New Keynesian Macroeconomic Models are worse than you think

Posted byThe Mountain GoatPosted inUncategorizedTags:, , , , , , ,

I have spent the past several years learning mainstream macroeconomics, in order to be sure that my heterodox views on the topic were justified.  When I began this project I expected that many of the predictions of mainstream models that I disagreed with would be a result of some of the unrealistic assumptions such models make. However, it turns out that dubious assumptions are not the most serious issue with the textbook New Keynesian(NK) model and the models based on it.  In the NK model many of the most important conclusions of the model do not follow logically from the assumptions at all, but are rather the result of mathematical fudging.  The fudging techniques used can be used to reach a wide variety of absurd conclusions, but in the textbook model they are used to ensure that monetary policy, and the Taylor rule have the expected effect on the economy.

The best explanation of how the Taylor rule works in the standard NK model is in the PHD macro II lecture notes of Eric Sims.  Eric Sims is a highly respected mainstream macroeconomist, and his lecture notes have often been recommended to me as the best source of knowledge on how the NK model works.  These notes are from a PHD macro II class he teaches.

According to Eric Sims when Taylor originally proposed the Taylor rule he thought it would control inflation in the following way. In his view, peoples’ propensity to consume is based on the real interest rate.  In order to reduce inflation the central bank must reduce consumption, and it does so by raising the real interest rate. To do so it must raise the nominal interest rate by more than the increase in inflation, since the nominal interest rate is approximately equal to the real interest rate plus the inflation rate.  

However, Sims states that Taylor’s original intuition is not how the Taylor rule works in the standard NK model.  Instead, the central bank uses the Taylor principle to rule out indeterminacy by creating explosive inflation dynamics.  If inflation gets above target the central bank increases inflation further, ensuring that the inflation rate eventually goes to infinity.  Somehow solutions with infinite inflation in inflation are ruled out, and so by destabilising the economy the central bank ensures inflation will stay on target.

Of course, I am not the only person to notice that the way the Taylor rule works in NK models is suspect.  John Cochrane has written extensively on this issue and David Andolfatto has blogged on the topic.  However, both authors do not seem to fully appreciate how much of a problem the approach taken by the NK model is.

I have struggled with how to write about this issue myself.  People without a strong background in math or economics are unlikely to have much prior knowledge about when it is okay to reject infinite solutions to a model, and the PHD economists who have actually studied this topic are unlikely to be receptive to the idea that the majority of macro models in the past 20 years should be rejected.  One approach would be to moderate my criticism and write for mainstream macroeconomists, however I believe it is important to emphasize just how much of a problem the standard approach is.

Instead, I have created a reductio ad absurdum argument that should make it clear to non-experts how problematic the way the Taylor rule works in NK models is.  Using the same logic that the NK model uses to rule out inflation indeterminacy, we can in fact show that the central bank can control practically any variable in the economy.

Eric Sims illustrates how the Taylor principle rules out indeterminacy in the standard model as follows.

Suppose the central bank sets interest rates according to the following rule. 

i_t=\sigma \pi_t +\theta,

where \pi is inflation, i_t is the nominal intererst rate, and \theta is a AR(1) error term with mean zero. \sigma is a parameter that governs how strongly the central bank responds to inflation.

The Euler equation gives us the following expression

Y_t=E(Y_t)-(i_t-E(\pi_{t+1})),

which gives us i_t=E(\pi_{t+1}) if Y_t is constant.  Combining the two expressions we get

E(\pi_{t+1})=\sigma \pi_t +\theta. 

We also have the boundary condition \lim_{t \to +\infty} E(\pi_{t+1})=0

The above two equations and boundary condition give us an infinite number of finite solutions in the case where \sigma is less than 1.  Any value of inflation today is a solution to the model.  If, on the other hand, \sigma is greater than 1 we only have one solution, where \pi_t=(1-\sigma) \theta.  By turning solutions that exist if \sigma is less than 1 into solutions where inflation goes to infinity the central bank somehow ensures they do not happen in reality, and thus inflation is made determinate.

