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on Econometrics |
| By: | Alain Guay (University of Quebec in Montreal); Florian Pelgrin (EDHEC Business School) |
| Abstract: | This paper proposes a joint methodology for the identification and inference of structural vector autoregressive models in the frequency domain. We show that identifying restrictions can be written naturally as an asymptotic least squares problem (Gourieroux, Monfort and Trognon, 1985) in which there is a continuum of nonlinear estimating equations. Following Carrasco and Florens (2000), we then develop a continuum asymptotic least squares estimator (C-ALS) that exploits efficiently the continuum of estimating equations thereby allowing to obtain optimal consistent estimates of impulse responses and reliable confidence intervals. Moreover the identifying restrictions can be formally tested using an appropriate J-stat and the frequency band can be selected with a data-driven procedure. Finally, we provide some new results using Monte Carlo simulations and applications regarding the hours-productivity debate and the impact of news shocks. |
| Keywords: | SVARs, Frequency domain, Asymptotic least squares, Continuum of identifying restrictions. |
| JEL: | C12 C32 C51 |
| Date: | 2021–08 |
| URL: | http://d.repec.org/n?u=RePEc:bbh:wpaper:21-07&r=ecm |
| By: | Harvey, David I; Leybourne, Stephen J; Taylor, AM Robert |
| Abstract: | Predictive regression methods are widely used to examine the predictability of (excess) stock returns by lagged financial variables characterised by unknown degrees of persistence and endogeneity. We develop a new hybrid test for predictability in these circumstances based on simple regression t-statistics. Where the predictor is endogenous, the optimal, but infeasible, test for predictability is based on the t-statistic on the lagged predictor in the basic predictive regression augmented with the current period innovation driving the predictor. We propose a feasible version of this augmented test, designed for the case where the predictor is an endogenous near-unit root process, using a GLS-based estimate of the innovation used in the infeasible test regression. The limiting null distribution of this statistic depends on both the endogeneity correlation parameter and the local-to-unity parameter characterising the predictor. A method for obtaining asymptotic critical values is discussed and response surfaces are provided. We compare the asymptotic power properties of the feasible augmented test with those of a (non-augmented) t-test recently considered in Harvey et al. (2021) and show that the augmented test is more powerful in the strongly persistent predictor case. We then propose using a weighted combination of the augmented statistic and the t-statistic of Harvey et al. (2021), where the weights are obtained using the p-values from a unit root test on the predictor. We find this can further improve asymptotic power in cases where the predictor has persistence at or close to that of a unit root process. Our final hybrid testing procedure then embeds the weighted statistic within a switching-based procedure which makes use of a standard predictive regression t-test, compared with standard normal critical values, when there is evidence for the predictor being weakly persistent. Monte Carlo simulations suggest that overall our new hybrid test displays superior finite sample performance to comparable extant tests. |
| Keywords: | predictive regression; augmented regression; persistence; endogeneity; weighted statistics |
| Date: | 2023–03–08 |
| URL: | http://d.repec.org/n?u=RePEc:esy:uefcwp:35133&r=ecm |
| By: | Zhenhong Huang; Zhaoyuan Li; Jianfeng Yao |
| Abstract: | This paper revisits the Lagrange multiplier type test for the null hypothesis of no cross-sectional dependence in large panel data models. We propose a unified test procedure and its power enhancement version, which show robustness for a wide class of panel model contexts. Specifically, the two procedures are applicable to both heterogeneous and fixed effects panel data models with the presence of weakly exogenous as well as lagged dependent regressors, allowing for a general form of nonnormal error distribution. With the tools from Random Matrix Theory, the asymptotic validity of the test procedures is established under the simultaneous limit scheme where the number of time periods and the number of cross-sectional units go to infinity proportionally. The derived theories are accompanied by detailed Monte Carlo experiments, which confirm the robustness of the two tests and also suggest the validity of the power enhancement technique. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.14387&r=ecm |
| By: | Federico A. Bugni; Ivan A. Canay; Steve McBride |
