
on Econometrics 
By:  Yuling Yan; Martin J. Wainwright 
Abstract:  In causal inference with panel data under staggered adoption, the goal is to estimate and derive confidence intervals for potential outcomes and treatment effects. We propose a computationally efficient procedure, involving only simple matrix algebra and singular value decomposition. We derive nonasymptotic bounds on the entrywise error, establishing its proximity to a suitably scaled Gaussian variable. Despite its simplicity, our procedure turns out to be instanceoptimal, in that our theoretical scaling matches a local instancewise lower bound derived via a Bayesian Cram\'{e}rRao argument. Using our insights, we develop a datadriven procedure for constructing entrywise confidence intervals with prespecified coverage guarantees. Our analysis is based on a general inferential toolbox for the SVD algorithm applied to the matrix denoising model, which might be of independent interest. 
Date:  2024–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2401.13665&r=ecm 
By:  Sandro Heiniger 
Abstract:  Matrix completion estimators are employed in causal panel data models to regulate the rank of the underlying factor model using nuclear norm minimization. This convex optimization problem enables concurrent regularization of a potentially highdimensional set of covariates to shrink the model size. For valid finite sample inference, we adopt a permutationbased approach and prove its validity for any treatment assignment mechanism. Simulations illustrate the consistency of the proposed estimator in parameter estimation and variable selection. An application to public health policies in Germany demonstrates the datadriven model selection feature on empirical data and finds no effect of travel restrictions on the containment of severe Covid19 infections. 
Date:  2024–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2402.01069&r=ecm 
By:  Felix Chan; Laszlo Matyas 
Abstract:  The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The paper shows that such estimator is consistent for carefully selected weights. Other properties, such as asymptotic distributions, have also been derived to facilitate valid statistical inference. Unlike traditional methods, such as Least Squares and Maximum Likelihood, among others, the estimated residual of this estimator is not by construction orthogonal to the explanatory variables of the model. This property allows a wide range of practical applications, such as the testing of endogeneity, i.e., the correlation between the explanatory variables and the disturbance terms, and potentially several others. 
Date:  2024–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2401.11229&r=ecm 
By:  Nora Bearth; Michael Lechner 
Abstract:  It is valuable for any decision maker to know the impact of decisions (treatments) on average and for subgroups. The causal machine learning literature has recently provided tools for estimating group average treatment effects (GATE) to understand treatment heterogeneity better. This paper addresses the challenge of interpreting such differences in treatment effects between groups while accounting for variations in other covariates. We propose a new parameter, the balanced group average treatment effect (BGATE), which measures a GATE with a specific distribution of a prioridetermined covariates. By taking the difference of two BGATEs, we can analyse heterogeneity more meaningfully than by comparing two GATEs. The estimation strategy for this parameter is based on double/debiased machine learning for discrete treatments in an unconfoundedness setting, and the estimator is shown to be $\sqrt{N}$consistent and asymptotically normal under standard conditions. Adding additional identifying assumptions allows specific balanced differences in treatment effects between groups to be interpreted causally, leading to the causal balanced group average treatment effect. We explore the finite sample properties in a smallscale simulation study and demonstrate the usefulness of these parameters in an empirical example. 
Date:  2024–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2401.08290&r=ecm 
By:  Jochmans, Koen 
Abstract:  We consider point estimation and inference based on modifications of the profile likelihood in models for dyadic interactions between n agents featuring agentspecific parameters. The maximumlikelihood estimator of such models has bias and standard deviation of order n1 and so is asymptotically biased. Estimation based on modified likelihoods leads to estimators that are asymptotically unbiased and likelihood ratio tests that exhibit correct size. 
