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arXiv2018

Fixed Effect Estimation of Large T Panel Data Models

This article reviews recent advances in fixed effect estimation of panel data models for long panels, where the number of time periods is relatively large. We focus on semiparametric models with unobserved individual and time effects, where the distribution of the outcome variable conditional on covariates and unobserved effects is specified parametrically, while the distribution of the unobserved effects is left unrestricted. Compared to existing reviews on long panels (Arellano and Hahn 2007; a section in Arellano and Bonhomme 2011) we discuss models with both individual and time effects, split-panel Jackknife bias corrections, unbalanced panels, distribution and quantile effects, and other extensions. Understanding and correcting the incidental parameter bias caused by the estimation of many fixed effects is our main focus, and the unifying theme is that the order of this bias is given by the simple formula p/n for all models discussed, with p the number of estimated parameters and n the total sample size.

econ.EM↗

arXiv2017

Bounds On Treatment Effects On Transitions

This paper considers the identification of treatment effects on conditional transition probabilities. We show that even under random assignment only the instantaneous average treatment effect is point identified. Since treated and control units drop out at different rates, randomization only ensures the comparability of treatment and controls at the time of randomization, so that long-run average treatment effects are not point identified. Instead we derive informative bounds on these average treatment effects. Our bounds do not impose (semi)parametric restrictions, for example, proportional hazards. We also explore various assumptions such as monotone treatment response, common shocks and positively correlated outcomes that tighten the bounds.

econ.EM↗

arXiv2017

Inference on Estimators defined by Mathematical Programming

We propose an inference procedure for estimators defined by mathematical programming problems, focusing on the important special cases of linear programming (LP) and quadratic programming (QP). In these settings, the coefficients in both the objective function and the constraints of the mathematical programming problem may be estimated from data and hence involve sampling error. Our inference approach exploits the characterization of the solutions to these programming problems by complementarity conditions; by doing so, we can transform the problem of doing inference on the solution of a constrained optimization problem (a non-standard inference problem) into one involving inference based on a set of inequalities with pre-estimated coefficients, which is much better understood. We evaluate the performance of our procedure in several Monte Carlo simulations and an empirical application to the classic portfolio selection problem in finance.

econ.EM↗

arXiv2017

Discrete Choice and Rational Inattention: a General Equivalence Result

This paper establishes a general equivalence between discrete choice and rational inattention models. Matejka and McKay (2015, AER) showed that when information costs are modelled using the Shannon entropy function, the resulting choice probabilities in the rational inattention model take the multinomial logit form. By exploiting convex-analytic properties of the discrete choice model, we show that when information costs are modelled using a class of generalized entropy functions, the choice probabilities in any rational inattention model are observationally equivalent to some additive random utility discrete choice model and vice versa. Thus any additive random utility model can be given an interpretation in terms of boundedly rational behavior. This includes empirically relevant specifications such as the probit and nested logit models.

econ.EM↗

arXiv2019

Sharp bounds and testability of a Roy model of STEM major choices

We analyze the empirical content of the Roy model, stripped down to its essential features, namely sector specific unobserved heterogeneity and self-selection on the basis of potential outcomes. We characterize sharp bounds on the joint distribution of potential outcomes and testable implications of the Roy self-selection model under an instrumental constraint on the joint distribution of potential outcomes we call stochastically monotone instrumental variable (SMIV). We show that testing the Roy model selection is equivalent to testing stochastic monotonicity of observed outcomes relative to the instrument. We apply our sharp bounds to the derivation of a measure of departure from Roy self-selection to identify values of observable characteristics that induce the most costly misallocation of talent and sector and are therefore prime targets for intervention. Special emphasis is put on the case of binary outcomes, which has received little attention in the literature to date. For richer sets of outcomes, we emphasize the distinction between pointwise sharp bounds and functional sharp bounds, and its importance, when constructing sharp bounds on functional features, such as inequality measures. We analyze a Roy model of college major choice in Canada and Germany within this framework, and we take a new look at the under-representation of women in~STEM.

econ.EM↗

arXiv2018

Zero-rating of Content and its Effect on the Quality of Service in the Internet

The ongoing net neutrality debate has generated a lot of heated discussions on whether or not monetary interactions should be regulated between content and access providers. Among the several topics discussed, `differential pricing' has recently received attention due to `zero-rating' platforms proposed by some service providers. In the differential pricing scheme, Internet Service Providers (ISPs) can exempt data access charges for on content from certain CPs (zero-rated) while no exemption is on content from other CPs. This allows the possibility for Content Providers (CPs) to make `sponsorship' agreements to zero-rate their content and attract more user traffic. In this paper, we study the effect of differential pricing on various players in the Internet. We first consider a model with a monopolistic ISP and multiple CPs where users select CPs based on the quality of service (QoS) and data access charges. We show that in a differential pricing regime 1) a CP offering low QoS can make have higher surplus than a CP offering better QoS through sponsorships. 2) Overall QoS (mean delay) for end users can degrade under differential pricing schemes. In the oligopolistic market with multiple ISPs, users tend to select the ISP with lowest ISP resulting in same type of conclusions as in the monopolistic market. We then study how differential pricing effects the revenue of ISPs.

