. I consider two production technologies. For a production function that is additive in worker inputs, I propose a regression estimator and show how to obtain unbiased estimates of variance components that measure the contributions of heterogeneity and sorting. To estimate nonlinear models with complementarity, I propose a mixture approach under the assumption that individual types are discrete, and rely on a mean-field variational approximation for estimation. To illustrate the methods, I estimate the impact of economists on their research output, and the contributions of inventors to the quality of their patents.

Teams: Heterogeneity, Sorting, and Complementarity

2021-02-03 02:52:12

Stephane Bonhomme

http://arxiv.org/abs/2102.01802v1, http://arxiv.org/pdf/2102.01802v1

econ.EM

em

This paper studies the joint inference on conditional volatility parameters and the innovation moments by means of bootstrap to test for the existence of moments for GARCH(p,q) processes. We propose a residual bootstrap to mimic the joint distribution of the quasi-maximum likelihood estimators and the empirical moments of the residuals and also prove its validity. A bootstrap-based test for the existence of moments is proposed, which provides asymptotically correctly-sized tests without losing its consistency property. It is simple to implement and extends to other GARCH-type settings. A simulation study demonstrates the test's size and power properties in finite samples and an empirical application illustrates the testing approach.

A Bootstrap Test for the Existence of Moments for GARCH Processes

2019-02-05 20:32:20

Alexander Heinemann

http://arxiv.org/abs/1902.01808v3, http://arxiv.org/pdf/1902.01808v3

econ.EM

em

We study discrete panel data methods where unobserved heterogeneity is revealed in a first step, in environments where population heterogeneity is not discrete. We focus on two-step grouped fixed-effects (GFE) estimators, where individuals are first classified into groups using kmeans clustering, and the model is then estimated allowing for group-specific heterogeneity. Our framework relies on two key properties: heterogeneity is a function - possibly nonlinear and time-varying - of a low-dimensional continuous latent type, and informative moments are available for classification. We illustrate the method in a model of wages and labor market participation, and in a probit model with time-varying heterogeneity. We derive asymptotic expansions of two-step GFE estimators as the number of groups grows with the two dimensions of the panel. We propose a data-driven rule for the number of groups, and discuss bias reduction and inference.

Discretizing Unobserved Heterogeneity

2021-02-03 19:03:19

Stéphane Bonhomme Thibaut Lamadon Elena Manresa

http://arxiv.org/abs/2102.02124v1, http://arxiv.org/pdf/2102.02124v1

econ.EM