Keywords:  Asymptotic bias; Dyadic data; Fixed effects ; Undirected random graph 
JEL:  C23 
Date:  2024–01–24 
URL:  http://d.repec.org/n?u=RePEc:tse:wpaper:129030&r=ecm 
By:  Chudamani Poudyal 
Abstract:  Numerous robust estimators exist as alternatives to the maximum likelihood estimator (MLE) when a completely observed groundup loss severity sample dataset is available. However, the options for robust alternatives to MLE become significantly limited when dealing with grouped loss severity data, with only a handful of methods like least squares, minimum Hellinger distance, and optimal bounded influence function available. This paper introduces a novel robust estimation technique, the Method of Truncated Moments (MTuM), specifically designed to estimate the tail index of a Pareto distribution from grouped data. Inferential justification of MTuM is established by employing the central limit theorem and validating them through a comprehensive simulation study. 
Date:  2024–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2401.14593&r=ecm 
By:  Isaac Loh 
Abstract:  We provide a means of computing and estimating the asymptotic distributions of test statistics based on an outer minimization of an inner maximization. Such test statistics, which arise frequently in moment models, are of special interest in providing hypothesis tests under partial identification. Under general conditions, we provide an asymptotic characterization of such test statistics using the minimax theorem, and a means of computing critical values using the bootstrap. Making some light regularity assumptions, our results provide a basis for several asymptotic approximations that have been provided for partially identified hypothesis tests, and extend them by mitigating their dependence on local linear approximations of the parameter space. These asymptotic results are generally simple to state and straightforward to compute (e.g. adversarially). 
Date:  2024–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2401.13057&r=ecm 
By:  Kaicheng Chen; Kyoo il Kim 
Abstract:  We study identification of the treatment effects in a class of nonseparable models with the presence of potentially endogenous control variables. We show that given the treatment variable and the controls are measurably separated, the usual conditional independence condition or availability of excluded instrument suffices for identification. 
Date:  2024–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2401.14395&r=ecm 
By:  Zachary Porreca 
Abstract:  Gradientbased solvers risk convergence to local optima, leading to incorrect researcher inference. Heuristicbased algorithms are able to ``break free" of these local optima to eventually converge to the true global optimum. However, given that they do not provide the gradient/Hessian needed to approximate the covariance matrix and that the significantly longer computational time they require for convergence likely precludes resampling procedures for inference, researchers often are unable to quantify uncertainty in the estimates they derive with these methods. This note presents a simple and relatively fast twostep procedure to estimate the covariance matrix for parameters estimated with these algorithms. This procedure relies on automatic differentiation, a computational means of calculating derivatives that is popular in machine learning applications. A brief empirical example demonstrates the advantages of this procedure relative to bootstrapping and shows the similarity in standard error estimates between this procedure and that which would normally accompany maximum likelihood estimation with a gradientbased algorithm. 
Date:  2024–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2401.07176&r=ecm 
By:  Haruki Kono 
Abstract:  The instrumental variable (IV) quantile regression model introduced by Chernozhukov and Hansen (2005) is a useful tool for analyzing quantile treatment effects in the presence of endogeneity, but when outcome variables are multidimensional, it is silent on the joint distribution of different dimensions of each variable. To overcome this limitation, we propose an IV model built on the optimaltransportbased multivariate quantile that takes into account the correlation between the entries of the outcome variable. We then provide a local identification result for the model. Surprisingly, we find that the support size of the IV required for the identification is independent of the dimension of the outcome vector, as long as the IV is sufficiently informative. Our result follows from a general identification theorem that we establish, which has independent theoretical significance. 
Date:  2024–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2401.11422&r=ecm 
By:  Zhenhao Gong (Shanxi University of Finance and Economics); Min Seong Kim (University of Connecticut) 
Abstract:  The use of multilevel regression models is prevalent in policy analysis to estimate the effect of group level policies on individual outcomes. In order to allow for the time varying effect of group heterogeneity and the group specific impact of time effects, we propose a group interactive fixed effects approach that employs interaction terms of group factor loadings and common factors in this model. For this approach, we consider the least squares estimator and associated inference procedure. We examine their properties under the large n and fixed T asymptotics. The number of groups, G; is allowed to grow but at a slower rate. We also propose a test for the level of grouping to specify group factor loadings, and a GMM approach to address policy endogeneity with respect to idiosyncratic errors. Finally, we provide empirical illustrations of the proposed approach using two empirical examples. 
