Dude, here is your model

Here is Scott Sumner:

“Whenever I get taunted about not having a “model,” I assume the commenter is probably younger than me, highly intelligent, but not particularly wise.”

So Scott has a problem – he does not have a fancy new model he can show off to the young guys. Well, Scott let me see if I can help you.

Here is your short-term static model:

An Eaglian (as in David Eagle) equation of exchange:

(1) N=PY

Where N is nominal GDP and P is the price level. Y is real GDP.

An Sumnerian Phillips curve:

(2) Y=Y*+a(N-NT)

Where NT is the target level for nominal GDP and N is nominal GDP . Y* is trend trend RGDP.

(1) is a definition so there can be no debate about that one. (2) is a well-established emprical fact. There is a very high correlation between Y and N in the short-run. If you need a microfoundation that’s easy – it’s called “sticky prices”.

N (and NT) is exogenous in the model and is of course determined by the central bank. And yes, yes N=MV where  M is the money and V is velocity.

In the short run P is “sticky” and N determines Y. Hence, the Sumnerian Phillips curve is upward sloping.

If you want a financial sector in the model we need to re-formulate it all in growth rates and we can introduce rational expectations. That not really overly complicated. Bond yield is a function of expected growth nominal GDP over a given period and so is stock prices.

In the long-run money is neutral so Y=Y* …so if you need a model for Y* you just go for a normal Solow growth model (or whatever you need…). I the long run the Sumnerian Phillips curve becomes vertical.

It don’t have to be more complicated than that…

That said, I think it is very important to demand to see people’s models. In fact I often challenge people to exactly spell out the model people have in their heads. That will show the inconsistencies in their arguments (the Austrian Business Cycle model is for example impossible to put on equations exactly because it is inconsistent). Mostly it turns out that people are doing national accouting economics and there is no money in their models – and if there is money in the model they do not have a explicit modeling of the central bank’s reaction function. So Scott you are certainly wrong when you tell of to get rid of the models. The problem is that far too many economists and especially central bankers are not spelling out their models and their reaction functions. I would love to see the kind of model that make the ECB think that monetary policy is easy in the euro zone…

That damn loss function

Scott further complains:

“Some general equilibrium models are used to find which stabilization policy regime is optimal from a welfare perspective.  Most of these models assume some sort of wage/price stickiness.  And 100% of the models taken seriously in the real world assume wage/price stickiness.  The problem is that there are many types of wage and price stickiness, and many ways of modeling the problem.  You can get pretty much whatever policy implication you want with the right set of assumptions.  Unfortunately, macroeconomists aren’t able to prove which model is best.  I think that’s because lots of models are partly true, and the extent to which specific assumptions are true depends on which country you are looking at, as well as which time period.  And then there’s the Lucas Critique.”

Translated this mean that implicit in most New Keynesian models is a assumption about the the central bank minimizing some sort of “loss function”. The problem with that is that assumes that there is some kind of representative agent. In terms of welfare analysis of monetary policy rules that is a massive problem – any Austrian economist would (rightly) tell you so and so would David Eagle. See my earlier post on the that damn “loss function” here.

Scott has one more complaint:

“To summarize, despite all the advances in modern macro, there is no model that anyone can point to that “proves” any particular policy target is superior to NGDPLT.  There might be a superior target (indeed I suspect a nominal wage target would be superior.)  But it can’t be shown with a model.  All we can do is construct a model that has that superiority built in by design.”

Scott, I am disappointed. Haven’t you read the insights of David Eagle? David has done excellent work on why NGDPLT Pareto dominates Price Level Targeting and inflation targeting. See here and here and here. Evan Koeing of course makes a similar point. And yes, neither David nor Evan use a “loss function”. They use proper welfare theory.

Anyway, no reason to be worried about models – they just need to be the right ones and the biggest complaint against most New Keynesian models is the problematic assumption about the representative agent. And then of course New Keynesian models have a very rudimentary formulation of asset markets, but that is easy to get around.

PS I am sure Scott would not disagree with much what I just wrote and I am frankly as frustrated with “models” that are used exactly because they are fancy rather because they make economic sense.

About these ads

Lets concentrate on the policy framework

Here is Scott Sumner:

I’ve noticed that when I discuss economic policy with other free market types, it’s easier to get agreement on broad policy rules than day-to-day discretionary decisions.

