why am i getting contradictory changes in the current account balance for a change in interest rates?

Question

CAB = X - M + NI

GDP = C + I +G + X - M

GNI = C + I + G + CAB

S = GNI - C - G

S = I + CAB

CAB = S - I

If interest rates are to rise you would expect rising savings and falling investment (S-I) leading to a higher current account balance (CAB), while simultaneously higher interest rates leading to an appreciation in the exchange rate leading to a lower net exports (X-M) due to reduced competitiveness and a lower level of net income from foreigners (NI) due to increased interest payments to foreigners in the primary income account leading to a lower CAB how can these both happen at once?

Answer 1

What actually happens is ambiguous because what you have are just bunch of accounting identities.

In macro models like this everything is endogenous and second order effects are important. For example, increase in interest rate does lead to appreciation of home currency if we use let's say monetary model of exchange rates, but in the model above it would also lead to fall in national income and according to same model of exchange rates fall in national income leads to depreciation of home currency.

Or for example, it is true that increase in interest rate would make people save more money, however, again increase with marginal propensity to save without increase in marginal propensity to invest would lead to lower national income and hence lower saving despite higher marginal propensity to save.

What a net effect is, is impossible to say unless you start giving these relationships a form. What you need to do first is to specify these relationships. For example, investment might be given as:

$I= 10 +0.3Y -100i$

Savings can be given as:

$S= (1-MPC(i))Y-100$ where you can further specify the relationship between MPC and i, and so on.

Once you specify behavior of all functions (or set them to some constant, for example G could be just set to 100), you can solve the system and say how much change in one variable like $i$ affects other variable like CAD.

Also note, you don't need to use numbers, I used numbers because you seem like high school student, you can also just use letters for parameters and just see direction of effect. So for example $I$ could be $I= \alpha + \beta Y - \gamma i$, and then when you solve the system just take total derivative.