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on Econometrics |
| By: | Max Welz |
| Abstract: | In empirical science, many variables of interest are categorical. Like any model, models for categorical responses can be misspecified, leading to possibly large biases in estimation. One particularly troublesome source of misspecification is inattentive responding in questionnaires, which is well-known to jeopardize the validity of structural equation models (SEMs) and other survey-based analyses. I propose a general estimator that is designed to be robust to misspecification of models for categorical responses. Unlike hitherto approaches, the estimator makes no assumption whatsoever on the degree, magnitude, or type of misspecification. The proposed estimator generalizes maximum likelihood estimation, is strongly consistent, asymptotically Gaussian, has the same time complexity as maximum likelihood, and can be applied to any model for categorical responses. In addition, I develop a novel test that tests whether a given response can be fitted well by the assumed model, which allows one to trace back possible sources of misspecification. I verify the attractive theoretical properties of the proposed methodology in Monte Carlo experiments, and demonstrate its practical usefulness in an empirical application on a SEM of personality traits, where I find compelling evidence for the presence of inattentive responding whose adverse effects the proposed estimator can withstand, unlike maximum likelihood. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.11954&r=ecm |
| By: | Yuya Shimizu |
| Abstract: | This paper develops a general asymptotic theory for nonparametric kernel regression in the presence of cluster dependence. We examine nonparametric density estimation, Nadaraya-Watson kernel regression, and local linear estimation. Our theory accommodates growing and heterogeneous cluster sizes. We derive asymptotic conditional bias and variance, establish uniform consistency, and prove asymptotic normality. Our findings reveal that under heterogeneous cluster sizes, the asymptotic variance includes a new term reflecting within-cluster dependence, which is overlooked when cluster sizes are presumed to be bounded. We propose valid approaches for bandwidth selection and inference, introduce estimators of the asymptotic variance, and demonstrate their consistency. In simulations, we verify the effectiveness of the cluster-robust bandwidth selection and show that the derived cluster-robust confidence interval improves the coverage ratio. We illustrate the application of these methods using a policy-targeting dataset in development economics. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.04766&r=ecm |
| By: | Rong J. B. Zhu; Weiwei Jiang |
| Abstract: | Treatment effects in regression discontinuity designs (RDDs) are often estimated using local regression methods. However, global approximation methods are generally deemed inefficient. In this paper, we propose a semiparametric framework tailored for estimating treatment effects in RDDs. Our global approach conceptualizes the identification of treatment effects within RDDs as a partially linear modeling problem, with the linear component capturing the treatment effect. Furthermore, we utilize the P-spline method to approximate the nonparametric function and develop procedures for inferring treatment effects within this framework. We demonstrate through Monte Carlo simulations that the proposed method performs well across various scenarios. Furthermore, we illustrate using real-world datasets that our global approach may result in more reliable inference. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.05803&r=ecm |
| By: | Mario Fiorini; Wooyong Lee; Gregor Pfeifer; Gregor-Gabriel Pfeifer |
| Abstract: | We establish identifying assumptions and estimation procedures for the ATT in a Difference-in-Differences setting with staggered treatment adoption in the presence of spillovers. We show that the ATT can be estimated by a simple TWFE method that extends the approach of Wooldridge [2022]’s fully interacted regression model. We broaden our framework to the non-linear case of count data, offering estimation of the ATT by a simple TWFE Poisson model, and we revisit a corresponding application from the crime literature. Monte Carlo simulations show that our estimator performs competitively. |
| Keywords: | difference-in-differences, staggered treatment adoption, spillovers, (non-)linear models |
| Date: | 2024 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_11011&r=ecm |
| By: | Aknouche, Abdelhakim; Almohaimeed, Bader; Dimitrakopoulos, Stefanos |
