An Intertemporal Benchmark Model for Turkey’s Current Account

The k-step ahead expectation is therefore given as
εt[Xt+k]=Ψ^kXt                                                                     (9)

Thus, εt (∆ zt+k )= [1 0 L 0]Ψ^k Xt                                               (10)

Combining equation (10) with equation (6) we can compute the optimal consumption
smoothing current account as

cat =-∑ ₇-¹_v [1 0 L O]Ψ X
j=1 (1+ r)^j

= -[1 0 L O](Ψ∕ 1 + r) ∑ -ɪ- Ψ ^jX_t
j=0 (1 + r)^j

= -[1 O L O][ψ/(1 + r)][I-Ψ/(1 + r)]^-1 X_t ≡ΓX_t

The coefficients from the VAR will allow us to compute the optimal consumption smoothing
current account. The optimal consumption smoothing current account equation given in equation
(11) is valid if the infinite sum converges, which is dependent on stationarity of the variables in
the VAR. The unit root tests to show evidence of stationarity of these variables will be presented
in the following section.

There are a few testable implications of this model noted in Ghosh and Ostry (1995), Adedeji
(2OO1) and others which we conduct as well. The first implication of the model is that the current
account Granger-causes subsequent movements in national cash flow. As shown in Campbell
(1987), an implication of the permanent income hypothesis is that savings increase when income
declines and vice versa. In this context, there is a current account surplus when net output is
expected to decline and a current account deficit when net output is expected to increase.

The second implication of the IBM is that the actual consumption smoothing current account
ca_t will be equal to the optimal consumption smoothing current account ca_t^* . From equation
(11), we note that the optimal consumption smoothing current account can be denoted as follows

1O

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