Review session

1
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.

2
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.

3
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.

4
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.
• Since I is falling in i, the IS curve slopes down
  in (Y, i).

5
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).

6
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.

7
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

8
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)

9
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 )

10
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)

11
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 downward-sloping.

12
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

13
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.

14
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 a u z
• And then transform prices into percentage change
  in prices (inflation), we get
• p pe (µ z) - a u
• Current inflation is a function of unemployment
  with parameters (pe, µ, z).
• So we have transformed our AS curve into the
  Phillips Curve.

15
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) / a
• And substituting back into the Phillips Curve
  equation, results in
• pt - pte a un - a ut - a (ut un)

16
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 Okuns law expressing a
  relationship between changes in unemployment and
  GDP growth
• ut ut-1 -ß (gYt gY)

17
Dynamic AD

• Intuition of Okuns 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
  years inflation rate, then the Phillips Curve
  becomes
• pt - pt-1 - a (ut un)
• Where we call 1/a the sacrifice ratio, as it
  represents the number of percent-years of
  unemployment required to reduce inflation by 1.

18
Dynamic AD

• RBA controls interest rates
• Yt Y(it, Gt, Tt) Yt / it
• Where Y is the natural rate of output Then
  putting this into growth rates, we get
• gYt gY - git
• If the RBA follows an interest rate target then
  the rule for the RBA might be
• git f(pt pT)
• gYt gY - f(pt pT)

19
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 pt

20
Dynamic AD

• So we have three relations in growth rates
• Okuns Law ut ut-1 -ß (gYt gY)
• Phillips curve pt - p t-1 - a (ut un)
• DAD gYt gY - f(pt pT)
• Or
• DAD gYt gMt pt
• Parameters gY, un, pT , gMt
• Variables to be solved gYt, ut, pt
• As these are growth models, we will typically be
  solving for values of variables over time.

21
Dynamic AD

• Unless we want to allow for a solution that
  spirals away, ie. pt gt pt-1 for all t, then we
  will require that pt pt-1.
• From our Phillips Curve, then ut un for all t,
  so through our Okuns Law, gYt gY for all t.
• Our DAD relations will then determine monetary
  policy.
• pt pT
• gMt gY pT
• So to maintain stability in our model, the path
  of money supply is determined by our targets and
  parameters.

22
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
  IS-LM/AD-AS framework in an explicit way.

23
Valuation of an asset

• Imagine an asset is expected to return in cash
  zet1 next year, zet2 the year after next,
  zet3 the year after that
• The value of the asset is the sum of the
  discounted values of these cash flows
• Vt zet1/(1it) zet2/(1it)(1iet1)
• This is the basis of financial valuation and the
  basic tool of finance.

24
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
  Pet1. In the meantime we get the expected
  dividend next year det1.
• Pt det1/(1it) Pet1/(1it)
• But the expected value of P next year must be the
  expected value of the dividend plus the sale
  price the year after next.

25
Value of a share

• So we get
• Pt det1/(1it) det2/(1iet1)
  Pet2/(1iet1) /(1it)
• We can keep doing this and finally get
• Pt det1/(1it) det2/(1iet1)(1it)
• 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.

26
Bringing in expectations

• Our new investment function
• It I(Real Profitse/(red))
• 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

27
Bringing in expectations

• Our new IS equation becomes
• Y C(Y, T, W(Ye, Te)) I(Profits(Ye, Te), r,
  re) G
• Avoiding the books ugly notation, lets just use
  IS for the right-hand side.
• Y IS(Y, T, r, Ye, Te, re, G)
• (, -, -, , -, -, )
• Where IS A G in the books notation and the
  /- are the relationships between and increase in
  the independent variable and Y.

28
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.

29
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 - (Et1e - 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.

30
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

31
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 cant sign e, as we cant
  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)
• (-, , -)

32
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 - pe
• And since the nominal exchange rate is pegged at
  E, we have
• e EP/P

33
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 pe) G
• NX(Y, Y, EP/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?

34
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 EP/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.

35
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(EP/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!