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on Econometrics |
| By: | Leonard Goff |
| Abstract: | Many identification results in instrumental variables (IV) models have the property that identification holds with no restrictions on the joint distribution of potential outcomes or how these outcomes are correlated with selection behavior. This enables many IV models to allow for arbitrary heterogeneity in treatment effects and the possibility of selection on gains in the outcome variable. I call this type of identification result "outcome-agnostic", and provide a necessary and sufficient condition for counterfactual means or treatment effects to be identified in an outcome-agnostic manner, when the instruments and treatments have finite support. In addition to unifying many existing IV identification results, this characterization suggests a brute-force approach to revealing all restrictions on selection behavior that yield identification of treatment effect parameters. While computationally intensive, the approach uncovers even in simple settings new selection models that afford identification of interpretable causal parameters. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.02835&r= |
| By: | Takahiro ITO (Graduate School of International Cooperation Studies, Kobe University) |
| Abstract: | This paper formulates a novel distribution-free maximum likelihood estimator for binary and ordered response models and demonstrates its finite sample performance in a Monte Carlo simulation. The simulation examines an ordered response model, focusing on estimating the effect of an exogenous regressor (e.g., randomly assigned treatment status) on the choice probability for an ordered outcome. Estimations are implemented based on a binary specification, which converts the outcome to dichotomous values {0, 1}, or an ordinal specification, which uses the outcome as is. The simulation results show that the proposed estimator outperforms conventional parametric/semiparametric estimators in most cases for both specifications. The results also show that the superiority of the proposed estimator holds even in the presence of conditionally heteroscedastic variance. In addition, the estimates based on the ordinal specification are always superior to those based on the binary specification in all simulation designs, implying that converting ordered responses to dichotomous responses and estimating based on the binary specification may not be the optimal approach. |
| Keywords: | semiparametric estimation, distribution-free maximum likelihood, binary choice model, ordered response model, Likert-type data, heteroscedastic variance |
| Date: | 2024–01 |
| URL: | https://d.repec.org/n?u=RePEc:kcs:wpaper:42&r= |
| By: | Lihua Lei |
| Abstract: | In studies of educational production functions or intergenerational mobility, it is common to transform the key variables into percentile ranks. Yet, it remains unclear what the regression coefficient estimates with ranks of the outcome or the treatment. In this paper, we derive effective causal estimands for a broad class of commonly-used regression methods, including the ordinary least squares (OLS), two-stage least squares (2SLS), difference-in-differences (DiD), and regression discontinuity designs (RDD). Specifically, we introduce a novel primitive causal estimand, the Rank Average Treatment Effect (rank-ATE), and prove that it serves as the building block of the effective estimands of all the aforementioned econometrics methods. For 2SLS, DiD, and RDD, we show that direct applications to outcome ranks identify parameters that are difficult to interpret. To address this issue, we develop alternative methods to identify more interpretable causal parameters. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.05548&r= |
| By: | Martin Huber; Kevin Kloiber; Lukas Laffers |
| Abstract: | We propose a test for the identification of causal effects in mediation and dynamic treatment models that is based on two sets of observed variables, namely covariates to be controlled for and suspected instruments, building on the test by Huber and Kueck (2022) for single treatment models. We consider models with a sequential assignment of a treatment and a mediator to assess the direct treatment effect (net of the mediator), the indirect treatment effect (via the mediator), or the joint effect of both treatment and mediator. We establish testable conditions for identifying such effects in observational data. These conditions jointly imply (1) the exogeneity of the treatment and the mediator conditional on covariates and (2) the validity of distinct instruments for the treatment and the mediator, meaning that the instruments do not directly affect the outcome (other than through the treatment or mediator) and are unconfounded given the covariates. Our framework extends to post-treatment sample selection or attrition problems when replacing the mediator by a selection indicator for observing the outcome, enabling joint testing of the selectivity of treatment and attrition. We propose a machine learning-based test to control for covariates in a data-driven manner and analyze its finite sample performance in a simulation study. Additionally, we apply our method to Slovak labor market data and find that our testable implications are not rejected for a sequence of training programs typically considered in dynamic treatment evaluations. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.13826&r= |
| By: | Justyna Wr\'oblewska; {\L}ukasz Kwiatkowski |
