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on Econometrics |
| By: | Matias D. Cattaneo; Michael Jansson; Kenichi Nagasawa |
| Abstract: | Westling and Carone (2020) proposed a framework for studying the large sample distributional properties of generalized Grenander-type estimators, a versatile class of nonparametric estimators of monotone functions. The limiting distribution of those estimators is representable as the left derivative of the greatest convex minorant of a Gaussian process whose covariance kernel can be complicated and whose monomial mean can be of unknown order (when the degree of flatness of the function of interest is unknown). The standard nonparametric bootstrap is unable to consistently approximate the large sample distribution of the generalized Grenander-type estimators even if the monomial order of the mean is known, making statistical inference a challenging endeavour in applications. To address this inferential problem, we present a bootstrap-assisted inference procedure for generalized Grenander-type estimators. The procedure relies on a carefully crafted, yet automatic, transformation of the estimator. Moreover, our proposed method can be made ``flatness robust" in the sense that it can be made adaptive to the (possibly unknown) degree of flatness of the function of interest. The method requires only the consistent estimation of a single scalar quantity, for which we propose an automatic procedure based on numerical derivative estimation and the generalized jackknife. Under random sampling, our inference method can be implemented using a computationally attractive exchangeable bootstrap procedure. We illustrate our methods with examples and we also provide a small simulation study. The development of formal results is made possible by some technical results that may be of independent interest. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.13598&r=ecm |
| By: | Rui Wang |
| Abstract: | This paper characterizes point identification results of the local average treatment effect (LATE) using two imperfect instruments. The classical approach (Imbens and Angrist (1994)) establishes the identification of LATE via an instrument that satisfies exclusion, monotonicity, and independence. However, it may be challenging to find a single instrument that satisfies all these assumptions simultaneously. My paper uses two instruments but imposes weaker assumptions on both instruments. The first instrument is allowed to violate the exclusion restriction and the second instrument does not need to satisfy monotonicity. Therefore, the first instrument can affect the outcome via both direct effects and a shift in the treatment status. The direct effects can be identified via exogenous variation in the second instrument and therefore the local average treatment effect is identified. An estimator is proposed, and using Monte Carlo simulations, it is shown to perform more robustly than the instrumental variable estimand. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.13795&r=ecm |
| By: | Gianluca Cubadda (CEIS, Università di Roma ‘Tor Vergata’); Marco Mazzali (Università di Roma ‘Tor Vergata’) |
| Abstract: | This paper extends the multivariate index autoregressive model by Reinsel (1983) to the case of cointegrated time series of order (1, 1). In this new modelling, namely the Vector Error-Correction Index Model (VECIM), the first differences of series are driven by some linear combinations of the variables, namely the indexes. When the indexes are significantly fewer than the variables, the VECIM achieves a substantial dimension reduction w.r.t. the Vector Error Correction Model. We show that the VECIM allows one to decompose the reduced form errors into sets of common and uncommon shocks, and that the former can be further decomposed into permanent and transitory shocks. Moreover, we offer a switching algorithm for optimal estimation of the VECIM. Finally, we document the practical value of the proposed approach by both simulations and an empirical application, where we search for the shocks that drive the aggregate fluctuations at different frequency bands in the US. |
| Keywords: | Vector autoregressive models, multivariate autoregressive index model, cointegration, reduced-rank regression, dimension reduction, main business cycle shock. |
| Date: | 2023–04–04 |
| URL: | http://d.repec.org/n?u=RePEc:rtv:ceisrp:556&r=ecm |
| By: | Holm, Anders; Breen, Richard |
| Abstract: | We propose a novel way of estimating direct and indirect causal effects for panel data. Our method applies when the treatment and the mediator can be coded as binary variables. We exploit pre-treatment and pre-mediator differences in outcomes between the mediated and non-mediated groups within the treated units. Our method is applicable when the mediator is realized both before and after treatment or when it is only a consequence of the treatment. We apply our method to the New Jersey minimum wage policy data and show that a minimal effect on overall employment is mediated through part-time employment. |
| Date: | 2023–03–23 |
| URL: | http://d.repec.org/n?u=RePEc:osf:socarx:kwscz&r=ecm |
| By: | Haroon Mumtaz (Queen Mary University London); Michele Piffer (King's College London) |
| Abstract: | This paper introduces a exible local projection that generalises the model by Jordá (2005) to a non-parametric setting using Bayesian Additive Regression Trees. Monte Carlo experiments show that our BART-LP model is able to capture non-linearities in the impulse responses. Our first application shows that the fiscal multiplier is stronger in recession than expansion only in response to contractionary fiscal shocks, but not in response to expansionary fiscal shocks. We then show that financial shocks generate effects on the economy that increase more than proportionately in the size of the shock when the shock is negative, but not when the shock is positive. |
