Hayekian capital theory – the math geek version

When I wrote my master thesis many years ago the topic was a mathematical formalization of Austrian Business Cycle Theory. In hindsight I think it is incredible that I able to pull it off and I am still pretty happy with that master thesis. It, however, convinced me that Hayek’s version of Austrian Business Cycle theory was seriously flawed. Furthermore, the math in my modeling never really satisfied me. It was just not good enough.

Now somebody more clever than me have tried a similar exercise.Here is the abstract from a new paper from the talented Arash Molavi Vasséi:

“This paper provides a systematic translation of F.A. Hayek’s informal exposition of capital theory in Utility Analysis and Interest and The Pure Theory of Capital into a model. The underlying premise is that Hayek adopts infant versions of `modern’ analytical tools such that a rational reconstruction of his capital theory by established neoclassical tools is admissible. The major result is that Hayek’s capital theory contains a generalization of the Ramsey-Cass-Koopmans model. In concrete, Hayek provides the solution to an infinite-horizon deterministic social planner optimization problem in a one-sector economy such that the rate of pure time preference encapsulated in the discount factor increases in prospective utility. With respect to stability properties, he emphasizes that the system converges even in the special case of constant returns to per-capita accumulation.”

How cool is that? Pretty cool if you ask me, but take a look at the paper yourself.

PS Arash has promised me that his next project will be on NGDP targeting and/or Market Monetarism.
PPS I hope you all remember Arash’s clever discussion on (dis)equilibrium in Market Monetarism.


“Ben Volcker” and the monetary transmission mechanism

I am increasingly realising that a key problem in the Market Monetarist arguments for NGDP level targeting is that we have not been very clear in our arguments concerning how it would actually work.

We argue that we should target a certain level for NGDP and then it seems like we just expect it too happen more or less by itself. Yes, we argue that the central bank should control the money base to achieve this target and this could done with the use of NGDP futures. However, I still think that we need to be even clearer on this point.

Therefore, we really need a Market Monetarist theory of the monetary transmission mechanism. In this post I will try to sketch such a theory.

Combining “old monetarist” insights with rational expectations

The historical debate between “old” keynesians and “old” monetarists played out in the late 1960s and the 1970s basically was centre around the IS/LM model.

The debate about the IS/LM model was both empirical and theoretical. On the hand keynesians and monetarists where debating the how large the interest rate elasticity was of money and investments respectively. Hence, it was more or less a debate about the slope of the IS and LM curves. In much of especially Milton Friedman writings he seems to accept the overall IS/LM framework. This is something that really frustrates me with much of Friedman’s work on the transmission mechanism and other monetarists also criticized Friedman for this. Particularly Karl Brunner and Allan Meltzer were critical of “Friedman’s monetary framework” and for his “compromises” with the keynesians on the IS/LM model.

Brunner and Meltzer instead suggested an alternative to the IS/LM model. In my view Brunner and Meltzer provides numerous important insights to the monetary transmission mechanism, but it often becomes unduly complicated in my view as their points really are relatively simple and straight forward.

At the core of the Brunner-Meltzer critique of the IS/LM model is that there only are two assets in the IS/LM model – basically money and bonds and if more assets are included in the model such as equities and real estate then the conclusions drawn from the model will be drastically different from the standard IS/LM model. It is especially notable that the “liquidity trap” argument breaks down totally when more than two assets are included in the model. This obviously also is key to the Market Monetarist arguments against the existence of the liquidity trap.

This mean that monetary policy not only works via the bond market (in fact the money market). In fact we could easily imagine a theoretical world where interest rates did not exist and monetary policy would work perfectly well. Imagining a IS/LM model where we have two assets. Money and equities. In such a world an increase in the money supply would push up the prices of equities. This would reduce the funding costs of companies and hence increase investments. At the same time it would increase holdholds wealth (if they hold equities in their portfolio) and this would increase private consumption. In this world monetary policy works perfectly well and the there is no problem with a “zero lower bound” on interest rates. Throw in the real estate market and a foreign exchange markets and then you have two more “channels” by which monetary policy works.

