
on Econometrics 
By:  Harsh Parikh; Carlos Varjao; Louise Xu; Eric Tchetgen Tchetgen 
Abstract:  The fundamental challenge of drawing causal inference is that counterfactual outcomes are not fully observed for any unit. Furthermore, in observational studies, treatment assignment is likely to be confounded. Many statistical methods have emerged for causal inference under unconfoundedness conditions given pretreatment covariates, including propensity scorebased methods, prognostic scorebased methods, and doubly robust methods. Unfortunately for applied researchers, there is no `onesizefitsall' causal method that can perform optimally universally. In practice, causal methods are primarily evaluated quantitatively on handcrafted simulated data. Such datagenerative procedures can be of limited value because they are typically stylized models of reality. They are simplified for tractability and lack the complexities of realworld data. For applied researchers, it is critical to understand how well a method performs for the data at hand. Our work introduces a deep generative modelbased framework, Credence, to validate causal inference methods. The framework's novelty stems from its ability to generate synthetic data anchored at the empirical distribution for the observed sample, and therefore virtually indistinguishable from the latter. The approach allows the user to specify ground truth for the form and magnitude of causal effects and confounding bias as functions of covariates. Thus simulated data sets are used to evaluate the potential performance of various causal estimation methods when applied to data similar to the observed sample. We demonstrate Credence's ability to accurately assess the relative performance of causal estimation techniques in an extensive simulation study and two realworld data applications from Lalonde and Project STAR studies. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2202.04208&r= 
By:  Christis Katsouris 
Abstract:  We revisit classical asymptotics when testing for a structural break in linear regression models by obtaining the limit theory of residualbased and Waldtype processes. First, we establish the Brownian bridge limiting distribution of these test statistics. Second, we study the asymptotic behaviour of the partialsum processes in nonstationary (linear) time series regression models. Although, the particular comparisons of these two different modelling environments is done from the perspective of the partialsum processes, it emphasizes that the presence of nuisance parameters can change the asymptotic behaviour of the functionals under consideration. Simulation experiments verify size distortions when testing for a break in nonstationary time series regressions which indicates that the Brownian bridge limit cannot provide a suitable asymptotic approximation in this case. Further research is required to establish the cause of size distortions under the null hypothesis of parameter stability. 
Date:  2022–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2202.00141&r= 
By:  José Luis Montiel Olea (Columbia University); Mikkel PlagborgMøller (Princeton University); Eric Qian (Princeton University) 
Abstract:  Two recent strands of the literature on Structural Vector Autoregressions (SVARs) use higher moments for identification. One of them exploits independence and nonGaussianity of the shocks; the other, stochastic volatility (heteroskedasticity). These approaches achieve point identification without imposing exclusion or sign restrictions. We review this work critically, and contrast its goals with the separate research program that has pushed for macroeconometrics to rely more heavily on credible economic restrictions and institutional knowledge, as is the standard in microeconometric policy evaluation. Identification based on higher moments imposes substantively stronger assumptions on the shock process than standard secondorder SVAR identification methods do. We recommend that these assumptions be tested in applied work. Even when the assumptions are not rejected, inference based on higher moments necessarily demands more from a finite sample than standard approaches do. Thus, in our view, weak identification issues should be given high priority by applied users. 
Keywords:  Structural Vector Autoregressions, macroeconometrics 
JEL:  C01 C10 
Date:  2021–08 
URL:  http://d.repec.org/n?u=RePEc:pri:econom:202124&r= 
By:  Crudu, Federico (University of Siena and CRENoS); Mellace, Giovanni (Department of Economics); Smits, Joeri (Harvard University) 
Abstract:  Many econometrics textbooks imply that under mean independence of the regressors and the error term, the OLS estimand has a causal interpretation. We provide counterexamples of datagenerating processes (DGPs) where the standard assumption of zero conditional mean error is satisfied, but where OLS identifies a pseudoparameter that does not have a causal interpretation. No such counterexamples can be constructed when the assumption needed is stated in the potential outcome framework, highlighting the fact that causal inference requires causal, and not just stochastic, assumptions. 
Keywords:  OLS; zero conditional mean error; causal inference 
JEL:  C10 C18 C21 C31 
Date:  2022–02–23 
URL:  http://d.repec.org/n?u=RePEc:hhs:sdueko:2022_003&r= 
By:  Pincheira, Pablo; Hardy, Nicolas 
Abstract:  In this paper, we propose a correlationbased test for the evaluation of two competing forecasts. Under the null hypothesis of equal correlations with the target variable, we derive the asymptotic distribution of our test using the Delta method. This null hypothesis is not necessarily equivalent to the null of equal Mean Squared Prediction Errors (MSPE). Specifically, it might be the case that the forecast displaying the lowest MSPE also exhibits the lowest correlation with the target variable: this is known as "The MSPE paradox" (Pincheira and Hardy; 2021). In this sense, our approach should be seen as complementary to traditional tests of equality in MSPE. Monte Carlo simulations indicate that our test has good size and power. Finally, we illustrate the use of our test in an empirical exercise in which we compare two different inflation forecasts for a sample of OECD economies. We find more rejections of the null of equal correlations than rejections of the null of equality in MSPE. 