To extend the above logic we simply need to realize that the model is indeterminate in every variable that we have not explicitly excluded elsewhere in the model. The standard model says absolutely nothing about the birth rate, for example.  Using the same approach it used to eliminate inflation indeterminacy the central bank in the model can eliminate these other indeterminacies, and set the birth rate to whatever it wants.

To do so we simply modify the central bank’s reaction function to add a term that only exists if the birth rate is a particular value.  If the birth rate is not equal to the birthrate target then the central bank reacts to inflation as follows  i_t=\sigma\pi_t+\theta_t+ 10t), while if the birth rate is on target it uses the normal reaction function  There are no finite solutions to the model using the modified reaction function unless the birth rate is equal to the birth rate target, so, using the same logic as above, we can conclude that the birthrate must now always equal to the birthrate target.

Of course if we model the process by which the birth rate is set in reality then the above approach would run into problems.  The birth rate would not be indeterminate in that context, so we would not be able to get the central bank to control it.  But the same applies to the way the Taylor rule rules out inflation indeterminacy.  Inflation is indeterminate in the standard model due to not including initial conditions and how expectations are actually formed.  If those features are included, for example, by having inflation expectations formed in an adaptive manner then the standard approach would also run into problems.

When I present this argument to economists who work with mainstream NK models I typically get one of the following responses.

By far the most common is to claim that the Taylor principle works according to Taylors’ original intuition in these models.  Since only PHD macro classes teach how the Taylor rule works in NK models that way, it is understandable that they are suffering from that misapprehension. However the fact that so many mainstream economists do not understand their own models suggests major problems in the field.

The next response is to claim that what I am doing with the birth rate is somehow different than what the standard model does.  But mathematically and economically the status of the two variables is identical, so this argument is without merit.

The final response is to claim that this is not a problem, because a model can be as absurd as you want as long as it reproduces the data (this argument mirrors Milton Friedmans’ argument in The Methodology of Positive Economics). There are two main problems with using that argument in this context.

1.  These models do not in fact replicate the data very well.  There are some studies showing that they can do as well on a carefully chosen series of empirical tests as simple empirical models, but these models also suffer from a large number of puzzles, ie anomalous empirical results.  Amoung these are the Barro-King curse and the forward guidance puzzle.

2.  The entire rationale behind microfounded models is to have models that, due to correct modelling of the underlying processes, can be trusted more than models based on past empirical regularities.  If the mechanisms in the model are absurd there is no reason to expect that, and hence no reason to prefer a “microfounded” model to a model without microfoundations.

The issue discussed above is not limited to the textbook NK model. Practically every modern macroeconomic model has the Taylor rule ruling out indeterminacy in the manner described above.  The extent to which individual the predictions of these models are affected is unclear, however clearly there is reason for general scepticism.

3 thoughts on “New Keynesian Macroeconomic Models are worse than you think”

  1. Typo here or am I misunderstanding?

    “In order to reduce inflation the central bank must reduce consumption, and it does so by **lowering** the real interest rate. To do so it must *raise* the nominal interest rate by more than the increase in inflation,

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  2. Please read this:

    https://new-wayland.com/blog/interest-price-spiral/

    “The standard line is this from the Bank of England

    when we raise Bank Rate, banks will usually increase how much they charge on loans and the interest they offer on savings. This tends to discourage businesses from taking out loans to finance investment, and to encourage people to save rather than spend.

    ”

    “Overall if loans go down, financial savings must go down by exactly the same amount.

    If you want the stock of bank loans to come down, while the stock of bank deposits goes up, then, unfortunately, reality won’t let you do that.”

    “As MMT shows the cost of credit is incorporated into the cost of all goods and services. The higher the interest rate, the higher the price.

    The Myth recommends pouring fuel on the fire. MMT recommends a permanently zero Bank Rate, and making central bankers, along with their expensive entourage, redundant.”

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