Econometrics

10 pages, 302 KB

Open AccessCommunication

Fractional Probit with Cross-Sectional Volatility: Bridging Heteroskedastic Probit and Fractional Response Models

by Songsak Sriboonchitta, Aree Wiboonpongse, Jittaporn Sriboonjit and Woraphon Yamaka

Econometrics 2025, 13(4), 43; https://doi.org/10.3390/econometrics13040043 - 3 Nov 2025

This paper introduces a new econometric framework for modeling fractional outcomes bounded between zero and one. We propose the Fractional Probit with Cross-Sectional Volatility (FPCV), which specifies the conditional mean through a probit link and allows the conditional variance to depend on observable heterogeneity. The model extends heteroskedastic probit methods to fractional responses and unifies them with existing approaches for proportions. Monte Carlo simulations demonstrate that the FPCV estimator achieves lower bias, more reliable inference, and superior predictive accuracy compared with standard alternatives. The framework is particularly suited to empirical settings where fractional outcomes display systematic variability across units, such as participation rates, market shares, health indices, financial ratios, and vote shares. By modeling both mean and variance, FPCV provides interpretable measures of volatility and offers a robust tool for empirical analysis and policy evaluation. Full article

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20 pages, 431 KB

Open AccessArticle

Counterfactual Duration Analysis

by Miguel A. Delgado and Andrés García-Suaza

Econometrics 2025, 13(4), 42; https://doi.org/10.3390/econometrics13040042 - 30 Oct 2025

Viewed by 229

Abstract

This article introduces new counterfactual standardization techniques for comparing duration distributions subject to random censoring through counterfactual decompositions. The counterfactual distribution of one population relative to another is computed after estimating the conditional distribution, using either a semiparametric or a nonparametric specification. We consider both the semiparametric proportional hazard model and a fully nonparametric partition-based estimator. The finite-sample performance of the proposed methods is evaluated through Monte Carlo experiments. We also illustrate the methodology with an application to unemployment duration in Spain during the period between 2004 and 2007, focusing on gender differences. The results indicate that observable characteristics account for only a small portion of the observed gap. Full article

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27 pages, 448 KB

Open AccessArticle

Consistency of the OLS Bootstrap for Independently but Not-Identically Distributed Data: A Permutation Perspective

by Alwyn Young

Econometrics 2025, 13(4), 41; https://doi.org/10.3390/econometrics13040041 - 23 Oct 2025

Viewed by 184

Abstract

This paper introduces a new approach to proving bootstrap consistency based upon the distribution of permutation statistics, using it to derive results covering fundamentally not-identically distributed groups of data, in which average moments do not converge to anything, with moment conditions that are [...] Read more.

17 pages, 339 KB

Open AccessReview

VAR Models with an Index Structure: A Survey with New Results

by Gianluca Cubadda

Econometrics 2025, 13(4), 40; https://doi.org/10.3390/econometrics13040040 - 22 Oct 2025

Viewed by 422

Abstract

The main aim of this paper is to review recent advances in the multivariate autoregressive index model [MAI] and their applications to economic and financial time series. MAI has recently gained momentum because it can be seen as a link between two popular but distinct multivariate time series approaches: vector autoregressive modeling [VAR] and the dynamic factor model [DFM]. Indeed, on the one hand, MAI is a VAR model with a peculiar reduced-rank structure that can lead to a significant dimension reduction; on the other hand, it allows for the identification of common components and common shocks in a similar way as the DFM. Our focus is on recent developments of the MAI, which include extending the original model with individual autoregressive structures, stochastic volatility, time-varying parameters, high-dimensionality, and co-integration. In addition, some gaps in the literature are filled by providing new results on the representation theory underlying previous contributions, and a novel model is provided. Full article

(This article belongs to the Special Issue Advancements in Macroeconometric Modeling and Time Series Analysis)

22 pages, 400 KB

Open AccessArticle

Demonstrating That the Autoregressive Distributed Lag Bounds Test Can Detect a Long-Run Levels Relationship When the Dependent Variable Is I(0)

by Chris Stewart

Econometrics 2025, 13(4), 39; https://doi.org/10.3390/econometrics13040039 - 22 Oct 2025

Viewed by 267

Abstract

The autoregressive distributed lag bounds t-test and F-test for a long-run relationship that allows level variables to be either

I (1)

I (0)

is widely used in the literature. However, a long-run levels relationship cannot be detected [...] Read more.