econ.EM↗

arXiv2021

Identification of hedonic equilibrium and nonseparable simultaneous equations

This paper derives conditions under which preferences and technology are nonparametrically identified in hedonic equilibrium models, where products are differentiated along more than one dimension and agents are characterized by several dimensions of unobserved heterogeneity. With products differentiated along a quality index and agents characterized by scalar unobserved heterogeneity, single crossing conditions on preferences and technology provide identifying restrictions in Ekeland, Heckman and Nesheim (2004) and Heckman, Matzkin and Nesheim (2010). We develop similar shape restrictions in the multi-attribute case. These shape restrictions, which are based on optimal transport theory and generalized convexity, allow us to identify preferences for goods differentiated along multiple dimensions, from the observation of a single market. We thereby derive nonparametric identification results for nonseparable simultaneous equations and multi-attribute hedonic equilibrium models with (possibly) multiple dimensions of unobserved heterogeneity. One of our results is a proof of absolute continuity of the distribution of endogenously traded qualities, which is of independent interest.

econ.EM↗

arXiv2019

Inference for Impulse Responses under Model Uncertainty

In many macroeconomic applications, confidence intervals for impulse responses are constructed by estimating VAR models in levels - ignoring cointegration rank uncertainty. We investigate the consequences of ignoring this uncertainty. We adapt several methods for handling model uncertainty and highlight their shortcomings. We propose a new method - Weighted-Inference-by-Model-Plausibility (WIMP) - that takes rank uncertainty into account in a data-driven way. In simulations the WIMP outperforms all other methods considered, delivering intervals that are robust to rank uncertainty, yet not overly conservative. We also study potential ramifications of rank uncertainty on applied macroeconomic analysis by re-assessing the effects of fiscal policy shocks.

econ.EM↗

arXiv2017

Quasi-random Monte Carlo application in CGE systematic sensitivity analysis

The uncertainty and robustness of Computable General Equilibrium models can be assessed by conducting a Systematic Sensitivity Analysis. Different methods have been used in the literature for SSA of CGE models such as Gaussian Quadrature and Monte Carlo methods. This paper explores the use of Quasi-random Monte Carlo methods based on the Halton and Sobol' sequences as means to improve the efficiency over regular Monte Carlo SSA, thus reducing the computational requirements of the SSA. The findings suggest that by using low-discrepancy sequences, the number of simulations required by the regular MC SSA methods can be notably reduced, hence lowering the computational time required for SSA of CGE models.

econ.EM↗

arXiv2019

Estimation of Peer Effects in Endogenous Social Networks: Control Function Approach

We propose a method of estimating the linear-in-means model of peer effects in which the peer group, defined by a social network, is endogenous in the outcome equation for peer effects. Endogeneity is due to unobservable individual characteristics that influence both link formation in the network and the outcome of interest. We propose two estimators of the peer effect equation that control for the endogeneity of the social connections using a control function approach. We leave the functional form of the control function unspecified and treat it as unknown. To estimate the model, we use a sieve semiparametric approach, and we establish asymptotics of the semiparametric estimator.

econ.EM↗

arXiv2017

Estimation of Graphical Models using the $L_{1,2}$ Norm

Gaussian graphical models are recently used in economics to obtain networks of dependence among agents. A widely-used estimator is the Graphical Lasso (GLASSO), which amounts to a maximum likelihood estimation regularized using the $L_{1,1}$ matrix norm on the precision matrix $Ω$. The $L_{1,1}$ norm is a lasso penalty that controls for sparsity, or the number of zeros in $Ω$. We propose a new estimator called Structured Graphical Lasso (SGLASSO) that uses the $L_{1,2}$ mixed norm. The use of the $L_{1,2}$ penalty controls for the structure of the sparsity in $Ω$. We show that when the network size is fixed, SGLASSO is asymptotically equivalent to an infeasible GLASSO problem which prioritizes the sparsity-recovery of high-degree nodes. Monte Carlo simulation shows that SGLASSO outperforms GLASSO in terms of estimating the overall precision matrix and in terms of estimating the structure of the graphical model. In an empirical illustration using a classic firms' investment dataset, we obtain a network of firms' dependence that exhibits the core-periphery structure, with General Motors, General Electric and U.S. Steel forming the core group of firms.

econ.EM↗

arXiv2017

Forecasting with Dynamic Panel Data Models

This paper considers the problem of forecasting a collection of short time series using cross sectional information in panel data. We construct point predictors using Tweedie's formula for the posterior mean of heterogeneous coefficients under a correlated random effects distribution. This formula utilizes cross-sectional information to transform the unit-specific (quasi) maximum likelihood estimator into an approximation of the posterior mean under a prior distribution that equals the population distribution of the random coefficients. We show that the risk of a predictor based on a non-parametric estimate of the Tweedie correction is asymptotically equivalent to the risk of a predictor that treats the correlated-random-effects distribution as known (ratio-optimality). Our empirical Bayes predictor performs well compared to various competitors in a Monte Carlo study. In an empirical application we use the predictor to forecast revenues for a large panel of bank holding companies and compare forecasts that condition on actual and severely adverse macroeconomic conditions.

