Exchange Rate Economics: Theories and Evidence

The economics of the PPP puzzle 75
which indicates that for this small open economy the wage is determined entirely
by factor productivity in tradables. Our final relationship,which ties down the
internal price ratio/productivity relationship may be derived in the following way.
Solving the capital-labour ratio in non-tradables from (3.12) gives:
k NT = (i/[q NT ,T N(1 − δ)]) 1/−δ . (3.15)
Perfect competition in the non-tradable sector requires that the following condition
holds:
q NT ,T Nf (k NT ) = ik NT + W . (3.16)
For a given interest rate it follows from (3.10),(3.14) and (3.15) that the relative
price of non-tradables is:
ˆq NT ,T = δŵ −ˆv = δ ˆη −ˆv,(3.17)
λ
where we have expressed the variables in log changes,with lower case letters
denoting log values (i.e. η = log H and v = log N),and a circumflex denoting
a change. The basic message from this equation is that deviations from PPP –
movements in the internal price ratio – are driven by productivity differences
between the traded and non-traded sectors. To quote Balassa (1964):
The greater are productivity differentials in the production of tradable goods
between countries,the larger will be differences in wages and in the prices of
services and correspondingly the greater will be the gap between purchasing
power parity and the equilibrium exchange rate.
The intuition for this result may be explained in the following way. Productivity
developments tend to be concentrated in the tradable sector but a shock to total
factor productivity in this sector cannot affect the price of the traded good,by
assumption (the LOOP rules out any changes in the relative price of traded goods).
Therefore to ensure the real wage continually equals the marginal product of
labour in the traded sector,the wage in the traded sector rises and this pulls up the
economy wide wage in proportion (i.e. wages in the traded and non-traded sectors
are equalised). The rise in the wage in the non-traded sector raises the price of nontraded
goods,the relative price of traded to non-traded goods and hence the CPIbased
real exchange. Rogoff (1992) and Obstfeld and Rogoff (1996) modified the
original Balassa–Samuelson story to be consistent with forward-looking,optimising
agents and their modification is considered in Chapter 10.
3.2.2 Testing for the Balassa–Samuelson effect
Tests of the BS hypothesis have proceeded in one of two ways. The first set of tests
are indirect and rely on testing which of the two relative price effects embedded in