Hence, the Market Monetarist perspective on monetary policy the following dictum holds:

“Monetary policy works through many channels”

Keynesians are still obsessed about interest rates

Fast forward to the debate today. New Keynesians have mostly accepted that there are ways out of the liquidity trap and the work of for example Lars E. O. Svensson is key. However, when one reads New Keynesian research today one will realise that New Keynesians are as obsessed with interest rates as the key channel for the transmission of monetary policy as the old keynesians were. What has changed is that New Keynesians believe that we can get around the liquidity trap by playing around with expectations. Old Keynesians assumed that economic agents had backward looking or static expectations while New Keynesians assume rational expectations – hence, forward-looking expectations.

Hence, New Keynesians still see interest rates at being at the core of monetary policy making. This is as problematic as it was 30 years ago. Yes, it is fine that New Keynesian acknowledges that agents are forward-looking but it is highly problematic that they maintain the narrow focus on interest rates.

In the New Keynesian model monetary policy works by increasing inflation expectation that pushes down real interest rates, which spurs private consumption and investments. Market Monetarists certainly do think this is one of many channels by which monetary policy work, but it is clearly not the most important channel.

Rules are at the centre of the transmission mechanism

Market Monetarist stresses the importance of monetary policy rules and how that impacts agents expectations and hence the monetary transmission mechanism. Hence, we are more focused on the forward-looking nature or monetary policy than the “old” monetarists were. In that regard we are similar to the New Keynesians.

It exactly because of our acceptance of rational expectations that we are so obsessed about NGDP level targeting. Therefore when we discuss the monetary policy transmission mechanism it is key whether we are in world with no credible rule in place or whether we are in a world of a credible monetary policy rule. Below I will discussion both.

From no credibility to a credible NGDP level target

Lets assume that the economy is in “bad equilibrium”. For some reason money velocity has collapsed, which continues to put downward pressures on inflation and growth and therefore on NGDP. Then enters a new credible central bank governor and he announces the following:

“I will ensure that a “good equilibrium” is re-established. That means that I will ‘print’ whatever amount of money is needed so to make up for the drop in velocity we have seen. I will not stop the expansion of the money base before market participants again forecasts nominal GDP to have returned to it’s old trend path. Thereafter I will conduct monetary policy in such a fashion so NGDP is maintained on a 5% growth path.”

Lets assume that this new central bank governor is credible and market participants believe him. Lets call him Ben Volcker.

By issuing this statement the credible Ben Volcker will likely set in motion the following process:

1) Consumers who have been hoarding cash because they where expecting no and very slow growth in the nominal income will immediately reduce there holding of cash and increase private consumption.
2) Companies that have been hoarding cash will start investing – there is no reason to hoard cash when the economy will be growing again.
3) Banks will realise that there is no reason to continue aggressive deleveraging and they will expect much better returns on lending out money to companies and households. It certainly no longer will be paying off to put money into reserves with the central bank. Lending growth will accelerate as the “money multiplier” increases sharply.
4) Investors in the stock market knows that in the long run stock prices track nominal GDP so a promise of a sharp increase in NGDP will make stocks much more attractive. Furthermore, with a 5% path growth rule for NGDP investors will expect a much less volatile earnings and dividend flow from companies. That will reduce the “risk premium” on equities, which further will push up stock prices. With higher stock prices companies will invest more and consumers will consume more.
5) The promise of loser monetary policy also means that the supply of money will increase relative to the demand for money. This effectively will lead to a sharp sell-off in the country’s currency. This obviously will improve the competitiveness of the country and spark export growth.

These are five channels and I did not mention interest rates yet…and there is a reason for that. Interest rates will INCREASE and so will bond yields as market participant start to price in higher inflation in the transition period in which we go from a “bad equilibrium” to a “good equilibrium”.