| Abstract: | This paper studies settings where there is interest in identifying and estimating an average causal effect of a binary treatment on an outcome of interest, under complete randomization or selection on observables assumptions. The outcome does not get immediately realized after treatment assignment, a feature that is ubiquitous in empirical settings, creating a time window in between the treatment and the realization of the outcome. The existence of such a time window, in turn, opens up the possibility of other observed endogenous actions to take place and affect the interpretation of popular parameters, including the average treatment effect. In this context, we study several regression-based estimands that are routinely used in empirical work, and present five results that shed light on how to interpret them in terms of ceteris paribus effects, indirect causal effects, and selection terms. Our three main takeaways are the following. First, the three most popular estimands do not satisfy what we call strong sign preservation, in the sense these estimands may be negative even when the treatment positively affects the outcome for any possible combination of other actions. Second, the by-far most popular estimand that ``controlls'' for the other actions in the regression does not improve upon a simple comparisons of means in the sense that negative weights multiplying relevant ceteris paribus effects become more prevalent. Finally, while non-parametric identification of the effects we study is straightforward under our assumptions and follows from saturated regressions, we also show that linear regressions that correctly control for the other actions by stratifying lead to estimands that always satisfy strong sign preservation. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.11505&r=ecm |
| By: | John Mullahy |
| Abstract: | With count-valued outcomes y in {0, 1, ..., M} identification and estimation of average treatment effects raise no special considerations beyond those involved in the continuous-outcome case. If partial identification of the distribution of treatment effects is of interest, however, count-valued outcomes present some subtle yet important considerations beyond those involved in continuous-outcome contexts. This paper derives appropriate bounds on the distribution of treatment effects for count-valued outcomes. |
| JEL: | C10 C25 I1 |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:31005&r=ecm |
| By: | Blankmeyer, Eric |
| Abstract: | A correlation between regressors and disturbances presents challenging problems in linear regression. Issues like omitted variables, measurement error and simultaneity render ordinary least squares (OLS) biased and inconsistent. In the context of heteroscedastic linear regression, this note proposes a bias test that is simple to apply. It does not reveal the size or sign of OLS bias but instead provides a statistic to assess the probable presence or absence of bias. The test is examined in simulation and in real data sets. |
| Keywords: | Linear regression, least squares bias, heteroscedasticity, Fisher transformation |
| JEL: | C1 C13 C2 C3 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:116605&r=ecm |
| By: | Matias D. Cattaneo; Luke Keele; Rocio Titiunik |
| Abstract: | We present a practical guide for the analysis of regression discontinuity (RD) designs in biomedical contexts. We begin by introducing key concepts, assumptions, and estimands within both the continuity-based framework and the local randomization framework. We then discuss modern estimation and inference methods within both frameworks, including approaches for bandwidth or local neighborhood selection, optimal treatment effect point estimation, and robust bias-corrected inference methods for uncertainty quantification. We also overview empirical falsification tests that can be used to support key assumptions. Our discussion focuses on two particular features that are relevant in biomedical research: (i) fuzzy RD designs, which often arise when therapeutic treatments are based on clinical guidelines, but patients with scores near the cutoff are treated contrary to the assignment rule; and (ii) RD designs with discrete scores, which are ubiquitous in biomedical applications. We illustrate our discussion with three empirical applications: the effect CD4 guidelines for anti-retroviral therapy on retention of HIV patients in South Africa, the effect of genetic guidelines for chemotherapy on breast cancer recurrence in the United States, and the effects of age-based patient cost-sharing on healthcare utilization in Taiwan. Complete replication materials employing publicly available statistical software in Python, R and Stata are provided, offering researchers all necessary tools to conduct an RD analysis. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.07413&r=ecm |
| By: | Zhenhong Huang; Chen Wang; Jianfeng Yao |
