Problems With
Woodford's Model of a Cashless Economy

Click here to download a paper I have written that discusses most of the logical problems I have found in Woodford's model of cashless economy.

In 2003, Dr. Michael Woodford of Princeton University wrote a book entitled, Interest and Prices, which is considered the cornerstone of the New Keynesian Economics. The basis of Woodford's book is his model of a cashless economy that he develops in Chapter 2. Woodford claims the model determines prices when the central bank sets the interest rate according to certain policies. Based on this model, Woodford claims that economists need not worry about any loss of control over prices if we let financial innovations eliminate any monetary frictions.

I view this model to be incomplete, and I find that the central bank in Woodford’s model will be unable to affect nominal interest rates on loans for which the central bank is not a party. Click below to see more details on each of these theoretical defects of Woodford’s analysis: 
     Incompleteness of Woodford’s Model
          Dr. Woodford’s Response

     Inability of Central Bank in Woodford’s Model to Affect Nominal Interest Rates
          Dr. Woodford’s Response

     Invalidity of Rational Expectations Precedent for Solving Expectational
     Difference Equations
          Dr. Tom Sargent’s Response

     Dr. Dale Domian's and My Papers With Models in Conflict with Dr. Woodford's Model

     My attempts to engage in a dialog before making this web site operational
Incompleteness of Woodford's Model:

In order to say his model determines prices, Woodford assumes his solution is bounded. Assuming a solution is bounded is the appropriate approach to take according to the rational expectations approach for solving expectational difference equations. However, Dr. Elizabeth Murff and I have found this precedent to be invalid. Instead, when we solve an expectational difference equation forward, we propose that we follow the more rigorous procedure of working with a finite version of the model to determine the terminal condition and then take the limit of that terminal condition as the horizon goes to infinity. (Click here to learn more about Dr. Murff’s and my analysis.) Doing that with Woodford’s model shows it to be incomplete because any finite version of Woodford’s model is incomplete.

Woodford himself admits that if price were to be determined in his model, it would be through Woodford’s Fisher equation (1.21). Remember, a Fisher equation relates the nominal interest rate to the real interest rate and expected inflation. However, in a finite model, Woodford’s Fisher equation does not apply to the final period as there is no interest on that terminal period. Therefore, with any finite version of Woodford’s model, there will be more unknowns than equations. You can read more details in Dr. Murff’s and my paper entitled, “Logical Pitfalls of Assuming Bounded Solutions to Expectational Difference Equations.”

Dr. Woodford’s Response: I have sent Dr. Woodford a note at the beginning of February 2004. I have also sent him the paper Dr. Murff and I wrote. I have even followed up with a telephone call at the end of March 2004 when Dr. Woodford said that he would send his comments “in a few days”. I have yet to receive any comments from Dr. Woodford. On April 23, 2004, I wrote Dr. Woodford inviting him to write a response to my web site and I would put in a link to his response. As of May 14, 2004, I have yet to hear from Dr. Woodford.

Inability of Central Bank in Woodford’s Model to Affect Nominal Interest Rates:

While in current real world economies, central banks can affect nominal interest rates; the economy Woodford assumes does not relate to any current real world economy. First, he assumes no monetary frictions, and second, he assumes complete markets. Under the complete markets assumption, there are securities that nominal bonds as far as exposure to risk. As a result, the only reason to hold nominal bonds will be to hedge against other nominal risk someone faces. Since Woodford’s government pays nominal subsidies or charges nominal taxes, consumers will use the nominal bonds to hedge against these nominal subsidies or taxes. Click here to see the note that I wrote Dr. Woodford explaining this issue to him. I will later write a paper on this issue.

Dr. Woodford’s Response: I have sent Dr. Woodford a note at the end of February 2004. I have even followed up with a telephone call at the end of March 2004 when Dr. Woodford said that he would send his comments “in a few days”. I have yet to receive any comments from Dr. Woodford. On April 23, 2004, I wrote Dr. Woodford inviting him to write a response to my web site and I would put in a link to his response. As of May 14, 2004, I have yet to hear from Dr. Woodford.