| Abstract: | This paper proposes a noisy GARCH model with two volatility sequences (an unobserved and an observed one) and a stochastic time-varying conditional kurtosis. The unobserved volatility equation, equipped with random coefficients, is a linear function of the past squared observations and of the past observed volatility. The observed volatility is the conditional mean of the unobserved volatility, thus following the standard GARCH specification, where its coefficients are equal to the means of the random coefficients. The means and the variances of the random coefficients as well as the unobserved volatilities are estimated using a three-stage procedure. First, we estimate the means of the random coefficients, using the Gaussian quasi-maximum likelihood estimator (QMLE), then, the variances of the random coefficients, using a weighted least squares estimator (WLSE), and finally the latent volatilities through a filtering process, under the assumption that the random parameters follow an Inverse Gaussian distribution, with the innovation being normally distributed. Hence, the conditional distribution of the model is the Normal Inverse Gaussian (NIG), which entails a closed form expression for the posterior mean of the unobserved volatility. Consistency and asymptotic normality of the QMLE and WLSE are established under quite tractable assumptions. The proposed methodology is illustrated with various simulated and real examples. |
| Keywords: | Noised volatility GARCH, Randon coefficient GARCH, Markov switching GARCH, QMLE, Weighted least squares, filtering volatility, time-varying conditional kurtosis. |
| JEL: | C13 C22 C51 C58 |
| Date: | 2024–03–15 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:120456&r=ecm |
| By: | Silvia Goncalves; Serena Ng |
| Abstract: | A crucial input into causal inference is the imputed counterfactual outcome. Imputation error can arise because of sampling uncertainty from estimating the prediction model using the untreated observations, or from out-of-sample information not captured by the model. While the literature has focused on sampling uncertainty, it vanishes with the sample size. Often overlooked is the possibility that the out-of-sample error can be informative about the missing counterfactual outcome if it is mutually or serially correlated. Motivated by the best linear unbiased predictor (\blup) of \citet{goldberger:62} in a time series setting, we propose an improved predictor of potential outcome when the errors are correlated. The proposed \pup\; is practical as it is not restricted to linear models, can be used with consistent estimators already developed, and improves mean-squared error for a large class of strong mixing error processes. Ignoring predictability in the errors can distort conditional inference. However, the precise impact will depend on the choice of estimator as well as the realized values of the residuals. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.08130&r=ecm |
| By: | Jean-Baptiste Bonnier (Université de Franche-Comté, CRESE, UR3190, F-25000 Besançon, France) |
| Abstract: | I devise a difference-in-differences design that accounts for the possibility that some treatment effect is split in the reactions to two or more events. At the intersection of settings with a single treatment and with multiple treatments, regression-based methods for this split-treatment design can be subject both to negative weights and contamination bias. I propose a simple solution, a first-difference regression with sample constraints in the spirit of Dube et al.’s (2023) LP-DiD, that allows to identify and estimate sensible causal parameters of interest. This estimator is efficient under random walk errors and unrestricted heterogeneity across groups and events. |
| Keywords: | Difference-in-differences, Heterogeneous treatment effects, Multiple treatments, Contamination bias. |
| JEL: | C21 C23 |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:crb:wpaper:2024-11&r=ecm |
| By: | Martín Almuzara; Víctor Sancibrián |
| Abstract: | We study estimation and inference in panel data regression models when the regressors of interest are macro shocks, which speaks to a large empirical literature that targets impulse responses via local projections. Our results hold under general dynamics and are uniformly valid over the degree of signal-to-noise of aggregate shocks. We show that the regression scores feature strong cross-sectional dependence and a known autocorrelation structure induced only by leads of the regressor. In general, including lags as controls and then clustering over the cross-section leads to simple, robust inference. |
| Keywords: | panel data; local projections; impulse responses; aggregate shocks; inference; heterogeneity |
| JEL: | C32 C33 C38 C51 |
| Date: | 2024–03–01 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fednsr:97956&r=ecm |
| By: | Raghavendra Addanki; Siddharth Bhandari |
