# Guest post: Central Banks Should Quit “Kicking Them While They Are Down!" (by David Eagle)

**Guest post: Central Banks Should Quit “Kicking Them While They Are Down!"**

**- Abandon Inflation Targeting! Embrace NGDP Level Targeting!**

*By David Eagle*

**The Evil NGDP Base Drift**: Let

*X*be a prearranged nominal loan payment, and let

_{t}*x*≡

_{t}*X*/

_{t}*P*be the real value of this nominal loan payment. By the equation of exchange (

_{t}*MV*=

*N*=

*PY*), we know that

*P*=

*N*/

*Y*. Therefore, the real value of

*X*is (

_{t}*X*/

_{t}*N*)

_{t}*Y*, which implies that the real value of

_{t}*X*is proportional to

_{t}*Y*when

_{t}*N*, which it will be under perfectly successful NT. Define

_{t}=E[N_{t}]*α*≡

_{t}*X*/

_{t}*N*to be the actual proportion that the real value of this nominal payment is to RGDP. Multiply the right side by

_{t}*N*/

_{t}^{*}*N*(which equals one) where

_{t}^{*}*N*is defined as the prerecession trend for NGDP (Under NT,

_{t}^{*}*N*would be the NGDP target). Rearranging slightly gives:

_{t}^{*}(1)* α _{t}*=(

*X*/

_{t}*N*)(

_{t}^{*}*N*/

_{t}^{*}*N*)

_{t}_{t}≡(N

_{t}─N

_{t}

^{*})/N

_{t}

^{*}. We can also write that NGAP

_{t}=

*N*/

_{t}*N*-1, or 1+NGAP

_{t}^{*}_{t}=

*N*/

_{t}*N*, which is the reciprocal of the last ratio in equation (1). Define

_{t}^{*}*α*≡

_{t}^{*}*X*/

_{t}*N*, which is what

_{t}^{*}*α*would if

_{t}*N*=

_{t}*N*, i.e., when NGAP

_{t}^{*}_{t}=0. With this new definition and our understanding of NGAP, we can rewrite equation (1) as: (2)

*α*=

_{t}*α*

*/(1+NGAP*

_{t}^{*}_{t}) This states that the proportion that the real value of the nominal loan payment is of RGDP equals the proportion it would be if NGDP is on its prerecession trend divided by 1+NGAP. Equation (2) is useful to show how borrowers and lenders are affected when NGDP deviates from its trend. When NGDP rises above trend, NGAP becomes positive, decreasing this proportion, making borrowers better off at the expense of lenders; in other words, borrowers gain while lenders lose. When NGDP falls below trend, NGAP becomes negative, increasing this proportion, making borrowers worse off and lenders better off; in other words, borrowers lose while lenders gain. NGDP base drift occurs when NGAP becomes positive or negative, and the central bank accepts this NGAP and commits to keeping this NGAP in the future as it does both with IT and ΔNT. This NGDP base drift then makes the effects on borrowers and lenders permanent. On the other hand, under NT, the central bank tries to reverse these effects by returning NGAP to zero as soon as possible so that the effects on borrowers and lenders are temporary not permanent. Because NGDP base drift causes the effects of NGAP on borrowers and lenders to be permanent, this NGDP base drift “kicks the loser when the loser is down.” Hence, I view NGDP base drift as evil.