Keywords:  Forecasting, timeseries, outofsample evaluation, mean squared prediction error, correlations. 
JEL:  C52 C53 E31 E37 F37 G17 
Date:  2022–02–16 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:112014&r= 
By:  Mikio Ito 
Abstract:  This article proposes an estimation method to detect breakpoints for linear time series models with their parameters that jump scarcely. Its basic idea owes the group LASSO (group least absolute shrinkage and selection operator). The method practically provides estimates of such timevarying parameters of the models. An example shows that our method can detect each structural breakpoint's date and magnitude. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2202.02988&r= 
By:  Hafner, C. M. 
Abstract:  We introduce a new class of semiparametric dynamic autoregressive models for the Amihud illiquidity measure, which captures both the longrun trend in the illiquidity series with a nonparametric component and the shortrun dynamics with an autoregressive component. We develop a GMM estimator based on conditional moment restrictions and an efficient semiparametric ML estimator based on an iid assumption. We derive large sample properties for both estimators. We further develop a methodology to detect the occurrence of permanent and transitory breaks in the illiquidity process. Finally, we demonstrate the model performance and its empirical relevance on two applications. First, we study the impact of stock splits on the illiquidity dynamics of the five largest US technology company stocks. Second, we investigate how the different components of the illiquidity process obtained from our model relate to the stock market risk premium using data on the S&P 500 stock market index. 
Keywords:  Nonparametric, Semiparametric, Splits, Structural Change 
JEL:  C12 C14 
Date:  2022–02–23 
URL:  http://d.repec.org/n?u=RePEc:cam:camdae:2214&r= 
By:  Heckman, James J. (University of Chicago); Pinto, Rodrigo (University of California, Los Angeles) 
Abstract:  This paper examines the econometric causal model for policy analysis developed by the seminal ideas of Ragnar Frisch and Trygve Haavelmo. We compare the econometric causal model with two popular causal frameworks: NeymanHolland causal model and the docalculus. The NeymanHolland causal model is based on the language of potential outcomes and was largely developed by statisticians. The docalculus, developed by Judea Pearl and coauthors, relies on Directed Acyclic Graphs (DAGs) and is a popular causal framework in computer science. We make the case that economists who uncritically use these approximating frameworks often discard the substantial benefits of the econometric causal model to the detriment of more informative economic policy analyses. We illustrate the versatility and capabilities of the econometric framework using causal models that are frequently studied by economists. 
Keywords:  policy analysis, econometric models, causality, identification, causal calculus, directed acyclic graphs, simultaneous treatment effects 
JEL:  C10 C18 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:iza:izadps:dp15081&r= 
By:  Caio Almeida (Princeton University); Jianqing Fan (Princeton University); Francesca Tang (Princeton University) 
Abstract:  We introduce a novel approach to capture implied volatility smiles. Given any parametric option pricing model used to fit a smile, we train a deep feedforward neural network on the modelâ€™s orthogonal residuals to correct for potential mispricings and boost performance. Using a large number of recent S&P500 options, we compare our hybrid machinecorrected model to several standalone parametric models ranging from adhoc corrections of BlackScholes to more structural noarbitrage stochastic volatility models. Empirical results based on outofsample fitting errors  in crosssectional and timeseries dimensions  consistently confirm that a machine can in fact correct existing models without overfitting. Moreover, we find that our twostep technique is relatively indiscriminate: regardless of the bias or structure of the original parametric model, our boosting approach is able to correct it to approximately the same degree. Hence, our methodology is adaptable and versatile in its application to a large range of parametric option pricing models. As an overarching theme, machine corrected methods, guided by an implied volatility model as a template, outperform pure machine learning methods. 
Keywords:  Deep Learning, Boosting, Implied Volatility, Stochastic Volatility, Model Correction 
JEL:  E37 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:pri:econom:202144&r= 
By:  Liu Yang; Kajal Lahiri; Adrian Pagan 
Abstract:  Judging the conformity of binary events in macroeconomics and finance has often been done with indices that measure synchronization. In recent years, the use of Receiver Operating Characteristic (ROC) curve has become popular for this task. This paper shows that the ROC and synchronization approaches are closely related, and each can be represented as a weighted average of correlation coefficients between a set of binary indicators and the target event. An advantage of such a representation is that inferences on the degree of conformity can be made robust to serial dependence in the underlying series in the standard framework of a linear regression model. Such serial correlation is common in macroeconomic and financial data. 
Keywords:  Receiver operating characteristic curve, Synchronization, Correlation, Economic recession, Serial dependence 
JEL:  C14 C52 C53 E37 
Date:  2022–01 
URL:  http://d.repec.org/n?u=RePEc:een:camaaa:202201&r= 