| Abstract: | Average Treatment Effect (ATE) estimation is a well-studied problem in causal inference. However, it does not necessarily capture the heterogeneity in the data, and several approaches have been proposed to tackle the issue, including estimating the Quantile Treatment Effects. In the finite population setting containing $n$ individuals, with treatment and control values denoted by the potential outcome vectors $\mathbf{a}, \mathbf{b}$, much of the prior work focused on estimating median$(\mathbf{a}) -$ median$(\mathbf{b})$, where median($\mathbf x$) denotes the median value in the sorted ordering of all the values in vector $\mathbf x$. It is known that estimating the difference of medians is easier than the desired estimand of median$(\mathbf{a-b})$, called the Median Treatment Effect (MTE). The fundamental problem of causal inference -- for every individual $i$, we can only observe one of the potential outcome values, i.e., either the value $a_i$ or $b_i$, but not both, makes estimating MTE particularly challenging. In this work, we argue that MTE is not estimable and detail a novel notion of approximation that relies on the sorted order of the values in $\mathbf{a-b}$. Next, we identify a quantity called variability that exactly captures the complexity of MTE estimation. By drawing connections to instance-optimality studied in theoretical computer science, we show that every algorithm for estimating the MTE obtains an approximation error that is no better than the error of an algorithm that computes variability. Finally, we provide a simple linear time algorithm for computing the variability exactly. Unlike much prior work, a particular highlight of our work is that we make no assumptions about how the potential outcome vectors are generated or how they are correlated, except that the potential outcome values are $k$-ary, i.e., take one of $k$ discrete values. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.10618&r=ecm |
| By: | Adam Lee |
| Abstract: | This paper considers hypothesis testing in semiparametric models which may be non-regular. I show that C($\alpha$) style tests are locally regular under mild conditions, including in cases where locally regular estimators do not exist, such as models which are (semi-parametrically) weakly identified. I characterise the appropriate limit experiment in which to study local (asymptotic) optimality of tests in the non-regular case, permitting the generalisation of classical power bounds to this case. I give conditions under which these power bounds are attained by the proposed C($\alpha$) style tests. The application of the theory to a single index model and an instrumental variables model is worked out in detail. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.05999&r=ecm |
| By: | Michael P. Leung |
| Abstract: | In settings with interference, it is common to utilize estimands defined by exposure mappings to summarize the impact of variation in treatment assignments local to the ego. This paper studies their causal interpretation under weak restrictions on interference. We demonstrate that the estimands can exhibit unpalatable sign reversals under conventional identification conditions. This motivates the formulation of sign preservation criteria for causal interpretability. To satisfy preferred criteria, it is necessary to impose restrictions on interference, either in potential outcomes or selection into treatment. We provide sufficient conditions and show that they are satisfied by a nonparametric model allowing for a complex form of interference in both the outcome and selection stages. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.08183&r=ecm |
| By: | Jonathan Fuhr (School of Business and Economics, University of T\"ubingen); Philipp Berens (Hertie Institute for AI in Brain Health, University of T\"ubingen); Dominik Papies (School of Business and Economics, University of T\"ubingen) |
| Abstract: | The estimation of causal effects with observational data continues to be a very active research area. In recent years, researchers have developed new frameworks which use machine learning to relax classical assumptions necessary for the estimation of causal effects. In this paper, we review one of the most prominent methods - "double/debiased machine learning" (DML) - and empirically evaluate it by comparing its performance on simulated data relative to more traditional statistical methods, before applying it to real-world data. Our findings indicate that the application of a suitably flexible machine learning algorithm within DML improves the adjustment for various nonlinear confounding relationships. This advantage enables a departure from traditional functional form assumptions typically necessary in causal effect estimation. However, we demonstrate that the method continues to critically depend on standard assumptions about causal structure and identification. When estimating the effects of air pollution on housing prices in our application, we find that DML estimates are consistently larger than estimates of less flexible methods. From our overall results, we provide actionable recommendations for specific choices researchers must make when applying DML in practice. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.14385&r=ecm |
