
on Econometrics 
By:  Yicong Lin (Vrije Universiteit Amsterdam); Hanno Reuvers (Erasmus University Rotterdam) 
Abstract:  We study a set of fully modified (FM) estimators in multivariate cointegrating polynomial regressions. Such regressions allow for deterministic trends, stochastic trends, and integer powers of stochastic trends to enter the cointegrating relations. A new feasible generalized least squares estimator is proposed. Our estimator incorporates: (1) the inverse autocovariance matrix of multidimensional errors and (2) secondorder bias corrections. The resulting estimator has the intuitive interpretation of applying a weighted least squares objective function to filtered data series. Moreover, the required secondorder bias corrections are convenient byproducts of our approach and lead to a conventional asymptotic inference. Based on different FM estimators, multiple multivariate KPSStype of tests for the null of cointegration are constructed. We then undertake a comprehensive Monte Carlo study to compare the performance of the FM estimators and the related tests. We find good performance of the proposed estimator and the implied test statistics for linear hypotheses and cointegration. 
Keywords:  Cointegrating Polynomial Regression, Cointegration Testing, Fully Modified Estimation, Generalized Least Squares 
JEL:  C12 C13 C32 
Date:  2022–12–15 
URL:  http://d.repec.org/n?u=RePEc:tin:wpaper:20220093&r=ecm 
By:  JeanPierre Florens; Elia Lapenta 
Abstract:  We consider a semiparametric partly linear model identified by instrumental variables. We propose an estimation method that does not smooth on the instruments and we extend the LandweberFridman regularization scheme to the estimation of this semiparametric model. We then show the asymptotic normality of the parametric estimator and obtain the convergence rates for the nonparametric estimator. Our estimator that does not smooth on the instruments coincides with a typical estimator that does smooth on the instruments but keeps the respective bandwidth fixed as the sample size increases. We propose a data driven method for the selection of the regularization parameter, and in a simulation study we show the attractive performance of our estimators. 
Date:  2022–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2212.11012&r=ecm 
By:  Wagner, Martin (Department of Economics University of Klagenfurt, Austria, Bank of Slovenia Ljubljana, Slovenia and Institute for Advanced Studies Vienna, Austria) 
Abstract:  We consider fully modified least squares estimation for systems of cointegrating polynomial regressions, i. e., systems of regressions that include deterministic variables, integrated processes and their powers as regressors. The errors are allowed to be correlated across equations, over time and with the regressors. Whilst, of course, fully modified OLS and GLS estimation coincide â€“ for any regular weighting matrix â€“ without restrictions on the parameters and with the same regressors in all equations, this equivalence breaks down, in general, in case of parameter restrictions and/or different regressors across equations. Consequently, we discuss in detail restricted fully modified GLS estimators and inference based upon them. 
Keywords:  Fully Modified Estimation, Cointegrating Polynomial Regression, Generalized, Least Squares, Hypothesis Testing 
JEL:  C12 C13 Q20 
Date:  2023–01 
URL:  http://d.repec.org/n?u=RePEc:ihs:ihswps:44&r=ecm 
By:  Elia Lapenta 
Abstract:  This paper provides a specification test for semiparametric models with nonparametrically generated regressors. Such variables are not observed by the researcher but are nonparametrically identified and estimable. Applications of the test include models with endogenous regressors identified by control functions, semiparametric sample selection models, or binary games with incomplete information. The statistic is built from the residuals of the semiparametric model. A novel wild bootstrap procedure is shown to provide valid critical values. We consider nonparametric estimators with an automatic bias correction that makes the test implementable without undersmoothing. In simulations the test exhibits good small sample performances, and an application to women's labor force participation decisions shows its implementation in a real data context. 
Date:  2022–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2212.11112&r=ecm 
By:  Costanza Naguib; Patrick Gagliardini 
Abstract:  In this paper we develop a novel seminonparametric panel copula model with external covariates for the study of wage rank dynamics. We focus on nonlinear dependence between the current and lagged worker’s ranks in the wage residuals distribution, conditionally on individual characteristics. We show the asymptotic normality of the Sieve estimator for our preferred mobility measure, which is an irregular functional of both the finite and infinitedimensional parameters, in the double asymptotics with N, T ?8. We derive an analytical bias correction for the incidental parameters bias induced by the individual fixedeffects. We apply our model to US data and we find that relative mobility at the bottom of the distribution is high for workers with a college degree and some experience. On the contrary, lesseducated individuals are likely to remain stuck at the bottom of the wage rank distribution year after year. 
