MACROECONOMICS: THE SARGENT & WALLACE POLICY INEFFECTIVENESS PROPOSITION, LUCAS CRITIQUE

POLICY INEFFECTIVENESS PROPOSITION

ASSUMPTIONS: PRICE FLEXIBILITY WAGE FLEXIBILITY RATIONAL EXPECTATIONS

Assume the following model of an economy: AD: πt = -b(yt – yt-1) + ΔMt + ΔG + μt

SRAS: yt = yt-1 + a(πt – Et-1πt) + εt Let us assume that G = 0 to simplify the

algebra (the result also holds if we assume M = 0)

POLICY INEFFECTIVENESS PROPOSITION

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Output is influenced by:

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Something we can’t make sense of – WHAT is the Expected value of inflation?

Random shocks

POLICY INEFFECTIVENESS PROPOSITION

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Now we need to TAKE EXPECTATIONS of the AD equation.

Et-1yt-1 is yt-1 (as it is already observable, and Et-

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POLICY INEFFECTIVENESS PROPOSITION

Thus throwing it all together:

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Output is influenced by:

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A Policy ‘Surprise’. This could also be a deviation from expected Government expenditure

Random shocks

POLICY INEFFECTIVENESS PROPOSITION

This suggests that Policy makers are ‘impotent’, as only a ‘surprise’ decision can alter short-run output.

HOWEVER. We can disprove the PIP by simply challenging one of the assumptions listed; namely wage flexibility.

Let us assume contracts are fixed for 2 periods, that is:

t-1: Contracts are being negotiated t t+1

Contracts are fixed

POLICY INEFFECTIVENESS PROPOSITION Taking off from the previous mathematical

derivation, this means: Expected inflation for ‘t’: Et-1πt = Et-1ΔMt Expected inflation for ‘t+1’: Etπt+1 = Et-1ΔMt Therefore (using a different parameter instead of ‘a’ as wages

are fixed): Yt = yt-1 + (f/1+fb)[ΔMt - Et-1ΔMt ] + (1/1+fb)[fμt + εt] Yt+1 = Yt + (f/1+fb)[ΔMt+1 - Et-1ΔMt ] + (1/1+fb)[fμt+1 + εt+1] We can see that we can sub in Yt into the equation for Yt+1.

This means that Yt+1 = g(μt , εt ) Hence, as the market can’t react to the shocks having

occurred in time ‘t’ (due to wages being fixed), there is a DESIRABLE and FUNCTIONAL role for the Government in order to react to the shocks (AD shifts).

We could show that the PIP holds for 1 period fixed contracts.

LUCAS CRITIQUE

Fundamentally, the Government is impotent. This is because the Government needs to know the slope of the AD/AS curves in order to exploit them.

HOWEVER, because these slopes are DETERMINED by Government policy, a change in Gov. Policy will also change the slope.

Thus, the Government will never be able to know what to do, as it’s actions alter the means of getting to the ends.

This lead to the new Keynesian school of economics which focuses on microfoundations.