Cochrane’s inconsistencies

I just came across a couple of weeks old post from John Cochrane’s blog. Cochrane seems to be very upset about the calls for easier monetary policy in the euro zone. Let’s just say it as it is. Even though Cochrane is a professor at the University of Chicago he is certainly not a monetarist. It is sad how the University of Chicago has totally abandoned its proud monetarist traditions.

Here is Cochrane:

“As you might have guessed, I think it’s a terrible idea (Cochrane refers to a weakening of the euro engineered by easier monetary policy)…The biggest reason is the vanity that you can do it just once. “Devalue and inflate the currency” is hardly a new idea. Portugal, Italy, Spain, and Greece lived on a cycle of continual devaluation and inflation until they joined the Euro.  Going on the Euro was a hard won transformation to precommit to get off this cycle. “

Hence, Cochrane thinks easier monetary policy is very evil. However, in the in the comment section Cochrane states the following:

“I like a price level target. I view money as a set of units for value, and I don’t think the government artfully devaluing the meter and kilo to give shopkeepers a boost is a good idea, any more than fooling with inflation to do so, even if it does “work,” at least once. I’m less of a fan of NGDP targets, and the link from interest rates to price level is pretty tenuous…More coming, a comment isn’t the place for an entire monetary-fiscal program.”

Again you would think that Milton Friedman would be screaming from economist heaven about Cochrane’s odd references to the “tenuous” link between the price level and interest rates – as if interest rates are telling us much about monetary policy. Anyway, note that Cochrane says he likes a price level targeting regime. Fine with me. Then why not endorse Price Level Targeting for the euro zone professor Cochrane?

The graph below shows the euro zone GDP deflator and a 2% trend path for prices. The 2% path is of course what the ECB would be targeting if it implemented a Price Level Target as supported by Cochrane. Now have a look at the graph again and tell me what the ECB should do now if it was a Price Level Targeter?

The graph is very clear: Monetary policy is far too tight in the euro zone and as a result the actual price level is far below the pre-crisis 2% path level.

If Professor Cochrane was consistent in his views then he would obviously conclude that the ECB’s failed monetary policies are keeping the euro zone price level depressed, but I am afraid he did not even care to study the numbers.

Cochrane should obviously be calling for massive monetary easing in the euro zone. Milton Friedman would do so.

I can only again say how sad it is that the University of Chicago professors continue to disregard the economics of Milton Friedman.

PS I hope I am wrong about the University of Chicago so I would be happy if my readers would be able to find just one staffer at UC that is actually a monetarist. Ok, I would be happy if you could just locate a student at UC who has read anything Milton Friedman had to say about monetary theory.

PPS I really do not like this kind of attack on what other economists are writing on their blogs. However, as an admirer of Milton Friedman the continued indirect badmouthing of Friedmanite monetarism by the present day University of Chicago professors upsets me a great deal.

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Related posts:

See here on another University of Chicago professor who doesn’t care about Milton Friedman.

Another post on why the ECB should target the GDP deflator rather than HICP.

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The dangers of targeting CPI rather than the GDP deflator – the case of the Czech Republic

It is no secret that Market Monetarists favour nominal GDP level targeting over inflation target. We do so for a number of reasons, but an important reason is that we believe that the central bank should not react to supply shocks are thereby distort the relative prices in the economy. However, for now the Market Monetarist quest for NGDP targeting has not yet lead any central bank in the world to officially switching to NGDP targeting. Inflation targeting still remains the preferred operational framework for central banks in the developed world and partly also in Emerging Markets.

However, when we talk about inflation targeting it is not given what inflation we are talking about. Now you are probably thinking “what is he talking about? Inflation is inflation”. No, there are a number of different measure of inflation and dependent on what measures of inflation the central bank is targeting it might get to very different conclusions about whether to tighten or ease monetary policy.

Most inflation targeting central banks tend to target inflation measured with some kind of consumer price index (CPI). The Consumer Price Index is a fixed basket prices of goods and services. Crucially CPI also includes prices of imported goods and services. Therefor a negative supply shock in the form of higher import prices will show up directly in higher CPI-inflation. Furthermore, increases in indirect taxes will also push up CPI.

Hence, try to imagine a small very open economy where most of the production of the country is exported and everything that is consumed domestically is imported. In such a economy the central bank will basically have no direct influence on inflation – or at least if the central bank targets headline CPI inflation then it will basically be targeting prices determined in the outside world (and by indirect taxes) rather than domestically.

Contrary to CPI the GDP deflator is a price index of all goods and services produced within the country. This of course is what the central bank can impact directly. Therefore, it could seem somewhat paradoxically that central banks around the world tend to focus on CPI rather than on the GDP deflator. In fact I would argue that many central bankers are not even aware about what is happening to the GDP deflator.

It is not surprising that many central bankers knowingly or unknowingly are ignorant of the developments in the GDP deflator. After all normally the GDP deflator and CPI tend to move more or less in sync so “normally” there are not major difference between inflation measured with CPI and GDP deflator. However, we are not in “normal times”.

The deflationary Czech economy

A very good example of the difference between CPI and the GDP deflator is the Czech economy. This is clearly illustrated in the graph below.

The Czech central bank (CNB) is targeting 2% inflation. As the graph shows both CPI and the GDP deflator grew close to a 2% growth-path from the early 2000s and until crisis hit in 2008. However, since then the two measures have diverged dramatically from each other. The consumer price index has clearly moved above the 2%-trend – among other things due to increases in indirect taxes. On the other hand the GDP deflator has at best been flat and one can even say that it until recently was trending downwards.

Hence, if you as a Czech central banker focus on inflation measured by CPI then you might be alarmed by the rise in CPI well above the 2%-trend. And this has in fact been the case with the CNB’s board, which has remained concerned about inflationary risks all through this crisis as the CNB officially targets CPI inflation.

However, if you instead look at the GDP deflator you would realise that the CNB has had too tight monetary policy. In fact one can easily argue that CNB’s policies have been deflationary and as such it is no surprise that the Czech economy now shows a growth pattern more Japanese in style than a catching-up economy. In that regard it should be noted that the Czech economy certainly cannot be said to be a very leveraged economy. Rather both the public and private debt in the Czech Republic is quite low. Hence, there is certainly no “balance sheet recession” here (I believe that such thing does not really exists…). The Czech economy is not growing because monetary policy is deflationary. The GDP deflator shows that very clearly. Unfortunately the CNB does not focus on the GDP deflator, but rather on CPI.