| Abstract: | We develop a Bayesian framework for cointegrated structural VAR models identified by two-state Markovian breaks in conditional covariances. The resulting structural VEC specification with Markov-switching heteroskedasticity (SVEC-MSH) is formulated in the so-called B-parameterization, in which the prior distribution is specified directly for the matrix of the instantaneous reactions of the endogenous variables to structural innovations. We discuss some caveats pertaining to the identification conditions presented earlier in the literature on stationary structural VAR-MSH models, and revise the restrictions to actually ensure the unique global identification through the two-state heteroskedasticity. To enable the posterior inference in the proposed model, we design an MCMC procedure, combining the Gibbs sampler and the Metropolis-Hastings algorithm. The methodology is illustrated both with a simulated as well as real-world data examples. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.03053&r= |
| By: | Retsef Levi; Elisabeth Paulson; Georgia Perakis; Emily Zhang |
| Abstract: | We address a core problem in causal inference: estimating heterogeneous treatment effects using panel data with general treatment patterns. Many existing methods either do not utilize the potential underlying structure in panel data or have limitations in the allowable treatment patterns. In this work, we propose and evaluate a new method that first partitions observations into disjoint clusters with similar treatment effects using a regression tree, and then leverages the (assumed) low-rank structure of the panel data to estimate the average treatment effect for each cluster. Our theoretical results establish the convergence of the resulting estimates to the true treatment effects. Computation experiments with semi-synthetic data show that our method achieves superior accuracy compared to alternative approaches, using a regression tree with no more than 40 leaves. Hence, our method provides more accurate and interpretable estimates than alternative methods. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.05633&r= |
| By: | David M. Ritzwoller; Joseph P. Romano; Azeem M. Shaikh |
| Abstract: | We review approaches to statistical inference based on randomization. Permutation tests are treated as an important special case. Under a certain group invariance property, referred to as the ``randomization hypothesis, '' randomization tests achieve exact control of the Type I error rate in finite samples. Although this unequivocal precision is very appealing, the range of problems that satisfy the randomization hypothesis is somewhat limited. We show that randomization tests are often asymptotically, or approximately, valid and efficient in settings that deviate from the conditions required for finite-sample error control. When randomization tests fail to offer even asymptotic Type 1 error control, their asymptotic validity may be restored by constructing an asymptotically pivotal test statistic. Randomization tests can then provide exact error control for tests of highly structured hypotheses with good performance in a wider class of problems. We give a detailed overview of several prominent applications of randomization tests, including two-sample permutation tests, regression, and conformal inference. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.09521&r= |
| By: | Steven Wilkins Reeves; Shane Lubold; Arun G. Chandrasekhar; Tyler H. McCormick |
| Abstract: | The stable unit treatment value assumption states that the outcome of an individual is not affected by the treatment statuses of others, however in many real world applications, treatments can have an effect on many others beyond the immediately treated. Interference can generically be thought of as mediated through some network structure. In many empirically relevant situations however, complete network data (required to adjust for these spillover effects) are too costly or logistically infeasible to collect. Partially or indirectly observed network data (e.g., subsamples, aggregated relational data (ARD), egocentric sampling, or respondent-driven sampling) reduce the logistical and financial burden of collecting network data, but the statistical properties of treatment effect adjustments from these design strategies are only beginning to be explored. In this paper, we present a framework for the estimation and inference of treatment effect adjustments using partial network data through the lens of structural causal models. We also illustrate procedures to assign treatments using only partial network data, with the goal of either minimizing estimator variance or optimally seeding. We derive single network asymptotic results applicable to a variety of choices for an underlying graph model. We validate our approach using simulated experiments on observed graphs with applications to information diffusion in India and Malawi. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.11940&r= |
| By: | Jianqing Fan; Yuling Yan; Yuheng Zheng |
| Abstract: | This article establishes a new and comprehensive estimation and inference theory for principal component analysis (PCA) under the weak factor model that allow for cross-sectional dependent idiosyncratic components under nearly minimal the factor strength relative to the noise level or signal-to-noise ratio. Our theory is applicable regardless of the relative growth rate between the cross-sectional dimension $N$ and temporal dimension $T$. This more realistic assumption and noticeable result requires completely new technical device, as the commonly-used leave-one-out trick is no longer applicable to the case with cross-sectional dependence. Another notable advancement of our theory is on PCA inference $ - $ for example, under the regime where $N\asymp T$, we show that the asymptotic normality for the PCA-based estimator holds as long as the signal-to-noise ratio (SNR) grows faster than a polynomial rate of $\log N$. This finding significantly surpasses prior work that required a polynomial rate of $N$. Our theory is entirely non-asymptotic, offering finite-sample characterizations for both the estimation error and the uncertainty level of statistical inference. A notable technical innovation is our closed-form first-order approximation of PCA-based estimator, which paves the way for various statistical tests. Furthermore, we apply our theories to design easy-to-implement statistics for validating whether given factors fall in the linear spans of unknown latent factors, testing structural breaks in the factor loadings for an individual unit, checking whether two units have the same risk exposures, and constructing confidence intervals for systematic risks. Our empirical studies uncover insightful correlations between our test results and economic cycles. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.03616&r= |