| Abstract: | This paper investigates the behavior of Stock and Yogo (2005)'s first-stage F statistic and the Cragg-Donald statistic (Cragg and Donald, 1993) when the number of instruments and the sample size go to infinity in a comparable magnitude. Our theory shows that the first-stage F test is oversized for detecting many weak instruments. We next propose an asymptotically valid correction of the F statistic for testing weakness of instruments. The theory is also used to construct confidence intervals for the strength of instruments. As for the Cragg-Donald statistic, we obtain an asymptotically valid correction in the case of two endogenous variables. Monte Carlo experiments demonstrate the satisfactory performance of the proposed methods in both situations of a single and multiple endogenous variables. The usefulness of the proposed tests is illustrated by an analysis of the returns to education data in Angrist and Keueger (1991). |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.14423&r=ecm |
| By: | Rui Miao; Zhengling Qi; Cong Shi; Lin Lin |
| Abstract: | Pricing based on individual customer characteristics is widely used to maximize sellers' revenues. This work studies offline personalized pricing under endogeneity using an instrumental variable approach. Standard instrumental variable methods in causal inference/econometrics either focus on a discrete treatment space or require the exclusion restriction of instruments from having a direct effect on the outcome, which limits their applicability in personalized pricing. In this paper, we propose a new policy learning method for Personalized pRicing using Invalid iNsTrumental variables (PRINT) for continuous treatment that allow direct effects on the outcome. Specifically, relying on the structural models of revenue and price, we establish the identifiability condition of an optimal pricing strategy under endogeneity with the help of invalid instrumental variables. Based on this new identification, which leads to solving conditional moment restrictions with generalized residual functions, we construct an adversarial min-max estimator and learn an optimal pricing strategy. Furthermore, we establish an asymptotic regret bound to find an optimal pricing strategy. Finally, we demonstrate the effectiveness of the proposed method via extensive simulation studies as well as a real data application from an US online auto loan company. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.12670&r=ecm |
| By: | Ningning Zhang; Ke Zhu |
| Abstract: | The conditional variance, skewness, and kurtosis play a central role in time series analysis. These three conditional moments (CMs) are often studied by some parametric models but with two big issues: the risk of model mis-specification and the instability of model estimation. To avoid the above two issues, this paper proposes a novel method to estimate these three CMs by the so-called quantiled CMs (QCMs). The QCM method first adopts the idea of Cornish-Fisher expansion to construct a linear regression model, based on $n$ different estimated conditional quantiles. Next, it computes the QCMs simply and simultaneously by using the ordinary least squares estimator of this regression model, without any prior estimation of the conditional mean. Under certain conditions that allow estimated conditional quantiles to be biased, the QCMs are shown to be consistent with the convergence rate $n^{-1/2}$. Simulation studies indicate that the QCMs perform well under different scenarios of estimated conditional quantiles. In the application, the study of QCMs for eight major stock indexes demonstrates the effectiveness of financial rescue plans during the COVID-19 pandemic outbreak, and unveils a new ``non-zero kink'' phenomenon in the ``news impact curve'' function for the conditional kurtosis. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.06799&r=ecm |
| By: | Giorgio Calzolari; Roxana Halbleib; Christian M\"ucher |
| Abstract: | We provide a simple method to estimate the parameters of multivariate stochastic volatility models with latent factor structures. These models are very useful as they alleviate the standard curse of dimensionality, allowing the number of parameters to increase only linearly with the number of the return series. Although theoretically very appealing, these models have only found limited practical application due to huge computational burdens. Our estimation method is simple in implementation as it consists of two steps: first, we estimate the loadings and the unconditional variances by maximum likelihood, and then we use the efficient method of moments to estimate the parameters of the stochastic volatility structure with GARCH as an auxiliary model. In a comprehensive Monte Carlo study we show the good performance of our method to estimate the parameters of interest accurately. The simulation study and an application to real vectors of daily returns of dimensions up to 148 show the method's computation advantage over the existing estimation procedures. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.07052&r=ecm |
| By: | CHANG Pao-Li; MAKIOKA Ryo; NG Bo Lin; YANG Zhenlin |
