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arXiv2020

Network and Panel Quantile Effects Via Distribution Regression

This paper provides a method to construct simultaneous confidence bands for quantile functions and quantile effects in nonlinear network and panel models with unobserved two-way effects, strictly exogenous covariates, and possibly discrete outcome variables. The method is based upon projection of simultaneous confidence bands for distribution functions constructed from fixed effects distribution regression estimators. These fixed effects estimators are debiased to deal with the incidental parameter problem. Under asymptotic sequences where both dimensions of the data set grow at the same rate, the confidence bands for the quantile functions and effects have correct joint coverage in large samples. An empirical application to gravity models of trade illustrates the applicability of the methods to network data.

econ.EM↗

arXiv2018

Causal Inference for Survival Analysis

In this paper, we propose the use of causal inference techniques for survival function estimation and prediction for subgroups of the data, upto individual units. Tree ensemble methods, specifically random forests were modified for this purpose. A real world healthcare dataset was used with about 1800 patients with breast cancer, which has multiple patient covariates as well as disease free survival days (DFS) and a death event binary indicator (y). We use the type of cancer curative intervention as the treatment variable (T=0 or 1, binary treatment case in our example). The algorithm is a 2 step approach. In step 1, we estimate heterogeneous treatment effects using a causalTree with the DFS as the dependent variable. Next, in step 2, for each selected leaf of the causalTree with distinctly different average treatment effect (with respect to survival), we fit a survival forest to all the patients in that leaf, one forest each for treatment T=0 as well as T=1 to get estimated patient level survival curves for each treatment (more generally, any model can be used at this step). Then, we subtract the patient level survival curves to get the differential survival curve for a given patient, to compare the survival function as a result of the 2 treatments. The path to a selected leaf also gives us the combination of patient features and their values which are causally important for the treatment effect difference at the leaf.

econ.EM↗

arXiv2022

Decentralized Pure Exchange Processes on Networks

We define a class of pure exchange Edgeworth trading processes that under minimal assumptions converge to a stable set in the space of allocations, and characterise the Pareto set of these processes. Choosing a specific process belonging to this class, that we define fair trading, we analyse the trade dynamics between agents located on a weighted network. We determine the conditions under which there always exists a one-to-one map between the set of networks and the set of limit points of the dynamics. This result is used to understand what is the effect of the network topology on the trade dynamics and on the final allocation. We find that the positions in the network affect the distribution of the utility gains, given the initial allocations

econ.EM↗

arXiv2020

Difference-in-Differences with Multiple Time Periods

In this article, we consider identification, estimation, and inference procedures for treatment effect parameters using Difference-in-Differences (DiD) with (i) multiple time periods, (ii) variation in treatment timing, and (iii) when the "parallel trends assumption" holds potentially only after conditioning on observed covariates. We show that a family of causal effect parameters are identified in staggered DiD setups, even if differences in observed characteristics create non-parallel outcome dynamics between groups. Our identification results allow one to use outcome regression, inverse probability weighting, or doubly-robust estimands. We also propose different aggregation schemes that can be used to highlight treatment effect heterogeneity across different dimensions as well as to summarize the overall effect of participating in the treatment. We establish the asymptotic properties of the proposed estimators and prove the validity of a computationally convenient bootstrap procedure to conduct asymptotically valid simultaneous (instead of pointwise) inference. Finally, we illustrate the relevance of our proposed tools by analyzing the effect of the minimum wage on teen employment from 2001--2007. Open-source software is available for implementing the proposed methods.

econ.EM↗

arXiv2019

Schooling Choice, Labour Market Matching, and Wages

We develop inference for a two-sided matching model where the characteristics of agents on one side of the market are endogenous due to pre-matching investments. The model can be used to measure the impact of frictions in labour markets using a single cross-section of matched employer-employee data. The observed matching of workers to firms is the outcome of a discrete, two-sided matching process where firms with heterogeneous preferences over education sequentially choose workers according to an index correlated with worker preferences over firms. The distribution of education arises in equilibrium from a Bayesian game: workers, knowing the distribution of worker and firm types, invest in education prior to the matching process. Although the observed matching exhibits strong cross-sectional dependence due to the matching process, we propose an asymptotically valid inference procedure that combines discrete choice methods with simulation.

