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on Econometrics |
| By: | Zetterqvist, Johan (Karolinska institutet); Waernbaum, Ingeborg (IFAU - Institute for Evaluation of Labour Market and Education Policy) |
| Abstract: | An estimand of interest in empirical studies with observational data is the average treatment effect of a multi-valued treatment in the treated subpopulation. We demonstrate three estimation approaches: outcome regression, inverse probability weighting and inverse probability weighted regression, where the latter estimator holds a so called doubly robust property. Here, we define the estimators in the framework of partial M-estimation and derive corresponding sandwich estimators of their variances. The finite sample properties of the estimators and the proposed variance estimators are evaluated in simulations that reproduce designs from a previous simulation study in the literature of multi-valued treatment effects. The proposed variance estimators are investigated and compared to a bootstrap estimator. |
| Keywords: | ATT; causal inference; inverse probability weighting; doubly robust; weighted ordinary least squares |
| JEL: | C14 |
| Date: | 2020–03–05 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:ifauwp:2020_004&r=all |
| By: | Songnian Chen; Shakeeb Khan; Xun Tang |
| Abstract: | We study the identification and estimation of treatment effect parameters in non-separable models. In their seminal work, Vytlacil and Yildiz (2007) showed how to identify and estimate the average treatment effect of a dummy endogenous variable in a weakly separable model under a monotonicity condition. We also consider similar weakly separable models, but relax the monotonicity condition for identification. Our approach exploits information from the distribution of the outcome. To illustrate the advantage of our approach, we provide several examples of models where our approach can identify parameters of interest whereas existing methods cannot be applied because monotonicity fails. These include models with multiple unobserved disturbance terms such as the Roy model and multinomial choice models with dummy endogenous variables, as well as potential outcome models with endogenous random coefficients. Our proposed method applies to a wide class of models and is easy to implement. We also establish standard asymptotic properties such as consistency and asymptotic normality. |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2003.04337&r=all |
| By: | Florian Huber; Gary Koop; Michael Pfarrhofer |
| Abstract: | 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. |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2002.10274&r=all |
| By: | Krikamol Muandet; Wittawat Jitkrittum; Jonas K\"ubler |
| Abstract: | We propose a new family of specification tests called kernel conditional moment (KCM) tests. Our tests are built on conditional moment embeddings (CMME)---a novel representation of conditional moment restrictions in a reproducing kernel Hilbert space (RKHS). After transforming the conditional moment restrictions into a continuum of unconditional counterparts, the test statistic is defined as the maximum moment restriction within the unit ball of the RKHS. We show that the CMME fully characterizes the original conditional moment restrictions, leading to consistency in both hypothesis testing and parameter estimation. The proposed test also has an analytic expression that is easy to compute as well as closed-form asymptotic distributions. Our empirical studies show that the KCM test has a promising finite-sample performance compared to existing tests. |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2002.09225&r=all |
| By: | Jean-Pierre H. Dubé; Ali Hortaçsu; Joonhwi Joo |
| Abstract: | Although typically overlooked, many purchase datasets exhibit a high incidence of products with zero sales. We propose a new estimator for the Random-Coefficients Logit demand system for purchase datasets with zero-valued market shares. The identification of the demand parameters is based on a pairwise-differencing approach that constructs moment conditions based on differences in demand between pairs of products. The corresponding estimator corrects non-parametrically for the potential selection of the incidence of zeros on unobserved aspects of demand. The estimator also corrects for the potential endogeneity of marketing variables both in demand and in the selection propensities. Monte Carlo simulations show that our proposed estimator provides reliable small-sample inference both with and without selection-on- unobservables. In an empirical case study, the proposed estimator not only generates different demand estimates than approaches that ignore selection in the incidence of zero shares, it also generates better out-of-sample fit of observed retail contribution margins. |
| JEL: | D12 L00 L66 L81 M3 |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:26795&r=all |
| By: | Marc Hallin; Gilles Mordant; Johan Segers |
