Review session
• In this lecture we will review the major models
that we have developed in the course.
• This course has focussed on developing several
macroeconomic models that are useful in
analysing the broad policies of the federal
government.
• We will cover the basic structure of each of the
models and show how each proceeds from or
extends the previous models.
Goals of the models
• What is it that we wish to explain in our models?
• Answer: We would like to better understand the
behaviour of the “big” macroeconomic variables
–
–
–
–
–
Output
Unemployment
Interest rates
Inflation
Exchange rates
• These are the variables we would like to have a
model to explain.
Basic IS-LM
• We started with the core closed-economy IS-LM
model:
IS: Y = C(Y – T) + I(Y, i) + G
LM: (Ms/P) = L(Y, i)
• We have two equations in two variables (Y, i),
and so this equation is (generally) solvable for a
unique solution (Y*, i*) that satisfies both
equations.
• Only one set of values (Y*, i*) will simultaneously
solve both the IS and LM equations. So only
one set of values will lead to equilibrium in both
the goods and money markets.
Basic IS-LM
• If we specify a functional form for C(Y-T)
and I(Y, i), then we could solve for Y as a
function of i in the goods market- an IS
curve.
Y  c 0  c1 (Y  T)  b 0  b1Y  b 2i  G
1
Y
(c 0  c1T  b 0  b 2i  G)
(1  c1  b1 )
• Since I is falling in i, the IS curve slopes
down in (Y, i).
Basic IS-LM
• Likewise if we specified a functional form for L(i),
we could derive a form for Y as a function of i in
the money market- an LM curve. Typically we
chose:
L(Y, i) = Y L(i)
• So we had the LM curve:
Y= Ms/(P L(i))
• Since L(i) is falling in i and L(i) appears in the
denominator on the right-hand side, the LM
curve slopes up in (Y, i).
Basic IS-LM
• We have a model with two endogenous
variables (Y, i) and four parameters (G, T, Ms, P).
• The two IS and LM curves jointly determine the
two endogenous variables. The four parameters
will each shift one of the two curves (since they
each only appear in one equation).
• Strengths of the model: Simplicity.
• Weaknesses: Only explains output and interest
rates.
Adding the labour market
• The basic IS-LM model had no labour market in
it, so out next step is to add a labour market
which will bring in wages/prices and
unemployment.
• We have a wage-setting equation relating wage
demands to labour market conditions:
W = Pe F(u, z)
• And we add in a price-setting equation relating
prices to labour cost:
P = (1 + μ ) W
Adding the labour market
• We have “normalized” (set the units) of labour so
that one unit of labour produces one real unit of
output. In this case, output is simply
employment (N):
Y=N
• Since we have a labour force of L,
unemployment is:
u = (L – N) / L = 1 – N / L = 1 – Y / L
• So we have a relation between wage demands
and output:
W = Pe F(1 – Y/L, z)
Adding the labour market
• We have two equations
W = Pe F(1 - Y/L, z)
W = P / (1 + μ )
• These are our labour market equations.
• We have introduced into our system two new
endogenous variables (W, P) and four new
exogenous variables (Pe, L, z, μ).
• Equilibrium in the labour market holds when the
wage demanded is equal to the wage assumed
by employers. We get:
Pe F(u, z) = P / (1 + μ )
Basic AD-AS
• Substituting Y in for unemployment, we get the
equation for the AS curve:
P = Pe (1 + μ )F(1 - Y/L, z)
• We have a relationship between the price level
and supply of output in the economy. Since
wage demands fall in u, P is rising in Y- the AS
curve is upward-sloping. Now we need a
relationship between the price level and demand
for output in the economy.
• Our IS-LM equations are:
IS: Y = C(Y – T) + I(Y, i) + G
LM: M/P = Y L(i)
Basic AD-AS
• Using our IS-LM equations, we can solve for the
solution values (Y*, i*) depending on the values
of the parameters (G, T, M, P).
• Then you can think of expressing Y* as a
function of the value of P. This relation is the AD
curve. The other parameters (G, T, M) will shift
the AD curve.
• Since a rise in P lowers M/P, shifting the LM
curve left and lowering Y*, P rises and Y falls
along the AD curve. The AD is downwardsloping.
Basic AD-AS
• We could express our AD-AS model in the same
form as our IS-LM:
AD: P = AD(Y, G, T, M)
AS: P = AS(Y, Pe, L, z, μ)
• So we have two equations with two endogenous
variables (P, Y) and seven parameters (G, T, M,
Pe, L, z, μ). Note that in solving the AD-AS
system, we also get i* from the IS-LM equations,
and unemployment:
u = 1 – Y/L
Basic AD-AS
• Strengths: Relative simplicity. Can
explain price movements and
unemployment.