| By: | Johannes W. Ligtenberg; Tiemen Woutersen |
| Abstract: | Estimates in judge designs run the risk of being biased due to the many judge identities that are implicitly or explicitly used as instrumental variables. The usual method to analyse judge designs, via a leave-out mean instrument, eliminates this many instrument bias only in case the data are clustered in at most one dimension. What is left out in the mean defines this clustering dimension. How most judge designs cluster their standard errors, however, implies that there are additional clustering dimensions, which makes that a many instrument bias remains. We propose two estimators that are many instrument bias free, also in multidimensional clustered judge designs. The first generalises the one dimensional cluster jackknife instrumental variable estimator, by removing from this estimator the additional bias terms due to the extra dependence in the data. The second models all but one clustering dimensions by fixed effects and we show how these numerous fixed effects can be removed without introducing extra bias. A Monte-Carlo experiment and the revisitation of two judge designs show the empirical relevance of properly accounting for multidimensional clustering in estimation. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.09473&r= |
| By: | Daniel Ober-Reynolds |
| Abstract: | Missing data is pervasive in econometric applications, and rarely is it plausible that the data are missing (completely) at random. This paper proposes a methodology for studying the robustness of results drawn from incomplete datasets. Selection is measured as the squared Hellinger divergence between the distributions of complete and incomplete observations, which has a natural interpretation. The breakdown point is defined as the minimal amount of selection needed to overturn a given result. Reporting point estimates and lower confidence intervals of the breakdown point is a simple, concise way to communicate the robustness of a result. An estimator of the breakdown point of a result drawn from a generalized method of moments model is proposed and shown root-n consistent and asymptotically normal under mild assumptions. Lower confidence intervals of the breakdown point are simple to construct. The paper concludes with a simulation study illustrating the finite sample performance of the estimators in several common models. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.06804&r= |
| By: | Carolina Caetano; Brantly Callaway |
| Abstract: | In this paper, we study difference-in-differences identification and estimation strategies where the parallel trends assumption holds after conditioning on time-varying covariates and/or time-invariant covariates. Our first main contribution is to point out a number of weaknesses of commonly used two-way fixed effects (TWFE) regressions in this context. In addition to issues related to multiple periods and variation in treatment timing that have been emphasized in the literature, we show that, even in the case with only two time periods, TWFE regressions are not generally robust to (i) paths of untreated potential outcomes depending on the level of time-varying covariates (as opposed to only the change in the covariates over time), (ii) paths of untreated potential outcomes depending on time-invariant covariates, and (iii) violations of linearity conditions for outcomes over time and/or the propensity score. Even in cases where none of the previous three issues hold, we show that TWFE regressions can suffer from negative weighting and weight-reversal issues. Thus, TWFE regressions can deliver misleading estimates of causal effect parameters in a number of empirically relevant cases. Second, we extend these arguments to the case of multiple periods and variation in treatment timing. Third, we provide simple diagnostics for assessing the extent of misspecification bias arising due to TWFE regressions. Finally, we propose alternative (and simple) estimation strategies that can circumvent these issues with two-way fixed regressions. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.15288&r= |
| By: | Hollenbach, Florian M (Copenhagen Business School); Egerod, Benjamin |