Keywords:  endogeneity; GMM estimation; group heterogeneity; group level test; least squares estimation; panel; repeated crosssections 
JEL:  C12 C13 C23 C54 
Date:  2024–01 
URL:  http://d.repec.org/n?u=RePEc:uct:uconnp:202401&r=ecm 
By:  Coady Wing; Seth M. Freedman; Alex Hollingsworth 
Abstract:  This paper introduces the concept of a "trimmed aggregate ATT, " which is a weighted average of a set of grouptime average treatment effect on the treated (ATT) parameters identified in a staggered adoption differenceindifferences (DID) design. The set of identified grouptime ATTs that contribute to the aggregate is trimmed to achieve compositional balance across an event window, ensuring that comparisons of the aggregate parameter over event time reveal dynamic treatment effects and differential pretrends rather than compositional changes. Taking the trimmed aggregate ATT as a target parameter, we investigate the performance of stacked DID estimators. We show that the most basic stacked estimator does not identify the target aggregate or any other average causal effect because it applies different implicit weights to treatment and control trends. The bias can be eliminated using corrective sample weights. We present a weighted stacked DID estimator, and show that it correctly identifies the target aggregate, providing justification for using the estimator in applied work. 
JEL:  C01 C13 I0 
Date:  2024–01 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:32054&r=ecm 
By:  Sylvia Kaufmann (Study Center Gerzensee); Markus Pape (RuhrUniversity Bochum) 
Abstract:  Factor modelling extracts common information from a highdimensional data set into few common components, where the latent factors usually explain a large share of data variation. Exploratory factor estimation induces sparsity into the loading matrix to associate units or series with those factors most strongly associated with them, eventually determining factor interpretation. We motivate geometrically under which circumstances it may be necessary to consider the existence of multiple sparse factor loading matrices with similar degrees of sparsity for a given data set. We propose two MCMC approaches for Bayesian inference and corresponding postprocessing algorithms to uncover multiple sparse representations of the factor loadings matrix. We investigate both approaches in a simulation study. Applied to data on countryspecific gross domestic product and U.S. price components series, we retrieve multiple sparse factor representations for each data set. Both approaches prove useful to discriminate between pervasive and weaker factors. 
Date:  2023–12 
URL:  http://d.repec.org/n?u=RePEc:szg:worpap:2304&r=ecm 
By:  Jonathan Roth 
Abstract:  This note discusses the interpretation of eventstudy plots produced by recent differenceindifferences methods. I show that even when specialized to the case of nonstaggered treatment timing, the default plots produced by software for three of the most popular recent methods (de Chaisemartin and D'Haultfoeuille, 2020; Callaway and SantAnna, 2021; Borusyak, Jaravel and Spiess, 2024) do not match those of traditional twoway fixed effects (TWFE) eventstudies: the new methods may show a kink or jump at the time of treatment even when the TWFE eventstudy shows a straight line. This difference stems from the fact that the new methods construct the pretreatment coefficients asymmetrically from the posttreatment coefficients. As a result, visual heuristics for analyzing TWFE eventstudy plots should not be immediately applied to those from these methods. I conclude with practical recommendations for constructing and interpreting eventstudy plots when using these methods. 
