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on Econometrics |
| By: | Karsten Reichold |
| Abstract: | This paper derives asymptotic theory for Breitung's (2002, Journal of Econometrics 108, 343-363) nonparameteric variance ratio unit root test when applied to regression residuals. The test requires neither the specification of the correlation structure in the data nor the choice of tuning parameters. Compared with popular residuals-based no-cointegration tests, the variance ratio test is less prone to size distortions but has smaller local asymptotic power. However, this paper shows that local asymptotic power properties do not serve as a useful indicator for the power of residuals-based no-cointegration tests in finite samples. In terms of size-corrected power, the variance ratio test performs relatively well and, in particular, does not suffer from power reversal problems detected for, e.g., the frequently used augmented Dickey-Fuller type no-cointegration test. An application to daily prices of cryptocurrencies illustrates the usefulness of the variance ratio test in practice. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.06288&r=ecm |
| By: | Anastasia Semykina (Department of Economics, Florida State University) |
| Abstract: | This paper considers estimating heterogeneous effects in panel data models when the outcome is binary. We argue that a common practice of splitting the sample and performing estimation separately for each subsample results in inconsistent estimators of heterogeneous parameters. The paper presents methods that account for a possibility of nonrandom sorting and produce consistent estimators of causal effects in two or more heterogeneous sub-populations. Monte Carlo simulations show that considered methods perform well in finite samples. As an empirical application, the paper studies gender differences in job satisfaction by occupation type. |
| Keywords: | binary response, heterogeneous effects, nonrandom sorting |
| JEL: | C33 C34 C35 |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:fsu:wpaper:wp2022_11_01&r=ecm |
| By: | Ziyu Wang; Yucen Luo; Yueru Li; Jun Zhu; Bernhard Sch\"olkopf |
| Abstract: | Many problems in causal inference and economics can be formulated in the framework of conditional moment models, which characterize the target function through a collection of conditional moment restrictions. For nonparametric conditional moment models, efficient estimation has always relied on preimposed conditions on various measures of ill-posedness of the hypothesis space, which are hard to validate when flexible models are used. In this work, we address this issue by proposing a procedure that automatically learns representations with controlled measures of ill-posedness. Our method approximates a linear representation defined by the spectral decomposition of a conditional expectation operator, which can be used for kernelized estimators and is known to facilitate minimax optimal estimation in certain settings. We show this representation can be efficiently estimated from data, and establish L2 consistency for the resulting estimator. We evaluate the proposed method on proximal causal inference tasks, exhibiting promising performance on high-dimensional, semi-synthetic data. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.16525&r=ecm |
| By: | Richard Post; Isabel van den Heuvel; Marko Petkovic; Edwin van den Heuvel |
| Abstract: | Causal inference from observational data requires untestable assumptions. If these assumptions apply, machine learning (ML) methods can be used to study complex forms of causal-effect heterogeneity. Several ML methods were developed recently to estimate the conditional average treatment effect (CATE). If the features at hand cannot explain all heterogeneity, the individual treatment effects (ITEs) can seriously deviate from the CATE. In this work, we demonstrate how the distributions of the ITE and the estimated CATE can differ when a causal random forest (CRF) is applied. We extend the CRF to estimate the difference in conditional variance between treated and controls. If the ITE distribution equals the CATE distribution, this difference in variance should be small. If they differ, an additional causal assumption is necessary to quantify the heterogeneity not captured by the CATE distribution. The conditional variance of the ITE can be identified when the individual effect is independent of the outcome under no treatment given the measured features. Then, in the cases where the ITE and CATE distributions differ, the extended CRF can appropriately estimate the characteristics of the ITE distribution while the CRF fails to do so. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.16547&r=ecm |
| By: | Eric Gautier (TSE); Christiern Rose (UQ) |
| Abstract: | We propose and implement an approach to inference in linear instrumental variables models which is simultaneously robust and computationally tractable. Inference is based on self-normalization of sample moment conditions, and allows for (but does not require) many (relative to the sample size), weak, potentially invalid or potentially endogenous instruments, as well as for many regressors and conditional heteroskedasticity. Our coverage results are uniform and can deliver a small sample guarantee. We develop a new computational approach based on semidefinite programming, which we show can equally be applied to rapidly invert existing tests (e.g,. AR, LM, CLR, etc.). |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.02249&r=ecm |
| By: | Paulo M.M. Rodrigues; Matei Demetrescu; Mehdi Hosseinkouchack |