Hence, there is no reason for the New Keynesian interest rate “fetish” – we got at least five other more powerful channels by which monetary policy works.

Monetary transmission mechanism with a credible NGDP level target

Ben Volcker has now with his announcement brought back the economy to a “good equilibrium”. In the process he might have needed initially to increase the money base to convince economic agents that he meant business. However, once credibility is established concerning the new NGDP level target rule Ben Volcker just needs to look serious and credible and then expectations and the market will take care of the rest.

Imagine the following situation. A positive shock increase the velocity of money and with a fixed money supply this pushed NGDP above it target path. What happens?

1) Consumers realise that Ben Volcker will tighten monetary policy and slow NGDP growth. With the expectation of lower income growth consumers tighten their belts and private consumption growth slows.
2) Investors also see NGDP growth slowing so they scale back investments.
3) With the outlook for slower growth in NGDP banks scale back their lending and increase their reserves.
4) Stock prices start to drop as expectations for earnings growth is scaled back (remember NGDP growth and earnings growth is strongly correlated). This slows private consumption growth and investment growth.
5) With expectations of a tightening of monetary conditions players in the currency market send the currency strong. This led to a worsening of the country’s competitiveness and to weaker export growth.
6) Interest rates and bond yields DROP on the expectations of tighter monetary policy.

All this happens without Ben Volcker doing anything with the money base. He is just sitting around repeating his dogma: “The central bank will control the money base in such a fashion that economic agents away expect NGDP to grow along the 5% path we already have announced.” By now he might as well been replaced by a computer…


Recommended reading on the “old” monetarist transmission mechanism

Milton Friedman: “Milton Friedman’s Monetary Framework: A Debate with His Critics”
Karl Brunner and Allan Meltzer: “Money and the Economy: Issues in Monetary Analysis”

For a similar discussion to mine with special focus on the Paradox of Thrieft see the following posts from some of our Market Monetarist friends:

Josh Hendrickson
David Beckworth
Bill Woolsey
Nick Rowe

And finally from Scott Sumner on the differences between New Keynesian and Market Monetarist thinking.


Update: Scott Sumner has a interesting comment on central banking “language” and “interest rates”.

Daylight saving time and NGDP targeting

Today I got up one hour later than normal. The reason is the same as for most other Europeans this morning – the last Sunday of October – we move our clocks back one hour due to the end of Daylight saving time (summertime).

That reminded me of Milton Friedman’s so-called Daylight saving argument for floating exchange rates. According to Friedman, the argument in favour of flexible exchange rates is in many ways the same as that for summer time. Instead of changing the clocks to summer time, everyone could instead “just” change their behaviour: meet an hour later at work, change programme times on the TV, let buses and trains run an hour later, etc. The reason we do not do this is precisely because it is easier and more practical to put clocks an hour forward than to change everyone’s behaviour at the same time. It is the same with exchange rates, one can either change countless prices or change just one – the exchange rate.

There is a similar argument in favour of NGDP level targeting. Lets illustrate it with the equation of exchange.


P*Y is of course the same as NGDP the equation of exchange can also be written as


What Market Monetarists are arguing is that if we hold NGDP constant (or it grows along a constant path) then any shock to velocity (V) should be counteracted by an increase or decrease in the money supply (M).

Obviously one could just keep M constant, but then any shock to V would feed directly through to NGDP, but NGDP is not “one number” – it is in fact made up of countless goods and prices. So an “accommodated” shock to V in fact necessitates changing numerous prices (and volumes for the matter). By having a NGDP level target the money supply will do the adjusting instead and no prices would have to change. Monetary policy would therefore by construction be neutral – as it would not influence relative prices and volumes in the economy.

So when you (re)read Friedman’s “The Case for Floating Exchange Rates” then try think instead of “The Case for NGDP Level Targeting” – it is really the same story.