| Abstract: | Goodness-of-fit tests based on the empirical Wasserstein distance are proposed for simple and composite null hypotheses involving general multivariate distributions. This includes the important problem of testing for multivariate normality with unspecified location and covariance and, more generally, testing for elliptical symmetry with given standard radial density, unspecified location and scatter parameters. The calculation of test statistics boils down to solving the well-studied semi-discrete optimal transport problem. Exact critical values can be computed for some important particular cases, such as null hypotheses of ellipticity with given standard radial density and unspecified location and scatter; else, approximate critical values are obtained via parametric bootstrap. Consistency is established, based on a result on the convergence to zero, uniformly over certain families of distributions, of the empirical Wasserstein distance---a novel result of independent interest. A simulation study establishes the practical feasibility and excellent performance of the proposed tests. |
| Keywords: | Copula; Elliptical distribution; Goodness-of- t; Multivariate normality; Optimal transport; Semi-discrete problem; Skew-t distribution; Wasserstein distance |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/303372&r=all |
| By: | Kung-Sik Chan; Simone Giannerini; Greta Goracci; Howell Tong |
| Abstract: | We propose a new unit-root test based on Lagrange Multipliers, where we extend the null hypothesis to an integrated moving-average process (IMA(1,1)) and the alternative to a first-order threshold autoregressive moving-average process (TARMA(1,1)). This new theoretical framework provides tests with good size without pre-modelling steps. Moreover, leveraging on the versatile capability of the TARMA(1,1), our test has power against a wide range of linear and nonlinear alternatives. We prove the consistency and asymptotic similarity of the test. The proof of tightness of the test is of independent and general theoretical interest. Moreover, we propose a wild bootstrap version of the statistic. Our proposals outperform most existing tests in many contexts. We support the view that rejection does not necessarily imply nonlinearity so that unit-root tests should not be used uncritically to select a model. Finally, we present an application to real exchange rates. |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2002.09968&r=all |
| By: | Firmin Doko Tchatoka (School of Economics, University of Adelaide); Qazi Haque (Business School, The University of Western Australia) |
| Abstract: | The asymptotic distributions of the recursive out-of-sample forecast accuracy test statistics depend on stochastic integrals of Brownian motion when the models under comparison are nested. This often complicates their implementation in practice because the computation of their asymptotic critical values is costly. Hansen and Timmermann (2015, Econometrica) propose a Wald approximation of the commonly used recursive F-statistic and provide a simple characterization of the exact density of its asymptotic distribution. However, this characterization holds only when the larger model has one extra predictor or the forecast errors are homoscedastic. No such closed-form characterization is readily available when the nesting involves more than one predictor and heteroskedasticity is present. We first show both the recursive F-test and its Wald approximation have poor finite-sample properties, especially when the forecast horizon is greater than one. We then propose an hybrid bootstrap method consisting of a block moving bootstrap (which is nonparametric) and a residual based bootstrap for both statistics, and establish its validity. Simulations show that our hybrid bootstrap has good finite-sample performance, even in multi-step ahead forecasts with heteroscedastic or autocorrelated errors, and more than one predictor. The bootstrap method is illustrated on forecasting core inflation and GDP growth. |
| Keywords: | Out-of-sample forecasts; HAC estimator; Moving block bootstrap; Bootstrap consistency |
| JEL: | C12 C15 C32 |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:adl:wpaper:2020-03&r=all |
| By: | Yulong Wang; Zhijie Xiao |
| Abstract: | 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. |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2002.09982&r=all |
| By: | Sven Otto; J\"org Breitung |
| Abstract: | It is well known that the conventional CUSUM test suffers from low power and large detection delay. We therefore propose two alternative detector statistics. The backward CUSUM detector sequentially cumulates the recursive residuals in reverse chronological order, whereas the stacked backward CUSUM detector considers a triangular array of backward cumulated residuals. While both the backward CUSUM detector and the stacked backward CUSUM detector are suitable for retrospective testing, only the stacked backward CUSUM detector can be monitored on-line. The limiting distributions of the maximum statistics under suitable sequences of alternatives are derived for retrospective testing and fixed endpoint monitoring. In the retrospective testing context, the local power of the tests is shown to be substantially higher than that for the conventional CUSUM test if a single break occurs after one third of the sample size. When applied to monitoring schemes, the detection delay of the stacked backward CUSUM is shown to be much shorter than that of the conventional monitoring CUSUM procedure. Moreover, an infinite horizon monitoring procedure and critical values are presented. |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2003.02682&r=all |
| By: | Oguzhan Akgun; Alain Pirotte; Giovanni Urga; Zhenlin Yang |