I have noticed the same thing – or rather I find that when pro-market economists are presented with Market Monetarist ideas based on the fact that we want to limit the discretionary powers of central banks then it is much easier to sell our views than when we just argue for monetary “stimulus”. I don’t want central bank to ease monetary policy. I don’t want central banks to tighten monetary policy. I simply want to central banks to stop distorting relative prices. I believe the best way to ensure that is with futures based NGDP targeting as this is the closest we get to the outcome that would prevail under a truly free monetary system with competitive issuance of money.

I have often argued that NGDP level targeting is not about monetary stimulus (See here, here and here) and argued that NGDP level targeting is the truly free market alternative (see here).

This in my view is the uniting view for free market oriented economists. We can disagree about whether monetary policy was too loose in the US and Europe prior to 2008 or whether it became too tight in 2008/9. My personal view is that both US and European monetary policy likely was (a bit!) too loose prior to 2008, but then turned extremely tight in 2008/09. The Great Depression was not caused by too easy monetary policy, but too tight monetary policy. However, in terms of policy recommendations is that really important? Yes it is important in the sense of what we think that the Fed or the ECB should do right now in the absence of a clear framework of NGDP targeting (or any other clear nominal target). However, the really important thing is not whether the Fed or the ECB will ease a little bit more or a little less in the coming month or quarter, but how we ensure the right institutional framework to avoid a future repeat of the catastrophic policy response in 2008/9 (and 2011!). In fact I would be more than happy if we could convince the ECB and the Fed to implement NGDP level target at the present levels of NGDP in Europe and the US – that would mean a lot more to me than a little bit more easing from the major central banks of the world (even though I continue to think that would be highly desirable as well).

What can Scott Sumner, George Selgin, Pete Boettke, Steve Horwitz, Bob Murphy and John Taylor all agree about? They want to limit the discretionary powers of central banks. Some of them would like to get rid of central banks all together, but as long as that option is not on the table they they all want to tie the hands of central bankers as much as possible. Scott, Steve and George all would agree that a form of nominal income targeting would be the best rule. Taylor might be convinced about that I think if it was completely rule based (at least if he listens to Evan Koeing). Bob of course want something completely else, but I think that even he would agree that a futures based NGDP targeting regime would be preferable to the present discretionary policies.

So maybe it is about time that we take this step by step and instead of screaming for monetary stimulus in the US and Europe start build alliances with those economists who really should endorse Market Monetarist ideas in the first place.

Here are the steps – or rather the questions Market Monetarists should ask other free market types (as Scott calls them…):

1) Do you agree that in the absence of Free Banking that monetary policy should be rule based rather than based on discretion?

2) Do you agree that markets send useful and appropriate signals for the conduct of monetary policy?

3) Do you agree that the market should be used to do forecasting for central banks and to markets should be used to implement policies rather than to leave it to technocrats? For example through the use of prediction markets and futures markets. (See my comments on prediction markets and market based monetary policy here and here).

4) Do you agree that there is good and bad inflation and good and bad deflation?

5) Do you agree that central banks should not respond to non-monetary shocks to the price level?

6) Do you agree that monetary policy can not solve all problems? (This Market Monetarists do not think so – see here)

7) Do you agree that the appropriate target for a central bank should be to the NGDP level?

I am pretty sure that most free market oriented monetary economists would answer “yes” to most of these questions. I would of course answer “yes” to them all.

So I suggest to my fellow Market Monetarists that these are the questions we should ask other free market economists instead of telling them that they are wrong about being against QE3 from the Fed. In fact would it really be strategically correct to argue for QE3 in the US right now? I am not sure. I would rather argue for strict NGDP level targeting and then I am pretty sure that the Chuck Norris effect and the market would do most of the lifting. We should basically stop arguing in favour of or against any discretionary policies.

PS I remain totally convinced that when economists in future discuss the causes of the Great Recession then the consensus among monetary historians will be that the Hetzelian-Sumnerian explanation of the crisis was correct. Bob Hetzel and Scott Sumner are the Hawtreys and Cassels of the day.

The Close Connection Between Evan Koenig and Market Monetarism

Evan Koenig – who is a long-time defender of NGDP targeting – is out with a new paper: “All in the Family: The Close Connection Between Nominal-GDP Targeting and the Taylor Rule”Evan of course is a Senior Economist and Vice President at the Dallas Fed.