The autoregressive distributed lag bounds t-test and F-test for a long-run relationship that allows level variables to be either

I (1)

I (0)

is widely used in the literature. However, a long-run levels relationship cannot be detected when the dependent variable is

I (0)

, because both tests will always reject their null hypotheses. It has subsequently been argued that a third test determines whether the dependent variable is

I (1)

, such that when all three tests reject their null hypotheses, a cointegrating equation with an

I (1)

dependent variable is identified. It is argued that all three tests rejecting their null hypotheses rules out the possibility that the dependent variable is

I (0)

, implying that the three tests cannot detect an equilibrium when the dependent variable is

I (0)

. Our first contribution is to demonstrate and explain that rejection of all three tests’ null hypotheses can also indicate an equilibrium when the dependent variable is

I (0)

and not only when it is

I (1)

. Our second contribution is to produce previously unavailable critical values for the third test in the cases where an intercept or trend is restricted into the equilibrium. Full article

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56 pages, 1777 KB

Open AccessReview

Vis Inertiae and Statistical Inference: A Review of Difference-in-Differences Methods Employed in Economics and Other Subjects

by Bruno Paolo Bosco and Paolo Maranzano

Econometrics 2025, 13(4), 38; https://doi.org/10.3390/econometrics13040038 - 30 Sep 2025

Viewed by 832

Abstract

Difference in Differences (DiD) is a useful statistical technique employed by researchers to estimate the effects of exogenous events on the outcome of some response variables in random samples of treated units (i.e., units exposed to the event) ideally drawn from an infinite population. The term “effect” should be understood as the discrepancy between the post-event realisation of the response and the hypothetical realisation of that same outcome for the same treated units in the absence of the event. This theoretical discrepancy is clearly unobservable. To circumvent the implicit missing variable problem, DiD methods utilise the realisations of the response variable observed in comparable random samples of untreated units. The latter are samples of units drawn from the same population, but they are not exposed to the event under investigation. They function as the control or comparison group and serve as proxies for the non-existent untreated realisations of the responses in treated units during post-treatment periods. In summary, the DiD model posits that, in the absence of intervention and under specific conditions, treated units would exhibit behaviours that are indistinguishable from those of control or untreated units during the post-treatment periods. For the purpose of estimation, the method employs a combination of before–after and treatment–control group comparisons. The event that affects the response variables is referred to as “treatment.” However, it could also be referred to as “causal factor” to emphasise that, in the DiD approach, the objective is not to estimate a mere statistical association among variables. This review introduces the DiD techniques for researchers in economics, public policy, health research, management, environmental analysis, and other fields. It commences with the rudimentary methods employed to estimate the so-called Average Treatment Effect upon Treated (ATET) in a two-period and two-group case and subsequently addresses numerous issues that arise in a multi-unit and multi-period context. A particular focus is placed on the statistical assumptions necessary for a precise delineation of the identification process of the cause–effect relationship in the multi-period case. These assumptions include the parallel trend hypothesis, the no-anticipation assumption, and the SUTVA assumption. In the multi-period case, both the homogeneous and heterogeneous scenarios are taken into consideration. The homogeneous scenario refers to the situation in which the treated units are initially treated in the same periods. In contrast, the heterogeneous scenario involves the treatment of treated units in different periods. A portion of the presentation will be allocated to the developments associated with the DiD techniques that can be employed in the context of data clustering or spatio-temporal dependence. The present review includes a concise exposition of some policy-oriented papers that incorporate applications of DiD. The areas of focus encompass income taxation, migration, regulation, and environmental management. Full article

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Econometrics, Volume 13, Issue 4 (December 2025) – 6 articles

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