econ.EM↗

arXiv2018

Inference for VARs Identified with Sign Restrictions

There is a fast growing literature that set-identifies structural vector autoregressions (SVARs) by imposing sign restrictions on the responses of a subset of the endogenous variables to a particular structural shock (sign-restricted SVARs). Most methods that have been used to construct pointwise coverage bands for impulse responses of sign-restricted SVARs are justified only from a Bayesian perspective. This paper demonstrates how to formulate the inference problem for sign-restricted SVARs within a moment-inequality framework. In particular, it develops methods of constructing confidence bands for impulse response functions of sign-restricted SVARs that are valid from a frequentist perspective. The paper also provides a comparison of frequentist and Bayesian coverage bands in the context of an empirical application - the former can be substantially wider than the latter.

econ.EM↗

arXiv2017

A Note on the Multi-Agent Contracts in Continuous Time

Dynamic contracts with multiple agents is a classical decentralized decision-making problem with asymmetric information. In this paper, we extend the single-agent dynamic incentive contract model in continuous-time to a multi-agent scheme in finite horizon and allow the terminal reward to be dependent on the history of actions and incentives. We first derive a set of sufficient conditions for the existence of optimal contracts in the most general setting and conditions under which they form a Nash equilibrium. Then we show that the principal's problem can be converted to solving Hamilton-Jacobi-Bellman (HJB) equation requiring a static Nash equilibrium. Finally, we provide a framework to solve this problem by solving partial differential equations (PDE) derived from backward stochastic differential equations (BSDE).

econ.EM↗

arXiv2019

A Justification of Conditional Confidence Intervals

To quantify uncertainty around point estimates of conditional objects such as conditional means or variances, parameter uncertainty has to be taken into account. Attempts to incorporate parameter uncertainty are typically based on the unrealistic assumption of observing two independent processes, where one is used for parameter estimation, and the other for conditioning upon. Such unrealistic foundation raises the question whether these intervals are theoretically justified in a realistic setting. This paper presents an asymptotic justification for this type of intervals that does not require such an unrealistic assumption, but relies on a sample-split approach instead. By showing that our sample-split intervals coincide asymptotically with the standard intervals, we provide a novel, and realistic, justification for confidence intervals of conditional objects. The analysis is carried out for a rich class of time series models.

econ.EM↗

arXiv2018

Rate-Optimal Estimation of the Intercept in a Semiparametric Sample-Selection Model

This paper presents a new estimator of the intercept of a linear regression model in cases where the outcome varaible is observed subject to a selection rule. The intercept is often in this context of inherent interest; for example, in a program evaluation context, the difference between the intercepts in outcome equations for participants and non-participants can be interpreted as the difference in average outcomes of participants and their counterfactual average outcomes if they had chosen not to participate. The new estimator can under mild conditions exhibit a rate of convergence in probability equal to $n^{-p/(2p+1)}$, where $p\ge 2$ is an integer that indexes the strength of certain smoothness assumptions. This rate of convergence is shown in this context to be the optimal rate of convergence for estimation of the intercept parameter in terms of a minimax criterion. The new estimator, unlike other proposals in the literature, is under mild conditions consistent and asymptotically normal with a rate of convergence that is the same regardless of the degree to which selection depends on unobservables in the outcome equation. Simulation evidence and an empirical example are included.

econ.EM↗

arXiv2017

Smooth Pinball Neural Network for Probabilistic Forecasting of Wind Power

Uncertainty analysis in the form of probabilistic forecasting can significantly improve decision making processes in the smart power grid for better integrating renewable energy sources such as wind. Whereas point forecasting provides a single expected value, probabilistic forecasts provide more information in the form of quantiles, prediction intervals, or full predictive densities. This paper analyzes the effectiveness of a novel approach for nonparametric probabilistic forecasting of wind power that combines a smooth approximation of the pinball loss function with a neural network architecture and a weighting initialization scheme to prevent the quantile cross over problem. A numerical case study is conducted using publicly available wind data from the Global Energy Forecasting Competition 2014. Multiple quantiles are estimated to form 10%, to 90% prediction intervals which are evaluated using a quantile score and reliability measures. Benchmark models such as the persistence and climatology distributions, multiple quantile regression, and support vector quantile regression are used for comparison where results demonstrate the proposed approach leads to improved performance while preventing the problem of overlapping quantile estimates.

stat.ML↗

arXiv2018

Finite Time Identification in Unstable Linear Systems

Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially regarding finite time bounds. For this setting, classical results on least-squares estimation of the dynamics parameters are not applicable and therefore new concepts and technical approaches need to be developed to address the issue. Unstable linear systems arise in key real applications in control theory, econometrics, and finance. This study establishes finite time bounds for the identification error of the least-squares estimates for a fairly large class of heavy-tailed noise distributions, and transition matrices of such systems. The results relate the time length (samples) required for estimation to a function of the problem dimension and key characteristics of the true underlying transition matrix and the noise distribution. To establish them, appropriate concentration inequalities for random matrices and for sequences of martingale differences are leveraged.

eess.SY↗