A easy fix for the Czech economy would therefore be for the CNB to acknowledge that CPI gives a wrong impression of inflationary/deflationary risks in the economy and that the CNB therefore in the future will target inflation measured from the GDP deflator and that it because it has undershot this measure of inflation in the past couple of years it will bring the GDP deflator back to it’s pre-crisis trend. That would necessitate an increase in level of the GDP deflator of 6-7% from the present level. There after the CNB could return to targeting growth rate in the GDP deflator around 2% trend level. This could in my view easily be implemented by announcing the policy and then start to implement it through a policy of buying of foreign currency. Such a policy would in my view be fully in line with the CNB’s 2% inflation target and would in no way jeopardize the long time nominal stability of the Czech economy. Rather it would be the best insurance against the present environment of stagnation turning into a debt and financial crisis.

Obviously I think it would make more sense to focus on targeting the NGDP level, but if the CNB insists on targeting inflation then it at least should focus on targeting an inflation measure it can influence directly. The CNB cannot influence global commodity prices or indirect taxes, but it can influence the price of domestically produced products so that is what it should be aiming at rather than to focus on CPI. It is time to replace CPI with the GDP deflator in it’s inflation target.

Guest blog: Why Price-Level Targeting Pareto Dominates Inflation Targeting (By David Eagle)

Guest blog: Why Price-Level Targeting Pareto Dominates Inflation Targeting

- And a Bizarre Tale of Blind Macroeconomists

By David Eagle

Some central banks throughout the world, including the Central bank of Canada and the Federal Reserve, have been considering Price-Level Targeting (PLT) as an alternative to Inflation Targeting (IT). In this guest blog, I present my argument why PLT Pareto dominates IT.  My argument is simple, and one that many readers will consider so obvious that they would expect most monetary economists to be already aware of this Pareto domination.

Please read the following quotation from Shukayev and Ueberfeldt (2010):

Various papers have suggested that Price-Level targeting is a welfare improving policy relative to Inflation targeting. … Research on Inflation targeting and Price-level Targeting monetary policy regimes shows that a credible Price-level Targeting (PT) regime dominates an Inflation targeting regime.

Reading the above quotation indicates that economists already know that PLT Pareto dominates IT.  However, there is a bizarre twist to this literature, which we will discuss later in this blog.  I ask you to continue patiently reading and trust that the ending to the blog will be well worth the journey, even to market monetarists who oppose both PLT and IT.

In my last guest blog for The Market Monetarist, I discussed what I called the Two Fundamental Welfare Principles of Monetary Economics.  The First Principle concerned the Pareto implications when nominal GDP (NGDP) changes, but real GDP (RGDP) does not.  The Second Principle concerned the Pareto implications when RGDP changes, but NGDP does not.  Since PLT and IT have the same Pareto implications when RGDP changes, but NGDP does not; let us focus on the First Principle.  To do so, assume an economy where RGDP is known with perfect foresight; then the First Principle always applies.

A Nominal-Loan Example – Initial Expectations

Let us again consider a long term nominal loan.  This time, I will explain my argument with an example.  For this example, assume a €200,000 nominal mortgage with a 7.2% p.a. interest rate, compounded monthly, and a term of 15-years, and fixed, fully amortizing nominal monthly payments.  The monthly payment would then be a nominal €1820.09.  Let us assume that individual B borrowed the €200,000 from individual A.   The €1820.09 is the nominal amount B must pay A each month.

Let us also assume that both A and B expect inflation to be 2.4% p.a., compounded monthly, during this period.  They therefore built that expected inflation rate into their 7.2% p.a. negotiated nominal interest rate.[1]   Please note that in Finance, we second-naturedly convert per annum rates to per month rates when the rate is compounded monthly.  Thus, the 7.2% p.a. is actually 0.6% per month, and the 2.4% p.a. inflation rate is 0.2% per month.  While this monthly compounding adds an extra step and a source of confusion, I believe the gain in the realism of the example is worth it.

If inflation is the 2.4% p.a. expected rate, then the real value of the monthly payment at time t will equal 1820.09/(1.002)t where t is the number of months from the loan’s origination.  Since both A and B expect the inflation rate to be 2.4% p.a., compounded monthly, their expected real value[2] of this monthly loan payment at time t will be 1820.09/(1.002)t

As I discussed in my second guest blog on the Market Monetarist, PLT and IT have the same effect on the economy as long as the central bank is successful at meeting its target, whether that target is a price-level target or an inflation target.  Let us assume that under IT, the central bank’s inflation target is 2.4% p.a., whereas under PLT, the central bank’s price-level target at time t is 100(1.002)t.  Hence, under both PLT and IT, the central bank’s initial price-level trajectory is 100(1.002)t.

Scenarios of Missing the Target

When PLT and IT differ is when the central bank misses its target.  Suppose inflation on average over the first year turns out to be 1.2% p.a. instead of the expected  2.4% p.a (both rates are compounded monthly).  To be more clear given the monthly compounding issue, the central bank’s initially trajectory of the price level at one year (or at time t=12 months) was 100(1.002)12 = 102.43; however, the actual price level at one year turned out to be 100(1.001)12 = 101.21.  Under PLT, the central bank will try to return the economy to its initial price-level target of 100(1.002)t.  However, under IT, the central bank would shift its price-level trajectory to 101.21(1.002)t-12, which is less than the initial price-level trajectory of 100(1.002)t.  This is the phenomenon we call price-level base drift, which is caused by the central bank under IT letting bygones be bygones and merely aiming for future inflation to be consistent with its inflation target; the central bank under IT does not try to make up for lost ground.

The real value of the nominal loan payment at time t=12 when the actual inflation rate turns out to be1.2% 1820.09/1.00112 = €1798.39, which is greater than the expected nominal loan payment of €1776.97.

