Monetary Approach to the Balance of Payments – Robert Mundell

1. Monetary Approach to the Balance of Payments – Robert Mundell

2. What it is • Relying on the fundamental equation of monetary economics MV = PY, monetary theory predicts various phenomena about international exchange rate adjustment and the balance of payments • Many of these predictions are contrary to those of the simple Keynesian model, which neglects the effects of changes in the money supply • According to MABP, credit creation by the central bank to stimulate the economy may be thwarted by an outflow of capital in the form of foreign exchange reserves, which are also part of the monetary base.

3. Who they are • The two most important theorists in MABP were the late Harry Johnson, who drank far too much baijiu for his own good and expired much too early in life and so never saw the Nobel prize, Lloyd Melzer, and Robert Mundell, who, am told by reliable sources, drank less and did live to receive it • See an interview with Mundell at http://nobelprize.org/mediaplayer/index.php?id=448&view=1

4. Development of the model • The model used in the MABP is derived as follows. • The demand for money L = kPYe-αi, where • P = the domestic price level, • Y = real output • i = the nominal interest rate, • α = the interest elasticity of money demand, and • k is a constant = 1/V, V = money velocity • The assumption of a constant money velocity is a keystone to monetarism

5. The interest rate and expected inflation • The nominal interest rate may also be written as i = r + Pe, where r is the real interest rate (when inflation is and is expected to remain 0), and Pe is expected inflation • One of the problems with using this expanded form is that Pe is unobservable • If we know r, however, Pe can be calculated by subtracting r from I • Another way to attempt to determine Pe is to assume expectations are rational and regress Pt on Pt-j, j = 1, 2, 3, … , k for some number of periods k • P-hat from the resulting prediction equation would then serve as the measure for Pe

6. The Money Supply • The supply of money is quite simple: M = A(R + D), where • A = the money multiplier • R = monetary foreign exchange reserves, and • D = official credit created by the central bank • Thus, R + D is base money

7. Equilibrium • At equilibrium, L = M, so kPYe-αi = A(R + D) • Next, we need to specify the exchange rate between the country and the world as P = EP0, where P0 is the world price level, however this is specified, and E is the exchange rate • Note that since E = home currency units/reserve currency unit, an increase in E is a depreciation of home’s currency • Also, since the US dollar is the reserve currency, P = P0 for the U.S., so we can let P0 = U.S. price level • We probably want to use the GDP deflator as the price level variable as this is the most general price index used • Thus, kEP0Ye^-αi = A(R + D)

8. Weighting Credit and Reserves • Taking natural logs we get • (1) ln(k) + ln(E) + ln(P0) + ln(Y) – αi = ln(A) + ln(R + D) • Now the first difference in natural log of x is the percent change in x, shown as follows • d(ln(x))/dx = 1/x, so d(ln(x)) = dx/x = percent change in x = x-dot • In addition, the % change in R + D = R-dot[R/(R+D)] + D-dot[D/(R+D)] since, by the chain rule of differentiation, d(ln(R+D))/dR = d(ln(R+D))/dD = 1/(R+D); thus, the total differential d(ln(R+D)) = δ[ln(R+D)]/δR*dR + δ[ln(R+D)]/δD*dD = dR/(R+D) + dD(R+D) = (dR/R)*R/(R+D) + (dD/D)*D/(R+D) = R-dot[R/(R+D)] + D-dot[D/(R+D)] • We’ll call these terms R-dot = r and D-dot = d with the understanding that these are really weighted percent changes

9. Final MABP Equation • Taking the first difference of equation (1) and rearranging terms yields • r – e = – a + p0 + y – d(αi) – d (the % change in k is assumed to be 0) • This equation states that the change in a country’s foreign exchange reserves plus the rate of appreciation of its currency relative to the dollar is positively affected by a rise in world prices and its own output, while it is negatively affected by an increase in the money multiplier, domestic credit and an increase in the interest elasticity of demand for money and/or the nominal interest rate

10. Interpretation of the model • The interest rate term might seem counter-intuitive; but, recall that the real rate is assumed to be constant so a rise in i means an increase in expected inflation, which, in turn, reduces the desirability of holding home’s currency • Also, for a country that is not inflating, rising rates of GDP growth lead to greater exports; who else will buy the excess output of the economy • In fact, this result is commonly observed empirically; rapidly growing economies do generate large current account surpluses • But Keynesian economists generally associate high rates of growth with increased consumer and producer demand

11. Estimation of the model • To estimate the model, we note first of all that there is only one slope coefficient to be estimated, α • All other variables are unit elastic • The dependent variable is • Z = r – e – p0 – y + d, which is regressed on i; the constant term is a-hat and the slope estimate is α-hat

12. What is done • What most studies do is to estimate the coefficients on all the variable to see how close these come to the theoretical values • My colleagues and I did such a model for China and due to data problems have not come up with meaningful results • I need to find good data to use in our model before I go home; I don’t think so!