Keywords:  Wage dynamics, rank, functional copula model, nonlinear autoregressive process, Sieve seminonparametric estimation 
JEL:  C14 J31 
Date:  2023–01 
URL:  http://d.repec.org/n?u=RePEc:ube:dpvwib:dp2302&r=ecm 
By:  Ben Jann; Karlson, Kristian Bernt 
Abstract:  Coefficients from logistic regression are affected by noncollapsibility, which means that the comparison of coefficients across models may be misleading. Several strategies have been proposed in the literature to respond to these difficulties, the most popular of which is to report average marginal effects (on the probability scale) rather than odds ratios. Average marginal effects (AMEs) have many desirable properties but at least in part they throw the baby out with the bathwater. The size of an AME strongly depends on the marginal distribution of the dependent variable; for events that are very likely or very unlikely the AME necessarily has to be small because the probability space is bounded. Logistic regression, in contrast, estimates odds ratios which are free from such flooring and ceiling effects. Hence, odds ratios may be more appropriate than AMEs for comparison of effect sizes in many applications. Yet, logistic regression estimates conditional odds ratios, which are not comparable across different specifications. In this paper, we aim to remedy the declining popularity of the odds ratio by introducing an estimand that we term the "marginal odds ratio"; that is, logit coefficients that have properties similar to AMEs, but which retain the odds ratio interpretation. We define the marginal odds ratio theoretically in terms of potential outcomes, both for binary and continuous treatments, we develop estimation methods using three different approaches (Gcomputation, inverse probability weighting, RIF regression), and we present an example that illustrates the usefulness and interpretation of the marginal odds ratio. 
Keywords:  marginal odds ratio, noncollapsibility, logistic regression, Gcomputation, inverse probability weighting, recentered influence functions 
JEL:  C01 C25 C87 
Date:  2023–01–06 
URL:  http://d.repec.org/n?u=RePEc:bss:wpaper:44&r=ecm 
By:  Jan Pablo Burgard; Matthias Neuenkirch; Dennis Umlandt 
Abstract:  Recursively identified vector autoregressive (VAR) models often lead to a counterintuitive response of prices (and output) shortly after a monetary policy shock. To overcome this problem, we propose to estimate the VAR parameters under the restriction that economic theory is not violated, while the shocks are still recursively identified. We solve this optimization problem under nonlinear constraints using an augmented Lagrange solution approach, which adjusts the VAR coefficients to meet the theoretical requirements. In a generalization, we allow for a (minimal) rotation of the Cholesky matrix in addition to the parameter restrictions. Based on a Monte Carlo study and an empirical application, we show that particularly the "almost recursively identified approach with parameter restrictions" leads to a solution that avoids an estimation bias, generates theoryconsistent impulse responses, and is as close as possible to the recursive scheme. 
Keywords:  Monetary Policy Transmission, NonLinear Optimization, Price Puzzle, Recursive Identification, Rotation, Sign Restrictions 
JEL:  C32 E52 E58 
Date:  2023 
URL:  http://d.repec.org/n?u=RePEc:trr:qfrawp:202301&r=ecm 
By:  Fresoli, Diego Eduardo; Poncela Blanco, Maria Pilar; Ruiz Ortega, Esther 
Abstract:  In economics, Principal Components, its generalized version that takes into account heteroscedasticity, and Kalman filter and smoothing procedures are among the most popular procedures for factor extraction in the context of Dynamic Factor Models. This paper analyses the consequences on point and interval factor estimation of using these procedures when the idiosyncratic components are wrongly assumed to be crosssectionally uncorrelated. We show that not taking into account the presence of crosssectional dependence increases the uncertainty of point estimates of the factors. Furthermore, the Mean Square Errors computed using the usual expressions based on asymptotic approximations, are underestimated and may lead to prediction intervals with extremely low coverages. 
