Quality & Quantity (2006) 40:1055–1060 © Springer 2006
Inaccurate Approximation in the Modelling
PETER G. MOFFATT
and EVENS SALIES
University of East Anglia, Norwich, UK;
Observatoire Franc¸ais des Conjonctures
Abstract. In time series macroeconometric models, the ﬁrst difference in the logarithm of a
variable is routinely used to represent the rate of change of that variable. It is often over-
looked that the assumed approximation is accurate only if the rates of change are small.
Models of hyper-inﬂation are a case in point, since in these models, by deﬁnition, changes
in price are large. In this letter, Cagan’s model is applied to Hungarian hyper-inﬂation data.
It is then demonstrated that use of the approximation in the formation of the price inﬂation
variable is causing an upward bias in the model’s key parameter, and therefore an exagger-
ation of the effect postulated by Cagan.
Key words: difference in logarithms, hyperinﬂation, model speciﬁcation
Models of hyper-inﬂation are considered very useful by macroeconomists
because during periods of very high inﬂation, the effects of expected inﬂa-
tion on key variables such as money demand tend to drown out all other
inﬂuences, allowing the econometrician to focus exclusively on the effect of
inﬂationary expectations, thereby estimating this effect with maximal preci-
sion (see, for example, Sargent and Wallace, 1973).
When the rate of price inﬂation appears as a variable in a macroecono-
metric model, the variable routinely used to represent it in estimation is:
that is, the ﬁrst difference in the natural logarithm of the price level P
Author for correspondence: Evens Salies, OFCE-I2C, 250, Rue Albert Einstein, 06560
Valbonne, France. Tel.: +33-4-93-95-41-52; E-mail: evens.salies@ideﬁ.cnrs.fr