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on Econometrics |
| By: | Linton, O. B.; Rücker, M.; Vogt, M.; Walsh, C. |
| Abstract: | We develop new econometric methods for estimation and inference in high-dimensional panel data models with interactive fixed effects. Our approach can be regarded as a non-trivial extension of the very popular common correlated effects (CCE) approach. Roughly speaking, we proceed as follows: We first construct a projection device to eliminate the unobserved factors from the model by applying a dimensionality reduction transform to the matrix of cross-sectionally averaged covariates. The unknown parameters are then estimated by applying lasso techniques to the projected model. For inference purposes, we derive a desparsified version of our lasso-type estimator. While the original CCE approach is restricted to the low-dimensional case where the number of regressors is small and fixed, our methods can deal with both lowand high-dimensional situations where the number of regressors is large and may even exceed the overall sample size. We derive theory for our estimation and inference methods both in the large-T-case, where the time series length T tends to infinity, and in the small-T-case, where T is a fixed natural number. Specifically, we derive the convergence rate of our estimator and show that its desparsified version is asymptotically normal under suitable regularity conditions. The theoretical analysis of the paper is complemented by a simulation study and an empirical application to characteristic based asset pricing. |
| Keywords: | Panel Data, Interactive Fixed Effects, CCE Estimator, High-Dimensional Model, Lasso, Desparsified Lasso |
| JEL: | C13 C23 C55 |
| Date: | 2024–11–21 |
| URL: | https://d.repec.org/n?u=RePEc:cam:camdae:2467 |
| By: | Aßmann, Christian; Boysen-Hogrefe, Jens; Pape, Markus |
| Abstract: | Orthonormality constraints are common in reduced rank models. They imply that matrix-variate parameters are given as orthonormal column vectors. However, these orthonormality restrictions do not provide identification for all parameters. For this setup, we show how the remaining identification issue can be handled in a Bayesian analysis via post-processing the sampling output according to an appropriately specified loss function. This extends the possibilities for Bayesian inference in reduced rank regression models with a part of the parameter space restricted to the Stiefel manifold. Besides inference, we also discuss model selection in terms of posterior predictive assessment. We illustrate the proposed approach with a simulation study and an empirical application. |
| Keywords: | Bayesian estimation, Post-processing, Reduced rank regression, Orthogonal transformation, Model selection, Stiefel manifold, Posterior predictive assessment |
| JEL: | C11 C31 C51 C52 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:ifwkie:306605 |
| By: | Silvia Goncalves; Ana María Herrera; Lutz Kilian; Elena Pesavento |
| Abstract: | Nonlinearities play an increasingly important role in applied work when studying the responses of macroeconomic aggregates to policy shocks. Seemingly natural adaptations of the popular local linear projection estimator to nonlinear settings may fail to recover the population responses of interest. In this paper we study the properties of an alternative nonparametric local projection estimator of the conditional and unconditional responses of an outcome variable to an observed identified shock. We discuss alternative ways of implementing this estimator and how to allow for data-dependent tuning parameters. Our results are based on data generating processes that involve, respectively, nonlinearly transformed regressors, state-dependent coefficients and nonlinear interactions between shocks and state variables. Monte Carlo simulations show that a local-linear specification of the estimator tends to work well in reasonably large samples and is robust to nonlinearities of unknown form. |
| Keywords: | impulse response; Local Projection; nonparametric estimation; nonlinear structural model; potential outcomes |
| JEL: | C14 C32 E52 |
| Date: | 2024–11–20 |
| URL: | https://d.repec.org/n?u=RePEc:fip:feddwp:99177 |
| By: | D'Haultfoeuille, Xavier; Gaillac, Christophe; Maurel, Arnaud |
| Abstract: | We study best linear predictions in a context where the outcome of interest and some of the covariates are observed in two different datasets that can-not be matched. Traditional approaches obtain point identification by relying, often implicitly, on exclusion restrictions. We show that without such restric-tions, coefficients of interest can still be partially identified and we derive a constructive characterization of the sharp identified set. We then build on this characterization to develop computationally simple and asymptotically normal estimators of the corresponding bounds. We show that these estimators exhibit good finite sample performances. |
