An Intertemporal Benchmark Model for Turkey’s Current Account

∞

∑β^t Ε[u(ct)]                                                                        (1)

t=0

where β is the discount rate [ 0 < β < 1 ], u is the utility function [ u '(c_t ) > 0 and u ''(c_t )< 0 ],
and c is consumption of a single traded good. Utility is maximized subject to a dynamic budget
constraint given by

b_t+1 =(1+r)b_t +q_t -c_t -i_t -g_t                                                                 (2)

where b is the level of foreign bonds held by the economy, r is the world rate of interest, q_t is
GDP, i_t is the level of investment, and g _t is government expenditure.

The current account balance is given by

ca_t = b_t+1 -b_t                                                                                   (3)

Assuming a no-Ponzi game and the first order conditions with the dynamic budget constraint,
the optimal consumption function is given by

where C_t^* is the optimal path of consumption and θ is the proportion that reflects consumption
tilting which is given by the relation between rate of interest (r) and the rate of time preference
(β).⁵ If θ < 1, then the country is consuming more than the national cash flow which means the
country is tilting consumption to the present. If θ > 1 then the country is consuming less than the
national cash flow which implies that the country is tilting consumption to the future. If θ = 1
then consumption equals the national cash flow. There is no consumption tilting in this case.

From optimal consumption C_t^* we can compute the optimal consumption smoothing current
account Ca _t^* as follows

**

Ca_t = y_t - i_t - g_t -θC_t

⁵ For example, if we assume a quadratic utility function, θ = βr (1 + r)∕[β (1 + r)2 -1].

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