{"title":"Nonlinear and nonseparable structural functions in regression discontinuity designs with a continuous treatment","authors":"Haitian Xie","doi":"10.1016/j.jeconom.2024.105784","DOIUrl":"https://doi.org/10.1016/j.jeconom.2024.105784","url":null,"abstract":"<div><p>Many empirical examples of regression discontinuity (RD) designs concern a continuous treatment variable, but the theoretical aspects of such models are less studied. This study examines the identification and estimation of the structural function in fuzzy RD designs with a continuous treatment variable. The structural function fully describes the causal impact of the treatment on the outcome. We show that the nonlinear and nonseparable structural function can be nonparametrically identified at the RD cutoff under shape restrictions, including monotonicity and smoothness conditions. Based on the nonparametric identification equation, we propose a three-step semiparametric estimation procedure and establish the asymptotic normality of the estimator. The semiparametric estimator achieves the same convergence rate as in the case of a binary treatment variable. As an application of the method, we estimate the causal effect of sleep time on health status by using the discontinuity in natural light timing at time zone boundaries.</p></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"242 1","pages":"Article 105784"},"PeriodicalIF":6.3,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141244886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A vector monotonicity assumption for multiple instruments","authors":"Leonard Goff","doi":"10.1016/j.jeconom.2024.105735","DOIUrl":"https://doi.org/10.1016/j.jeconom.2024.105735","url":null,"abstract":"<div><p>When a researcher combines multiple instrumental variables for a single binary treatment, the monotonicity assumption of the local average treatment effects (LATE) framework can become restrictive: it requires that all units share a common direction of response even when separate instruments are shifted in opposing directions. What I call <em>vector monotonicity</em>, by contrast, simply assumes treatment uptake to be monotonic in all instruments. I characterize the class of causal parameters that are point identified under vector monotonicity, when the instruments are binary. This class includes, for example, the average treatment effect among units that are in any way responsive to the collection of instruments, or those that are responsive to a given subset of them. The identification results are constructive and yield a simple estimator for the identified treatment effect parameters. An empirical application revisits the labor market returns to college.</p></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"241 1","pages":"Article 105735"},"PeriodicalIF":6.3,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140618471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The law of large numbers for large stable matchings","authors":"Jacob Schwartz , Kyungchul Song","doi":"10.1016/j.jeconom.2024.105742","DOIUrl":"https://doi.org/10.1016/j.jeconom.2024.105742","url":null,"abstract":"<div><p>In many empirical studies of a large two-sided matching market (such as in a college admissions problem), the researcher performs statistical inference under the assumption that they observe a random sample from a large matching market. In this paper, we consider a setting in which the researcher observes either all or a nontrivial fraction of outcomes from a stable matching. We establish a concentration inequality for empirical matching probabilities assuming strong correlation among the colleges’ preferences while allowing students’ preferences to be fully heterogeneous. Our concentration inequality yields laws of large numbers for the empirical matching probabilities and other statistics commonly used in empirical analyses of a large matching market. To illustrate the usefulness of our concentration inequality, we prove consistency for estimators of conditional matching probabilities and measures of positive assortative matching.</p></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"241 1","pages":"Article 105742"},"PeriodicalIF":6.3,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140638424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Estimation and inference for high dimensional factor model with regime switching","authors":"Giovanni Urga , Fa Wang","doi":"10.1016/j.jeconom.2024.105752","DOIUrl":"https://doi.org/10.1016/j.jeconom.2024.105752","url":null,"abstract":"<div><p>This paper proposes maximum (quasi)likelihood estimation for high dimensional factor models with regime switching in the loadings. The model parameters are estimated jointly by the EM (expectation maximization) algorithm, which in the current context only requires iteratively calculating regime probabilities and principal components of the weighted sample covariance matrix. When regime dynamics are taken into account, smoothed regime probabilities are calculated using a recursive algorithm. Consistency, convergence rates and limit distributions of the estimated loadings and the estimated factors are established under weak cross-sectional and temporal dependence as well as heteroscedasticity. It is worth noting that due to high dimension, regime switching can be identified consistently after the switching point with only one observation period. Simulation results show good performance of the proposed method. An application to the FRED-MD dataset illustrates the potential of the proposed method for detection of business cycle turning points.