| Abstract: | This paper shows that cross-sectional dependence (CSD) is an indicator of misspecification in panel QR rather than just a nuisance that may be accounted for with panel-robust standard errors. This motivates the development of a novel test for panel QR misspecification based on detecting CSD. The test possesses a standard normal limiting distribution under joint N; T asymptotics with restrictions on the relative rate at which N and T go to infinity. A finitesample correction improves the applicability of the test for panels with larger N. An empirical application illustrates the use of the proposed cross-sectional dependence test. |
| JEL: | C12 C23 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:ptu:wpaper:w202213&r=ecm |
| By: | Kotlyarova, Yulia; Schafgans, Marcia M.A.; Zinde-Walsh, Victoria |
| Abstract: | In this paper, we summarize results on convergence rates of various kernel based non- and semiparametric estimators, focusing on the impact of insufficient distributional smoothness, possibly unknown smoothness and even non-existence of density. In the presence of a possible lack of smoothness and the uncertainty about smoothness, methods of safeguarding against this uncertainty are surveyed with emphasis on nonconvex model averaging. This approach can be implemented via a combined estimator that selects weights based on minimizing the asymptotic mean squared error. In order to evaluate the finite sample performance of these and similar estimators we argue that it is important to account for possible lack of smoothness. |
| Keywords: | combined estimator; convergence rates; degree of smoothness; kernel based estimation; model averaging; nonparametric estimation |
| JEL: | J1 N0 |
| Date: | 2021–11–18 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:113436&r=ecm |
| By: | John Cai; Weinan Wang |
| Abstract: | To effectively optimize and personalize treatments, it is necessary to investigate the heterogeneity of treatment effects. With the wide range of users being treated over many online controlled experiments, the typical approach of manually investigating each dimension of heterogeneity becomes overly cumbersome and prone to subjective human biases. We need an efficient way to search through thousands of experiments with hundreds of target covariates and hundreds of breakdown dimensions. In this paper, we propose a systematic paradigm for detecting, surfacing and characterizing heterogeneous treatment effects. First, we detect if treatment effect variation is present in an experiment, prior to specifying any breakdowns. Second, we surface the most relevant dimensions for heterogeneity. Finally, we characterize the heterogeneity beyond just the conditional average treatment effects (CATE) by studying the conditional distributions of the estimated individual treatment effects. We show the effectiveness of our methods using simulated data and empirical studies. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.01547&r=ecm |
| By: | Takuya Ishihara; Daisuke Kurisu |
| Abstract: | This study examines the problem of determining whether to treat individuals based on observed covariates. The most common decision rule is the conditional empirical success (CES) rule proposed by Manski (2004), which assigns individuals to treatments that yield the best experimental outcomes conditional on observed covariates. By contrast, using shrinkage estimators, which shrink unbiased but noisy preliminary estimates toward the average of these estimates, is a common approach in statistical estimation problems because it is well-known that shrinkage estimators have smaller mean squared errors than unshrunk estimators. Inspired by this idea, we propose a computationally tractable shrinkage rule that selects the shrinkage factor by minimizing an upper bound of the maximum regret. Then, we compare the maximum regret of the proposed shrinkage rule with that of CES and pooling rules when the parameter space is correctly specified and misspecified. The theoretical and numerical results show that our shrinkage rule performs well in many cases when the parameter space is correctly specified. In addition, we show that the results are robust against the misspecification of the parameter space. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.17063&r=ecm |
| By: | Chris Muris; Konstantin Wacker |
| Abstract: | A common task in empirical economics is to estimate \emph{interaction effects} that measure how the effect of one variable $X$ on another variable $Y$ depends on a third variable $H$. This paper considers the estimation of interaction effects in linear panel models with a fixed number of time periods. There are at least two ways to estimate interaction effects in this setting, both common in applied work. Our theoretical results show that these two approaches are distinct, and only coincide under strong conditions on unobserved effect heterogeneity. Our empirical results show that the difference between the two approaches is large, leading to conflicting conclusions about the sign of the interaction effect. Taken together, our findings may guide the choice between the two approaches in empirical work. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.01557&r=ecm |
| By: | Bansak, Kirk; Nowacki, Tobias |
| Abstract: | Research investigating subgroup differences in treatment effects recovered using regression discontinuity (RD) designs has become increasingly popular. For in- stance, scholars have investigated whether incumbency effects on candidate per- sistence or winning again vary by candidate characteristics (e.g., gender) or local context. Under what conditions can we interpret subgroup differences in treat- ment effects as a causal result of the moderating characteristic? In this study, we explore the difference between RD effect conditionality that is simply associated with versus causally driven by another variable. To make this distinction explicit and formal, we define two alternative estimands and lay out identification as- sumptions required for each, along with corresponding estimation procedures. In doing so, we highlight how investigating RD effect conditionality that is causally driven by another variable involves several additional challenges related to in- terpretation, identification, and estimation. We apply our framework to recent studies and offer practical advice for applied researchers considering these alter- native quantities of interest. |