| Keywords: | Best linear prediction; data combination; partial identification; inference. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:tse:wpaper:130028 |
| By: | Jad Beyhum; Martin Mugnier |
| Abstract: | We consider a linear panel data model with nonseparable two-way unobserved heterogeneity corresponding to a linear version of the model studied in Bonhomme et al. (2022). We show that inference is possible in this setting using a straightforward two-step estimation procedure inspired by existing discretization approaches. In the first step, we construct a discrete approximation of the unobserved heterogeneity by (k-means) clustering observations separately across the individual (i) and time (t) dimensions. In the second step, we estimate a linear model with two-way group fixed effects specific to each cluster. Our approach shares similarities with methods from the double machine learning literature, as the underlying moment conditions exhibit the same type of bias-reducing properties. We provide a theoretical analysis of a cross-fitted version of our estimator, establishing its asymptotic normality at parametric rate under the condition max(N, T) = o(min(N, T)³. Simulation studies demonstrate that our methodology achieves excellent finite-sample performance, even when T is negligible with respect to N. |
| Date: | 2024–12–16 |
| URL: | https://d.repec.org/n?u=RePEc:azt:cemmap:29/24 |
| By: | Masahiro Kato |
| Abstract: | This study proposes a debiasing method for smooth nonparametric estimators. While machine learning techniques such as random forests and neural networks have demonstrated strong predictive performance, their theoretical properties remain relatively underexplored. Specifically, many modern algorithms lack assurances of pointwise asymptotic normality and uniform convergence, which are critical for statistical inference and robustness under covariate shift and have been well-established for classical methods like Nadaraya-Watson regression. To address this, we introduce a model-free debiasing method that guarantees these properties for smooth estimators derived from any nonparametric regression approach. By adding a correction term that estimates the conditional expected residual of the original estimator, or equivalently, its estimation error, we obtain a debiased estimator with proven pointwise asymptotic normality, uniform convergence, and Gaussian process approximation. These properties enable statistical inference and enhance robustness to covariate shift, making the method broadly applicable to a wide range of nonparametric regression problems. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.20173 |
| By: | Guastadisegni, Lucia; Cagnone, Silvia; Moustaki, Irini; Vasdekis, Vassilis |
| Abstract: | This paper introduces the generalized Hausman test as a novel method for detecting the non-normality of the latent variable distribution of the unidimensional latent trait model for binary data. The test utilizes the pairwise maximum likelihood estimator for the parameters of the latent trait model, which assumes normality of the latent variable, and the maximum likelihood estimator obtained under a semi-non-parametric framework, allowing for a more flexible distribution of the latent variable. The performance of the generalized Hausman test is evaluated through a simulation study and compared with other test statistics available in the literature for testing latent variable distribution fit and an overall goodness-of-fit test statistic. Additionally, three information criteria are used to select the best-fitted model. The simulation results show that the generalized Hausman test outperforms the other tests under most conditions. However, the results obtained from the information criteria are somewhat contradictory under certain conditions, suggesting a need for further investigation and interpretation. The proposed test statistics are used in three datasets. |
| Keywords: | semi-non-parametric-IRT model; misspecification test; correlated binary data 1 |
| JEL: | C1 |
| Date: | 2024–12–26 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:126270 |
| By: | Mugnier, Martin (Paris School of Economics); Wang, Ao (University of Warwick and CAGE Research Centre) |