On the other hand, assume that the inflation rate on average over the first year was 3.6% p.a. rather than the targeted 2.4% p.a. This means that the actual price level at one year turned out to be 100(1.003)12 = 103.66.  Under PLT, the central bank would have tried to return the economy to its initial price-level target of 100(1.002)t.  However, under IT, the central bank would shift its price-level trajectory to 103.66(1.002)t-12, which is greater than the initial price-level trajectory of 100(1.002)t.

The real value of the nominal loan payment at time t=12 when the actual inflation rate was 3.6% instead of 2.4% is 1820.09/1.00312 = €1755,83, which is less that the initially expected value of €1776.97.

Comparing Actual to Expectations Beyond 12 Months

Because we are talking about four different scenarios, let PLT- and IT- represent PLT and IT when the inflation rate on average for the first year turns out to be 1.2% rather than 2.4%.  Let PLT+ and IT+ represent PLT and IT when the inflation on average for the first year turns out to be 3.6% rather than the expected 2.4%.  Under all four scenarios, assume that starting in at time t=24, which is 2 years after the loan began, the central bank is able to perfectly meet is price-level trajectory whether under PLT or IT and it does so for the remaining of the 15 years.

Under these assumptions, the real value of the monthly payment under PLT starting at time t=24 will be the same as expected because the central bank will get the price level back to its preannounced price-level target.  However, when the actual inflation rate for the first year turned out being 1.2%, the real value of the nominal monthly payment under IT would be 1820.09/((1.001)12(1.002)t-12) for t≥24 under the assumption the central bank (CB) then meets its target.  On the other hand, when the actual inflation rate for the first year turned out being 3.6%, the real value of the nominal monthly payment under IT would be 1820.09/((1.003)12(1.002)t-12) for t≥24 assuming the CB then meets its target.

The table below shows how the actual real values of these nominal loan payments compare to A and B’s original expectation under all four scenarios.

Note: This table only reports the payment at the end of each year.

That PLT Pareto dominates IT should be obvious from the table.  Under PLT, the central bank (CB) tries to get the real value of nominal loan payments to be back to what borrowers and lenders initially expected.  In other words, under PLT, the CB tries to reverse its mistakes.  Under IT, the CB makes its mistakes permanent.  Note that in the table under PLT, the real value of the nominal loan payments are as expected from time t=24 months on.  However, under IT, the real value of the nominal loan payments are either 1.21% less than expected when the CB fell short of its target, or 1.19% higher than expected when the CB overshot its target.  Clearly, both risk-averse borrowers and risk-averse lenders will be better off with the temporary deviations from expectations under PLT than under the permanent deviations under IT.

Kicking Borrowers or Lenders When They are Down

John Taylor referred to the price-level basis drift as the CB “letting bygones be bygones.”  After writing this blog, I have another view:  I view IT as meaning that when the CB hurts either borrowers or lenders because it is unable to meet its target, then the CB turns around and kicks that down borrower or lender again and again to make them suffer for the duration of their loan.  I have long opposed IT, but writing this blog makes me oppose it even more.  Why cannot other economists see IT for the Pareto damaging regime it is?

The issue of why PLT Pareto dominates IT is simple.  The risk to borrowers and lenders is not inflation risk; it is price-level risk.  To minimize price-level risk, we should not minimize inflation, we should minimize the deviation of the price-level from its expected value.  As such, when a central banking missing its target, it should not keep kicking those suffering from the CB’s past mistakes; the central bank should not make that miss permanent as in IT, but rather the CB should try to reverse that damage as it will try to do under PLT.  Hence PLT Pareto dominates IT.

The Bizarre Tale of the Blind Economists

Thank you all for bearing with me through my argument.  However, from the quote by Shukayev and Ueberfeldt, you knew that the economic profession already knew this.  After all, this is obvious.  (Lars, drink something before you read on; we don’t want your blood to boil too much.)

However, the argument that I gave is not the argument that the literature that Shukayev and Ueverfeldt cited.  That literature did not use the Pareto criterion; it used a loss function that included inflation.  (Yes, Lars, that xxxx loss function again.)

What the literature starting with Svenson (1999) found is that paradoxically when the central bank is trying to minimize a loss function involving inflation, it may actually be better able to do that through PLT than with IT.  That is what Shukayev and Ueverfeld (2010) meant when they said that the literature had found PLT welfare dominates IT.  That literature was referring to “welfare” as defined by their ad hoc loss function, not by their applying the Pareto criterion to the well being of borrowers and lenders.

Economists have been blinded from the obvious by their ad hoc assumption of a loss function involving inflation.  This bizarre twist to this literature is an example of the dangers that economists’ prejudices can enter into their ad hoc loss functions, causing them to miss the obvious.  In this case they have missed the obvious impacts on individual borrowers and lenders of PLT vs. IT.

Of course, there are other targeting regimes than just PLT and IT, but this blog focused on those two.  In my future writing, I plan to explain why NGDP level targeting Pareto dominates NGDP growth rate targeting, although the logic of that is really the same as I have just discussed; we just allow RGDP to vary so that the Second Fundamental Principle of Monetary Economics also applies.

Also, think about how the “kick them while they are down” characteristic of IT is relevant to the aftermath of the Financial crisis concerning the sovereign debt issues in Europe and the debt burdens on mortgage borrowers in the U.S. and elsewhere.  I guess I have to be careful here as I might be accused of starting riots.

References

Eagle, David and Dale Domian (2011), “Quasi-Real-Indexed Mortgages to the Rescue,” working paper delivered at the Western Economic Associating Meetings in San Diego, CA, http://www.cbpa.ewu.edu/~deagle/WEAI2011/QRIMs.doc

Shukayev, Malik and Alexander Ueberfeldt (2010).  “Price Level Targeting: What Is the Right Price?” Bank of Canada Working Paper 2010-8

Svensson, Lars E O, 1999. “Price-level Targeting versus Inflation Targeting: A Free Lunch?,”

Journal of Money, Credit and Banking, Blackwell Publishing, vol. 31(3), pages 277-95, August.

© Copyright (2012) by David Eagle


[1] The traditional Fisher equation states that i @ r + E[π] where i is the nominal interest rate, r is the real interest rate, and π is the inflation rate.  A more exact relationship we use in Finance is (1+i)=(1+r)(1+E[π) where these rates are per compound period, in this case per month.  According to the approximate and traditional Fisher equation, the real interest rate would be 4.8%, which equals the 7.2% nominal rate less the 2.4% expected inflation (the more precise Fisher equation using the monthly rates concludes the real rate will be 4.79%).