| Keywords: | Non-linear models, non-parametric techniques, identification |
| JEL: | C14 C11 C32 E52 |
| Date: | 2022–04–21 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:938&r=ecm |
| By: | Jerome R. Simons |
| Abstract: | This paper argues that the symmetrisability condition in Tyler(1981) is not necessary to establish asymptotic inference procedures for eigenvectors. We establish distribution theory for a Wald and t-test for full-vector and individual coefficient hypotheses, respectively. Our test statistics originate from eigenprojections of non-symmetric matrices. Representing projections as a mapping from the underlying matrix to its spectral data, we find derivatives through analytic perturbation theory. These results demonstrate how the analytic perturbation theory of Sun(1991) is a useful tool in multivariate statistics and are of independent interest. As an application, we define confidence sets for Bonacich centralities estimated from adjacency matrices induced by directed graphs. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.18233&r=ecm |
| By: | Christophe Bruneel-Zupanc |
| Abstract: | This paper proposes a novel approach to identify models with a discrete endogenous variable, that I study in the general context of nonseparable models with continuous potential outcomes. I show that nonparametric identification of the potential outcome and selection equations, and thus of the individual treatment effects, can be obtained with semi-instrumental variables (semi-IVs), which are relevant but only partially excluded from the potential outcomes, i.e., excluded from one or more potential outcome equations, but not necessarily all. This contrasts with the full exclusion restriction imposed on standard instrumental variables (IVs), which is stronger than necessary for identification: IVs are only a special case of valid semi-IVs. In practice, there is a trade-off between imposing stronger exclusion restrictions, and finding semi-IVs with a larger support and stronger relevance assumptions. Since, in empirical work, the main obstacle for finding a valid IV is often the full exclusion restriction, tackling the endogeneity problem with semi-IVs instead should be an attractive alternative. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.12667&r=ecm |
| By: | Xiaorong Yang; Jia Chen; Degui Li; Runze Li |
| Abstract: | This paper considers estimating functional-coefficient models in panel quantile regression with individual effects, allowing the cross-sectional and temporal dependence for large panel observations. A latent group structure is imposed on the heterogenous quantile regression models so that the number of nonparametric functional coefficients to be estimated can be reduced considerably. With the preliminary local linear quantile estimates of the subject-specific functional coefficients, a classic agglomerative clustering algorithm is used to estimate the unknown group structure and an easy-to-implement ratio criterion is proposed to determine the group number. The estimated group number and structure are shown to be consistent. Furthermore, a post-grouping local linear smoothing method is introduced to estimate the group-specific functional coefficients, and the relevant asymptotic normal distribution theory is derived with a normalisation rate comparable to that in the literature. The developed methodologies and theory are verified through a simulation study and showcased with an application to house price data from UK local authority districts, which reveals different homogeneity structures at different quantile levels. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.13218&r=ecm |
| By: | Kevin Dano |
| Abstract: | This paper introduces an algebraic approach to derive identifying moments in dynamic logit models with strictly exogenous regressors and additive fixed effects. It is based upon two common features in this class of models. First, many (individual-specific) transition probabilities can be expressed as conditional expectations of functions of the data and common parameters given the initial condition, the regressors and the fixed effects. We call such functions transition functions. Second, after a certain time period, multiple transition functions map to the same transition probabilities. This motivates a differencing strategy leveraging the multiplicity of transition functions to produce valid moment conditions in panels of adequate length. We detail the construction of identifying moments in scalar models of arbitrary lag order as well as first-order panel vector autoregressions and dynamic multinomial logit models. A simulation study illustrates the small sample performance of GMM estimators based on our methodology. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.00083&r=ecm |
| By: | Nabil Bouamara; S\'ebastien Laurent; Shuping Shi |