**NGDP Targeting (NT) – The “Pi” or “e” of Monetary Economics**In my previous guest blog post where I explained why IT “kicks them while they are down,” I restricted that discussion to where real GDP (RGDP) remains the same. That is because the First Principle from my blog on the Two Fundamental Welfare Principles of Monetary Economics states that Pareto Efficiency requires the consumption of individuals to be the same only as long as RGDP remains the same. When RGDP changes, the Second Principle applies, which states that Pareto efficiency requires that the consumption of an individual with average relative risk aversion be proportional to RGDP. NT helps individuals achieve this consumption proportional to RGDP by trying to make the real value of prearranged nominal payments (such as loan payments) proportional to RGDP. NT does this by trying to keep NGAP equal to zero. As seen in equation (2), as long as NGAP is zero and consumers expect NGAP to be zero, then this proportion will be proportional to RGDP. Nominal contracts work efficiently in a Pareto sense whenever NGDP is as expected. People are not trying to guarantee real payments between each other; rather they want to let the natural feature of nominal contracts properly distribute the RGDP risk among the parties of the contract. As long as NGDP is as expected, the real value of the nominal contract’s payment will be proportionate to RGDP, which is what an individual with average relative risk aversion needs according to the Second Principle. In a previous guest blog post, I noted that when RGDP remains the same, the uncertainty borrowers and lenders face is not inflation risk, but rather price-level risk. While simple and obvious, that statement nevertheless has profound implications concerning the issue of price-level targeting (PLT) vs. IT. However, when we broaden our perspective to include when RGDP changes, we need to go beyond the concept of price-level risk. Instead of inflation risk or price-level risk, economic agents should really be concerned about NGDP risk. NGDP risk is what I view to be the true monetary risk in an economy. Minimizing NGDP risk helps meet both The Two Fundamental Welfare Principles of Monetary Economics. First, by minimizing NGDP risk we minimize the price-level risk when RGDP does remain the same. Second, minimizing NGDP risk helps consumption levels be proportional to RGDP by helping the real value of nominal payments to be proportional to RGDP. Many proponents of NGDP targeting have described NGDP targeting as a reasonable compromise to the dual mandate of monetary policy. That is not my view. My view is that NGDP targeting is the ideal, not a compromise. NGDP targeting comes out of theory as the Pareto-efficient monetary policy, much as in mathematics the numbers “pi” and “e” come out of pure theory.

**Why NT Pareto Dominates**

**ΔNT**: NT targets the level of NGDP whereas ΔNT targets the growth rate of NGDP. As explained in my second guest blog post, as long as the central bank meets its target, NT and ΔNT have the same effect. The difference between NT and ΔNT occurs when the central bank misses its target. Under NT, when NGDP is less (greater) than its trajectory, the central bank tries to increase (decrease) NGDP back to its original trajectory. However, with ΔNT the central bank “lets bygones be bygones” and shifts its NGDP trajectory to be consistent with its targeted NGDP growth. When the central bank misses its target under NT or ΔNT, borrowers and lenders experience zero-sum gains and losses as a result of NGDP differing from expected NGDP. For example, assume NGDP initially is 10 (trillion monetary units), the targeted growth rate for NGDP under ΔNT is 5%, and the targeted level of NGDP under NT is 10(1.05)

^{t}. Then the initial NGDP trajectory under both NT and ΔNT is 10(1.05)

^{t}, and the public’s initial expectation of NGDP at time t is this NGDP trajectory of 10(1.05)

^{t}. In particular, the public’s expectation of NGDP at time t=1 is 10.50. However, assume NGDP

_{1}=10.29 instead of 10.50. This means NGAP is -2%, which causes the proportion in equation (2) to rise, causing the borrowers to lose and the lenders to gain. Under NT, the central bank tries to return NGDP back up to its initial trajectory where NGAP will be 0%. On the other hand, under ΔNT the central bank shifts its NGDP trajectory from 10(1.05)

^{t}to 10.29(1.05)

^{t-1}, which means that the expected future NGAP will be -2%, meaning the borrower’s loss will be made permanent. In other words, central banks following ΔNT “kick the losers (the borrowers in this case) when they are down.” On the other hand, suppose NGDP

_{1}=10.71 instead of the 10.50 expected NGDP. This is a positive NGAP of 2%, which implies that the proportion in equation (2) decreases, making the borrower better off at the expense of the loser. With NT, the central bank will try to reverse its mistake and return to its initial NGDP trajectory, return NGAP to 0%, and return the proportion of the real payment to RGDP back to as originally expected. However, with ΔNT, the central bank tries to make its mistake permanent, trying to keep NGAP at +2%, thus making the borrower permanently better off and the lender permanently worse off. Thus, the difference between NT and ΔNT is that under NT, the central bank tries to reverse the losses and gains faced by both borrowers and lenders, whereas under ΔNT, the central bank tries to make those losses and gains permanent. Thus, ΔNT “kicks the losers when they are down.” A priori, both the borrower and lender are better off knowing that the central bank is going to reverse its mistakes rather than making its mistakes and the resulting gains and losses permanent. Therefore, NT Pareto dominates ΔNT.

