# 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)

*where*

^{t}*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)

*. Hence, under both PLT and IT, the central bank’s initial price-level trajectory is 100(1.002)*

^{t}*.*

^{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)

*. However, under IT, the central bank would shift its price-level trajectory to 101.21(1.002)*

^{t}*, which is less than the initial price-level trajectory of 100(1.002)*

^{t-12}*. 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}*t*=12 when the actual inflation rate turns out to be1.2% 1820.09/1.001

^{12}= €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)

*. However, under IT, the central bank would shift its price-level trajectory to 103.66(1.002)*

^{t}*, which is greater than the initial price-level trajectory of 100(1.002)*

^{t-12}*. The real value of the nominal loan payment at time*

^{t}*t*=12 when the actual inflation rate was 3.6% instead of 2.4% is 1820.09/1.003

^{12}= €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).

2012-01-29