Keywords:  EM Algorithm; Kalman Filter; Principal Components; StateSpace Model 
JEL:  C32 C38 C55 
Date:  2022–12–12 
URL:  http://d.repec.org/n?u=RePEc:cte:wsrepe:36251&r=ecm 
By:  Julien Hambuckers; Li Sun; Luca Trapin 
Abstract:  We study tail risk dynamics in highfrequency financial markets and their connection with trading activity and market uncertainty. We introduce a dynamic extreme value regression model accommodating both stationary and local unitroot predictors to appropriately capture the timevarying behaviour of the distribution of highfrequency extreme losses. To characterize trading activity and market uncertainty, we consider several volatility and liquidity predictors, and propose a twostep adaptive $L_1$regularized maximum likelihood estimator to select the most appropriate ones. We establish the oracle property of the proposed estimator for selecting both stationary and local unitroot predictors, and show its good finite sample properties in an extensive simulation study. Studying the highfrequency extreme losses of nine large liquid U.S. stocks using 42 liquidity and volatility predictors, we find the severity of extreme losses to be well predicted by low levels of price impact in period of high volatility of liquidity and volatility. 
Date:  2023–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2301.01362&r=ecm 
By:  Christian Tien 
Abstract:  Instruments can be used to identify causal effects in the presence of unobserved confounding, under the famous relevance and exclusion assumptions. As exclusion is difficult to justify and to some degree untestable, it often invites criticism in applications. Hoping to alleviate this problem, we propose a novel identification approach, which relaxes traditional IV exclusion to exclusion conditional on some unobserved common confounders. We assume there exist some relevant proxies for the unobserved common confounders. Unlike typical proxies, our proxies can have a direct effect on the endogenous regressor and the outcome. We provide point identification results with a linearly separable outcome model in the disturbance, and alternatively with strict monotonicity in the first stage. Using this novel method with NLS97 data, we demonstrate the insignificant role of ability bias compared to general selection bias in the economic returns to education problem. Beyond economics, the approach is just as relevant in health treatment evaluation with an unobserved underlying health status, or a psychological study where character traits are unobserved common confounders. 
Date:  2023–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2301.02052&r=ecm 
By:  Annika Camehl (Erasmus University Rotterdam); Dennis Fok (Erasmus University Rotterdam); Kathrin Gruber (Erasmus University Rotterdam) 
Abstract:  In multipleoutput quantile regression the simultaneous study of multiple response variables requires multivariate quantiles. Current definitions of such quantiles often lack a clear probability interpretation, as the defined quantiles can cover large parts of the distribution where little probability mass is located or their enclosed area does not equal the quantile level. We suggest superlevelsets of conditional multivariate density functions as an alternative multivariate quantile definition. Such a quantile set contains all points in the domain for which the density exceeds a certain level. By applying this to a conditional density, the quantile becomes a function of the conditioning variables. We show that such a quantile has favorable mathematical and intuitive features. For implementation, we, first, use an overfitted Gaussian mixture model to fit the multivariate density and, next, calculate the multivariate quantile for a conditional or marginal density of interest. Operating on the same estimated multivariate density guarantees logically consistent quantiles. In particular, the quantiles at multiple percentiles are noncrossing. We use simulation to demonstrate that we recover the true quantiles for distributions with correlation, heteroskedasticity, or asymmetry in the disturbances and we apply our method to study heterogeneity in household expenditures. 
Keywords:  Multiple Response, Bayesian Quantile Regression, Gaussian Mixture Model 
Date:  2022–12–22 
URL:  http://d.repec.org/n?u=RePEc:tin:wpaper:20220094&r=ecm 
By:  Luofeng Liao; Christian Kroer 
Abstract:  We initiate the study of statistical inference and A/B testing for firstprice pacing equilibria (FPPE). The FPPE model captures the dynamics resulting from largescale firstprice auction markets where buyers use pacingbased budget management. Such markets arise in the context of internet advertising, where budgets are prevalent. We propose a statistical framework for the FPPE model, in which a limit FPPE with a continuum of items models the longrun steadystate behavior of the auction platform, and an observable FPPE consisting of a finite number of items provides the data to estimate primitives of the limit FPPE, such as revenue, Nash social welfare (a fair metric of efficiency), and other parameters of interest. We develop central limit theorems and asymptotically valid confidence intervals. Furthermore, we establish the asymptotic local minimax optimality of our estimators. We then show that the theory can be used for conducting statistically valid A/B testing on auction platforms. Numerical simulations verify our central limit theorems, and empirical coverage rates for our confidence intervals agree with our theory. 