[2] You may note that the real value of the monthly nominal payment is expected to decline over time.  In the mortgage literature, this is known as the “tilt effect” (See Eagle and Domian, 2011).


Let the Fed target a Quasi-Real PCE Price Index (QRPCE)

The Federal Reserve on Wednesday said it would target a long-run inflation target of 2%. Some of my blogging Market Monetarist friends are not too happy about this – See Scott Sumner and Marcus Nunes. But I have an idea that might bring the Fed very close to the Market Monetarist position without having to go back on the comments from Wednesday.

We know that the Fed’s favourite price index is the deflator for Private Consumption Expenditure (PCE) for and the Fed tends to adjust this for supply shocks by referring to “core PCE”. Market Monetarists of course would welcome that the Fed would actually targeting something it can influence directly and not react to positive and negative supply shocks. This is kind of the idea behind NGDP level targeting (as well as George Selgin’s Productivity Norm).

Instead of using the core PCE I think the Fed should decomposed the PCE deflator between demand inflation and supply by using a Quasi Real Price Index. I have spelled out how to do this in an earlier post.

In my earlier post I show that demand inflation (pd) can be calculated in the following way:

(1) Pd=n-yp

Where n is nominal GDP growth and yp is trend growth in real GDP.

Private Consumption Expenditure growth and NGDP growth is extremely highly correlated over time and the amplitude in PCE and NGDP growth is nearly exactly the same. Therefore, we can easily calculate Pd from PCE:

(2) Pd=pce-yp

Where pce is the growth rate in PCE. An advantage of using PCE rather than NGDP is that the PCE numbers are monthly rather than quarterly which is the case for NGDP.

Of course the Fed is taking about the “long-run”. To Market Monetarists that would mean that the Fed should target the level rather growth of the index. Hence, we really want to go back to a Price Index.

If we write (2) in levels rather than in growth rates we basically get the following:

(3) QRPCE=PCE/RGDP*

Where QRPCE is what we could term a Quasi-Real PCE Price Index, PCE is the nominal level of Private Consumption Expenditure and RGDP* is the long-term trend in real GDP. Below I show a graph for QRPCE assuming 3% RGDP in the long-run. The scale is natural logarithm.

I have compared the QRPCE with a 2% trend starting the 2000. The starting point is rather arbitrary, but nonetheless shows that Fed policy ensured that QRPCE grew around a 2% growth path in the half of the decade and then from 2004-5 monetary policy became too easy to ensure this target. However, from 2008 QRPCE dropped sharply below the 2% growth path and is presently around 9% below the “target”.

So if the Fed really wants to use a price index based on Private Consumption Expenditure it should use a Quasi-Real Price Index rather than a “core” measure and it should of course state that long-run inflation of 2% means that this target is symmetrical which means that it will be targeting the level for the price index rather the year-on-year growth rate of the index. This would effectively mean that the Fed would be targeting a NGDP growth path around 5% but it would be packaged as price level targeting that ensures 2% inflation in the long run. Maybe Fed chairman Bernanke could be convince that QRPCE is actually the index to look at rather than PCE core? Packaging actually do matter in politics – and maybe that is also the case for monetary policy.

Guest Blog: The Two Fundamental Welfare Principles of Monetary Economics (By David Eagle)

I am extremely happy that David Eagle is continuing his series of guest blogs on my blog.

I strongly believe that David’s ideas are truly revolutionary and anybody who takes monetary policy and monetary theory serious should study  these ideas carefully. In this blog David presents what he has termed the “Two Fundamental Welfare Principles of Monetary Economics” as an clear alternative to the ad hoc loss functions being used in most of the New Keynesian monetary literature.

To me David Eagle here provides the clear microeconomic and welfare economic foundation for Market Monetarism. David’s thinking and ideas have a lot in common with George Selgin’s view of monetary theory – particularly in “Less than zero” (despite their clear methodological differences – David embraces math while George use verbal logic). Anybody that reads and understands David’s and George’s research will forever abandon the idea of a “Taylor function” and New Keynesian loss functions.

Enjoy this long, but very, very important blog post.

Lars Christensen

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Guest Blog: The Two Fundamental Welfare Principles of Monetary Economics

by David Eagle

Good Inflation vs. Bad Inflation

At one time, doctors considered all cholesterol as bad.  Now they talk about good cholesterol and bad cholesterol.  Today, most economists considered all inflation uncertainty as bad, at least all core inflation uncertainty.  However, some economists including George Selgin (2002), Evan Koenig (2011), Dale Domian, and myself (and probably most of the market monetarists) believe that while aggregate-demand-caused inflation uncertainty is bad, aggregate-supply-caused inflation or deflation actually improves the efficiency of our economies.  Through inflation or deflation, nominal contracts under Nominal GDP (NGDP) targeting naturally provide the appropriate real-GDP risk sharing between borrowers and lenders, between workers and employers, and more generally between the payers and receivers of any prearranged nominal payment.  Inflation targeting (IT), price-level targeting (PLT), and conventional inflation indexing actually interfere with the natural risk sharing inherent in nominal contracts.

I am not the first economist to think this way as George Selgin (2002, p. 42) reports that “Samuel Bailey (1837, pp. 115-18) made much the same point.”  Also, the wage indexation literature that originated in the 1970s, makes the distinction between demand-induced inflation shocks and supply-induced inflation shocks, although that literature did not address the issue of risk sharing.

The Macroeconomic Ad Hoc Loss Function vs. Parerto Efficiency

The predominant view of most macroeconomists and monetary economists is that all inflation uncertainty is bad regardless the cause.  This view is reflected in the ad hoc loss function that forms the central foundation for conventional macroeconomic and monetary theory.  This loss function is often expressed as a weighted sum of the variances of (i) deviations of inflation from its target and (ii) output gap.  Macro/monetary economists using this loss function give the impression that their analyses are “scientific” because they often use control theory to minimize this function.  Nevertheless, as Sargent and Wallace (1975) noted, the form of this loss function is ad hoc; it is just assumed by the economist making the analysis.

