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) + GLM: (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.

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

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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 equationsW = 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) + GLM: 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 downward-sloping.

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

Valuation of an asset

• Imagine an asset is expected to return in cash $ze

t+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) + $ze

t+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 Pe

t+1. In the meantime we get the expected dividend next year de

t+1.

Pt = det+1/(1+it) + Pe

t+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) + [de

t+2/(1+iet+1) + Pet+2/(1+iet+1)] /(1+it)

• We can keep doing this and finally get:

Pt = det+1/(1+it) + de

t+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!]