Frankly speaking I have not yet have time to read the paper, but I wanted to share the link with my readers nonetheless.

Here is the abstract:

“The classic Taylor rule for adjusting the stance of monetary policy is formally a special case of nominal- gross-domestic-product (GDP) targeting. Suitably implemented, moreover, nominal-GDP targeting satisfies the definition of a flexible inflation targeting policy rule. However, nominal-GDP targeting would require more discipline from policymakers than some analysts think is realistic.”

So what Koeing is basically arguing that we should not see NGDP level targeting as something so fundamentally different from the Taylor rule – at least in relation to Federal Reserve’s mandate. I am not sure I totally agree, but I would certainly agree that if a Taylor rule can be said to be within the Fed’s mandate so can a NGDP level target.

I have two earlier posts relating to NGDP targeting and Fed’s mandate:

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

NGDP level targeting and the Fed’s mandate

I hope I will be able to read all of Evan’s paper in the coming days and I highly recommend to read Evan’s other papers on NGDP targeting. He has written a few. See here and here.

Our friend Bill Woolsey also has great post on on Evan’s paper.

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

—————–

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.

Selgin and Eagle should be best friends

David Eagle has a comment on Integral’s piece on Evan Koeing. Here is some of the comment:

“This is my first comment, Integral’s review states that Koenig “notes that since nominal debts are paid out of nominal income, any adverse shock to income will lead to financial disruption, not just shocks to the price level.” This drew my attention for reasons I will state in a moment so I looked at what Koenig wrote on p. 1, which is “Households and firms obligated to make fixed nominal payments are exposed to financial stress whenever nominal income flows deteriorate relative to expectations extant when the obligations were accepted, independent of whether the deterioration is due to lower-than-expected inflation or to lower-than-expected real income growth.” Both of these statements seem to indicate that the financial distress from an aggregate-supply shock is due to the income being in nominal form. I disagree; the financial distress related to aggregate-supply shocks will occur on average to people regardless whether their income is in real terms or nominal terms. The reason is because real aggregate supply is basically also real income. If real aggregate supply falls so must real income and so must average real income, by the same proportion. Hence what happens to a household’s income on average is the same whether the income is in real or nominal terms. Now we look at two households A and B where B is making a nominal payment to A. Also, assume that these households are average in the sense that both of their real incomes not including this nominal payment change proportionately to real aggregate supply as they do in Koenig’s model. Under successful price-level or inflation targeting, the real value of that nominal payment will be unchanged. Hence household B will be squeezed between his declining real income and the constant real payment he must make to A. On the other hand, while A is only exposed to her own real income declining, not the real value of the payment she is receiving from B. Therefore, under price-level or inflation targeting, the payer of the nominal payments absorbs more of the aggregate-supply risk than does the receiver.”

Note especially the bold part. Here is George Selgin in “Less than Zero” (page 41-42):

“… if the price level is kept constant in the face of unexpected improvements in productivity, readily adjusted money incomes, including profits, dividends,and some wage /payments, will increase; and recipients of these flexible money payments will benefit from the improvements in real output. Creditors, however, will not be allowed to reap any gains from the same improvements, as debtors’ real interest payments will not increase despite a general improvement in real earnings. Although an unchanged price level does fulfil creditors’ price-level expectations, creditors may still regret having engaged in fixed nominal contracts, rightly sensing that they have missed out on their share of an all-around advance of real earnings, which share they might have been able to insist upon had they (and debtors also) known about the improvement in productivity in advance.

Now imagine instead that the price level is allowed to fall in response to improvements in productivity. 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, while the nominal payments burden borne by debtors is unchanged. Debtors can, in other words, afford to pay higher real rates of interest; they might therefore, for all we know, have been quite happy to agree to the’ same fixed nominal interest rate had both they and creditors been equipped with perfect foresight. Therefore the debtors’ only possible cause for regretting the (unexpected) drop in prices is their missed opportunity to benefit from an alternative (zero inflation) that would in this case have given them an artificial advantage over creditors.” 

It seems to me that David and George more or less have the same model in their heads…what do you think?

