21
gains, and re-arranging terms, we obtain
∆ b„ = tb;+r +( '«+ kg∙' > ь-1- -⅛-ι>l, -1 (6)
1 + γ1t 1 + Ytt
where tbi* is the ratio to GDP of the balance of goods, services, and current transfers; iit + kgit is the
nominal rate of return on outstanding net foreign assets (nominal yield iit plus capital gains∕losses);
and γ is the rate of change of GDP measured in current dollars. Note that 1 + γ = (1 + g)(1 + ε)(1 + π*,
where g is the real GDP growth rate, ε is the rate of real exchange rate appreciation of the home
country’s currency vis-à-vis the US$ and π * isUS inflation.
In turn, we can re-arrange equation (6) to relate the “transfer-corrected” trade balance to our
estimate of the change in the net foreign asset position, given in equation (4)
tb* + trk = Abit---———ε~- bt 1 + νit = Abit-ψit + νit (7)
it it it t—1 it it it it
(1 + git )(1 + εit )
where rit is the real rate of return on net foreign assets, measured in US dollars.33 The “transfer-
corrected” trade balance is related to three factors. The first term on the RHS of this equation reflects
the change in the net foreign asset position that is required for convergence to its long-run
fundamental value, as captured by the ECM representation in section 4.1; the second term (-Ψit ) is
the combined effect of overall returns, output growth, and real exchange rate changes, interacted with
the past net foreign asset position; and the third term is the component of the change in net foreign
assets that is not explained by the dynamics of its long-run fundamentals. Consider for example a
debtor country for which the rate of return on its net liabilities is higher than its growth rate. In this
case if the “fundamental” net foreign asset position does not change, the country will need to run a
trade surplus equal to Ψ it.
33 In the presence of differences in rates of return between external assets and liabilities the RHS would also
include the term (r ttL — r ttA )b it-1 l where r ttL — r a is the rate of return differential between liabilities and assets
and bit-1 l is the stock of gross liabilities. We implicitly include this term in the adjusted returns Ψ it.