I do not agree with this loss function and hence I am at odds with the vast majority of the macro/monetary economists.  However, I have neoclassical microfoundations on my side – our side when we include Selgin, Bailey, Koenig, Domian, and many of the market monetarists.  This ad hoc social loss function used as the basis for much of macroeconomic and monetary theory is basically the negative of an ad hoc social utility function.  The microeconomic profession has long viewed the Pareto criterion as vastly superior to and more “scientific” than ad hoc social utility functions that are based on the biased preconceptions of economists.  By applying the Pareto criterion instead of a loss function, Dale Domian and I found what I now call, “The Two Fundamental Welfare Principles of Monetary Economics.”  My hope is that these Fundamental Principles will in time supplant the standard ad hoc loss function approach to macro/monetary economics.

These Pareto-theoretic principles support what George Selgin (p. 42) stated in 2002 and what Samuel Bailey (pp. 115-18) stated in 1837.  Some economists have dismissed Selgin’s and Bailey’s arguments as “unscientific.”  No longer can they legitimately do so.  The rigorous application of neoclassical microeconomics and the Pareto criterion give the “scientific” support for Selgin’s and Bailey’s positions.  The standard ad-hoc-loss-function approach in macro- and monetary economics, on the other hand, is based on pulling this ad hoc loss function out of thin air without any “scientific” microfoundations basis.

Macroeconomists and monetary economists have applied the Pareto criterion to models involving representative consumers.  However, representative consumers miss the important ramifications of monetary policy on diverse consumers.  In particular, models of representative consumers miss (i) the well-known distributional effect that borrowers and lenders are affected differently when the price level differs from their expectations, and (ii) the Pareto implications about how different individuals should share in changes in RGDP.

The Two Direct Determinants of the Price Level

Remember the equation of exchange (also called the “quantity equation), which says that MV=N=PY where M is the money supply, V is income velocity, N is nominal aggregate spending as measured by nominal GDP, P is the price level, and Y is aggregate supply as measured by real GDP.  Focusing on the N=PY part of this equation and solving for P, we get:

(1) P=N/Y

This shows there are two and only two direct determinants of the price level:

(i)             nominal aggregate spending as measured by nominal GDP, and

(ii)           aggregate supply as measured by real GDP.

This also means that these are the two and only two direct determinants of inflation.

The Two Fundamental Welfare Principles of Monetary Economics

When computing partial derivatives in calculus, we treat one variable as constant while we vary the other variable.  Doing just that with respect to the direct determinants of the price level leads us to The Two Fundamental Welfare Principles of Monetary Economics:

Principle #1:    When all individuals are risk averse and RGDP remains the same, Pareto efficiency requires that each individual’s consumption be unaffected by the level of NGDP.

Principle #2:    For an individual with average relative risk aversion, Pareto efficiency requires that individual’s consumption be proportional to RGDP.[1]

Dale Domian and I (2005) proved these two principles for a simple, pure-exchange economy without storage, although we believe the essence of these Principles go well beyond pure-exchange economies and apply to our actual economies.

My intention in this blog is not to present rigorous mathematical proofs for these principles.  These proofs are in Eagle and Domian (2005).  Instead, this blog presents these principles, discusses the intuition behind the principles, and gives examples applying the principles.

Applying the First Principle to Nominal Loans:

I begin by applying the First Principle to borrowers and lenders; this application will give the sense of the logic behind the First Principle.  Assume the typical nominal loan arrangement where the borrower has previously agreed to pay a nominal loan payment to the lender at some future date.  If NGDP at this future date exceeds its expected value whereas RGDP is as expected, then the price level must exceed its expected level because P=N/Y.  Since the price level exceeds its expected level, the real value of the loan payment will be lower than expected, which will make the borrower better off and the lender worse off.  On the other hand, if NGDP at this future date is less than its expected value when RGDP remains as expected, then the price level will be less than expected, and the real value of the loan payment will be higher than expected, making the borrower worse off and the lender better off.  A priori both the borrower and the lender would be better off without this price-level risk.  Hence, a Pareto improvement can be made by eliminating this price-level risk.

One way to eliminate this price-level risk is for the central bank to target the price level, which if successful will eliminate the price-level risk; however, doing so will interfere will the Second Principle as we will explain later.  A second way to eliminate this price-level risk when RGDP stays the same (which is when the First Principle applies), is for the central bank to target NGDP; as long as both NGDP and RGDP are as expected, the price level will also be as expected, i.e., no price-level risk..

Inflation indexing is still another way to eliminate this price-level risk.  However, conventional inflation indexing will also interfere with the Second Principle as we will soon learn.

That borrowers gain (lose) and lenders lose (gain) when the price level exceeds (fall short of) its expectations is well known.  However, economists usually refer to this as “inflation risk.” Technically, it is not inflation risk; it is price-level risk, which is especially relevant when we are comparing inflation targeting (IT) with price-level targeting (PLT).

An additional clarification that the First Principle makes clear concerning this price-level risk faced by borrowers and lenders is that risk only applies as long as RGDP stays the same.  When RGDP changes, the Second Principle applies.

Applying the Second Principle to Nominal Loans under IT, PLT, and NT:

The Second Principle is really what differentiates Dale Domian’s and my position and the positions of Bailey, Selgin, and Koenig from the conventional macroeconomic and monetary views.  Nevertheless, the second principle is really fairly easy to understand.  Aggregate consumption equals RGDP in a pure exchange economy without storage, capital, or government.  Hence, when RGDP falls by 1%, aggregate consumption must also fall by 1%.  If the total population has not changed, then average consumption must fall by 1% as well.  If there is a consumer A whose consumption falls by less than 1%, there must be another consumer B whose consumption falls by more than 1%.  While that could be Pareto justified if A has more relative risk aversion than does B, when both A and B have the same level of relative risk aversion, their Pareto-efficient consumption must fall by the same percent.  In particular, when RGDP falls by 1%, then the consumption level of anyone with average relative risk aversion should fall by 1%.  (See Eagle and Domian, 2005, and Eagle and Christensen, 2012, for the basis of these last two statements.)