| Abstract: | We study a class of two-way fixed effects index function models with a nonparametric link function and individual- (or time-) specific slopes. Our model alleviates potential misspecification errors due to the common practice of specifying a known link function such as Gaussian and its tail behavior. It also enables to incorporate richer unobserved heterogeneity in the marginal effects of covariates via heterogeneous slopes across individuals. We show the identification of the link function as well as the slopes and fixed effects parameters when both individual and time dimensions are large. We propose a nonparametric consistency result for the fixed effects sieve maximum likelihood estimators. Finally, we apply our method to the study of establishing exportation and illustrate the consequences of imposing Gaussian link function and homogeneity on the slope of distance. |
| Keywords: | Nonlinear Panel Models ; Fixed Effects ; Slope Heterogeneity ; Nonparametric ; Sieve JEL Codes: C23 ; C24 ; C25 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:wrk:warwec:1531 |
| By: | Frederik Krabbe |
| Abstract: | A Markov-switching observation-driven model is a stochastic process $((S_t, Y_t))_{t \in \mathbb{Z}}$ where (i) $(S_t)_{t \in \mathbb{Z}}$ is an unobserved Markov process taking values in a finite set and (ii) $(Y_t)_{t \in \mathbb{Z}}$ is an observed process such that the conditional distribution of $Y_t$ given all past $Y$'s and the current and all past $S$'s depends only on all past $Y$'s and $S_t$. In this paper, we prove the consistency and asymptotic normality of the maximum likelihood estimator for such model. As a special case hereof, we give conditions under which the maximum likelihood estimator for the widely applied Markov-switching generalised autoregressive conditional heteroscedasticity model introduced by Haas et al. (2004b) is consistent and asymptotic normal. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.19555 |
| By: | Mohammad R. Jahan-Parvar; Charles Knipp; Pawel J. Szerszen |
| Abstract: | We propose a generalized multivariate unobserved components model to decompose macroeconomic data into trend and cyclical components. We then forecast the series using Bayesian methods. We document that a fully Bayesian estimation, that accounts for state and parameter uncertainty, consistently dominates out-of-sample forecasts produced by alternative multivariate and univariate models. In addition, allowing for stochastic volatility components in variables improves forecasts. To address data limitations, we exploit cross-sectional information, use the commonalities across variables, and account for both parameter and state uncertainty. Finally, we find that an optimally pooled univariate model outperforms individual univariate specifications, andperforms generally closer to the benchmark model. |
| Keywords: | Bayesian estimation; Maximum likelihood estimation; Online forecasting; Out-of-sample forecasting; Parameter uncertainty; Sequential Monte Carlo methods; Trend-cycle decomposition |
| JEL: | C11 C22 C32 C53 |
| Date: | 2024–12–30 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fedgfe:2024-100 |
| By: | Jean-Jacques Forneron; Zhongjun Qu |
| Abstract: | This paper considers filtering, parameter estimation, and testing for potentially dynamically misspecified state-space models. When dynamics are misspecified, filtered values of state variables often do not satisfy model restrictions, making them hard to interpret, and parameter estimates may fail to characterize the dynamics of filtered variables. To address this, a sequential optimal transportation approach is used to generate a model-consistent sample by mapping observations from a flexible reduced-form to the structural conditional distribution iteratively. Filtered series from the generated sample are model-consistent. Specializing to linear processes, a closed-form Optimal Transport Filtering algorithm is derived. Minimizing the discrepancy between generated and actual observations defines an Optimal Transport Estimator. Its large sample properties are derived. A specification test determines if the model can reproduce the sample path, or if the discrepancy is statistically significant. Empirical applications to trend-cycle decomposition, DSGE models, and affine term structure models illustrate the methodology and the results. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.20204 |
| By: | António Rua; Junho Lee; Miguel de Carvalho; Julio Avila |
| Abstract: | We propose a Bayesian time-varying model that learns about the dynamics governing joint extreme values over time. Our model relies on dual measures of time-varying extremal dependence, that are modelled via a suitable class of generalized linear models conditional on a large threshold. The simulation study indicates that the proposed methods perform well in a variety of scenarios. The application of the proposed methods to some of the world’s most important stock markets reveals complex patterns of extremal dependence over the last 30 years, including passages from asymptotic dependence to asymptotic independence. |