econ.EM↗

arXiv2023

Efficient Discovery of Heterogeneous Quantile Treatment Effects in Randomized Experiments via Anomalous Pattern Detection

In the recent literature on estimating heterogeneous treatment effects, each proposed method makes its own set of restrictive assumptions about the intervention's effects and which subpopulations to explicitly estimate. Moreover, the majority of the literature provides no mechanism to identify which subpopulations are the most affected--beyond manual inspection--and provides little guarantee on the correctness of the identified subpopulations. Therefore, we propose Treatment Effect Subset Scan (TESS), a new method for discovering which subpopulation in a randomized experiment is most significantly affected by a treatment. We frame this challenge as a pattern detection problem where we efficiently maximize a nonparametric scan statistic (a measure of the conditional quantile treatment effect) over subpopulations. Furthermore, we identify the subpopulation which experiences the largest distributional change as a result of the intervention, while making minimal assumptions about the intervention's effects or the underlying data generating process. In addition to the algorithm, we demonstrate that under the sharp null hypothesis of no treatment effect, the asymptotic Type I and II error can be controlled, and provide sufficient conditions for detection consistency--i.e., exact identification of the affected subpopulation. Finally, we validate the efficacy of the method by discovering heterogeneous treatment effects in simulations and in real-world data from a well-known program evaluation study.

stat.ME↗

arXiv2019

Panel Data Analysis with Heterogeneous Dynamics

This paper proposes a model-free approach to analyze panel data with heterogeneous dynamic structures across observational units. We first compute the sample mean, autocovariances, and autocorrelations for each unit, and then estimate the parameters of interest based on their empirical distributions. We then investigate the asymptotic properties of our estimators using double asymptotics and propose split-panel jackknife bias correction and inference based on the cross-sectional bootstrap. We illustrate the usefulness of our procedures by studying the deviation dynamics of the law of one price. Monte Carlo simulations confirm that the proposed bias correction is effective and yields valid inference in small samples.

econ.EM↗

arXiv2021

Continuous Record Asymptotics for Change-Points Models

For a partial structural change in a linear regression model with a single break, we develop a continuous record asymptotic framework to build inference methods for the break date. We have T observations with a sampling frequency h over a fixed time horizon [0, N] , and let T with h 0 while keeping the time span N fixed. We impose very mild regularity conditions on an underlying continuous-time model assumed to generate the data. We consider the least-squares estimate of the break date and establish consistency and convergence rate. We provide a limit theory for shrinking magnitudes of shifts and locally increasing variances. The asymptotic distribution corresponds to the location of the extremum of a function of the quadratic variation of the regressors and of a Gaussian centered martingale process over a certain time interval. We can account for the asymmetric informational content provided by the pre- and post-break regimes and show how the location of the break and shift magnitude are key ingredients in shaping the distribution. We consider a feasible version based on plug-in estimates, which provides a very good approximation to the finite sample distribution. We use the concept of Highest Density Region to construct confidence sets. Overall, our method is reliable and delivers accurate coverage probabilities and relatively short average length of the confidence sets. Importantly, it does so irrespective of the size of the break.

math.ST↗

arXiv2018

Tests for Forecast Instability and Forecast Failure under a Continuous Record Asymptotic Framework

We develop a novel continuous-time asymptotic framework for inference on whether the predictive ability of a given forecast model remains stable over time. We formally define forecast instability from the economic forecaster's perspective and highlight that the time duration of the instability bears no relationship with stable period. Our approach is applicable in forecasting environment involving low-frequency as well as high-frequency macroeconomic and financial variables. As the sampling interval between observations shrinks to zero the sequence of forecast losses is approximated by a continuous-time stochastic process (i.e., an Ito semimartingale) possessing certain pathwise properties. We build an hypotheses testing problem based on the local properties of the continuous-time limit counterpart of the sequence of losses. The null distribution follows an extreme value distribution. While controlling the statistical size well, our class of test statistics feature uniform power over the location of the forecast failure in the sample. The test statistics are designed to have power against general form of insatiability and are robust to common forms of non-stationarity such as heteroskedasticty and serial correlation. The gains in power are substantial relative to extant methods, especially when the instability is short-lasting and when occurs toward the tail of the sample.