</p></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"241 2","pages":"Article 105752"},"PeriodicalIF":6.3,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140825926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The local to unity dynamic Tobit model","authors":"Anna Bykhovskaya , James A. Duffy","doi":"10.1016/j.jeconom.2024.105764","DOIUrl":"https://doi.org/10.1016/j.jeconom.2024.105764","url":null,"abstract":"<div><p>This paper considers highly persistent time series that are subject to nonlinearities in the form of censoring or an occasionally binding constraint, such as are regularly encountered in macroeconomics. A tractable candidate model for such series is the dynamic Tobit with a root local to unity. We show that this model generates a process that converges weakly to a non-standard limiting process, that is constrained (regulated) to be positive. Surprisingly, despite the presence of censoring, the OLS estimators of the model parameters are consistent. We show that this allows OLS-based inferences to be drawn on the overall persistence of the process (as measured by the sum of the autoregressive coefficients), and for the null of a unit root to be tested in the presence of censoring. Our simulations illustrate that the conventional ADF test substantially over-rejects when the data is generated by a dynamic Tobit with a unit root, whereas our proposed test is correctly sized. We provide an application of our methods to testing for a unit root in the Swiss franc/euro exchange rate, during a period when this was subject to an occasionally binding lower bound.</p></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"241 2","pages":"Article 105764"},"PeriodicalIF":6.3,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140901880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yuehao Bai , Liang Jiang , Joseph P. Romano , Azeem M. Shaikh , Yichong Zhang
{"title":"Covariate adjustment in experiments with matched pairs","authors":"Yuehao Bai , Liang Jiang , Joseph P. Romano , Azeem M. Shaikh , Yichong Zhang","doi":"10.1016/j.jeconom.2024.105740","DOIUrl":"https://doi.org/10.1016/j.jeconom.2024.105740","url":null,"abstract":"<div><p>This paper studies inference for the average treatment effect (ATE) in experiments in which treatment status is determined according to “matched pairs” and it is additionally desired to adjust for observed, baseline covariates to gain further precision. By a “matched pairs” design, we mean that units are sampled i.i.d. from the population of interest, paired according to observed, baseline covariates, and finally, within each pair, one unit is selected at random for treatment. Importantly, we presume that not all observed, baseline covariates are used in determining treatment assignment. We study a broad class of estimators based on a “doubly robust” moment condition that permits us to study estimators with both finite-dimensional and high-dimensional forms of covariate adjustment. We find that estimators with finite-dimensional, linear adjustments need not lead to improvements in precision relative to the unadjusted difference-in-means estimator. This phenomenon persists even if the adjustments interact with treatment; in fact, doing so leads to no changes in precision. However, gains in precision can be ensured by including fixed effects for each of the pairs. Indeed, we show that this adjustment leads to the minimum asymptotic variance of the corresponding ATE estimator among all finite-dimensional, linear adjustments. We additionally study an estimator with a regularized adjustment, which can accommodate high-dimensional covariates. We show that this estimator leads to improvements in precision relative to the unadjusted difference-in-means estimator and also provides conditions under which it leads to the “optimal” nonparametric, covariate adjustment. A simulation study confirms the practical relevance of our theoretical analysis, and the methods are employed to reanalyze data from an experiment using a “matched pairs” design to study the effect of macroinsurance on microenterprise.</p></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"241 1","pages":"Article 105740"},"PeriodicalIF":6.3,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140621415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Parametric risk-neutral density estimation via finite lognormal-Weibull mixtures","authors":"Yifan Li , Ingmar Nolte , Manh Cuong Pham","doi":"10.1016/j.jeconom.2024.105748","DOIUrl":"https://doi.org/10.1016/j.jeconom.2024.105748","url":null,"abstract":"<div><p>This paper proposes a new parametric risk-neutral density (RND) estimator based on a finite lognormal-Weibull mixture (LWM) density. We establish the consistency and asymptotic normality of the LWM method in a general misspecified parametric framework. Based on the theoretical results, we propose a sequential test procedure to evaluate the goodness-of-fit of the LWM model, which leads to an adaptive choice for the number and type of mixture components. Our simulation results show that, in finite samples with various observation error specifications, the LWM method can approximate complex RNDs generated by state-of-the-art multi-factor stochastic volatility models with a few (typically less than 4) mixtures. Application of the LWM model on index options confirms its reliability in recovering empirical RNDs with a heavy left tail or bimodality, which can be incorrectly identified as bimodality or a heavy left tail by existing (semi)-nonparametric methods if the goodness-of-fit to the observed data is ignored.