Multicollinearity caused by Specification Errors

The advantages of using linear least squares regressions induce us to adopt
functions which are linear in parameters. Often this imposes unrealistically
rigid constraints which may create multicollinearity. Using more realistic
non-linear forms and non-linear least squares regressions is likely to overcome
this problem as shown in a study of a production function.
Keywords: MULTICOLLINEARITY AND SPECIFICATION; NON-LINEAR LEAST SQUARES
REGRESSION;NON-LINEAR FUNCTIONS AND MULTICOLLINEARITY ;PRODUCTION
FUNCTIONS
THEpurpose of this paper is to suggest a method for overcoming multicollinearity by
changing the mathematical form of the independent variables.
Consider y =f(x,z) where x is a vector of uncorrelated independent variables but
where some or all variables in x are multicollinear with variables in z. If the
mathematical form of z is not predetermined on theoretical grounds, changing the
form in which z enters, including additions of extra parameters, may both overcome
the multicollinearity and give a functional form more closely approximating reality.
Frequently all variables are entered into economic behavioural functions in the same
form (e.g. linear in parameters) even though, for some variables, this is in conflict
with economic realism. This preference for linear forms is based on the desirability
of using linear least squares regressions. Nowadays, however, non-linear least squares
regression programs are easily available and much is known about the properties of
their estimators (Draper and Smith, 1966). Hence the preference for linear forms has
far less validity particularly when it imposes unrealistically rigid constraints on some
variables. The method here suggested seems to be particularly applicable to timeseries
studies where time itself is one of the independent variables.