econ.EM↗

arXiv2018

An Empirical Analysis of Constrained Support Vector Quantile Regression for Nonparametric Probabilistic Forecasting of Wind Power

Uncertainty analysis in the form of probabilistic forecasting can provide significant improvements in decision-making processes in the smart power grid for better integrating renewable energies 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 an approach for nonparametric probabilistic forecasting of wind power that combines support vector machines and nonlinear quantile regression with non-crossing constraints. A numerical case study is conducted using publicly available wind data from the Global Energy Forecasting Competition 2014. Multiple quantiles are estimated to form 20%, 40%, 60% and 80% prediction intervals which are evaluated using the pinball loss function and reliability measures. Three benchmark models are used for comparison where results demonstrate the proposed approach leads to significantly better performance while preventing the problem of overlapping quantile estimates.

stat.ML↗

arXiv2019

Bi-Demographic Changes and Current Account using SVAR Modeling

The paper aims to explore the impacts of bi-demographic structure on the current account and growth. Using a SVAR modeling, we track the dynamic impacts between these underlying variables. New insights have been developed about the dynamic interrelation between population growth, current account and economic growth. The long-run net impact on economic growth of the domestic working population growth and demand labor for emigrants is positive, due to the predominant contribution of skilled emigrant workers. Besides, the positive long-run contribution of emigrant workers to the current account growth largely compensates the negative contribution from the native population, because of the predominance of skilled compared to unskilled workforce. We find that a positive shock in demand labor for emigrant workers leads to an increasing effect on native active age ratio. Thus, the emigrants appear to be more complements than substitutes for native workers.

econ.EM↗

arXiv2018

Mortality in a heterogeneous population - Lee-Carter's methodology

The EU Solvency II directive recommends insurance companies to pay more attention to the risk management methods. The sense of risk management is the ability to quantify risk and apply methods that reduce uncertainty. In life insurance, the risk is a consequence of the random variable describing the life expectancy. The article will present a proposal for stochastic mortality modeling based on the Lee and Carter methodology. The maximum likelihood method is often used to estimate parameters in mortality models. This method assumes that the population is homogeneous and the number of deaths has the Poisson distribution. The aim of this article is to change assumptions about the distribution of the number of deaths. The results indicate that the model can get a better match to historical data, when the number of deaths has a negative binomial distribution.

econ.EM↗

arXiv2020

Continuous Record Laplace-based Inference about the Break Date in Structural Change Models

Building upon the continuous record asymptotic framework recently introduced by Casini and Perron (2018a) for inference in structural change models, we propose a Laplace-based (Quasi-Bayes) procedure for the construction of the estimate and confidence set for the date of a structural change. It is defined by an integration rather than an optimization-based method. A transformation of the least-squares criterion function is evaluated in order to derive a proper distribution, referred to as the Quasi-posterior. For a given choice of a loss function, the Laplace-type estimator is the minimizer of the expected risk with the expectation taken under the Quasi-posterior. Besides providing an alternative estimate that is more precise|lower mean absolute error (MAE) and lower root-mean squared error (RMSE)|than the usual least-squares one, the Quasi-posterior distribution can be used to construct asymptotically valid inference using the concept of Highest Density Region. The resulting Laplace-based inferential procedure is shown to have lower MAE and RMSE, and the confidence sets strike the best balance between empirical coverage rates and average lengths of the confidence sets relative to traditional long-span methods, whether the break size is small or large.

econ.EM↗

arXiv2018

Should We Adjust for the Test for Pre-trends in Difference-in-Difference Designs?