| JEL: | C11 C40 C58 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:ptu:wpaper:w202406 |
| By: | Xu, Yongdeng (Cardiff Business School) |
| Abstract: | This paper introduces an extended multivariate EGARCH model that overcomes the zero-return problem and allows for negative news and volatility spillover effects, making it an attractive tool for multivariate volatility modeling. Despite limitations, such as noninvertibility and unclear asymptotic properties of the QML estimator, our Monte Carlo simulations indicate that the standard QML estimator is consistent and asymptotically normal for larger sample sizes (i.e., T ≥ 2500). Two empirical examples demonstrate the model’s superior performance compared to multivariate GJR-GARCH and Log-GARCH models in volatility modeling. The first example analyzes the daily returns of three stocks from the DJ30 index, while the second example investigates volatility spillover effects among the bond, stock, crude oil, and gold markets. Overall, this extended multivariate EGARCH model offers a flexible and comprehensive framework for analyzing multivariate volatility and spillover effects in empirical finance research. |
| Keywords: | Multivariate EGARCH, QML Estimator, Volatility Spillovers, Zero Return |
| JEL: | C32 C58 G17 |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:cdf:wpaper:2024/24 |
| By: | Paul, Joseph R.; Schaffer, Mark E. |
| Abstract: | This paper introduces conformal inference, a powerful and flexible framework for constructing prediction intervals with guaranteed coverage in finite samples. Unlike conventional methods, conformal inference makes no assumptions about the underlying data distribution other than exchangeability. The paper begins with some simple examples of full and split conformal prediction that highlight the key assumption of exchangeability. We then provide more formal treatments of full and split conformal prediction along with extensions of the basic framework, including the Jackknife+ and CV+ algorithms, both of which offer a better balance between computational and statistical efficiency compared to full and split conformal prediction. The paper then discusses the limitations to achieving exact conditional coverage and several methods that aim to improve conditional coverage in practice. The final section briefly discusses areas of current research the software options for implementing conformal methods. |
| Keywords: | conformal inference, conformal prediction, distribution-free inference, machine learning |
| JEL: | C12 C14 C53 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:hwuaef:308058 |
| By: | Raffaella Giacomini; Jason Lu; Katja Smetanina |
| Abstract: | This paper develops a novel approach that leverages the information contained in expectations datasets to derive empirical measures of beliefs regarding economic shocks and their dynamic effects. Utilizing a panel of expectation revisions for a single variable across multiple horizons, we implement a time-varying factor model to nonparametrically estimate the latent shocks and their associated impulse responses at every point in time. The method is designed to accommodate small sample sizes and relies on weak assumptions, requiring no explicit modeling of expectations or assumptions about agents’ forecasting models, information sets, or rationality. Our empirical application to consensus inflation expectations identifies a single perceived shock that closely aligns with observed inflation surprises. The time-varying impulse responses indicate a significant decline in the perceived persistence of this shock, suggesting that inflation expectations have become more “anchored” over time. |
| Date: | 2024–11–25 |
| URL: | https://d.repec.org/n?u=RePEc:azt:cemmap:21/24 |
| By: | Soren Blomquist; Anil Kumar; Whitney K. Newey |
| Abstract: | This paper introduces an estimator for the average of heterogeneous elasticities of taxable income (ETI), addressing key econometric challenges posed by nonlinear budget sets. Building on an isoelastic utility framework, we derive a linear-in-logs taxable income specification that incorporates the entire budget set while allowing for individual-specific ETI and productivity growth. To account for endogenous budget sets, we employ panel data and estimate individual-specific ridge regressions, constructing a debiased average of ridge coefficients to obtain the average ETI. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2501.00633 |
| By: | Lorenzo Frattarolo |