| Abstract: | In difference-in-differences designs with staggered treatment timing and dynamic treatment effects, the two-way fixed effects estimator fails to recover an interpretable causal estimate. A large number of estimators have been proposed to remedy this issue. The flexibility of these estimators, however, increases their variance. This can lead to statistical tests with low statistical power. As a consequence, small effects are unlikely to be discovered. Additionally, under low power, if a statistically significant estimate is recovered, the estimate is often wrongly signed and/or greatly exaggerated. Using simulations on real-world data on US States, we show that effect sizes of 10 to 15% are necessary for the recently developed estimators for staggered difference-in-differences to produce statistical tests that achieve 80% power. Further, conditional on statistical significance, when the intervention generates weak effects, estimators recover the wrong sign in approximately 10% of the simulations and overestimate the true effect by several hundred percent on average. We use data on publicly traded firms to investigate which sample size is needed for a staggered difference-in-differences analysis to be informative. We find that depending on the dependent variable and effect size, even the most efficient estimators generally need more than 250 units to achieve reasonable power. We conclude with a discussion of how this type of ‘design analysis’ ought to be used by researchers before estimating staggered difference-in-differences models. We also discuss how power may under certain conditions be improved if a study is re-designed, e.g., by examining county-level outcomes with state-level interventions. |
| Date: | 2024–06–18 |
| URL: | https://d.repec.org/n?u=RePEc:osf:osfxxx:ac5ru&r= |
| By: | Shi, Xiangyu |
| Abstract: | In this paper, I argue that in situations of complex network dependence, the traditional and widely used Hausman-style instrumental variable estimation may not be valid for causal identification. This is the case for inter-regional migration networks when evaluating place-based labor market policies, and for correlated unobserved consumer tastes in the product and geographic space in demand estimation. I build an economic model for these two cases, respectively, to derive the estimating equation and to shed light on the fallacy---omitted variable bias and the resulting violation of exclusion restriction---of the traditional econometric framework. I then build an alternative econometric framework and propose a new approach to estimation that exploits higher-order network neighbors and, then, I establish its desirable properties. I conduct Monte Carlo simulations and two empirical analyses that each correspond to the two economic models to validate this new approach of estimation. |
| Keywords: | treatment effect; network; instrumental variable; Hausman IV; spatial linkages; migration network; demand estimation |
| JEL: | C0 C1 C3 |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:121349&r= |
| By: | Chen Tong; Peter Reinhard Hansen; Ilya Archakov |
| Abstract: | We introduce a novel multivariate GARCH model with flexible convolution-t distributions that is applicable in high-dimensional systems. The model is called Cluster GARCH because it can accommodate cluster structures in the conditional correlation matrix and in the tail dependencies. The expressions for the log-likelihood function and its derivatives are tractable, and the latter facilitate a score-drive model for the dynamic correlation structure. We apply the Cluster GARCH model to daily returns for 100 assets and find it outperforms existing models, both in-sample and out-of-sample. Moreover, the convolution-t distribution provides a better empirical performance than the conventional multivariate t-distribution. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.06860&r= |
| By: | Tibor Szendrei; Arnab Bhattacharjee; Mark E. Schaffer |
| Abstract: | Mixed frequency data has been shown to improve the performance of growth-at-risk models in the literature. Most of the research has focused on imposing structure on the high-frequency lags when estimating MIDAS-QR models akin to what is done in mean models. However, only imposing structure on the lag-dimension can potentially induce quantile variation that would otherwise not be there. In this paper we extend the framework by introducing structure on both the lag dimension and the quantile dimension. In this way we are able to shrink unnecessary quantile variation in the high-frequency variables. This leads to more gradual lag profiles in both dimensions compared to the MIDAS-QR and UMIDAS-QR. We show that this proposed method leads to further gains in nowcasting and forecasting on a pseudo-out-of-sample exercise on US data. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.15157&r= |
| By: | Badi H. Baltagi (Center for Policy Research, Maxwell School, Syracuse University, 426 Eggers Hall, Syracuse, NY 13244); Long Liu (Department of Economics, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431) |
| Abstract: | This note shows that for a spatial regression with a weight matrix depicting a complete bipartite network, the Moran I test for zero spatial correlation is never rejected when the alternative is positive spatial correlation no matter how large the true value of the spatial correlation coefficient. In contrast, the null hypothesis of zero spatial correlation is always rejected (with probability one asymptotically) when the alternative is negative spatial correlation and the true value of the spatial correlation coefficient is near -1. |
| Keywords: | Spatial Error Model, Moran I Test, Complete Bipartite Network. |
| JEL: | C12 C21 C31 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:max:cprwps:264&r= |
| By: | Lukas Hack; Klodiana Istrefi; Matthias Meier |
| Abstract: | Conventional strategies to identify monetary policy shocks rest on the implicit assumption that systematic monetary policy is constant over time. We formally show that these strategies do not isolate monetary policy shocks in an environment with time-varying systematic monetary policy. Instead, they are contaminated by systematic monetary policy and macroeconomic variables, leading to contamination bias in estimated impulse responses. Empirically, we show that Romer and Romer (2004) monetary policy shocks are indeed predictable by fluctuations in systematic monetary policy. Instead, we propose a new monetary policy shock that is orthogonal to systematic monetary policy. Our shock suggests U.S. monetary policy has shorter lags and stronger effects on inflation and output. |