The common practice in difference-in-difference (DiD) designs is to check for parallel trends prior to treatment assignment, yet typical estimation and inference does not account for the fact that this test has occurred. I analyze the properties of the traditional DiD estimator conditional on having passed (i.e. not rejected) the test for parallel pre-trends. When the DiD design is valid and the test for pre-trends confirms it, the typical DiD estimator is unbiased, but traditional standard errors are overly conservative. Additionally, there exists an alternative unbiased estimator that is more efficient than the traditional DiD estimator under parallel trends. However, when in population there is a non-zero pre-trend but we fail to reject the hypothesis of parallel pre-trends, the DiD estimator is generally biased relative to the population DiD coefficient. Moreover, if the trend is monotone, then under reasonable assumptions the bias from conditioning exacerbates the bias relative to the true treatment effect. I propose new estimation and inference procedures that account for the test for parallel trends, and compare their performance to that of the traditional estimator in a Monte Carlo simulation.

econ.EM↗

arXiv2021

A Bayesian panel VAR model to analyze the impact of climate change on high-income economies

In this paper, we assess the impact of climate shocks on futures markets for agricultural commodities and a set of macroeconomic quantities for multiple high-income economies. To capture relations among countries, markets, and climate shocks, this paper proposes parsimonious methods to estimate high-dimensional panel VARs. We assume that coefficients associated with domestic lagged endogenous variables arise from a Gaussian mixture model while further parsimony is achieved using suitable global-local shrinkage priors on several regions of the parameter space. Our results point towards pronounced global reactions of key macroeconomic quantities to climate shocks. Moreover, the empirical findings highlight substantial linkages between regionally located climate shifts and global commodity markets.

econ.EM↗

arXiv2019

Simultaneous Mean-Variance Regression

We propose simultaneous mean-variance regression for the linear estimation and approximation of conditional mean functions. In the presence of heteroskedasticity of unknown form, our method accounts for varying dispersion in the regression outcome across the support of conditioning variables by using weights that are jointly determined with the mean regression parameters. Simultaneity generates outcome predictions that are guaranteed to improve over ordinary least-squares prediction error, with corresponding parameter standard errors that are automatically valid. Under shape misspecification of the conditional mean and variance functions, we establish existence and uniqueness of the resulting approximations and characterize their formal interpretation and robustness properties. In particular, we show that the corresponding mean-variance regression location-scale model weakly dominates the ordinary least-squares location model under a Kullback-Leibler measure of divergence, with strict improvement in the presence of heteroskedasticity. The simultaneous mean-variance regression loss function is globally convex and the corresponding estimator is easy to implement. We establish its consistency and asymptotic normality under misspecification, provide robust inference methods, and present numerical simulations that show large improvements over ordinary and weighted least-squares in terms of estimation and inference in finite samples. We further illustrate our method with two empirical applications to the estimation of the relationship between economic prosperity in 1500 and today, and demand for gasoline in the United States.

econ.EM↗

arXiv2018

Statistical inference for autoregressive models under heteroscedasticity of unknown form

This paper provides an entire inference procedure for the autoregressive model under (conditional) heteroscedasticity of unknown form with a finite variance. We first establish the asymptotic normality of the weighted least absolute deviations estimator (LADE) for the model. Second, we develop the random weighting (RW) method to estimate its asymptotic covariance matrix, leading to the implementation of the Wald test. Third, we construct a portmanteau test for model checking, and use the RW method to obtain its critical values. As a special weighted LADE, the feasible adaptive LADE (ALADE) is proposed and proved to have the same efficiency as its infeasible counterpart. The importance of our entire methodology based on the feasible ALADE is illustrated by simulation results and the real data analysis on three U.S. economic data sets.

stat.ME↗

arXiv2020

Varying Random Coefficient Models

This paper provides a new methodology to analyze unobserved heterogeneity when observed characteristics are modeled nonlinearly. The proposed model builds on varying random coefficients (VRC) that are determined by nonlinear functions of observed regressors and additively separable unobservables. This paper proposes a novel estimator of the VRC density based on weighted sieve minimum distance. The main example of sieve bases are Hermite functions which yield a numerically stable estimation procedure. This paper shows inference results that go beyond what has been shown in ordinary RC models. We provide in each case rates of convergence and also establish pointwise limit theory of linear functionals, where a prominent example is the density of potential outcomes. In addition, a multiplier bootstrap procedure is proposed to construct uniform confidence bands. A Monte Carlo study examines finite sample properties of the estimator and shows that it performs well even when the regressors associated to RC are far from being heavy tailed. Finally, the methodology is applied to analyze heterogeneity in income elasticity of demand for housing.

econ.EM↗