| Abstract: | Financial crises are usually associated with increased cross-sectional dependence between asset returns, causing asymmetry between the lower and upper tail of return distribution. The detection of asymmetric dependence is now understood to be essential for market supervision, risk management, and portfolio allocation. I propose a non-parametric test procedure for the hypothesis of copula central symmetry based on the Cram\'er-von Mises distance of the empirical copula and its survival counterpart, deriving the asymptotic properties of the test under standard assumptions for stationary time series. I use the powerful tie-break bootstrap that, as the included simulation study implies, allows me to detect asymmetries with up to 25 series and the number of observations corresponding to one year of daily returns. Applying the procedure to US portfolio returns separately for each year in the sample shows that the amount of copula central asymmetry is time-varying and less present in the recent past. Asymmetry is more critical in portfolios based on size and less in portfolios based on book-to-market and momentum. In portfolios based on industry classification, asymmetry is present during market downturns, coherently with the financial contagion narrative. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2501.00634 |
| By: | Matias Quiroz (University of Technology Sydney, Australia); Laleh Tafakori (RMIT University, Australia); Hans Manner (University of Graz, Austria) |
| Abstract: | We investigate methods for forecasting multivariate realized covariances matrices applied to a set of 30 assets that were included in the DJ30 index at some point, including two novel methods that use existing (univariate) log of realized variance models that account for attenuation bias and time-varying parameters. We consider the implications of some modeling choices within the class of heterogeneous autoregressive models. The following are our key findings. First, modeling the logs of the marginal volatilities is strongly preferred over direct modeling of marginal volatility. Thus, our proposed model that accounts for attenuation bias (for the log-response) provides superior one-step-ahead forecasts over existing multivariate realized covariance approaches. Second, accounting for measurement errors in marginal realized variances generally improves multivariate forecasting performance, but to a lesser degree than previously found in the literature. Third, time-varying parameter models based on state-space models perform almost equally well. Fourth, statistical and economic criteria for comparing the forecasting performance lead to some differences in the model's rankings, which can partially be explained by the turbulent post-pandemic data in our out-of-sample validation dataset using sub-sample analyses. |
| Keywords: | State space model, Heterogeneous autoregressive, Realized measures, Volatility forecasting. |
| JEL: | C51 C53 G17 |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:grz:wpaper:2024-20 |
| By: | Kirill Borusyak; Peter Hull; Xavier Jaravel |
| Abstract: | A recent econometric literature shows two distinct paths for identification with shift-share instruments, leveraging either many exogenous shifts or exogenous shares. We present the core logic of both paths and practical takeaways via simple checklists. A variety of empirical settings illustrate key points. |
| Date: | 2024–12–12 |
| URL: | https://d.repec.org/n?u=RePEc:azt:cemmap:22/24 |
| By: | Kirill Borusyak; Matan Kolerman-Shemer |
| Abstract: | We extend the regression discontinuity (RD) design to settings where each unit's treatment status is an average or aggregate across multiple discontinuity events. Such situations arise in many studies where the outcome is measured at a higher level of spatial or temporal aggregation (e.g., by state with district-level discontinuities) or when spillovers from discontinuity events are of interest. We propose two novel estimation procedures - one at the level at which the outcome is measured and the other in the sample of discontinuities - and show that both identify a local average causal effect under continuity assumptions similar to those of standard RD designs. We apply these ideas to study the effect of unionization on inequality in the United States. Using credible variation from close unionization elections at the establishment level, we show that a higher rate of newly unionized workers in a state-by-industry cell reduces wage inequality within the cell. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2501.00428 |
| By: | Leo Krippner |
| Abstract: | The eigenvalue/eigenvector structure underlying a standard N-variable P -lag vector autoregression (VAR) may be transformed into a system of NP scalar AR1 processes, each with an eigenvalue as its coefficient. This perspective allows a VAR to be assessed, analyzed, and manipulated using the mathematical and statistical convenience of elementary AR1 processes. Illustrative empirical applications demonstrate the inherent benefits: (1) the persistence of a VAR’s dynamics is interpreted from its AR1 processes; (2) closed-form VAR forecasts are obtained from AR1 forecasts; (3) equality or zero constraints on selected AR1 coefficients are tested and imposed for VAR parsimony; (4) a median-unbiased estimate of the largest AR1 coefficient is generated and imposed to produce a more persistent VAR; (5) a unit root for the largest AR1 coefficient is tested and imposed to produce a cointegrated VAR, which also produces an estimate of the associated cointegrating vector. |
