Unit Roots and the Dynamics of Market Shares: An Analysis Using Italian Banking Micro-Panel

The paper proposes the use of panel data unit root tests to assess market share instability in order to have (preliminary) indications of the industry dynamic. The idea is to consider the movements in market shares not only as element of the market structure but rather reflecting conduct that arise from that market. If shares are mean-reverting, the firm actions only have a temporary effect on shares. On the other hand, if they are evolving, as signaled by the presence of unit roots, the gain in shares respect with the competitors could be long-term. To illustrate the potential of unit roots tests, I consider an application to the Italian retail banking industry.

Maximum Likelihood Estimation and Inference Methods for the Covariance Stationary Panel AR(1)/Unit Root Model

International audienc

Estimation of dynamic panel data models with a lot of heterogeneity

The commonly used 1-step and 2-step System GMM estimators for the panel AR(1) model are inconsistent under mean stationarity when the ratio of the variance of the individual e§ects to the variance of the idiosyncratic errors is unbounded when N ! 1. The reason for their inconsistency is that their weight matrices select moment conditions that do not identify the autoregressive parameter. This paper proposes a new 2-step System estimator that is still consistent in this case provided that T > 3: Unlike the commonly used 2-step System estimator, the new estimator uses an estimator of the optimal weight matrix that remains consistent in this case. We also show that the commonly used 1-step and 2-step Arellano-Bond GMM estimators and the Random E§ects Quasi MLE remain consistent under the same conditions. To illustrate the usefulness of our new System estimator we revisit the growth study of Levine et al. (2000)

A further look at Modified ML estimation of the panel AR(1) model with fixed effects and arbitrary initial conditions

In this paper we consider two kinds of generalizations of Lancaster's (Review of Economic Studies, 2002) Modified ML estimator (MMLE) for the panel AR(1) model with fixed effects and arbitrary initial conditions and possibly covariates when the time dimension, T, is fixed. When the autoregressive parameter ρ=1, the limiting modified profile log-likelihood function for this model has a stationary point of inflection and ρ is first-order underidentified but second-order identified. We show that the generalized MMLEs exist w.p.a.1 and are uniquely defined w.p.1. and consistent for any value of ρ≥-1. When ρ=1, the rate of convergence of the MMLEs is N^{1/4}, where N is the cross-sectional dimension of the panel. We then develop an asymptotic theory for GMM estimators when one of the parameters is only second-order identified and use this to derive the limiting distributions of the MMLEs. They are generally asymmetric when ρ=1. One kind of generalized MMLE depends on a weight matrix W_{N} and we show that a suitable choice of W_{N} yields an asymptotically unbiased MMLE. We also show that Quasi LM tests that are based on the modified profile log-likelihood and use its expected rather than observed Hessian, with an additional modification for ρ=1, and confidence regions that are based on inverting these tests have correct asymptotic size in a uniform sense when |ρ|≤1. Finally, we investigate the finite sample properties of the MMLEs and the QLM test in a Monte Carlo study