| Date: | 2022–06–29 |
| URL: | http://d.repec.org/n?u=RePEc:osf:socarx:vj34m&r=ecm |
| By: | Xiao Huang |
| Abstract: | Assessing the statistical significance of parameter estimates is an important step in high-dimensional vector autoregression modeling. Using the least-squares boosting method, we compute the p-value for each selected parameter at every boosting step in a linear model. The p-values are asymptotically valid and also adapt to the iterative nature of the boosting procedure. Our simulation experiment shows that the p-values can keep false positive rate under control in high-dimensional vector autoregressions. In an application with more than 100 macroeconomic time series, we further show that the p-values can not only select a sparser model with good prediction performance but also help control model stability. A companion R package boostvar is developed. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.02215&r=ecm |
| By: | Härtl, Tilmann |
| JEL: | C32 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc22:264071&r=ecm |
| By: | Beiser-McGrath, Liam F. |
| Abstract: | When separation is a problem in binary dependent variable models, many researchers use Firth's penalized maximum likelihood in order to obtain finite estimates (Firth, 1993; Zorn, 2005; Rainey, 2016). In this paper, I show that this approach can lead to inferences in the opposite direction of the separation when the number of observations are sufficiently large and both the dependent and independent variables are rare events. As large datasets with rare events are frequently used in political science, such as dyadic data measuring interstate relations, a lack of awareness of this problem may lead to inferential issues. Simulations and an empirical illustration show that the use of independent weakly-informative prior distributions centered at zero, for example, the Cauchy prior suggested by Gelman et al. (2008), can avoid this issue. More generally, the results caution researchers to be aware of how the choice of prior interacts with the structure of their data, when estimating models in the presence of separation. |
| Keywords: | Bayesian; categorical data analysis; discrete choice models |
| JEL: | C1 |
| Date: | 2020–12–11 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:117222&r=ecm |
| By: | Yuya Sasaki; Yulong Wang |
| Abstract: | The conventional cluster-robust (CR) standard errors may not be robust. They are vulnerable to data that contain a small number of large clusters. When a researcher uses the 51 states in the U.S. as clusters, the largest cluster (California) consists of about 10\% of the total sample. Such a case in fact violates the assumptions under which the widely used CR methods are guaranteed to work. We formally show that the conventional CR method fails if the distribution of cluster sizes follows a power law with exponent less than two. Besides the example of 51 state clusters, some examples are drawn from a list of recent original research articles published in a top journal. In light of these negative results about the existing CR methods, we propose a weighted CR (WCR) method as a simple fix. Simulation studies support our arguments that the WCR method is robust while the conventional CR method is not. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.16991&r=ecm |
| By: | Tamimy, Zenab; van Bergen, Elsje (Vrije Universiteit Amsterdam); van der Zee, Matthijs D.; Dolan, Conor V.; Nivard, Michel Guillaume (Vrije Universiteit) |
| Abstract: | We present the Multi Co-moment Structural Equation Model (MCM-SEM), a novel approach to estimating the direction and magnitude of causal effects in the presence of confounding. In MCM-SEM, not only covariance structures but also co-skewness and co-kurtosis structures are leveraged. Co-skewness and co-kurtosis provide information on the joint non-normality. In large scale non-normally distributed data, we can use these higher-order co-moments to identify and estimate both bidirectional causal effects and latent confounding effects, which would not have been identified in regular SEM. We performed an extensive simulation study which showed that MCM-SEM correctly reveals the direction of causality in the presence of confounding. Subsequently, we applied the model empirically to data of (1) height and weight and to (2) education and income, and compared the results to those obtained through instrumental variable regression. In the empirical application, MCM-SEM yielded expected results for (1), but also highlighted some caveats when applied to (2). We provide an MCM-SEM R-package and recommendations for future use. |
| Date: | 2022–06–30 |
| URL: | http://d.repec.org/n?u=RePEc:osf:socarx:ynam2&r=ecm |
| By: | Tzougas, George; Makariou, Despoina |