</p></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"241 2","pages":"Article 105748"},"PeriodicalIF":6.3,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0304407624000940/pdfft?md5=f465fdac6f8ce04ea8c1db064b06c8cc&pid=1-s2.0-S0304407624000940-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140813191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Robust inference of panel data models with interactive fixed effects under long memory: A frequency domain approach","authors":"Shuyao Ke , Peter C.B. Phillips , Liangjun Su","doi":"10.1016/j.jeconom.2024.105761","DOIUrl":"https://doi.org/10.1016/j.jeconom.2024.105761","url":null,"abstract":"<div><p>This paper studies a linear panel data model with interactive fixed effects wherein regressors, factors and idiosyncratic error terms are all stationary but with potential long memory. The setup involves a new formulation of panel data models, where weakly dependent regressors, factors and idiosyncratic errors are embedded as a special case. Standard methods based on principal component decomposition and least squares estimation, as in Bai (2009), are found to be biased and distorted in inference. To cope with this failure and to provide a simple implementable estimation procedure, a frequency domain least squares estimation is proposed. The limit distribution of the frequency domain estimator is established and a self-normalized approach to inference without the need for plug-in estimation of memory parameters is developed. Simulations show that the frequency domain estimator performs robustly under short memory and outperforms the time domain estimator when long range dependence is present. An empirical illustration is provided, examining the long-run relationship between stock returns and realized volatility.</p></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"241 2","pages":"Article 105761"},"PeriodicalIF":6.3,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140818618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Estimation and inference of seller’s expected revenue in first-price auctions","authors":"Federico Zincenko","doi":"10.1016/j.jeconom.2024.105734","DOIUrl":"https://doi.org/10.1016/j.jeconom.2024.105734","url":null,"abstract":"<div><p>I propose an estimator for the seller’s expected revenue function in a first-price sealed-bid auction with independent private values and symmetric bidders, who can exhibit constant relative risk aversion and bid according to the Bayesian Nash equilibrium. I build the proposed estimator from pseudo-private values, which can be estimated from observed bids, and show that it is pointwise and uniformly consistent: the corresponding optimal nonparametric rates of convergence can be achieved. Then I construct asymptotically valid confidence intervals and uniform confidence bands. Suggestions for critical values are based on first-order asymptotics, as well as on the bootstrap method.</p></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"241 1","pages":"Article 105734"},"PeriodicalIF":6.3,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140605771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Identifiability and estimation of possibly non-invertible SVARMA Models: The normalised canonical WHF parametrisation","authors":"Bernd Funovits","doi":"10.1016/j.jeconom.2024.105766","DOIUrl":"https://doi.org/10.1016/j.jeconom.2024.105766","url":null,"abstract":"<div><p>This article focuses on the parametrisation, identifiability, and (quasi-) maximum likelihood (QML) estimation of possibly non-invertible structural vector autoregressive moving average (SVARMA) models. SVAR models are routinely adopted due to their well-known implementation strategy. However, for various economic and statistical reasons, multivariate SVARMA settings are often more suitable. These settings introduce complexity in the analysis, primarily due to the presence of the moving average (MA) polynomial. We propose a novel representation of the MA polynomial matrix using the Wiener–Hopf factorization (WHF). A significant advantage of the WHF is its ability to handle possible non-invertibility and thus models with informational asymmetry between economic agents and outside observers. Since solutions of Dynamic Stochastic General Equilibrium (DSGE) models often involve this informational asymmetry, SVARMA models in WHF parametrisation can be considered data-driven alternatives to DSGE models and used for their evaluation. Furthermore, we provide low-level conditions for the asymptotic normality of the (Q)ML estimator and analytic expressions for the score and information matrix. As application, we estimate the Blanchard and Quah model, and compare our results and implied impulse response function with the ones in the SVAR model by Blanchard and Quah and a non-invertible SVARMA model by Gouriéroux and co-authors. Importantly, we have implemented this novel method in a well-documented R-package, making it readily accessible for researchers and practitioners.</p></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"241 2","pages":"Article 105766"},"PeriodicalIF":6.3,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S030440762400112X/pdfft?md5=31d8eea116ae38418b22b6b324439bd8&pid=1-s2.0-S030440762400112X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141068097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}