Date:  2024–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2401.12309&r=ecm 
By:  Rubin, Mark (Durham University) 
Abstract:  During multiple testing, researchers often adjust their alpha level to control the familywise error rate for a statistical inference about a joint union alternative hypothesis (e.g., “H1 or H2”). However, in some cases, they do not make this inference. Instead, they make separate inferences about each of the individual hypotheses that comprise the joint hypothesis (e.g., H1 and H2). For example, a researcher might use a Bonferroni correction to adjust their alpha level from the conventional level of 0.050 to 0.025 when testing H1 and H2, find a significant result for H1 (p < 0.025) and not for H2 (p > .0.025), and so claim support for H1 and not for H2. However, these separate individual inferences do not require an alpha adjustment. Only a statistical inference about the union alternative hypothesis “H1 or H2” requires an alpha adjustment because it is based on “at least one” significant result among the two tests, and so it depends on the familywise error rate. When a researcher corrects their alpha level during multiple testing but does not make an inference about the union alternative hypothesis, their correction is redundant. In the present article, I discuss this redundant correction problem, including its reduction in statistical power for tests of individual hypotheses and its potential causes visàvis error rate confusions and the alpha adjustment ritual. I also provide three illustrations of redundant corrections from recent psychology studies. I conclude that redundant corrections represent a symptom of statisticism, and I call for a more nuanced inferencebased approach to multiple testing corrections. 
Date:  2024–01–24 
URL:  http://d.repec.org/n?u=RePEc:osf:metaar:d6a8s&r=ecm 
By:  Lars Ericson; Xuejun Zhu; Xusi Han; Rao Fu; Shuang Li; Steve Guo; Ping Hu 
Abstract:  In the financial services industry, forecasting the risk factor distribution conditional on the history and the current market environment is the key to market risk modeling in general and value at risk (VaR) model in particular. As one of the most widely adopted VaR models in commercial banks, Historical simulation (HS) uses the empirical distribution of daily returns in a historical window as the forecast distribution of risk factor returns in the next day. The objectives for financial time series generation are to generate synthetic data paths with good variety, and similar distribution and dynamics to the original historical data. In this paper, we apply multiple existing deep generative methods (e.g., CGAN, CWGAN, Diffusion, and Signature WGAN) for conditional time series generation, and propose and test two new methods for conditional multistep time series generation, namely EncoderDecoder CGAN and Conditional TimeVAE. Furthermore, we introduce a comprehensive framework with a set of KPIs to measure the quality of the generated time series for financial modeling. The KPIs cover distribution distance, autocorrelation and backtesting. All models (HS, parametric and neural networks) are tested on both historical USD yield curve data and additional data simulated from GARCH and CIR processes. The study shows that top performing models are HS, GARCH and CWGAN models. Future research directions in this area are also discussed. 
Date:  2024–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2401.10370&r=ecm 
By:  Jozef Barunik; Lukas Vacha 
Abstract:  Time variation and persistence are crucial properties of volatility that are often studied separately in oilbased volatility forecasting models. Here, we propose a novel approach that allows shocks with heterogeneous persistence to vary smoothly over time, and thus model the two together. We argue that this is important because such dynamics arise naturally from the dynamic nature of shocks in oilbased commodities. We identify such dynamics from the data using localised regressions and build a model that significantly improves volatility forecasts. Such forecasting models, based on a rich persistence structure that varies smoothly over time, outperform stateoftheart benchmark models and are particularly useful for forecasting over longer horizons. 
Date:  2024–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2402.01354&r=ecm 
By:  Stephen P. Holland; Erin T. Mansur; Valentin Verdier; Andrew J. Yates 
Abstract:  Environmental policy is increasingly concerned with measuring emissions resulting from local changes to electricity consumption. These marginal emissions are challenging to measure because electricity grids encompass multiple locations and the information available to identify the effect of each location’s consumption on gridwide emissions is limited. We formalize this as a highdimensional aggregation problem: The effect of electricity consumption on emissions can be estimated precisely for each electricity generating unit (generator), but not precisely enough to obtain reliable estimates of marginal emissions by summing these effects across all generators in a grid. We study how two economic constraints can address this problem: electricity supply equals demand and an assumption of monotonicity. We show that these constraints can be used to formulate a ‘naturally regularized’ estimator, which implements an implicit penalization that does not need to be directly tuned. Under an additional assumption of sparsity, we show that our new estimator solves the highdimensional aggregation problem, i.e., it is consistent for marginal emissions where the usual regression estimator would not be. We also develop an asymptotically valid method for inference to accompany our estimator. When applied to the U.S. electricity grid with 13 separate consumption regions, our method yields plausible patterns of marginal generation across fuel types and geographic location. Our estimates of regionlevel marginal emissions are precise, account for imports/exports between regions, and allow for all fuel types to potentially be on the margin. 