| Abstract: | We introduce a simple tool to control for false discoveries and identify individual signals when there are many tests, the test statistics are correlated, and the signals are potentially sparse. The tool applies the Cauchy combination test recursively on a sequence of expanding subsets of $p$-values and is referred to as the sequential Cauchy combination test. While the original Cauchy combination test aims for a global statement over a set of null hypotheses by summing transformed $p$-values, the sequential version determines which $p$-values trigger the rejection of the global null. The test achieves strong familywise error rate control and is less conservative than existing controlling procedures when the test statistics are dependent, leading to higher global powers and successful detection rates. As illustrations, we consider two popular financial econometric applications for which the test statistics have either serial dependence or cross-sectional dependence: monitoring drift bursts in asset prices and searching for assets with a nonzero alpha. The sequential Cauchy combination test is a preferable alternative in both cases in simulation settings and leads to higher detection rates than benchmark procedures in empirics. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.13406&r=ecm |
| By: | Alisa Tazhitdinova; Gonzalo Vazquez-Bare |
| Abstract: | We study a difference-in-differences (DiD) framework where groups experience unequal treatment statuses in the pre-policy change period. This approach is commonly employed in empirical studies but it contradicts the canonical model's assumptions. We show that in such settings, the standard DiD approach fails to recover the average treatment effect (ATT), unless the treatment effect is immediate and constant over time. Furthermore, the usual parallel trends test is invalid, meaning one may find pre-trends when the parallel trends assumption holds, and vice versa. We discuss two solutions. First, we show that including a linear term trend will recover the ATT if the differences in trends are constant over time (both in unequal baseline and canonical DiD settings) but not otherwise. Second, estimation in reverse also recovers the ATT if the potential outcomes do not depend on past treatments and post-policy statuses are converging. |
| JEL: | C21 C23 |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:31063&r=ecm |
| By: | Keigo Inukai; Yuta Shimodaira; Kohei Shiozawa |
| Abstract: | The convex time budget (CTB) method is a widely used experimental technique for eliciting an individual’s time preference in intertemporal choice problems. This paper investigates the accuracy of the estimation of the discount factor parameter and the present bias parameter in the quasi-hyperbolic discounting utility function for the CTB experiment. In this paper, we use a simulation technique called “parameter recovery.” We found that the precision of present bias parameter estimation is poor within the scope of previously reported parameter estimates, making it difficult to detect the effect of present bias. Our results recommend against using a combination of the CTB experimental task and the quasi-hyperbolic discounting utility model to explore the effect of present bias. This paper contributes to addressing the replicability issue in experimental economics and highlights the importance of auditing the accuracy of parameter estimates before conducting an experiment. |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:dpr:wpaper:1185r&r=ecm |
| By: | Giorgia De Nora (Queen Mary University of London) |
| Abstract: | I extend the Bayesian Factor-Augmented Vector Autoregressive model (FAVAR) to incorporate an identification scheme based on an exogenous variable approach. A Gibbs sampling algorithm is provided to estimate the posterior distributions of the models parameters. I estimate the effects of a monetary policy shock in the United States using the proposed algorithm, and find that an increase in the Federal Fund Rate has contractionary effects on both the real and financial sides of the economy. Furthermore, the paper suggests that data-rich models play an important role in mitigating price and real economic puzzles in the estimated impulse responses as well as the discrepancies among the impulse responses obtained with different monetary policy instruments. |
| Keywords: | information sufficiency, factor-augmented VARs, instrumental variables, monetary policy, structural VARs |
| JEL: | C32 C38 E52 |
| Date: | 2021–12–15 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:934&r=ecm |
| By: | Marc Hallin; Bas Werker; Bo Zhou |
| Abstract: | The classical concept of bounded completeness and its relation to sufficiency and ancillarity play a fundamental role in unbiased estimation, unbiased testing, and the validity of inference in the presence of nuisance parameters. In this short note, we provide a direct proof of a little-known result by Farrell (1962) on a characterization of bounded completeness based on an L1 denseness property of the linear span of likelihood ratios. As an application, we show that an experiment with infinite-dimensional observation space is boundedly complete iff suitably chosen restricted subexperiments with finitedimensional observation spaces are. |
| Keywords: | sufficiency, completeness, ancillarity, Brownian motion, Mazur’s theorem |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/357401&r=ecm |
| By: | Sascha A. Keweloh |
| Abstract: | This study proposes an estimator that combines statistical identification with economically motivated restrictions on the interactions. The estimator is identified by (mean) independent non-Gaussian shocks and allows for incorporation of uncertain prior economic knowledge through an adaptive ridge penalty. The estimator shrinks towards economically motivated restrictions when the data is consistent with them and stops shrinkage when the data provides evidence against the restriction. The estimator is applied to analyze the interaction between the stock and oil market. The results suggest that what is usually identified as oil-specific demand shocks can actually be attributed to information shocks extracted from the stock market, which explain about 30-40% of the oil price variation. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.13281&r=ecm |