Fixed effect estimation of large T panel data models

Abstract

This article reviews recent advances in fixed effect estimation of panel data models for long panels, where the number of time periods is relatively large. We focus on semiparametric models with unobserved individual and time effects, where the distribution of the outcome variable conditional on covariates and unobserved effects is specified parametrically, while the distribution of the unobserved effects is left unrestricted. Compared to existing reviews on long panels (Arellano & Hahn, 2007; a section in Arellano & Bonhomme, 2011) we discuss models with both individual and time effects, split-panel Jackknife bias corrections, unbalanced panels, distribution and quantile effects, and other extensions. Understanding and correcting the incidental parameter bias caused by the estimation of many fixed effects is our main focus, and the unifying theme is that the order of this bias is given by the simple formula p/n for all models discussed, with p the number of estimated parameters and n the total sample size.

Solid-State NMR and MD Study of the Structure of the Statherin Mutant SNa15 on Mineral Surfaces

“…In the mineral systems, F7 and F14 are pointing in different directions. This is consistent with chemical shift data, relaxation dynamics (T 1 /T 1ρ ) 20,27 , 13 C{ 31 P} REDOR 20 , 2 H ssNMR 27 , and NEXAFS 24 data, which all conclude that F7 is far from the HAP surface (at least 7 Å) while F14 is close to (within 4 Å) and interacting with the surface. The ΔCS values in this study support this theory, since there are significant perturbations for F14 ( 13 Cγ, 13 Cδ, 13 Cε, and 13 Cζ data), yet much smaller perturbations for the same shifts of F7.…”

“…The role of phenylalanine residues in the binding of statherin to HAP has been studied extensively. 20,24,27 Gibson and coworkers 20 studied the role of F7 and F14 in SN15 adsorption to HAP through isotropic chemical shift perturbations, 13 C{ 31 P} REDOR, and T 1ρ relaxation measurements. They found that when compared to F7, F14 is closer to the surface and is more dynamically constrained.…”

“…[11][12][13][14][15][16][17][18] These protein-surface systems include either small extracellular matrix (ECM) proteins or ECM protein domains that are adsorbed onto hydroxyapatite (HAP) crystals. 14,[19][20][21][22][23][24][25][26][27][28][29] These studies suggest that protein secondary structure can change when adsorbed to surfaces. They also hypothesize that the interaction of amino acid side-chains with inorganic surfaces are dependent on the secondary structures of adsorbed proteins.…”

“…They also hypothesize that the interaction of amino acid side-chains with inorganic surfaces are dependent on the secondary structures of adsorbed proteins. 20,22,24,25,27,30 Thus, all components of protein-surface interaction can be determined only when the structure of the adsorbed protein is resolved.…”

“…The structure of statherin adsorbed onto HAP has been resolved. 29,[31][32][33] Statherin has been studied by calorimetric methods 12,25 , adsorption isotherms, 31,34 solution NMR, 35,36 solid-state NMR (ssNMR), [19][20][21]23,24,26,27,29,32,33,37,38 and circular dichroism. 31,39 These studies indicate that statherin is unstructured in solution but structures when adsorbed onto HAP surfaces.…”