| Abstract: | We introduce a multivariate Poisson-Generalized Inverse Gaussian regression model with varying dispersion and shape for modeling different types of claims and their associated counts in nonlife insurance. The multivariate Poisson-Generalized Inverse Gaussian regression model is a general class of models which, under the approach adopted herein, allows us to account for overdispersion and positive correlation between the claim count responses in a flexible manner. For expository purposes, we consider the bivariate Poisson-Generalized Inverse Gaussian with regression structures on the mean, dispersion, and shape parameters. The model's implementation is demonstrated by using bodily injury and property damage claim count data from a European motor insurer. The parameters of the model are estimated via the Expectation-Maximization algorithm which is computationally tractable and is shown to have a satisfactory performance. |
| JEL: | F3 G3 M40 J1 |
| Date: | 2022–10–17 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:117197&r=ecm |
| By: | Toru Kitagawa; Hugo Lopez; Jeff Rowley |
| Abstract: | This paper proposes a novel method to estimate individualised treatment assignment rules. The method is designed to find rules that are stochastic, reflecting uncertainty in estimation of an assignment rule and about its welfare performance. Our approach is to form a prior distribution over assignment rules and to update this prior based upon an empirical welfare criterion. The social planner then assigns treatment by drawing a policy from the resulting posterior. We show analytically a welfare-optimal way of updating the prior using empirical welfare. The posterior obtained by implementing the optimal updating rule is not feasible to compute, so we propose a variational Bayes approximation for the optimal posterior. We characterise the welfare regret convergence of the assignment rule based upon this variational Bayes approximation and show that it converges to zero at a rate of ln(n)/sqrt(n). We apply our methods to experimental data from the Job Training Partnership Act Study and extensive numerical simulations to illustrate the implementation of our methods. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.01537&r=ecm |
| By: | Fève, Patrick; Beaudry, Paul; Collard, Fabrice; Guay, Alain; Portier, Franck |
| Abstract: | Most macroeconomic models, both fully structural models as well as SVAR models, view economic outcomes as the product of a combination of endogenous and exogenous dynamic forces. In particular, the exogenous forces are generally modeled as a set of linearly independent dynamics processes. In this paper we begin by showing that this dual dynamic structure is sufficient to identify the entire set of structural impulse responses inherent to any such model. No extra restrictions are necessary. We then use this observation to suggest how it can be used to evaluate common SVAR restrictions (impact restrictions, long-run restrictions and proxy-VAR), as well as help transpire the role of cross-equation restrictions inherent to more structural models. |
| Keywords: | Structural Shocks; Dynamic Identification; SVARs; DSGE models |
| JEL: | C32 E32 |
| Date: | 2022–11–18 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:127516&r=ecm |
| By: | Maciej Wysocki (University of Warsaw, Faculty of Economic Sciences; Quantitative Finance Research Group); Paweł Sakowski (University of Warsaw, Faculty of Economic Sciences; Quantitative Finance Research Group) |
| Abstract: | This paper investigates an important problem of an appropriate variance-covariance matrix estimation in the Modern Portfolio Theory. In this study we propose a novel framework for variance-covariance matrix estimation for purposes of the portfolio optimization, which is based on deep learning models. We employ the long short-term memory (LSTM) recurrent neural networks (RNN) along with two probabilistic deep learning models: DeepVAR and GPVAR to the task of one-day ahead multivariate forecasting. We then use these forecasts to optimize portfolios that consisted of stocks and cryptocurrencies. Our analysis presents results across different combinations of observation windows and rebalancing periods to compare performances of classical and deep learning variance-covariance estimation methods. The conclusions of the study are that although the strategies (portfolios) performance differed significantly between different combinations of parameters, generally the best results in terms of the information ratio and annualized returns are obtained using the LSTM-RNN models. Moreover, longer observation windows translate into better performance of the deep learning models indicating that these methods require longer windows to be able to efficiently capture the long-term dependencies of the variance-covariance matrix structure. Strategies with less frequent rebalancing typically perform better than these with the shortest rebalancing windows across all considered methods. |
| Keywords: | Portfolio Optimization, Deep Learning, Variance-Covariance Matrix Forecasting, Investment Strategies, Recurrent Neural Networks, Long Short-Term Memory Neural Networks |
| JEL: | C4 C14 C45 C53 C58 G11 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:war:wpaper:2022-12&r=ecm |
| By: | Darjus Hosszejni; Sylvia Fr\"uhwirth-Schnatter |
| Abstract: | Despite the popularity of factor models with sparse loading matrices, little attention has been given to formally address identifiability of these models beyond standard rotation-based identification such as the positive lower triangular constraint. To fill this gap, we present a counting rule on the number of nonzero factor loadings that is sufficient for achieving generic uniqueness of the variance decomposition in the factor representation. This is formalized in the framework of sparse matrix spaces and some classical elements from graph and network theory. Furthermore, we provide a computationally efficient tool for verifying the counting rule. Our methodology is illustrated for real data in the context of post-processing posterior draws in Bayesian sparse factor analysis. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.00671&r=ecm |