JEL:  C23 Q42 Q48 Q53 
Date:  2024–01 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:32065&r=ecm 
By:  Kjell G. Nyborg (University of Zurich  Department of Banking and Finance; Centre for Economic Policy Research (CEPR); Swiss Finance Institute); Jiri Woschitz (BI Norwegian Business School) 
Abstract:  Differenceindifferences (DiD) analysis is commonly used to study fixedincome pricing. Using simulations, we show that the standard DiD approach applied to variables with a term structure systematically produces false and mismeasured treatment effects, even under random treatment assignment. Standard DiD is misspecified because of endemic heterogeneity over the maturity spectrum and nonmatched treated and controlbond samples. Neither bond fixed effects nor standard termstructure controls resolve the problem. We provide solutions using termstructure modeling that allow for heterogeneous effects over the maturity spectrum. These issues are not unique to DiD analysis, but are generic to groupassignment settings. 
Keywords:  Fixedincome pricing, yield curve, term structure, differenceindifferences analysis, false and mismeasured treatment effects 
JEL:  C20 G12 E43 E47 
Date:  2024–01 
URL:  http://d.repec.org/n?u=RePEc:chf:rpseri:rp2403&r=ecm 
By:  Santavirta, Torsten (University of Helsinki); Stuhler, Jan (Universidad Carlos III de Madrid) 
Abstract:  Recent studies use names  first and surnames  to estimate intergenerational mobility in sources that lack direct family links. While generating novel evidence on intergenerational transmission processes, it remains unclear how different estimators compare and how reliable they are. This paper evaluates the most popular namebased methods, using newly digitised records from Finland and U.S. Census data. We illustrate that their interpretation depends on sampling properties of the data, such as the overlap between the parent and child samples, which differ widely across studies. We correct for the attenuation bias from limited overlap and address other common problems encountered in applications. 
Keywords:  intergenerational mobility, names, grouping estimator, splitsample IV 
JEL:  J62 
Date:  2024–01 
URL:  http://d.repec.org/n?u=RePEc:iza:izadps:dp16725&r=ecm 
By:  Matteo Iacopini; Aubrey Poon; Luca Rossini; Dan Zhu 
Abstract:  A widespread approach to modelling the interaction between macroeconomic variables and the yield curve relies on three latent factors usually interpreted as the level, slope, and curvature (Diebold et al., 2006). This approach is inherently focused on the conditional mean of the yields and postulates a dynamic linear model where the latent factors smoothly change over time. However, periods of deep crisis, such as the Great Recession and the recent pandemic, have highlighted the importance of statistical models that account for asymmetric shocks and are able to forecast the tails of a variable's distribution. A new version of the dynamic threefactor model is proposed to address this issue based on quantile regressions. The novel approach leverages the potential of quantile regression to model the entire (conditional) distribution of the yields instead of restricting to its mean. An application to US data from the 1970s shows the significant heterogeneity of the interactions between financial and macroeconomic variables across different quantiles. Moreover, an outofsample forecasting exercise showcases the proposed method's advantages in predicting the yield distribution tails compared to the standard conditional mean model. Finally, by inspecting the posterior distribution of the three factors during the recent major crises, new evidence is found that supports the greater and longerlasting negative impact of the great recession on the yields compared to the COVID19 pandemic. 
