Sampling Designs for Short Panel Data

Some aspects of the design and analysis of short panel data are considered. It is assumed
that each individual may be at any instant in one of two states, for example employed and
unemployed, and that individuals may switch from one to the other state. Alternative ways
of observing individuals in discrete time are compared via the Fisher information matrix.
The effect of the observational interval on the efficiency of the estimation is stressed and
optimal time intends for alternative sampling schemes are computed. A generalization to
a model with covariates is outlined.
1 . INTRODUCTION
PANELDATA are becoming increasingly common in economic and social studies
(see Heckman and Flinn [5], Lancaster [ 6 ] ,Lancaster and Nickel1 [7]). In this
paper we show that it is possible to design equivalently efficient sampling schemes
for the analysis of two-state Markov processes, so that survey costs may be
controlled. If, for example, the aim of a study is the estimation of the proportion
of time spent in unemployment, criteria are given to balance the amount of
information to be recorded at each time point (e.g., "Are you unemployed at
present?" or "How many unemployment spells did you experience over the last
year? and Are you unemployed now?"), the dimension of the sample size, and
the interval between observations in order to achieve a desired degree of efficiency.
Consider a population of individuals each of whom is at any instant in one
of two states, labelled 0 and 1. For example, the states might represent unemployment
and employment. We assume that individuals switch from time to time
from one state to the other and, initially, take the individuals as homogenous:
the dependence of the transition rates on explanatory variables is an important
issue and will be considered in the last section. We assume also that the systcm
is stationary and, at least in the initial analysis, that the times spent in state 0 or
in state 1 are independent exponentially distributed random variables with
parameters p, and p,, respectively. Thus the equilibrium probability of being in
state 0 is p,/(p,+p,).