Date:  2023–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2301.02276&r=ecm 
By:  Einmahl, John (Tilburg University, Center For Economic Research); Krajina, Andrea 
Keywords:  asymptotic theory; distributionfree; empirical likelihood; empirical process; multivariate tail; regular variation; tail index 
Date:  2023 
URL:  http://d.repec.org/n?u=RePEc:tiu:tiucen:261583f5c57148c68cea945ba6542026&r=ecm 
By:  Jinan Zou; Qingying Zhao; Yang Jiao; Haiyao Cao; Yanxi Liu; Qingsen Yan; Ehsan Abbasnejad; Lingqiao Liu; Javen Qinfeng Shi 
Abstract:  The stock market prediction has been a traditional yet complex problem researched within diverse research areas and application domains due to its nonlinear, highly volatile and complex nature. Existing surveys on stock market prediction often focus on traditional machine learning methods instead of deep learning methods. Deep learning has dominated many domains, gained much success and popularity in recent years in stock market prediction. This motivates us to provide a structured and comprehensive overview of the research on stock market prediction focusing on deep learning techniques. We present four elaborated subtasks of stock market prediction and propose a novel taxonomy to summarize the stateoftheart models based on deep neural networks from 2011 to 2022. In addition, we also provide detailed statistics on the datasets and evaluation metrics commonly used in the stock market. Finally, we highlight some open issues and point out several future directions by sharing some new perspectives on stock market prediction. 
Date:  2022–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2212.12717&r=ecm 
By:  Lin William Cong; Guanhao Feng; Jingyu He; Xin He 
Abstract:  We develop a new class of treebased models (PTree) for analyzing (unbalanced) panel data utilizing global (instead of local) split criteria that incorporate economic guidance to guard against overfitting while preserving interpretability. We grow a PTree topdown to split the cross section of asset returns to construct stochastic discount factor and test assets, generalizing sequential security sorting and visualizing (asymmetric) nonlinear interactions among firm characteristics and macroeconomic states. Datadriven PTree models reveal that idiosyncratic volatility and earningstoprice ratio interact to drive crosssectional return variations in U.S. equities; market volatility and inflation constitute the most critical regimeswitching that asymmetrically interact with characteristics. PTrees outperform most known observable and latent factor models in pricing individual stocks and test portfolios, while delivering transparent trading strategies and riskadjusted investment outcomes (e.g., outofsample annualized Sharp ratios of about 3 and monthly alpha around 0.8%). 
JEL:  C1 G11 G12 
Date:  2022–12 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:30805&r=ecm 
By:  Mark Ponder; Amil Petrin; Boyoung Seo 
Abstract:  The standard Berry, Levinsohn, and Pakes (1995) (BLP) approach to estimation of demand and supply parameters assumes that the product characteristic observed by consumers and producers but not the researcher is conditionally mean independent of observed characteristics. We extend BLP to allow all product characteristics to be endogenous, so the unobserved characteristic can be correlated with the observed characteristics. We derive moment conditions based on the assumption that firms choose product characteristics to maximize expected profits given their beliefs at that time about market conditions and that the “mistake” in the amount of the characteristic that is revealed once all products are on the market is conditionally mean independent of the firm's information set. Using the original BLP dataset we find that observed and unobserved product characteristics are highly positively correlated, biasing demand elasticities upward, as average estimated price elasticities double in absolute value and average markups fall by 50%. 
JEL:  C25 L0 
Date:  2022–12 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:30778&r=ecm 
By:  Victor Chernozhukov (MIT  Massachusetts Institute of Technology); Alfred Galichon (NYU  New York University [New York]  NYU  NYU System, ECON  Département d'économie (Sciences Po)  Sciences Po  Sciences Po  CNRS  Centre National de la Recherche Scientifique); Marc Henry (Penn State  Pennsylvania State University  Penn State System); Brendan Pass (University of Alberta) 
Abstract:  This paper derives conditions under which preferences and technology are nonparametrically identified in hedonic equilibrium models. With products differentiated along a quality index and agents characterized by scalar unobserved heterogeneity, singlecrossing conditions on preferences and technology provide identifying restrictions in previous work. We develop similar shape restrictions in the multiattribute case. These shape restrictions, based on optimal transport theory and generalized convexity, allow us to identify preferences for goods differentiated along multiple dimensions from the observation of a single market. We thereby derive identification results for nonseparable simultaneous equations and multiattribute hedonic equilibrium models with (possibly) multiple dimensions of unobserved heterogeneity. One of our results is a proof of absolute continuity of the distribution of endogenously traded qualities, which is of independent interest. 
Keywords:  Hedonic equilibrium, Nonparametric identification, Multidimensional unobserved heterogeneity, Optimal transport 
Date:  2021–03–01 
URL:  http://d.repec.org/n?u=RePEc:hal:spmain:hal03893143&r=ecm 