See my posts on Friedman’s arguments for floating exchange rates:

Milton Friedman on exchange rate policy #1
Milton Friedman on exchange rate policy #2
Milton Friedman on exchange rate policy #3

Milton Friedman on exchange rate policy #3

The fears of economists and politicians with regard to flexible exchange rates can largely be traced back to the policies of the 1920s following the collapse of the gold standard. The most famous criticism of flexible exchange rates is probably that made by the Estonian economist Ragnar Nurkse. Nurkse[1] claimed that the 1920s demonstrated that flexible exchange rates are destabilising.

Friedman, however, is fiercely critical of Nurkse’s view. First of all Friedman claims that currency speculation is stabilising and, second, that much of the historical volatility that can be observed in flexible exchange rates is in fact due to poor economic policy – primarily poor monetary policy – and not a result of “currency speculators”.

As mentioned Milton Friedman claims that currency speculation is stabilising not destabilising. The purpose of currency speculation is basically to buy cheap and sell expensive. If a currency deviates from its fundamental value – ie, is overvalued or undervalued – it would be rational for the “currency speculator” to expect that the currency would sooner or later move towards its fundamental exchange rate. If the currency is, for example, undervalued – ie, is cheap relative to the fundamental exchange rate – it would be rational to expect that the currency will eventually strengthen, and thus the rational speculator will buy the currency. If the majority of speculators act in this way, the exchange rate will all else equal be driven in the direction of the currency’s fundamental value – thus currency speculation is stabilising. Friedman argues furthermore that speculators who do not speculate rationally – ie, who sell when the currency is undervalued and buy when it is overvalued – will not earn money in the long run. Such speculators will soon be looking for a new job, and thus there will be a tendency for the number of “stabilising speculators” to be relatively greater than the number of “destabilising speculators”.

According to Friedman floating exchange rates will remain relatively stable if the FX market is left to its own devices. However, the problem is that governments and central banks have had problems keeping their hands off. Even in the 1920s and after the collapse of Bretton Woods in 1971 when flexible exchange rates were the norm, governments and central banks intervened in global FX markets. Friedman claims this has actually increased volatility in FX markets rather than stabilised exchange rates. As both the 1920s and the 1970s were marked by inappropriate monetary policies, this further contributed to unstable exchange rates. Put another way, floating exchange rates require sensible monetary policy. This implies that to ensure low and stable inflation one must let the supply of money grow at a low and stable rate.

Flexible exchange rates provide no guarantee of sensible monetary policy, but they are a precondition for an independent monetary policy. If a small country pursues a fixed exchange rate policy it will automatically be forced to follow the monetary policy of the nation(s) that dominate the currency system. This will be a particular problem if the “small” country’s economy is hit by what in the modern theoretical literature is called an asymmetric shock.

An asymmetric shock is an economic event (for example a strike or a shift in fiscal policy) that only affects one of the countries in a fixed exchange rate mechanism and not the others. One example of this is the reunification of Germany. Both fiscal and monetary policy were eased considerably in Germany at the time of reunification. This stoked inflationary pressure in Germany to a level that caused the German central bank, the Bundesbank, to tighten monetary policy again in 1992. Most EU currencies were at the time linked to the German mark under the European Monetary System (EMS). In the early 1990s, the other EU countries were struggling to break out of a period of low growth and the majority of the European economies had absolutely no need for the monetary tightening they were indirectly subject to via their fixed exchange rate policy with Germany. In 1992 Milton Friedman predicted the consequences for the EMS[2]:

“I suspect that EMS, too, will break down if Germany ever becomes unwilling to follow those policies, as it well may as a result of the unification of East and West Germany.”

The EMS broke down (partially) in 1993, proving Milton Friedman – as had been the case with the Canadian fixed exchange rate policy 43 years earlier – correct.

See also my posts in this series:

Milton Friedman on exchange rate policy #1

Milton Friedman on exchange rate policy #2


[1] Nurkse, Ragnar, “International Currency Experience: Lessons of Interwar Experience”, Genéve, 1944.

[2]“Money Mischief”, page 245.

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