Date:  2024–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2401.09874&r=ecm 
By:  M. Hashem Pesaran; Ron P. Smith 
Abstract:  Forecasts play a central role in decision making under uncertainty. After a brief review of the general issues, this paper considers ways of using highdimensional data in forecasting. We consider selecting variables from a known active set, known knowns, using Lasso and OCMT, and approximating unobserved latent factors, known unknowns, by various means. This combines both sparse and dense approaches. We demonstrate the various issues involved in variable selection in a highdimensional setting with an application to forecasting UK inflation at different horizons over the period 2020q12023q1. This application shows both the power of parsimonious models and the importance of allowing for global variables. 
Date:  2024–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2401.14582&r=ecm 
By:  Yechan Park; Yuya Sasaki 
Abstract:  Combining shortterm experimental data with observational data enables credible longterm policy evaluation. The literature offers two key but nonnested assumptions, namely the latent unconfoundedness (LU; Athey et al., 2020) and equiconfounding bias (ECB; Ghassami et al., 2022) conditions, to correct observational selection. Committing to the wrong assumption leads to biased estimation. To mitigate such risks, we provide a novel bracketing relationship (cf. Angrist and Pischke, 2009) repurposed for the setting with data combination: the LUbased estimand and the ECBbased estimand serve as the lower and upper bounds, respectively, with the true causal effect lying in between if either assumption holds. For researchers further seeking point estimates, our Lalondestyle exercise suggests the conservatively more robust LUbased lower bounds align closely with the holdout experimental estimates for educational policy evaluation. We investigate the economic substantives of these findings through the lens of a nonparametric class of selection mechanisms and sensitivity analysis. We uncover as key the submartingale property and sufficientstatistics role (Chetty, 2009) of the potential outcomes of student test scores (Chetty et al., 2011, 2014). 
Date:  2024–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2401.12050&r=ecm 
By:  Bryan T. Kelly (Yale SOM; AQR Capital Management, LLC; National Bureau of Economic Research (NBER)); Boris Kuznetsov (Swiss Finance Institute; EPFL); Semyon Malamud (Ecole Polytechnique Federale de Lausanne; Centre for Economic Policy Research (CEPR); Swiss Finance Institute); Teng Andrea Xu (École Polytechnique Fédérale de Lausanne) 
Abstract:  We open up the black box behind Deep Learning for portfolio optimization and prove that a sufficiently wide and arbitrarily deep neural network (DNN) trained to maximize the Sharpe ratio of the Stochastic Discount Factor (SDF) is equivalent to a large factor model (LFM): A linear factor pricing model that uses many nonlinear characteristics. The nature of these characteristics depends on the architecture of the DNN in an explicit, tractable fashion. This makes it possible to derive endtoend trained DNNbased SDFs in closed form for the first time. We evaluate LFMs empirically and show how various architectural choices impact SDF performance. We document the virtue of depth complexity: With enough data, the outofsample performance of DNNSDF is increasing in the NN depth, saturating at huge depths of around 100 hidden layers. 
Date:  2023–12 
URL:  http://d.repec.org/n?u=RePEc:chf:rpseri:rp23121&r=ecm 
By:  Luca Barbaglia; Lorenzo Frattarolo; Niko Hauzenberger; Dominik Hirschbuehl; Florian Huber; Luca Onorante; Michael Pfarrhofer; Luca Tiozzo Pezzoli 
Abstract:  Timely information about the state of regional economies can be essential for planning, implementing and evaluating locally targeted economic policies. However, European regional accounts for output are published at an annual frequency and with a twoyear delay. To obtain robust and more timely measures in a computationally efficient manner, we propose a mixedfrequency dynamic factor model that accounts for national information to produce highfrequency estimates of the regional gross value added (GVA). We show that our model produces reliable nowcasts of GVA in 162 regions across 12 European countries. 
Date:  2024–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2401.10054&r=ecm 