| Keywords: | vector autoregression, VAR, companion matrix, eigenvalues, eigenvectors |
| JEL: | C13 C32 C53 |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:een:camaaa:2024-71 |
| By: | Hollenbach, Johannes; Schmitz, Hendrik; Westphal, Matthias |
| Abstract: | We show that two-stage least squares (2SLS) estimates of interactions can be misleading in settings with essential heterogeneity (e.g., selection into gains) and where complier status to the instrument depends on the interaction variable. The 2SLS estimator cannot disentangle interaction effects from shifts in complier groups. Estimating marginal treatment effects addresses this problem by fixing the underlying population and unobserved heterogeneity. We illustrate this using the example of gene-environment studies, where the central parameter is the interaction effect between an endogenous, instrumented measure of environment or behavior and a predetermined measure of genetic endowment. Our application examines the effect of education on cognitive performance in old age. The results show complementarities between education and genetic predisposition in determining cognitive abilities. The marginal treatment effect estimates reveal a substantially larger gene-environment interaction, exceeding the 2SLS estimate by a factor of at least 2.5. |
| Abstract: | Wir zeigen, dass die zweistufige Kleinste-Quadrate-Methode (2SLS) unter bestimmten Bedingungen keine zuverlässige Schätzung von Interaktionstermen liefert, selbst wenn starke und valide Instrumente verwendet werden. Dieses Problem tritt dann auf, wenn unbeobachtete Heterogenität der Interaktionsvariable sowohl das Treatment als auch dessen Effekt auf das Outcome beeinflusst. In diesem Fall kann der 2SLS-Schätzer nicht zwischen beiden Arten von Heterogenität differenzieren, was aber für die beabsichtigte Interpretation des Interaktionseffektes als reiner Einfluss der Interaktionsvariable auf den kausalen Effekt des Treatments essenziell ist. Wir zeigen, dass die Schätzung marginaler Treatmenteffekte dieses Problem lösen kann, und illustrieren dies am Beispiel von Gen-Umgebung-Interaktionsstudien. Der zentrale Parameter in diesen Studien ist der Interaktionseffekt zwischen einem endogenen, instrumentierten Maß für die Umgebung (oder Entscheidungen in dieser) und genetischer Prädisposition. In unserer Anwendung untersuchen wir den Effekt von Bildung auf die kognitive Leistungsfähigkeit im Alter. Unsere Ergebnisse zeigen, dass der Bildungseffekt auf kognitive Fähigkeiten größer ist, je vorteilhafter die genetische Veranlagung. Während eine 2SLS-Schätzung nur schwache, statistisch nicht signifikante Effektunterschiede nahelegt, zeigen die auf marginalen Treatmenteffekten basierenden Schätzwerte, dass genetische Veranlagung einen relevanten und statistisch signifikanten Einfluss auf den Bildungseffekt hat: Dieser übersteigt den Interaktionsparameter der 2SLS-Schätzung mindestens um den Faktor 2, 5. |
| Keywords: | Two-stage least squares estimation, marginal treatment effects, gene-environment interactions, cognitive decline |
| JEL: | C31 J14 J24 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:rwirep:306835 |
| By: | Andrade, Philippe (Federal Reserve Bank of Boston); Ferroni, Filippo (Federal Reserve Bank of Chicago); Melosi, Leonardo (University of Warwick, EUI, DNB & CEPR) |
| Abstract: | We introduce a method that exploits some non-gaussian features of structural shocks to identify structural vector autoregressive models. More specifically, we propose to combine inequality restrictions on the higher-order moments of the structural shocks of interest with other set-identifying constraints, typically sign restrictions. We illustrate how, both in large or small sample settings, higher-moment restrictions considerably narrows the identification of monetary policy shocks compared to what is obtained with minimal sign restrictions typically used in the SVAR literature. The proposed methodology also delivers new insights on the macroeconomic effects of sovereign risk in the Euro Area, and on the transmission of geopolitical risk to the US economy. |
| Keywords: | Shock identification ; skewness ; kurtosis ; sign restrictions ; monetary policy ; sovereign risk ; geopolitical risk. JEL Codes: C32 ; E27 ; E32 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:wrk:warwec:1537 |