• Weaknesses: We really want inflation, not
price level movements.
• So how are we to move to a model in
inflation rather than P? We need to begin
with the Phillips Curve.
Phillips Curve
• We can derive an interesting result by
rearranging the equation for equilibrium in the
labour market. If we linearize F(.):
F (u, z) = 1 – α u + z
• And then transform prices into percentage
change in prices (inflation), we get:
π = πe + (μ + z) - α u
• Current inflation is a function of unemployment
with parameters (πe, μ, z).
• So we have transformed our AS curve into the
Phillips Curve.
Phillips Curve
• There are several different transforms of the
Phillips Curve. One is to use the deviation from
natural rate of unemployment. Since the natural
rate of unemployment occurs when inflation
equals expected inflation, we get:
un = (μ + z) / α
• And substituting back into the Phillips Curve
equation, results in:
πt - πte = α un - α ut = - α (ut – un)
Dynamic AD
• The Phillips Curve relation is expressed in
convenient variables- unemployment and
inflation- for policy discussion. Can we express
the rest of our AD-AS model in this form?
• Yes, the result is the dynamic AD model. In this
model, we have Okun’s law expressing a
relationship between changes in unemployment
and GDP growth:
ut – ut-1 = -β (gYt – g*Y)
Dynamic AD
• Intuition of Okun’s law: The labour market is
growing (in numbers and productivity) every
year. Output must grow at least this fast, or the
economy will not absorb all of the labour.
• If inflationary expectations are merely last year’s
inflation rate, then the Phillips Curve becomes:
πt - πt-1 = - α (ut – un)
• Where we call 1/α the “sacrifice ratio”, as it
represents the number of percent-years of
unemployment required to reduce inflation by
1%.
Dynamic AD
• RBA controls interest rates
Yt = Y(it, Gt, Tt) = Y*t / it
• Where Y* is the natural rate of output Then
putting this into growth rates, we get:
gYt = g*Y - git
• If the RBA follows an interest rate target then the
rule for the RBA might be
git = φ(πt – πT)
gYt = g*Y - φ(πt – πT)
Dynamic AD
• RBA controls money supply
Yt = Y((Mt/Pt), Gt, Tt) = (Mt/Pt) f(Gt, Tt)
• If we hold G and T constant, then they
drop out in a growth relation:
gYt = gMt – gPt
• But gP is just inflation, so we have:
gYt = gMt – πt
Dynamic AD
• So we have three relations in growth rates:
Okun’s Law: ut – ut-1 = -β (gYt – g*Y)
Phillips curve: πt - π t-1 = - α (ut – un)
DAD: gYt = g*Y - φ(πt – πT)
• Or
DAD: gYt = gMt – πt
• Parameters: g*Y, un, πT , gMt
• Variables to be solved: gYt, ut, πt
• As these are growth models, we will typically be
solving for values of variables over time.
Dynamic AD
• Unless we want to allow for a solution that
spirals away, ie. πt > πt-1 for all t, then we will
require that πt = πt-1.
• From our Phillips Curve, then ut = un for all t, so
through our Okun’s Law, gYt = g*Y for all t.
• Our DAD relations will then determine monetary
policy.
– πt = πT
– gMt = g*Y + πT
• So to maintain stability in our model, the path of
money supply is determined by our targets and
parameters.
Dynamic AD
• We have a model which expresses most of our
variables of interest (except exchange rates) in
the form which we desire for policy discussion.
• Strengths: Contains variables in the right form.
• Weaknesses: Complicated. The explanation of
expectations is not rational- expectations here
can be consistently wrong.
• We would like to bring expectations into the ISLM/AD-AS framework in an explicit way.
Valuation of an asset
• Imagine an asset is expected to return in
cash $zet+1 next year, $zet+2 the year after
next, $zet+3 the year after that …
• The value of the asset is the sum of the
discounted values of these cash flows:
Vt = $zet+1/(1+it) + $zet+2/(1+it)(1+iet+1) + …
• This is the basis of financial valuation and
the basic tool of finance.
Value of a share
• Example: The price of a share should be equal
to its cash flow value. Imagine we buy a share
today at price Pt and sell it next year at price
Pet+1. In the meantime we get the expected
dividend next year det+1.