| Keywords: | Systematic monetary policy, monetary policy shocks, identification |
| JEL: | E32 E43 E52 E58 |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2024_557&r= |
| By: | Kejin Wu (Department of Mathematics, University of California San Diego); Sayar Karmakar (Department of Statistics, University of Florida); Rangan Gupta (Department of Economics, University of Pretoria) |
| Abstract: | In this work, we explore the forecasting ability of a recently proposed normalizing and variance-stabilizing (NoVaS) transformation with the possible inclusion of exogenous variables. From an applied point-of-view, extra knowledge such as fundamentals- and sentiments-based information could be beneficial to improve the prediction accuracy of market volatility if they are incorporated into the forecasting process. In the classical approach, these models including exogenous variables are typically termed GARCHX-type models. Being a Model-free prediction method, NoVaS has generally shown more accurate, stable and robust (to misspecifications) performance than that compared to classical GARCH-type methods. This motivates us to extend this framework to the GARCHX forecasting as well. We derive the NoVaS transformation needed to include exogenous covariates and then construct the corresponding prediction procedure. We show through extensive simulation studies that bolster our claim that the NoVaS method outperforms traditional ones, especially for long-term time aggregated predictions. We also provide an interesting data analysis to exhibit how our method could possibly shed light on the role of geopolitical risks in forecasting volatility in national stock market indices for three different countries in Europe. |
| Keywords: | Volatility forecasting, Model-free prediction, GARCH, GARCHX |
| JEL: | C32 C53 C63 Q54 |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:pre:wpaper:202425&r= |
| By: | Markus Bibinger |
| Abstract: | The scope of this manuscript is to review some recent developments in statistics for discretely observed semimartingales which are motivated by applications for financial markets. Our journey through this area stops to take closer looks at a few selected topics discussing recent literature. We moreover highlight and explain the important role played by some classical concepts of probability and statistics. We focus on three main aspects: Testing for jumps; rough fractional stochastic volatility; and limit order microstructure noise. We review jump tests based on extreme value theory and complement the literature proposing new statistical methods. They are based on asymptotic theory of order statistics and the R\'{e}nyi representation. The second stage of our journey visits a recent strand of research showing that volatility is rough. We further investigate this and establish a minimax lower bound exploring frontiers to what extent the regularity of latent volatility can be recovered in a more general framework. Finally, we discuss a stochastic boundary model with one-sided microstructure noise for high-frequency limit order prices and its probabilistic and statistical foundation. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.07388&r= |
| By: | Tony Chernis; Gary Koop; Emily Tallman; Mike West |
| Abstract: | The macroeconomy is a sophisticated dynamic system involving significant uncertainties that complicate modelling. In response, decision makers consider multiple models that provide different predictions and policy recommendations which are then synthesized into a policy decision. In this setting, we introduce and develop Bayesian predictive decision synthesis (BPDS) to formalize monetary policy decision processes. BPDS draws on recent developments in model combination and statistical decision theory that yield new opportunities in combining multiple models, emphasizing the integration of decision goals, expectations and outcomes into the model synthesis process. Our case study concerns central bank policy decisions about target interest rates with a focus on implications for multi-step macroeconomic forecasting. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.03321&r= |
| By: | Marco Cozzi (Department of Economics, University of Victoria) |
| Abstract: | I propose a modified implementation of the popular Hamilton filter, to make the cyclical component extracted from an aggregate variable consistent with the aggregation of the cyclical components extracted from its underlying variables. This procedure is helpful in many circumstances, for instance when dealing with a variable that comes from a definition or when the empirical relationship is based on an equilibrium condition of a growth model. The procedure consists of the following steps: 1) build the aggregate variable, 2) run the Hamilton filter regression on the aggregate variable and store the related OLS estimates, 3) use these estimated parameters to predict the trends of all the underlying variables, 4) rescale the constant terms to obtain mean-zero cyclical components that are aggregation-consistent. I consider two applications, exploiting U.S. and Canadian data. The former is based on the GDP expenditure components, while the latter on the GDP of its Provinces and Territories. I find sizable differences between the cyclical components of aggregate GDP computed with and without the adjustment, making it a valuable procedure for both assessing the output gap and validating empirically DSGE models. |
| Keywords: | Business cycles, Filtering, Hamilton filter, Output gap, Trend-cycle decomposition. JEL Classifications: C22, E30, E32. |
| Date: | 2024–05 |
| URL: | https://d.repec.org/n?u=RePEc:vic:vicddp:2401&r= |