| Abstract: | This paper develops novel tests to compare the predictive ability of two forecasters using panels. We consider two different equal predictive ability (EPA) hypotheses. First hypothesis states that the predictive ability of two forecasters is equal on average over all periods and units. Under the second one, the EPA hypothesis holds jointly for all units. We study the asymptotic properties of proposed tests using sequential limits under strong and weak cross-sectional dependence. Their finite sample properties are investigated via Monte Carlo simulations. They are applied to compare the economic growth forecasts of OECD and IMF using data from OECD countries. |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2003.02803&r=all |
| By: | Xiaochun Meng; James W. Taylor; Souhaib Ben Taieb; Siran Li |
| Abstract: | Interest in predicting multivariate probability distributions is growing due to the increasing availability of rich datasets and computational developments. Scoring functions enable the comparison of forecast accuracy, and can potentially be used for estimation. A scoring function for multivariate distributions that has gained some popularity is the energy score. This is a generalization of the continuous ranked probability score (CRPS), which is widely used for univariate distributions. A little-known, alternative generalization is the multivariate CRPS (MCRPS). We propose a theoretical framework for scoring functions for multivariate distributions, which encompasses the energy score and MCRPS, as well as the quadratic score, which has also received little attention. We demonstrate how this framework can be used to generate new scores. For univariate distributions, it is well-established that the CRPS can be expressed as the integral over a quantile score. We show that, in a similar way, scoring functions for multivariate distributions can be "disintegrated" to obtain scoring functions for level sets. Using this, we present scoring functions for different types of level set, including those for densities and cumulative distributions. To compute the scoring functions, we propose a simple numerical algorithm. We illustrate our proposals using simulated and stock returns data. |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2002.09578&r=all |
| By: | Jarek Duda |
| Abstract: | While standard estimation assumes that all datapoints are from probability distribution of the same fixed parameters $\theta$, we will focus on maximum likelihood (ML) adaptive estimation for nonstationary time series: separately estimating parameters $\theta_T$ for each time $T$ based on the earlier values $(x_t)_{t |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2003.02149&r=all |
| By: | Moyu Liao |
| Abstract: | This paper studies the identification and estimation problem in incomplete economic models with testable assumptions. Testable assumptions give strong and interpretable empirical content to the models but they also carry the possibility that our distribution of observed outcome may reject these assumptions. A natural way is to find a set of relaxed assumptions $\tilde{A}$ that cannot be rejected by any reasonable distribution of observed outcome and preserves identified set of parameter of interest. The main contribution of this paper is to characterize the property of such relaxed assumption $\tilde{A}$ using a generalized definition of refutability and confirmability. A general estimation and inference procedure is proposed, and can be applied to most incomplete economic models. As the key application, I study the Imbens and Angrist Monotonicity assumption in potential outcome framework. I give a set of relaxed assumptions $\tilde{A}$ that can never be rejected and always preserve the identified set of local average treatment effect (LATE). The LATE is point identified and easy to estimate under $\tilde{A}$ |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2002.10415&r=all |
| By: | Andree,Bo Pieter Johannes; Spencer,Phoebe Girouard; Azari,Sardar; Chamorro,Andres; Wang,Dieter; Dogo,Harun |
| Abstract: | This paper introduces a Spatial Vector Autoregressive Moving Average (SVARMA) model in which multiple cross-sectional time series are modeled as multivariate, possibly fat-tailed, spatial autoregressive ARMA processes. The estimation requires specifying the cross-sectional spillover channels through spatial weights matrices. the paper explores a kernel method to estimate the network topology based on similarities in the data. It discusses the model and estimation, focusing on a penalized Maximum Likelihood criterion. The empirical performance of the estimator is explored in a simulation study. The model is used to study a spatial time series of pollution and household expenditure data in Indonesia. The analysis finds that the new model improves in terms of implied density, and better neutralizes residual correlations than the VARMA, using fewer parameters. The results suggest that growth in household expenditures precedes pollution reduction, particularly after the expenditures of poorer households increase; that increasing pollution is followed by reduced growth in expenditures, particularly reducing the growth of poorer households; and that there are significant spillovers from bottom-up growth in expenditures. The paper does not find evidence for top-down growth spillovers. Feedback between the identified mechanisms may contribute to pollution-poverty traps and the results imply that pollution damages are economically significant. |
| Keywords: | Global Environment,Inequality,Brown Issues and Health,Air Quality&Clean Air,Pollution Management&Control,Health Service Management and Delivery |
