004: Macroeconomic Theory

004: Macroeconomic Theory

Lecture 4

Mausumi Das

Lecture Notes, DSE

August 1, 2014

Keynes & the Classics: Role of Expectations

Even though we have deliberately kept expectations out of the picture so far, expectations play a major role in at least two of the

behavioural equations speci…ed earlier.

In the standard Classical System, we have assumed that workers’

labour supply schedule depends on the real wage rate.

It is often argued that since prices are determined in the goods market while nominal wages are set in the labour market, workers often do not have perfect information about the price behaviour. So they determine their labour supply on the basis of the‘expected’real wage.

Hence the labour supply equation would now be:

N^S :W =P^eg(N); g⁰ >0

If we incorporate this assumption in our standard Classical system, then the AS schedule under the classical system may change its character - as you will see in a moment.

Keynes & the Classics: Role of Expectations (Contd.)

Another equation where expectations play a major role is the LM equation that characterises the money market equilibrium.

In our earlier speci…cation (of both the Classical as well as the

Keynesian system) we have assumed that real and the nominal interest rates are the same. In other words we have asumed that the expected rate of in‡ation is zero.

If we allow that expected rate of in‡ation to be non-zero, than the real and the nominal interest rate would di¤er:

r =i π^e

This will a¤ect the money demand function such that the equation of the LM curve would now be:

LM: ¯M =PL(Y,i); L_Y >0;L_i <0

If we incorporate this assumption in our standard Keynesian/Classical system, then the AD schedule gets a¤ected by changes in people expectations. We shall come back to this point in a while.

Keynes & the Classics: Role of Expectations (Contd.)

Notice that the investment demand is always a function of the real interest rate. So the investment function and therefore the IS curve remains unchanged.

Question: Why is the LM curve a function of the ‘nominal’interest rate, instead of the ‘real’one?

AS Schedule in the Classical System when Labour Supply depends on Expected Real Wage:

As we have argued before, when the workers determine their labour supply on the basis of the ‘expected’real wage, the labour supply equation is given by:

N^S :W =P^eg(N); g⁰ >0

The labour demand equation remains unchanged (because producers’

are assumed to have more information about the price of the product that they themselves would be selling):

W =PF_N(N,K¯)

The labour market equilibrium now depends crucially on how price expectations are formed.

If workers can perfectly anticipate the actual price level, thenP^e =P and we are back to the old Classical world with a vertical AS curve.

AS Schedule in the Classical System when Labour Supply depends on Expected Real Wage (Contd.):

If, on the other hand, P^e is determined quite independent of the actual price level, then AS completely changes its character.

So the AS schedule is now upward sloping - just as it was in the Keynesian system!

Thus standard …scal and monetary policies would be e¤ective in this

‘modi…ed’Classical system - although there is no wage or price rigidity!

How are Expected Prices Determined?

It seems a little unrealistic to assume that the agent’s expectations would be completely independent of the actual value of the variable.

But to see exactly how they are related we have to look for some theories of expectation formation, which we shall discuss towards the end of the lecture.

AD Schedule when Expected Rate of In‡ation is Non-zero (say, Positive):

As we have seen before, in this case: r =i π^e This in turn changes the equation of the LM curve:

LM: ¯M =PL(Y,i) =PL(Y,r+π^e)

We can still draw the IS and the LM curves in theY-r plane, but for that we have to …x the expected rate of in‡ation at an arbitrary level.

AD Schedule when Expected Rate of In‡ation is Positive (Contd.):

Any increasein the expected rate of in‡ation now shifts the LM curve to the right in the r-Y plane (Why?)

Correspondingly the AD curve shifts to the right too.

This as such is not a problem if expected rate of in‡ation changes arbitrarily.

But if peoples’expectations about the rate of in‡ation are in‡uenced by governement policies then this would have serious implications for the e¤ectiveness of various government policies.

AD Schedule when Expected Rate of In‡ation is Positive (Contd.):

For example:

Suppose an expansionary …scal policy ("^inG¯)triggers o¤ an expectation that current price level would rise relative to the future price level.

This would then lead to afallinπ^e_t (sinceπ^e_t

P_t^e₊₁ P_t Pt ). Thus the IS curve shifts to the right (due to a"^inG¯ ) while the LM shifts to the left (due to a#^{in πe )}

So the ultimate e¤ect of an"^inG¯ on the AD curve is now ambiguous!

Needless to say, it all depends crucially on how expectations are formed - which is the topic that we now turn to.

Various Theories of Expectation Formation:

Static Expectations:

Today’s expected value of the variable (x) depends on previous period’s actual value. In particular:

x_t^e =x_{t 1}

Adaptive Expectations:

Today’s expected value of the variable (x) depends on previous period’s actual value and previous period’s expected value. In particular:

x_t^e =x_t^e ₁+λ[x_{t 1} x_t^e ₁]; 0<λ<1 Notice that Static Expectations is a special case of Adaptive Expectations (when λ=1)

Various Theories of Expectation Formation (Contd.):

Perfect Foresight:

Agent’sguess about the value of the variable (by some devine power) exactly matches its actual value. In particular:

x_t^e =x_t Notice that guessing isNOT knowing!

Rational Expectations:

Agent applies mathematical tools of expectation formation, using the available information set, to come up with the expected value of the variable. In particular:

x_t^e =E[x_tj^{It 1}]

Notice that under complete knowledge and complete certainty, Perfect Foresight and Rational Expectations are equivalent.