Page 26 - Contributed Paper Session (CPS) - Volume 1

CPS658 Sagaren P.
The impact of mis-specification of the
deterministic components in the Co-integration
model: An application to the bivariate case on
South African employment costs and gross
earnings
Sagaren Pillay
Statistics Finland

Abstract
This paper investigates the impact of different specifications of deterministic
compontens in the vector error correction model (VECM) form estimated with
Johansen’s multivariate maximum likelihood approach. Using time series for
employment costs and gross earnings data we show the impact of the
misspecification of the deterministic components of the estimated Co-
integration model. The study suggests that great care must be exercised in
model specification. The inclusion or exclusion of the deterministic trend
should be clearly justified to avoid misleading results.

Keywords
Deterministic; cointegration; trends

1. Introduction
Johansen’s (1988) multivariate maximum likelihood approach to Co-
integration is arguably the most popular approach in estimating long-run
economic relationships. The main objective of Co-integration analysis is to
determine the Co-integration rank of the model. Many studies have focused
considerable attention on the modelling of economic relationship between
variables, and variables to include in the model. Johansen (1995) has
emphasized that the choice of the deterministic components of a model has
important implications for the asymptotic distribution of the test statistics.
There are five different ways that the deterministic components could be
included in a Johansen Cointegration model. The choice of deterministic
components included in the model has a very significant influence on the
empirical results. It is therefore very important that, in actual application, the
modelling of the deterministic components of Co-integration models needs
to be carefully considered. Consider the Var(p) process without determinant
terms. Suppose all individual variables are I(1) or I(0)

= + ⋯ + + (1)
−
1 −1

The corresponding VECM may be written as

∆ = Π −1 + ∆ −1 + ⋯ −1 ∆ −+1 + (2)

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