The Only Way out of the Romer Conundrum is to Dump Wicksells Rocking Horse

A great deal of discussion on the blogosphere about Paul Romers paper critical of neoclassical modelling.

Heres the diplomatic authorised version

Once macroeconomists concluded that it was reasonable to invoke an imaginary forcing variables, they added more. The resulting menagerie, together with my suggested names now includes:

A general type of phlogiston that increases the quantity of consumption goods produced by given inputs

– An “investment-specific” type of phlogiston that increases the quantity of capital goods produced by given inputs

-A troll who makes random changes to the wages paid to all workers

-A gremlin who makes random changes to the price of output

-Aether, which increases the risk preference of investors

-Caloric, which makes people want less leisure.

I think much of the discussion has reverted to catalogs of why people don’t like DGSE models rather than the implicit criticism of modelling startegies based on ímaginary forcing variables’creating ”shocks”.  The kind of models now dominant in ALL modelling approaches derived from real business cycle models including New Keynsian.

All of these models are based on a parable of equilibrium based on Wicksell’s Rocking Horse model.  We now know this to be mathematically false, so why don’t we just replace it?

His famous quote from 1918

“If you hit a rocking horse with a stick, the movement of the horse will be very different from the stick. The hits are the cause of the movement, but the system’s own equilibrium laws condition the form of movement”

Wicksells model was one of damped equilibrium.  In nature equilibrium is a state of rest, so a pendulum for example will eventually stopped swinging.  So the only way to make the rocking horse rock is to hit it with a stick.

So equilibrium models based on this framework cannot explain business cycles.  This was a real problem for early theorists who tried to explain business cycles endogenously.

Take for example Marx, whose verbal model in Capital IIexplained cycles as a combination of ‘lags’in replacement of fixed capital and wages caused by changes to profits.  He tried to explain it mathematically but gave up (letter to Engels 1872) as it was beyond his mathematical abilities.

Kalecki took up the investment part in his celebrated business cycle model, in Essay on the Business Cycle Theory 1933.   Clearly influenced by Marx but expressed in clear form as difference equations.

This was criticized by Ragnar Frisch

“The Characteristic Solutions of a Mixed Difference and Differential Equation Occurring in Economic Dynamics”, with H. Holme, 1935, Econometrica

Essentially this is Wicksell’s rocking horse rendered mathematically.  To keep the horse rocking there had to be periodic ‘shocks’- the cycle could not be endogenous.

But we now know this to be false.  Slutsky (1927) showed how periodic cycles could be explained by small variations in endogenous variables.  He had provided the maths that was beyond Marx.  We now of course have a much richer mathematical toolkit of teh regions of stability that generate limit cycles, those that create damped occilations and those that lead to shifts in attractors and chaos.  This has barely penetrated post grad economics which still uses a discredited 8- year old set of equations.

Where the economics profession – following Lucas – got it wrong was to take Slutskys proof that random variations can generate cycles – which became the ‘stochastic’part of DGSE from his wider demonstration that ANY endogenous change can generate cycles – which takes us to endogenous theories of the business cycle – the path of Marx, Hawtry, Kalecki and Kaldor.   You can ‘fit’a series of waves to explain a graph of past data, but that is the same technique a DX9 synthesizer uses Fourier synthesis to generate waves that simulate instruments.  A DX9 programmed to simulate the noise of a flute is not a flute.  Slutsky himself used the example of rainfall falling over many days influencing crop yields and criticised ‘spurious’statistical correlations.

Over time emphasis in business cycle theory has shifted between ímpulse’ and ‘propigation'(socks – the hitting of the rocking horse) – but the underlying assumption that shocks are necessary to ensure propagation.

To get away from models where change is generated by philosogen and chaloric we have to abandon the  assumption that what drives cycles is outside the model.  To get a rocking horse to rick requires energy, and how much it swings depends on its centre of mass.  The economy is much more like a powered rocking horse where its centre of gravity is subject to rare but violent shifts to new equilibria.


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