# 6.4 Techniques of Testing PPP Theory in Economic-History Literature

## 6.4.1 Comparative-Static Computation

Let *E*_{0} denote *E* in period 0. An obvious test of PPP theory is to measure *P* and *P*^{*} as index numbers with value unity in base period 0 and compute *V* = (*P*/*P*^{*})*E*_{0} for either one period, a few discontinuous periods or a continuous sequence of periods. The computed *V* are then compared with the corresponding values of *E*, in a table or graph. Alternatively, (*E*/*E*_{0})/(*P*/*P*^{*}) is compared with unity. In either case, the closer the computed value to the norm, PPP-predicted, value, the closer is PPP theory to fulfillment. Any noticeable divergences are then explained in terms of non-PPP influences on the exchange rate (augmented PPP theory). One can allow for a lagged effect of *R* on *E*. Further, investigations of lead-lag relationships are used to test the PPP-postulated direction of causality, from prices to the exchange rate. This entire approach has the advantage of lying outside formal statistical analysis.

## 6.4.2 Regression Analysis

The use of regression analysis was a natural development in testing PPP theory. For example (using lower-case letters to denote logarithms), *e* is regressed on *P* and *p*^{*} or on *r*^{−1}; *q* is regressed on a constant. Properties such as symmetry and proportionality can be readily tested in terms of elasticities.

## 6.4.3 Testing for Causality

The PPP relationship tested can either be an equilibrium relationship or a causal relationship, each being tested directly. A hybrid ...