The Integral Reviews: Paper 1 – Koenig (2011)

I am always open to accept different guest blogs and I therefore very happy that “Integral” has accepted my invitation to do a number of reviews of different papers that are relevant for the discussion of monetary theory and the development of Market Monetarism.

“Integral” is a regular commentator on the Market Monetarist blogs. Integral is a pseudonym and I am familiar with his identity.

We start our series with Integral’s review of Evan Koeing’s paper “Monetary Policy, Financial Stability, and the Distribution of Risk”. I recently also wrote a short (too short) comment on the paper so I am happy to see Integral elaborating on the paper, which I believe is a very important contribution to the discussion about NGDP level targeting. Marcus Nunes has also earlier commented on the paper.

Lars Christensen

The Integral Reviews: Papers 1 – Koenig (2011)
By “Integral”

Reviewed: Evan F. Koenig, “Monetary Policy, Financial Stability, and the Distribution of Risk.” FRB Dallas Working Paper No.1111

Consider the typical debt-deflation storyline. An adverse shock pushes the price level down (relative to expected trend) and increases consumers’ real debt load. This leads to defaults, liquidation, and general disruption of credit markets. This is often-times used as justification for the central bank to target inflation or the price level, to mitigate the effect of such shocks on financial markets.

Koenig takes a twist on this view that is quite at home to Market Monetarists: he notes that since nominal debts are paid out of nominal income, any adverse shock to income will lead to financial disruption, not just shocks to the price level. One conclusion he draws out is that the central bank can target nominal income to insulate the economy against debt-deflation spirals.

He also makes a theoretical point that will resonate well with Lars’ discussion of David Eagle’s work. Recall that Eagle views NGDP targeting as the optimal way to prevent the “monetary veil” from damaging the underlying “real” economy, which he views as an Arrow-Debreu type general equilibrium economy. Koenig makes a similar observation with respect to financial risk (debt-deflation) and in particular the distribution of risk.

In a world with complete, perfect capital markets, agents will sign Arrow-Debreu state-contingent contracts to fully insure themselves against future risk (think shocks). Money is a veil in the sense that fluctuations in the price level, and monetary policy more generally, have no effect on the distribution of risk. However, the real world is much incomplete in this regard and it is difficult to imagine that one could perfectly insure against future income, price, or nominal income uncertainty. Koenig thus dispenses of complete Arrow-Debreau contracts and introduces a single debt instrument, a nominal bond. This is where the central bank comes in.

Koenig considers two policy regimes: one in which the central bank commits to a pre-announced price-level target and one in which the central bank commits to a pre-announced nominal-income target. While the price-level target neutralizes uncertainty about the future price level, it provides no insulation against fluctuations in future output. He shows that a price level target will have adverse distributional consequences: harming debtors but helping creditors. Note that this is exactly the outcome that a price-level target is supposed to avoid. By contrast a central bank policy of targeting NGDP fully insulates the economy from the combination of price and income fluctuations. It will not only have no adverse distributional consequences, it obtain a consumption pattern across debtors and creditors which is identical to that which is obtained when capital markets are complete.

At an empirical level, Koenig documents that loan delinquency is more closely related to surprise changes in NGDP than in P, providing corroborating evidence that it is nominal income, not the price level, which matters for thinking about the sustainability of the nominal debt load.

Koenig’s conclusion is succinct:

“If there are complete markets in contingent claims, so that agents can insure themselves against fluctuations in aggregate output and the price level, then “money is a veil” as far as the allocation of risk is concerned: It doesn’t matter whether the monetary authority allows random variation in the price level or nominal value of output. If such insurance is not available, monetary policy will affect the allocation of risk. When debt obligations are fixed in nominal terms, a price-level target eliminates one source of risk (price-level shocks), but shifts the other risk (real output shocks) disproportionately onto debtors. A more balanced risk allocation is achieved by allowing the price level to move opposite to real output. An example is presented in which the risk allocation achieved by a nominal-income target reproduces exactly the allocation observed with complete capital markets. Empirically, measures of financial stress are much more strongly related to nominal-GDP surprises than to inflation surprises. These theoretical and empirical results call into question the debt-deflation argument for a price-level or inflation target. More generally, they point to the danger of evaluating alternative monetary policy rules using representative-agent models that have no meaningful role for debt.”

Follow

Get every new post delivered to your Inbox.

Join 3,182 other followers

%d bloggers like this: