Transcript Lecture VIII Monetary Approach to the Balance of

Monetary Approach to the Balance of
Payments – Robert Mundell
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.
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
Development of the model
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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
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
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
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)
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)] + Ddot[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
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
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
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
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!