Common Correlated Effects Estimation of Heterogeneous: Dynamic Panel Quantile Regression Models

Abstract

This paper proposes a quantile regression estimator for a heterogeneous panel model with lagged dependent variables and interactive effects. The paper adopts the Common Correlated Effects (CCE) approach proposed by Pesaran (2006) and Chudik and Pesaran (2015) and demonstrates that the extension to the estimation of dynamic quantile regression models is feasible under similar conditions to the ones used in the literature. We establish consistency and derive the asymptotic distribution of the new quantile regression estimator. Monte Carlo studies are carried out to study the small sample behavior of the proposed approach. The evidence shows that the estimator can significantly improve on the performance of existing estimators as long as the time series dimension of the panel is large. We present an application to the evaluation of Time-of-Use pricing using a large randomized control trial. JEL-Codes: C210, C310, C330, D120, L940. The paper is organized as follows. The next section introduces the model and the proposed estimator. It also establishes the asymptotic properties of the estimator. Section 3 provides simulation experiments to investigate the small sample performance of the proposed estimator. Section 4 demonstrates how the estimator can be used in practice by exploring an application of electricity pricing and smart technology. Section 5 concludes. Mathematical proofs are provided in the Appendix and additional Monte Carlo results are offered in an online Supplement. Notations: Generic positive finite constants are denoted by K a , K b , . . ., and can take different values at different instances and are bounded in N and T (the panel dimensions). The largest and the smallest eigenvalues of the N × N real symmetric matrix A = (a ij ) are denoted by ζ max (A) and ζ min (A), respectively, and its spectral (or operator) norm by ∥A∥ = ζ 1/2 max (A ′ A). a.s. −→ denotes almost sure convergence, ℓ 1 −→ convergence in the ℓ 1 norm, p −→ convergence in probability, and d −→ convergence in distribution. We denote ∥x∥ 1 = ∑ n i=1 |x i | as the ℓ 1 norm of vector x. All asymptotics are carried out under N and T → ∞, jointly. Model and assumptionsWe consider a dynamic panel data model for i = 1, 2, . . . , N and t = 1, 2, . . . , T , where y it ∈ R is the response variable for cross-sectional unit i at time t and y it−1 denotes a lagged dependent variable. Consider the following conditional panel quantile function:The variable x it is a p x × 1 vector of regressors specific to cross-sectional unit i at time t,is a vector of latent factor loadings, and α i (τ ) is an individual effect potentially correlated with the regressor variables, x it . The term f ′ t γ i (τ ) can be interpreted as a quantile-specific function capturing unobserved heterogeneity that was not adequately controlled by the inclusion of x it .The model can be considered to be semi-parametric since the functional form of the conditionalis left unspecified and no parametric assumption is imposed on the relation between the regressors and the latent va...

Understanding the determinants of climate change adaptation strategies among smallholder maize farmers in South-west, Nigeria

“…With the assumption of the error terms in the equations is uncorrelated conditional on all covariates, the standard errors from separate estimations are also valid for conducting statistical inference. If the conditionally uncorrelated errors assumption does not hold, coefficient estimates from separate regressions will be biased (Heckman, 1977;Harding et al, 2020). According to Wooldridge (2002), testing for conditionally uncorrelated errors follows the same method as well as the Heckman test for selection bias.…”