A MONTE CARLO STUDY OF THE PHILLIPS CURVE WITH ERRORS IN VARIABLES
| Author | D. A. PEEL,K. HOLDEN |
| DOI | http://doi.org/10.1111/j.1468-0084.1975.mp37002006.x |
| Date | 01 May 1975 |
| Published date | 01 May 1975 |
A MONTE CARLO STUDY OF THE PHILLIPS CURVE
WITH ERRORS IN VARIABLES
By K. HOLDEN and D. A. PEEL
INTRODUCTION
This note is concerned with the basic Phillips-type relationship1
O=a+ßpt+yut+vt (1)
where a, ß and y are parameters, * = (w - w -1)/we -1' = (Pt - Pt - i)/pt -1' w is
wages, p is prices, u is unemployment and v is a random residual. Studies of (1)
have generally ignored the possibility of errors of measurement of the variables
even though it is well known that such errors can affect econometric relationships.2
A special feature of (1) is that while w and p are observed, it is * and f) which are
relevant in the Phillips curve. The complication of possible bias resulting from
the simultaneous determination of wages and prices is ignored in this note.
SOURCES OF ERROR
Two types of error in aggregate statistics are considered: rounding and compila-
tion. The former occurs as a result of recording the value of a variable observed to
a limited number of digits. For example the true value of the percentage un-
employed recorded as 2.1% may be assumed to lie between 2.05% and 2.15%.
Thus it is reasonable to postulate that the rounding error has a rectangular distribu-
tion over the range 0.05 to +0.05. The second source of error results from the
fact that aggregate statistics are compiled from numerous independent observations
and errors occur in both the raw data and the computation of aggregates. If there
are a large number of independent errors then the aggregate error will be approxi-
mately normally distributed. In the absence of any a priori information on the
direction of bias it is assumed that the mean of the error is zero.
The analytical derivation of the properties of the estimators of a, fi and y in (1)
with errors in the levels of the variables is difficult. Our approach is to construct a
set of data on w, p, and u based on United Kingdom experience in the period
1950-1966, which gives an exact fit to (1). This is our 'true' data. The effects of
errors in measurement are then examined by repeating the experiment of adding
random errors to the series on w, p, and u, estimating the parameters of (1) and
comparing the resulting estimates with the true values. The exact equation used is
= 0.062297 + 0.603 127 f)- 0.01725 1 u, (2)
THE ERROR MODELS
Three simple errors in variables models are now presented. The notation
adopted is:
N = normally distributed error with mean zero and standard deviation a
1 See, for example, Bodkin (1966).
2 See, for example, Denton and Kuiper (1965) or Holden (1969).
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