Invalidity of R.E. Precedent for Solving Expectational Difference Equations:

The Rational Expectation (R.E.) precedent for solving expectational difference equations has been to solve stable roots backwards, unstable roots forward, and declare indeterminacy for unit roots. Also, this precedent assumes solutions are bounded when solving forward. Dr. Elizabeth Murff and I have traced this precedent to less than rigorous foundations. These foundations include a couple of examples where the bounded assumption was appropriate, a misapplication of a justification to rule out “speculative bubbles”, and an unsupported claim that we are free to do so. We have also found that the precedent leads to erroneous solutions for many finance and infinitely repeated game examples. More rigorous procedures would be for us to assume a model with a finite horizon to determine the terminal condition and then take the limit of that terminal condition as the horizon goes to infinity. For more details, click on the title of Dr. Elizabeth Murff’s and my paper, entitled, “Logical Pitfalls of Assuming Bounded Solutions to Expectational Difference Equations.” This paper has been rejected by Econometrica not because of logical issues but because Dr. David Levine, a co-editor, said that "We do not ordinarily publish a paper pointing out a conceptual error in research that we did not publish..." Also, he stated:
           You may not be aware that there is a large literature in economics that attacks 
	the issue of the boundedness of solutions to infinite horizon problems generally
	with the use of examples and models from economics... .  In the case of single
	person optimization problems, this falls under the category of transversality
	conditions. Infinite horizon existence results generally follow from carefully
	relating a finite horizon truncated economy to the infinite horizon economy.  In
	some cases, boundedness follows naturally from economic assumptions.  In other
	cases (most obviously models of growth) they do not.

If what Dr. Levine says is correct, then one cannot always assume the solution is bounded for infinite economies. If this large literature exists (which I am trying to track down), then that literature just adds to Dr. Murff's and my arguments that Woodford's analysis is unsound.

Dr. Tom Sargent’s Response: Since Dr. Tom Sargent is largely responsible for the rational expectations precedent for solving expectational difference equations, I have contacted him. In September 2004, he responded by saying that he has "not followed the literature that you are working on for awhile." He also said that, "Everything that I know about the issue is in Gabel and Roberts and in Whiteman." I am now communicating with Dr. Charles Whiteman at the University of Iowa concerning this issue of how to correctly solve expectational difference equations and his understanding of the literature.

My attempts to engage in a dialog before making this web site operational: 
          I wrote this web site originally on January 27, 2004, about two weeks after I first 
          emailed Dr. Woodford and after I tried calling him.  On January 28, Dr. Woodford 
          contacted me; he had been out of the country.  I then isolated this web site from my
          professional web site so that he and I could engage in a dialog.  Dr. Woodford said 
          that he would comment on a note I promised him.  He did clarify his position which 
          did help me find where our differences lay.  However, when I did send him my note,
          followed later by additional notes, I never did receive any comments from Dr. Woodford.
          As a result, on April 23, 2004, I reconnected this web site to my professional web site.

     While I have given Dr. Woodford plenty of opportunity to respond to my concerns, I want
     to encourage a debate between him and myself concerning the issues I raise.  As a result,
     I am offering to make links to any rebuttals Dr. Woodford wishes to write in response to
     the criticisms of his model that I write on this web site.  My purpose is not to put
     Dr. Woodford down, but to encourage an on-line debate between Dr. Woodford and myself.
     According to philosophers, if we make the same assumptions, then logic should lead us to
     the same conclusion.  An on-line debate is one way to try to get us to work out the
     differences in logic between us.

     Being on line, in public, will help promote a logical discussion.  Unfortunately, this
     on-line debate may be one sided as one tactic Dr. Woodford may take is just to ignore me.
     It is a sad day when ignoring people replaces rigor as the determinant of economic thought.

Dr. Dale Domian's and My Papers In Conflict With Woodford's Model:

The reason I am so concerned about his model is that it conflicts with Dr. Dale Domian's and my models which we use in two of our papers. See Quasi-Real Indexing -- The Pareto-Efficient Solution to Inflation Indexing and Sounding the Alarm on Inflation Indexing and Strict Inflation Targeting. While Woodford believes that interest-targeting is all that is required to determine price levels in a cashless economy, we found we needed some other mechanism to replace structural velocity, which determines prices in an economy with monetary frictions.