| Date: | 2019–02–25 |
| URL: | http://d.repec.org/n?u=RePEc:wbk:wbrwps:8757&r=all |
| By: | Steven Y. K. Wong (University of Technology Sydney); Jennifer Chan (University of Sydney); Lamiae Azizi (University of Sydney); Richard Y. D. Xu (University of Technology Sydney) |
| Abstract: | We consider the problem of neural network training in a time-varying context. Machine learning algorithms have excelled in problems that do not change over time. However, problems encountered in financial markets are often non-stationary. We propose the online early stopping algorithm and show that a neural network trained using this algorithm can track a function changing with unknown dynamics. We applied the proposed algorithm to the stock return prediction problem studied in Gu et al. (2019) and achieved mean rank correlation of 4.69%, almost twice as high as the expanding window approach. We also show that prominent factors, such as the size effect and momentum, exhibit time varying stock return predictiveness. |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2003.02515&r=all |
| By: | Roy Allen; John Rehbeck |
| Abstract: | This paper provides nonparametric identification results for random coefficient distributions in perturbed utility models. We cover discrete and continuous choice models. We establish identification using variation in mean quantities, and the results apply when an analyst observes aggregate demands but not whether goods are chosen together. We require exclusion restrictions and independence between random slope coefficients and random intercepts. We do not require regressors to have large supports or parametric assumptions. |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2003.00276&r=all |
| By: | Oksana Bashchenko (HEC Lausanne; Swiss Finance Institute); Alexis Marchal (EPFL; SFI) |
| Abstract: | We develop a new method that detects jumps nonparametrically in financial time series and significantly outperforms the current benchmark on simulated data. We use a long short- term memory (LSTM) neural network that is trained on labelled data generated by a process that experiences both jumps and volatility bursts. As a result, the network learns how to disentangle the two. Then it is applied to out-of-sample simulated data and delivers results that considerably differ from the benchmark: we obtain fewer spurious detection and identify a larger number of true jumps. When applied to real data, our approach for jump screening allows to extract a more precise signal about future volatility. |
| Keywords: | Jumps, Volatility Burst, High-Frequency Data, Deep Learning, LSTM |
| JEL: | C14 C32 C45 C58 G17 |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp2010&r=all |
| By: | Kubinec, Robert (Princeton University) |
| Abstract: | I propose a new model, ordered beta regression, for data collected from human subjects using slider scales/visual analog scales with lower and upper bounds. This model employs the cutpoint technique popularized by ordered logit to simultaneously estimate the probability that the outcome is at the upper bound, lower bound, or any continuous number in between. This model is contrasted with existing approaches, including ordinary least squares (OLS) regression and the zero-one-inflated beta regression (ZOIB) model. Simulation evidence shows that the proposed model, relative to existing approaches, estimates effects with more accuracy while capturing the full uncertainty in the distribution. Furthermore, an analysis of data on U.S. public opinion towards college professors reveals that the proposed model is better able to combine variation across continuous and degenerate responses. The model can be fit with the R package brms. |
| Date: | 2020–03–02 |
| URL: | http://d.repec.org/n?u=RePEc:osf:socarx:2sx6y&r=all |
| By: | Marijn A. Bolhuis; Brett Rayner |
| Abstract: | We leverage insights from machine learning to optimize the tradeoff between bias and variance when estimating economic models using pooled datasets. Specifically, we develop a simple algorithm that estimates the similarity of economic structures across countries and selects the optimal pool of countries to maximize out-of-sample prediction accuracy of a model. We apply the new alogrithm by nowcasting output growth with a panel of 102 countries and are able to significantly improve forecast accuracy relative to alternative pools. The algortihm improves nowcast performance for advanced economies, as well as emerging market and developing economies, suggesting that machine learning techniques using pooled data could be an important macro tool for many countries. |
| Date: | 2020–02–28 |
| URL: | http://d.repec.org/n?u=RePEc:imf:imfwpa:20/44&r=all |
| By: | Savi Virolainen |
| Abstract: | We introduce a new mixture autoregressive model which combines Gaussian and Student's $t$ mixture components. The model has very attractive properties analogous to the Gaussian and Student's $t$ mixture autoregressive models, but it is more flexible as it enables to model series which consist of both conditionally homoscedastic Gaussian regimes and conditionally heteroscedastic Student's $t$ regimes. The usefulness of our model is demonstrated in an empirical application to the monthly U.S. interest rate spread between the 3-month Treasury bill rate and the effective federal funds rate. |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2003.05221&r=all |