Pt = det+1/(1+it) + Pet+1/(1+it)
• But the expected value of P next year must be
the expected value of the dividend plus the sale
price the year after next.
Value of a share
• So we get
Pt = det+1/(1+it) + [det+2/(1+iet+1) + Pet+2/(1+iet+1)]
/(1+it)
• We can keep doing this and finally get:
Pt = det+1/(1+it) + det+2/(1+iet+1)(1+it) + …
• The value of a share must be equal to the
present value of the expected dividends from
the share.
• Share prices and dividends and expected
dividends should move in the same direction.
Bringing in expectations
• Our new investment function
It = I(Real Profitse/(re+δ))
• Allows for the fact that investment depends on
expectations of future profits and interest rates.
• We have to adopt a new form
Ct = C(Yt , Wt )
• Where Wt is our household wealth, which will be
the sum of our financial and housing assets, At ,
plus our human wealth, Ht .
Wt = At + Ht
Bringing in expectations
• Our new IS equation becomes:
Y = C(Y, T, W(Ye, Te)) + I(Profits(Ye, Te), r, re) + G
• Avoiding the book’s ugly notation, let’s just use
IS for the right-hand side.
Y = IS(Y, T, r, Ye, Te, re, G)
(+, -, -, +, -, -, +)
• Where IS = A + G in the book’s notation and the
+/- are the relationships between and increase in
the independent variable and Y.
Bringing in expectations
• However our LM equation in unchanged:
LM: M/P = Y L(r)
• This model is useful for discussion
problems that involve linked changes in
present and future parameters.
• However we still have yet to bring in any
explanation of exchange rates. The next
set of models add external trade.
Adding external markets
• If we have financial openness, investors must
expect equal returns on domestic and overseas
assets.
• The uncovered interest rate parity condition
expresses this result:
it = it* - [(Et+1e - Et)/ Et]
• The domestic interest rate must be equal to the
foreign interest rate less the expected rate of
appreciation.
• Or it - it* = Expected appreciation of A$.
The new IS equation
• Exports are measured in Australian goods, but
imports are foreign goods, so we have to
translate into Australian good through the real
exchange rate, e, so net exports are:
NX = X(Y*, e) – IM(Y, e)/e
• This becomes a component of our AD, so
equilibrium in the goods market requires:
Y = C(Y-T) + I(Y, r) + G + NX
Y = C(Y-T) + I(Y, r) + G + X(Y*, e) – IM(Y, e)/e
Net exports
• In the last class we defined net exports as:
NX(Y, Y*, e) = X(Y*, e) – IM(Y, e)/e
(-, +, ?)
( +, -)
(+, +) +
• So NX is decreasing in Y, increasing in Y* and
ambiguous is e. We can’t sign e, as we can’t
sign IM(Y, e)/e.
• The Marshall-Lerner condition is the condition
that ensures that NX falls as e rises. If the
Marshall-Lerner is true:
NX(Y, Y*, e)
(-, +, -)
IS-LM under fixed rates
• Our goods market equilibrium is:
IS: Y = C(Y-T) + I(Y, r) + G + NX(Y, Y*, e)
• Our money market equilibrium is:
LM: (M/P) = Y L(i)
• We have our Fisher equation:
r = i - πe
• And since the nominal exchange rate is pegged
at E’, we have
e = E’P/P*
IS-LM under fixed rates
• We also have our interest parity condition:
i = i*
• Our IS-LM equations become:
IS: Y = C(Y-T) + I(Y, i* – πe) + G
+ NX(Y, Y*, E’P/P*)
LM: (M/P) = Y L(i*)
• We can use these two to solve for our AD
equation. We have to ask “what happens as P
rises?”
IS-LM under fixed rates
• As P rises, the RBA must move M so as to keep
i = i*, so the nominal interest rate will be
unaffected. However the real exchange rate will
change, as E’ and P* are fixed. As P rises, e
rises as:
e = E’P/P*
• So a change in P affects the economy only
through the change in the real exchange rate.
• As P rises, e rises, so NX must fall if the
Marshall-Lerner condition is satisfied. We can
use this fact to trace out our AD curve.
AD under fixed rates
• As P falls, NX rises, so AD increases. This
means our AD curve is downward-sloping.
• Our AD curve holds constant G, T, E’ and P*.
We can express our AD curve as:
AD: Y = AD(E’P/P*, G, T)
• Changes in G, T, E’ and P* will shift our AD
curve. A rise in G and P* shift the AD right. A
rise in T and E’ shift the AD left.
• [Note: Be sure that you understand why!]