Time series data are often well modeled by using
the device of an autoregressive root that is local to unity.
Unfortunately, the localizing parameter (c) is not
consistently estimable using existing time series econometric
techniques and the lack of a consistent estimator complicates
inference. This paper develops procedures for the estimation
of a common localizing parameter using panel data. Pooling
information across individuals in a panel aids the identification
and estimation of the localizing parameter and leads to consistent
estimation in simple panel models. However, in the important
case of models with concomitant deterministic trends, it is
shown that pooled panel estimators of the localizing parameter
are asymptotically biased. Some techniques are developed to
overcome this difficulty, and consistent estimators of
c in the region c < 0 are developed
for panel models with deterministic and stochastic trends.
A limit distribution theory is also established, and test
statistics are constructed for exploring interesting hypotheses,
such as the equivalence of local to unity parameters across
subgroups of the population. The methods are applied to the
empirically important problem of the efficient extraction of
deterministic trends. They are also shown to deliver consistent
estimates of distancing parameters in nonstationary panel models
where the initial conditions are in the distant past. In the
development of the asymptotic theory this paper makes use of
both sequential and joint limit approaches. An important limitation
in the operation of the joint asymptotics that is sometimes
needed in our development is the rate condition n/T
→ 0. So the results in the paper are likely to be most
relevant in panels where T is large and n is
moderately large.
Change Point in Panel Data with Small Fixed Panel Size: Ratio and Non-ratio Test Statistics