| By: | Yunyun Wang; Tatsushi Oka; Dan Zhu |
| Abstract: | Macro variables frequently display time-varying distributions, driven by the dynamic and evolving characteristics of economic, social, and environmental factors that consistently reshape the fundamental patterns and relationships governing these variables. To better understand the distributional dynamics beyond the central tendency, this paper introduces a novel semi-parametric approach for constructing time-varying conditional distributions, relying on the recent advances in distributional regression. We present an efficient precision-based Markov Chain Monte Carlo algorithm that simultaneously estimates all model parameters while explicitly enforcing the monotonicity condition on the conditional distribution function. Our model is applied to construct the forecasting distribution of inflation for the U.S., conditional on a set of macroeconomic and financial indicators. The risks of future inflation deviating excessively high or low from the desired range are carefully evaluated. Moreover, we provide a thorough discussion about the interplay between inflation and unemployment rates during the Global Financial Crisis, COVID, and the third quarter of 2023. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.12456&r=ecm |
| By: | Tomiyama, Hideyuki; Otsu, Taisuke |
| Abstract: | By extending de Paula and Tang (2012) and Aradillas-López and Gandhi (2016), we derive testable restrictions for uniqueness of equilibrium in games with multi-dimensional actions. We discuss two models of payoff functions which imply certain covariance restrictions for players’ actions. These restrictions can be used to construct an identified set of strategic parameters under multiple equilibria. |
| Keywords: | multiple equilibria; partial identification; moment inequalities |
| JEL: | C14 |
| Date: | 2022–06–01 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:114341&r=ecm |
| By: | Liang, Yuli (Department of Economics and Statistics); Hao, Chengcheng (Departmet of Data Science, School of Statistics and Information, Shanghai University of International Business and Economics, China); Dai, Deliang (Department of Economics and Statistics) |
| Abstract: | Under a model having a Kronecker product covariance structure with compound symmetry or circular symmetry, two-sample hypothesis testing for the equality of two correlation parameters is considered. Different tests are proposed by using the ratio of independent F distributions. Several tests are compared with the proposed ones and practical recommendations are made based on their type I error probabilities and powers. Finally, all mentioned tests are applied to a real data example. |
| Keywords: | Kronecker covariance structure; Higher order asymptotics; Ratio of F distributions |
| JEL: | C12 |
| Date: | 2024–03–25 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:vxesta:2024_006&r=ecm |
| By: | Martin Lettau |
| Abstract: | This paper proposes latent factor models for multidimensional panels called 3D-PCA. Factor weights are constructed from a small set of dimension-specific building blocks, which give rise to proportionality restrictions of factor weights. While the set of feasible factors is restricted, factors with long/short structures often found in pricing factors are admissible. I estimate the model using a 3-dimensional data set of double-sorted portfolios of 11 characteristics. Factors estimated by 3D-PCA have higher Sharpe ratios and smaller cross-sectional pricing errors than models with PCA or Fama-French factors. Since factor weights are subject to restrictions, the number of free parameters is small. Consequently, the model produces robust results in short time series and performs well in recursive out-of-sample estimations. |
| JEL: | C38 G0 G12 |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:32261&r=ecm |
| By: | Roberto Leon-Gonzalez (National Graduate Institute for Policy Studies, Japan; Rimini Centre for Economic Analysis); Blessings Majoni (National Graduate Institute for Policy Studies, Japan) |
| Abstract: | Common factor stochastic volatility (CSV) models capture the commonality that is often observed in volatility patterns. However, they assume that all the time variation in volatility is driven by a single multiplicative factor. This paper has two contributions. Firstly we develop a novel CSV model in which the volatility follows an inverse gamma process (CSV-IG), which implies fat Student’s t tails for the observed data. We obtain an analytic expression for the likelihood of this CSV model, which facilitates the numerical calculation of the marginal and predictive likelihood for model comparison. We also show that it is possible to simulate exactly from the posterior distribution of the volatilities using mixtures of gammas. Secondly, we generalize this CSV-IG model by parsimoniously substituting