**Real life example #1: Homeowners and Mortgages:**During the last recession, NGDP sharply fell and central banks have been experiencing significant negative NGDP base drift. While some say that this negative NGDP base drift is due to central banks being unable to increase NGDP, the fact is that negative NGDP base drift has been associated with most U.S. recessions even when the Federal Reserve was by no means considered impotent (I will report these empirical findings in a later blog post). The negative NGDP base drift has made borrowers worse off and the continuing of that NGDP base drift continues those borrowers’ misery. For example, consider homeowners who before the recession bought homes and financed those with fixed-payment mortgages. When NGDP fell below its expected trend, average nominal income fell below what the homeowners had expected. On average, these homeowners were squeezed between reduced nominal income and their fixed mortgage payments. With central banks continuing rather than reversing the negative NGDP base drift, these homeowners will continue to be squeezed until (i) they finally pay off their mortgage after greater financial strain than they expected, or (ii) they default on their mortgages because of their inability to pay them. If central banks were to pursue NT, eliminating this NGDP base drift, reducing NGAP to 0%, then average nominal income would again be as initially expected, ending the squeeze on the average homeowner once the central bank returns to its NGDP target path. However, as they have in past recessions, central banks are letting the negative NGDP base drift continue and are therefore kicking these borrowers while they are down.

**Real life example #2: European Sovereign Governments:**When NGDP fell during the last recession in Europe, the reduction of NGDP resulted in lower tax revenues to sovereign governments, but these governments’ nominal loan payments were fixed, squeezing these governments. The European Central Bank by allowing this NGDP base drift to continue are committing these governments to a perpetual squeeze; the European Central Bank is kicking these governments while they are down. How bad is this negative NGDP base drift in Euro area? See the following graph: The negative NGDP base drift in the aftermath of the last recession in the Euro area is very significant. However, this NGDP base drift is even more evil than normally. Not only is NGAP significantly negative, but it keeps getting worse. In the second quarter of 2009, NGAP was -10.28%. Since then NGAP has continued to get worse reaching -14.90% in the third quarter of 2011. If instead the European Central Bank were to target NGDP and try to return NGDP to its prerecession trend and were successful, these governments’ tax revenue should increase to initially expected levels, eliminating the squeeze. Many will claim that the European Central Bank is impotent, unable to eliminate this NGAP. However, as the following graph shows, the European Central Bank has experienced NGDP base previously when it was not impotent. Because of my work with the issue of price determinacy, I know that expectations is very important to a central bank’s ability to meet its targets. Since the European Central Bank has let NGDP base drift persist in the past, then the public’s expectation is that they will let the NGDP base drift persist now. To succeed in eliminating this NGDP base drift, to return NGAP to zero, we need to change expectations. By committing to NT and following other suggestions the market monetarists and I have, the European Central Bank can change these expectations and eliminate the evil of NGDP base drift. Rather than kicking the sovereign government borrowers and other debtors while they are down, central banks can return NGAP to zero and help lift these debtors to their feet, which is a lot nicer than kicking them while they are down.

**Making Both Borrowers and Lenders Worse off**Up until now I have described the negative NGDP base drift caused by ΔNT and IT as making borrowers worse off while making lenders better off. However, the latest recession has made so many borrowers so worse off as to cause many borrowers be unable to pay, leading to loan defaults. Hence, not only has this negative NGDP base drift made borrowers worse off, it has also made lenders worse off. Reversing the negative NGDP base by following NT rather than IT or ΔNT would thus help not only borrowers, but lenders as well. Unfortunately, the central banks have either committed to inflation targeting or acted as if they were inflation targeters. As a result, the expectation of those who recently entered into loan contracts after the negative NGAP occurred is that the central banks would not reverse this NGAP. If they central banks do reverse this NGAP, then it will make these recent borrowers better off and the recent lenders worse off. Had the central banks instead committed to a nominal GDP target, then these recent borrowers and lenders would have anticipated the elimination of NGAP. This then does put the central banks in a difficult position. Should they reverse the NGAP and return the borrowers and lenders back to their original expected proportions at the expense of more recent borrowers and lenders? Or should they keep to their promise of nonreversal of NGAP which is consistent with more recent loans, but which will continue to kick the original borrowers while they are down. It is a difficult decision. Perhaps they can compromise and partially reverse the NGAP and then commit to a nominal GDP target in the future.

© Copyright (2012) David Eagle

2012-03-26