My presentation of the Second Principle is such that it focuses on the average consumer, a consumer with average relative risk aversion.  My belief is that monetary policy should do what is optimal for consumers with average relative risk aversions rather than for the central bank to second guess how the relative-risk-aversion coefficients of different groups (such as borrowers and lenders) compare to the average relative risk aversion.

Let us now apply the Second Principle to borrowers and lenders where we assume that both the borrowers and the lenders have average relative risk aversion.  (By the way “relative risk aversion” is a technical economic term invented Kenneth Arrow, 1957, and John Pratt, 1964.)  Let us also assume that the real net incomes of both the borrower and the lender other than the loan payment are proportional to RGDP.  Please note that this assumption really must hold on average since RGDP is real income.  Hence, average real income = RGDP/m where m is the number of households, which means average real income is proportional to RGDP by definition (the proportion is 1/m).

The Second Principle says that since both the borrower and lender have average relative risk aversion, Pareto efficiency requires that both of their consumption levels must be proportional to RGDP.  When their other real net incomes are proportional to RGDP, their consumption levels can be proportional to RGDP only if the real value of their nominal loan payment is also proportional to RGDP.

However, assume the central bank successfully targets either inflation or the price level so that the price level at the time of this loan payment is as expected no matter what happens to RGDP.  Then the real value of this loan payment will be constant no matter what happens to RGDP.  That would mean the lenders will be guaranteed this real value of the loan payment no matter what happens to RGDP, and the borrowers will have to pay that constant real value even though their other net real incomes have declined when RGDP declined.  Under successful IT or PLT, borrowers absorb the RGDP risk so that the lenders don’t have to absorb any RGDP risk.  This unbalanced exposure to RGDP risk is Pareto inefficient when both borrowers and lenders have average relative risk aversion as the Second Principle states.

Since IT and PLT violate the Second Principle, we need to search for an alternative targeting regime that will automatically and proportionately adjust the real value of a nominal loan payment when RGDP changes?  Remember that the real value of the nominal loan payment is xt=Xt/P.  Replace P with N/Y to get xt=(Xt/Nt)Yt, which means the proportion of xt to Yt equals Xt/Nt.  When Xt is a fixed nominal payment, the only one way for the proportion Xt/Nt to equal a constant is for Nt to be a known in advance.  That will only happen under successful NGDP targeting.

What this has shown is that the proportionality of the real value of the loan payment, which is needed for the Pareto-efficient sharing of RGDP risk for people with average relative risk aversion, happens naturally with nominal fixed-payment loans under successful NGDP targeting.  When RGDP decreases (increases) while NGDP remains as expected by successful NGDP targeting, the price level increases (decreases), which decreases (increases) the real value of the nominal payment by the same percentage by which RGDP decreases (increases).

The natural ability of nominal contracts (under successful NGDP targeting) to appropriately distribute the RGDP risk for people with average relative risk aversion pertains not just to nominal loan contracts, but to any prearranged nominal contract including nominal wage contracts.  However, inflation targeting and price-level targeting will circumvent the nominal contract’s ability to appropriate distribute this RGDP risk by making the real value constant rather than varying proportionately with RGDP.

Inflation Indexing and the Two Principles:

Earlier in this blog I discussed how conventional inflation indexing could eliminate that price-level risk when RGDP remains as expected, but NGDP drifts away from its expected value.  While that is true, conventional inflation indexing leads to violations in the Second Principle.  Consider an inflation indexed loan when the principal and hence the payment are adjusted for changes in the price level.  Basically, the payment of an inflation-indexed loan would have a constant real value no matter what, no matter what the value of NGDP and no matter what the value of RGDP.  While the “no matter what the value of NGDP” is good for the First Principle, the “no matter what the value of RGDP” is in violation of the Second Principle.

What is needed is a type of inflation indexing that complies with both Principles.  That is what Dale Domian’s and my “quasi-real indexing” does.  It adjusts for the aggregate-demand-caused inflation, but not to the aggregate-supply-caused inflation that is necessary for the Pareto-efficient distribution of RGDP among people with average relative risk aversion.

Previous Literature:

Up until now, I have just mentioned Bailey (1837) and Selgin (2002) without quoting them.  Now I will quote them.  Selgin (2002, p. 42) states, ““ …the absence of unexpected price-level changes” is “a requirement … for avoiding ‘windfall’ transfers of wealth from creditors to debtors or vice-versa.”  This “argument … is perfectly valid so long as aggregate productivity is unchanging. But if productivity is subject to random changes, the argument no longer applies.”  When RGDP increases causing the price level to fall, “Creditors will automatically enjoy a share of the improvements, while debtors will have no reason to complain: although the real value of the debtors’ obligations does rise, so does their real income.”

Also, Selgin (2002, p. 41) reports that “Samuel Bailey (1837, pp. 115-18) made much the same point.  Suppose … A lends £100 to B for one year, and that prices in the meantime unexpectedly fall 50 per cent. If the fall in prices is due to a decline in spending, A obtains a real advantage, while B suffers an equivalent loss. But if the fall in prices is due to a general improvement in productivity, … the enhanced real value of B’s repayment corresponds with the enhanced ease with which B and other members of the community are able to produce a given amount of real wealth. …Likewise, if the price level were … to rise unexpectedly because of a halving of productivity, ‘both A and B would lose nearly half the efficiency of their incomes’, but ‘this loss would arise from the diminution of productive power, and not from the transfer of any advantage from one to the other’.”

The wage indexation literature as founded by Grey and Fischer recognized the difference between unexpected inflation caused by aggregate-demand shocks and aggregate-supply shocks; the main conclusion of this literature is that when aggregate-supply shocks exist, partial rather than full inflation indexing should take place.  Fischer (1984) concluded that the ideal form of inflation indexing would be a scheme that would filter out the aggregate-demand-caused inflation but leave the aggregate-supply-caused inflation intact.  However, he stated that no such inflation indexing scheme had yet been derived, and it would probably be too complicated to be of any practical use.  Dale Domian and I published our quasi-real indexing (QRI) in 1995 and QRI is not that much more complicated than conventional inflation indexing.  Despite the wage indexation literature leading to these conclusions, the distinction between aggregate-demand-caused inflation and aggregate-supply-caused inflation has not been integrated into mainstream macroeconomic theory.  I hope this blog will help change that.

