Maximum likelihood estimation of fixed effects dynamic panel data models covering short time periods

Accuracy and Efficiency of Various GMM Inference Techniques in Dynamic Micro Panel Data Models

“…Through linear transformation 15 we demonstrate that the sets of moment conditions for the equation in levels and for the equation in first-differences have a non empty intersection. First we consider the moment conditions associated with the strictly exogenous regressors.…”

“…For the equation in first differences these are E(x T i ∆ε it ) = E[∆ε it (x i1 ...x iT ) ] = 0, for t = 2, ..., T. They can also be represented 16 by the combination E[∆ε it (∆x i2 ...∆x iT ) ] = 0 and E(x it ∆ε it ) = 0. However, by a similar transformation 17 (here of the disturbances instead of the instruments), the conditions for the equation in levels E[∆x ith (η i ι T + ε i )] = 0, where h = 1, ..., K x (and again t = 2, ..., T), can 15 In this Appendix we repeatedly use the result that the p conditions E(aCb) = 0, where a is a random scalar, b a p × 1 random vector and C a deterministic nonsingular p × p matrix, are equivalent with the p conditions E(ab) = 0, because E(ab) = 0 ⇔ CE(ab) = 0 ⇔ E(aCb) = 0. 16 Here C = (D e T,t ) ⊗ I Kx .…”

“…For example: the simulation results in Arellano and Bover [3], Hahn and Kuersteiner [4], Alvarez and Arellano [5], Hahn et al [6], Kiviet [7], Kruiniger [8], Okui [9], Roodman [10], Hayakawa [11] and Han and Phillips [12] just concern the panel AR(1) model under homoskedasticity. Although an extra regressor is included in the simulation studies in Arellano and Bond [1], Kiviet [13], Bowsher [14], Hsiao et al [15], Bond and Windmeijer [16], Bun and Carree [17,18], Bun and Kiviet [19], Gouriéroux et al [20], Hayakawa [21], Dhaene and Jochmans [22], Flannery and Hankins [23], Everaert [24] and Kripfganz and Schwarz [25], this regressor is (weakly-)exogenous and most experiments just concern homoskedastic disturbances and stationarity regarding the impact of individual effects. Blundell et al [26] and Bun and Sarafidis [27] include an endogenous regressor, but their design does not allow us to control the degree of simultaneity; moreover, they stick to homoskedasticity.…”

Quasi ML estimation of the panel AR(1) model with arbitrary initial conditions

“…Both Chamberlain (1980) and Anderson and Hsiao (1982) proposed the same Random Effects MLE for the conditional panel AR(1) model. Recently, Hsiao et al (2002) and Kruiniger (2001) have independently shown that the conditional panel AR (1) model with fixed effects (FE) and homogenously distributed errors can be consistently estimated by (Quasi) ML if the difference between the initial observations and the individual effects (or equivalently the differenced data) satisfy a particular condition.…”

Alternative GMM estimators for first-order autoregressive panel model: An improving efficiency approach

“…Some of these methods are based on modifications of the profile likelihood, such as Lancaster (2002) and Dhaene and Jochmans (2012). Other methods start from the likelihood function of the first differences, such as Hsiao et al (2002), Binder et al (2005) and Hayakawa and Pesaran (2014).…”