conditionally homoscedastic shocks with heteroscedastic factors which interact multiplicatively with the common factor in an approximate factor model (CSV-IG-AF). In empirical applications we compare these models to other multivariate stochastic volatility models, including different types of CSV models and exact factor stochastic volatility (FSV) models. The models are estimated using daily exchange rate returns of 8 currencies. A second application estimates the models using 20 macroeconomic variables for each of four countries: US, UK, Japan and Brazil. The comparison method is based on the predictive likelihood. In the application to exchange rate data we find strong evidence of CSV and that the best model is the IG-CSV-AF. In the Macro application we find that 1) the CSV-IG model performs better than all other CSV models, 2) the CSV-IG-AF is the best model for the US, 3) the CSV-IG is the best model for Brazil and 4) exact factor SV models are the best for UK and JP. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:24-04&r=ecm |
| By: | Joseph Briggs (Goldman Sachs); Andrew Chaplin (New York University, NBER); Soeren Leth-Petersen (Department of Economics, University of Copenhagen); Christopher Tonetti (Stanford Graduate School of Business, NBER) |
| Abstract: | We develop a method to identify the individual latent propensity to select into treatment and marginal treatment effects. Identification is achieved with survey data on individuals’ subjective expectations of their treatment propensity and of their treatmentcontingent outcomes. We use the method to study how child birth affects female labor supply in Denmark. We find limited latent heterogeneity and large short-term effects that vanish by 18 months after birth. We support the validity of the identifying assumptions in this context by using administrative data to show that the average treatment effect on the treated computed using our method and traditional event-study methods are nearly equal. Finally, we study the effects of counterfactual changes to child care cost and quality on female labor supply. |
| Keywords: | marginal treatment effects, survey data, expectations |
| JEL: | C32 C52 C83 J13 J22 |
| Date: | 2024–04–11 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kucebi:2406&r=ecm |
| By: | Jeff Dominitz; Charles F. Manski |
| Abstract: | We argue that comprehensive out-of-sample (OOS) evaluation using statistical decision theory (SDT) should replace the current practice of K-fold and Common Task Framework validation in machine learning (ML) research. SDT provides a formal framework for performing comprehensive OOS evaluation across all possible (1) training samples, (2) populations that may generate training data, and (3) populations of prediction interest. Regarding feature (3), we emphasize that SDT requires the practitioner to directly confront the possibility that the future may not look like the past and to account for a possible need to extrapolate from one population to another when building a predictive algorithm. SDT is simple in abstraction, but it is often computationally demanding to implement. We discuss progress in tractable implementation of SDT when prediction accuracy is measured by mean square error or by misclassification rate. We summarize research studying settings in which the training data will be generated from a subpopulation of the population of prediction interest. We also consider conditional prediction with alternative restrictions on the state space of possible populations that may generate training data. We conclude by calling on ML researchers to join with econometricians and statisticians in expanding the domain within which implementation of SDT is tractable. |
| JEL: | C44 C45 C53 |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:32269&r=ecm |
| By: | Janoś Gabler; Sebastian Gsell; Tim Mensinger; Mariam Petrosyan |
| Abstract: | We propose the tranquilo algorithm, a trust-region optimizer that aims to facilitate optimization problems that arise during the method of simulated moments estimation (MSM). The algorithm is particularly suited for this type of problem as it (1) can utilize the least-squares structure of the MSM problem, (2) can be parallelized on the level of the algorithm, and (3) can adaptively deal with noise in the objective function. The adaptive nature of tranquilo makes it particularly suited for domain experts such as statisticians and social science researchers without extensive training in numerical optimization. Extensive benchmarks show that tranquilo is competitive with state-of-the-art algorithms in noise-free settings and outperforms them in the presence of substantial noise. |
| Keywords: | derivative-free optimization, least-squares, trust region methods, stochastic optimization, mathematical software, method of simulated moments estimation |
| JEL: | C61 |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2024_522&r=ecm |