Conclusions:

As the wage indexation literature has realized, there are two types of inflation:  (i) aggregate-demand-caused inflation and (ii) aggregate-supply-caused inflation.  The aggregate-demand-caused inflation is bad inflation because it unnecessary imposes price-level risk on the parties of a prearranged nominal contract.  However, aggregate-supply-caused inflation is good in that that inflation is necessary for nominal contracts to naturally spread the RGDP risk between the parties of the contract.  Nominal GDP targeting tries to keep the bad aggregate-demand-caused unexpected inflation or deflation to a minimum, while letting the good aggregate-supply-caused inflation or deflation take place so that both parties in the nominal contract proportionately share in RGDP risk.  Inflation targeting (IT), price-level targeting (PLT), and conventional inflation indexing interfere with the natural ability of nominal contracts to Pareto efficiently distribute RGDP risk.  Quasi-real indexing, on the other hand, gets rid of the bad inflation while keeping the good inflation.

Note that successful price-level targeting and conventional inflation indexing basically have the same effect on the real value of loan payments.   As such, we can look at conventional inflation indexing as insurance against the central bank not meeting its price-level target.

Note that successfully NGDP targeting and quasi-real indexing have the same effect on the real value of loan payments.  As such quasi-real indexing should be looked at as being insurance against the central bank not meeting its NGDP target.

A couple of exercises some readers could do to get more familiar with the Two Fundamental Welfare Principles of Welfare Economics is to apply them to the mortgage borrowers in the U.S. and to the Greek government since the negative NGDP base drift that occurred in the U.S. and the Euro zone after 2007.  In a future blog I very likely present my own view on how these Principles apply in these cases.

References:

Arrow, K.J. (1965) “The theory of risk aversion” in Aspects of the Theory of Risk Bearing, by Yrjo Jahnssonin Saatio, Helsinki.

Bailey, Samuel (1837) “Money and Its Vicissitudes in Value” (London: Effingham Wilson).

Debreu, Gerard, (1959) “Theory of Value” (New York:  John Wiley & Sons, Inc.), Chapter 7.

Eagle, David & Dale Domian, (2005). “Quasi-Real Indexing– The Pareto-Efficient Solution to Inflation Indexing” Finance 0509017, EconWPA, http://ideas.repec.org/p/wpa/wuwpfi/0509017.html.

Eagle, David & Lars Christensen (2012). “Two Equations on the Pareto-Efficient Sharing of Real GDP Risk,” future URL: http://www.cbpa.ewu.edu/papers/Eq2RGDPrisk.pdf.

Sargent, Thomas and Neil Wallace (1975). “’Rational’ Expectations, the Optimal Monetary Instrument, and the Optimal Money Supply Rule”. Journal of Political Economy 83 (2): 241–254.

Selgin, George (2002), Less than Zero: The Case for a Falling Price Level in a Growing Economy. (London: Institute of Economic Affairs).

Koenig, Evan (2011). “Monetary Policy, Financial Stability, and the Distribution of Risk,” Federal Reserve Bank of Dallas Research Department Working Paper 1111.

Pratt, J. W., “Risk aversion in the small and in the large,” Econometrica 32, January–April 1964, 122–136.

© Copyright (2012) by David Eagle

 


[1] Technically, the Second Principle should replace “average relative risk aversion” with “average relative risk tolerance,” which is from a generalization and reinterpretation by Eagle and Christensen (2012) of the formula Koenig (2011) derived.

A method to decompose supply and demand inflation

It is a key Market Monetarist position that there is good and bad deflation and therefore also good and bad inflation. (For a discussion of this see Scott Sumner’s and David Beckworth’s posts here and here). Basically one can say that bad inflation/deflation is a result of demand shocks, while good inflation/deflation is a result of supply shocks. Demand inflation is determined by monetary policy, while supply inflation is independent of whatever happens to monetary policy.

The problem is that the only thing that normally can be observed is “headline” inflation, which of course mostly is a result of both supply shocks and changes in monetary policy. However, inspired by David Eagle’s work on Quasi-Real Indexing (QRI) I will here suggest a method to decompose monetary policy induced changes in consumer prices from supply shock driven changes in consumer prices. I use US data since 1960 to illustrate the method.

Eagle’s simple equation of exchange

David Eagle in a number of his papers QRI starts out with the equation of exchange:

(1) M*V=P*Y

Eagle rewrites this to what he calls a simple equation of exchange:

(2) N=P*Y where N=M*V

This can be rewritten to

(3) P=N/Y

(3) Shows that consumer prices (P) are determined by the relationship between nominal GDP (N), which is determined by monetary policy (M*V) and by supply factors (Y, real GDP).

We can rewrite as growth rates:

(4) p=n-y

Where p is US headline inflation, n is nominal GDP growth and y is real GDP growth.

Introducing supply shocks

If we assume that we can separate underlining trend growth in y from supply shocks then we can rewrite (4):

(5) p=n-(yp+yt)

Where yp is the permanent growth in productivity and yt is transitory (shocks) changes in productivity.

Defining demand and supply inflation

We can then use (5) to define demand inflation pd:

(6) pd=n- yp

And supply inflation, ps, can then be defined as

(7) ps=p-pd (so p= ps+pd)

Below is shown the decomposition of US inflation since 1960. In the calculation of demand inflation I have assumed a constant growth rate in yp around 3% y/y (or 0.7% q/q). More advanced methods could of course be used to estimate yp (which is unlikely to be constant over time), but it seems like the long-term growth rate of GDP has been pretty stable around 3% of the last couple of decade. Furthermore, slightly higher or lower trend growth in RGDP does not really change the overall results.

We can of course go back from growth rates to the level and define a price index for demand prices as a Quasi-Real Price Index (QRPI). This is the price index that the monetary authorities can control.

The graph illustrates the development in demand inflation and supply inflation. There graph reveals a lot of insights to US monetary policy – for example that the increase in inflation in the 1970s was driven by demand inflation and hence caused by the Federal Reserve rather than by an increase in oil prices. Second and most interesting from today’s perspective demand inflation already started to ease in 2006 and in 2008 we saw a historically sharp drop in the Quasi-Real Price Index. Hence, it is very clear from our measure of the Quasi-Real Price Index that US monetary policy turning strongly deflationary already in early 2008 – and before (!) the collapse of Lehman Brothers.