| Abstract: | This paper proposes a three-stage GMM estimation procedure for estimating firm-level productivity in the presence of potential spatial dependence across firms via the product market, the input market, and the supply chain. The procedure builds on Ackerberg, Caves and Frazer (2015) and Wooldridge (2009), but in addition, allows the productivity process to depend on the lagged output levels and input usages of related firms, and to accommodate spatially correlated productivity shocks across firms. The procedure provides the estimates of the production function parameters (the capital and labor shares in value-added, and the degree of serial correlation in the productivity process), and the spatial dependence parameters (of productivity on related firms’ past outputs and inputs, and current innovation shocks), where the set of related firms can differ across the three dimensions of spatial dependence. We establish the asymptotic properties of the proposed estimator, and conduct Monte Carlo simulations to validate these properties. In particular, our proposed estimator is consistent under DGPs with or without spatial dependence. In contrast, the conventional estimators are biased when the true DGPs are indeed characterized by spatial dependence. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:eti:dpaper:23016&r=ecm |
| By: | Emir Malikov; Shunan Zhao; Jingfang Zhang |
| Abstract: | There is growing empirical evidence that firm heterogeneity is technologically non-neutral. This paper extends Gandhi et al.'s (2020) proxy variable framework for structurally identifying production functions to a more general case when latent firm productivity is multi-dimensional, with both factor-neutral and (biased) factor-augmenting components. Unlike alternative methodologies, our model can be identified under weaker data requirements, notably, without relying on the typically unavailable cross-sectional variation in input prices for instrumentation. When markets are perfectly competitive, we achieve point identification by leveraging the information contained in static optimality conditions, effectively adopting a system-of-equations approach. We also show how one can partially identify the non-neutral production technology in the traditional proxy variable framework when firms have market power. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.13429&r=ecm |
| By: | Sascha A. Keweloh; Mathias Klein; Jan Pr\"user |
| Abstract: | Different proxy variables commonly used in fiscal policy SVARs lead to contradicting conclusions implying that some of the exogeneity assumptions may not be fulfilled. We combine data-driven identification with a novel proxy shrinkage prior which enables us to estimate the effects of fiscal policy shocks without relying on strong assumptions about the validity of the proxy variables. Our results suggest that increasing government spending is a more effective tool to stimulate the economy than reducing taxes. Additionally, we provide evidence that the commonly used proxies in the literature are endogenously related to the structural shocks which leads to biased estimates. We construct new exogenous proxies that can be used in the traditional proxy VAR approach resulting in similar estimates compared to our proxy shrinkage model. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.13066&r=ecm |
| By: | Lorena Torres Lahoz (DTU Management, Technical University of Denmark); Francisco Camara Pereira (DTU Management, Technical University of Denmark); Georges Sfeir (DTU Management, Technical University of Denmark); Ioanna Arkoudi (DTU Management, Technical University of Denmark); Mayara Moraes Monteiro (DTU Management, Technical University of Denmark); Carlos Lima Azevedo (DTU Management, Technical University of Denmark) |
| Abstract: | Latent Class Choice Models (LCCM) are extensions of discrete choice models (DCMs) that capture unobserved heterogeneity in the choice process by segmenting the population based on the assumption of preference similarities. We present a method of efficiently incorporating attitudinal indicators in the specification of LCCM, by introducing Artificial Neural Networks (ANN) to formulate latent variables constructs. This formulation overcomes structural equations in its capability of exploring the relationship between the attitudinal indicators and the decision choice, given the Machine Learning (ML) flexibility and power in capturing unobserved and complex behavioural features, such as attitudes and beliefs. All of this while still maintaining the consistency of the theoretical assumptions presented in the Generalized Random Utility model and the interpretability of the estimated parameters. We test our proposed framework for estimating a Car-Sharing (CS) service subscription choice with stated preference data from Copenhagen, Denmark. The results show that our proposed approach provides a complete and realistic segmentation, which helps design better policies. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.09871&r=ecm |