Abstract

Panel data, by blending inter-individual differences and intra-individual dynamics, have greater capacity for capturing the complexity of human behavior than data sets with only a temporal or a cross-sectional dimension (e.g., Hsiao 2003, 2007). However, typical panels focus on individual outcomes. Factors affecting individual outcomes are numerous. It is rare that the conditional density of the outcomes, y_it , conditional on certain variables, x ˜ i t is independently, identically distributed across individual i and over time, t. To capture the effects of those omitted factors, empirical researchers often assume that, in addition to the effects of observed x ˜ i t , there exist unobserved individual-specific effects (i and time-specific effects A _t . These unobserved individual-specific and/or time-specific effects, (i and A _t , are supposed to capture the impacts of those omitted variables that vary across individuals but stay constant over time and the impact of those variables that vary over time but are the same for all individuals at a given time. They can be either treated as fixed constants or random variables, respectively called fixed effects (FE) or random effects (RE) model. The advantage of the FE modeling is that there is no need to postulate the relationship between the unobserved effects and the conditioning variables. The disadvantage is that it introduces the classical “incidental parameter” problems if either the time series dimension T or cross-sectional dimension, N, is finite (e.g., Neyman and Scott 1948). The advantage of the random effects modeling is that the number of unknown parameters stay constant as N and/or T increases. The disadvantage is that the relationships between the effects and the observed conditional variables have to be postulated, say, the conditional distribution of the effects given the observed factors (e.g., Hsiao 2007).