Lets target a 2% growth path for QRPI

It is clear that many people (including many economists) have a hard time comprehending NGDP level targeting. However, I am pretty certain that most people would agree that the central bank should target something it can actually directly influence. The Quasi-Real Price Index is just another modified price index (in the same way as for example core inflation) so why should the Federal Reserve not want to target a path level for QRPI with a growth path of 2%? (the clever reader will of course realise that will be exactly the same as a NGDP path level target of 5% – under an assumption of long term growth of RGDP of 3%).

In the coming days I will have a look at the QRPI and US monetary history since the 1960s through the lens of the decomposition of inflation between supply inflation and demand inflation.

Pedersen on Price Level Targeting

My good colleague Jens N. Pedersen has today successfully defended his master thesis at the Department on Economics at the University of Copenhagen.

 Jens’ thesis should be of interest to Market Monetarists.

 Here is a bit from the introduction of Jens’ thesis “Price Level Targeting -  Optimal anchoring of expectations in a New Keynesian model”:

 “The recent experience of the Financial Crisis has highlighted the potential drawbacks of a policy targeting the changes and not the level of the prices. When the zero lower bound on the nominal interest rate binds, the inflation target presents a lower constraint on the real interest rate because inflation expectations are anchored at the target. Following the crisis, a number of major central banks have been forced to keep the policy rate close to zero and in the mean time use unconventional tools to keep monetary policy effective. Price level targeting, however, presents the optimal way of anchoring expectations by increasing inflation expectations in a deflationary environment and vice versa. This improves monetary policy in general and in a zero interest rate environment, which keeps the conventional interest rate operating procedure effective. This thesis attempts to study, how the central bank can optimally utilise the expectational channel, when setting monetary policy, by announcing a price level target. The investigation will take on both a theoretical and an empirical stand point. The theoretical part of the thesis revisits the arguments for and against adopting price level targeting. The empirical part of the thesis attempts to evaluate the optimality of monetary policy by inspecting the statistical properties of the price level.”

I am grateful to Jens for always challenging some of my views on monetary policy and Jens is always an excellent sparring partner not only on monetary issues but also on such interesting subjects as sportometrics and fine dining.

So dear readers please have a look at Jens’ excellent thesis. And to Jens – Congratulations! It is well-deserved and you can truly be proud of your thesis.

 

 

Please listen to Nicholas Craft!

Professor Nicholas Craft as written a report for the British think tank Centre Forum on “Delivering growth while reducing deficits: lessons from the 1930s”. The report is an excellent overview of the British experience during the 1930s, where monetary easing through exchange rate depreciation combined with fiscal tightening delivered results that certainly should be of interest to today’s policy makers.

If you are the lazy type then you can just read the conclusion:

“The 1930s offers important lessons for today’s policymakers. At that time, the UK was attempting fiscal consolidation with interest rates at the lower bound but devised a policy package that took the economy out of a double-dip recession and into a strong recovery. The way this was achieved was through monetary rather than fiscal stimulus.

The key to recovery both in the UK and the United States in the 1930s was the adoption of credible policies to raise the price level and in so doing to reduce real interest rates. This provided monetary stimulus even though, as today, nominal interest rates could not be cut further. In the UK, the ‘cheap money’ policy put in place in 1932 provided an important offset to the deflationary impact of fiscal consolidation that had pushed the economy into a double-dip recession in that year.

If economic recovery falters in 2012, it may be necessary to go beyond further quantitative easing as practised hitherto. It is important to recognize that at that point there would be an alternative to fiscal stimulus which might be preferable given the weak state of public finances. The key requirement would be to reduce real interest rates by raising inflationary expectations.

At that point, inflation targeting as currently practised in the UK would no longer be appropriate. A possible reform would be to adopt a price level target which commits the MPC to increase the price level by a significant amount, say 15 per cent, over four years. In the 1930s, the Treasury succeeded in developing a clear and credible policy to raise prices. It maybe necessary to adopt a similar strategy in the near future.

It would be attractive if this kind of monetary stimulus worked, as in the 1930s, through encouraging housebuilding. This suggests that an important complementary policy reform would be to liberalize the planning restrictions which make it most unlikely that we will ever see the private sector again build 293000 houses in a year as happened in 1934/5.”

If I have any reservations against Craft’s views then it is the focus on real interest rates in the monetary transmission mechanism. I think that is a far to narrow description of the transmission mechanism in which I think interest rates plays a rather minor role. See my previous comment on the transmission mechanism.

That minor issue aside Craft provides some very insightful comments on the 1930s and the present crisis and  I hope some European policy makers would read Craft’s report…

I got this reference from David Glasner who also has written a comment on Craft’s report.

Bank of Canada is effectively targeting the price level

Last week the Bank of Canada and Canadian government announced – not overly surprising – that it will continue its 2% inflation targeting regime.

This is a slight disappointment to Market Monetarists, but that said maybe the BoC is not really having a inflation targeting. In fact research show that BoC effectively has been targeting the price level rather than inflation.

This at least is the conclusion in a IMF paper from 2008. Here is the abstract:

“One of the pioneers of inflation targeting (IT), the Bank of Canada is now considering a possibility of switching to price-level-path targeting (PLPT), where past deviations of inflation from the target would have to be offset in the future, bringing the price level back to a predetermined path. This paper draws attention to the fact that the price level in Canada has strayed little from the path implied by the two percent inflation target since its introduction in December 1994, and has tended to revert to that path after temporary deviations. Econometric analysis using Bayesian estimation suggests that a low probability can be assigned to explaining this behavior by sheer luck manifesting itself in mutually offsetting shocks. Much more plausible is the assumption that inflation expectations and interest rates are determined in a way that is consistent with an element of PLPT. This suggests that the difference between IT as it is actually practiced (or perceived) and PLPT may be less stark than what pure theoretical constructs posit, and that the transition to a full- fledged PLPT regime will likely be considerably easier than what was previously thought. The paper also shows that inflation expectations are a major driver of actual inflation in Canada, which makes it easier to keep inflation close to the target without large output costs.”

HT Jens Pedersen

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