PRACTITIONERS CORNER: On Using Ridge‐Type Estimators For a Distributed Lag Model
| Author | P. K. Trivedi,Stephen J. Yeo |
| Date | 01 February 1989 |
| Published date | 01 February 1989 |
| DOI | http://doi.org/10.1111/j.1468-0084.1989.mp51001006.x |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 51,1(1989)
0305-9049 $3.00
PRACTITIONERS CORNER
On Using Ridge-Type Estimators For a Distributed
Lag Model
Stephen J. Yeo and P. K. Trivedi
I. INTRODUCTION
In this paper we point out a difficulty involved in applying certain ridge-type
estimators to the problem of distributed lag estimation. There is a huge litera-
ture on distributed lag estimation and on ridge regression individually but
there is very little published work on distributed lag estimation using ridge
regression. As a major motivation for using ridge-type estimators is the
presence of collinearity among regressors, usually present in distributed lag
models, such estimators have a superficial appeal. However, distributed lag
estimation seems tractable only when prior information on the lag co-
efficients is incorporated; ridge regression introduces yet another representa-
tion of such prior information and hence is a possible estimation procedure.
Most existing methods of distributed lag estimation involve the use of some
constraints on the lag coefficients. This desire to constrain the lag coefficients
is partly due to the difficulty of estimating precisely a possibly large number
of coefficients given the collinearity usually found in lagged values for
economic time series. Ridge regression has often been put forward as a
possible solution to the problem of multicollinearity. Some limited experience
with ridge-type estimators for distributed lag models has been reported by
Maddala (1977). However, it is not as yet clearly understood in what
situations such estimators can be expected to perform satisfactorily. There is
also the further question of how ridge-type estimators might compare with
other biased estimators based on imposing data-based (as opposed to theory-
based) prior information. For example, pre-test estimators are more appeal-
ing in one respect, viz., that unlike the Principal Components Estimator
which imposes restrictions on a reparametrized form of the original model,
they lead to restrictions on the 'natural' parametrization of the model (see
below). See Hocking (1975) for a comparative analysis of other biased esti-
mators. The results of this paper throw some light on these issues.
We outline some possible ridge-type estimators in Section II; in Section III
we point out a specific difficulty which afflicts certain members of this class
and which impairs their usefulness. A numerical illustration is also provided.
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