We continue the series of guest blogs by David Eagle on his research on NGDP targeting and related topics.

See also David’s first guest post *“Why I Support NGDP Targeting”.*

Enjoy the reading.

Lars Christensen

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**Guest blog: Growth vs. level targeting**

*by David Eagle*

In my first guest blog for *“The Market Monetarist”* I stated that I am in favor of targeting the level of Nominal GDP (NGDP) and not the growth rate of NGDP. Some economists such as Bennett McCallum (2011) are in favor of NGDP-growth-rate targeting (ΔNT) over NGDP Targeting (NT).

I have long opposed inflation targeting (IT) and I view ΔNT as almost as bad as IT because both cause what we call *negative NGDP base drift*. In order to understand my arguments against ΔNT and against IT, we need to understand the concepts of NGAP and NGDP base drift.

In this blog, I use an example to illustrate these concepts and the difference between NT and ΔNT. It also uses another example to help us understand the concepts of PGAP and price-level base drift, and the difference between price-level targeting (PLT) and IT.

**Growth vs. Level NGDP Targeting**

To see the similarities and differences between targeting the *growth rate* of NGDP (ΔNT) and the *level* of NGDP (NT), assume the central bank’s target for NGDP *growth* would be 5%. As long as the central bank (CB) meets that target, NGDP would follow the path *N*_{t} = *N*_{0} (1.05)^{t} where *N*_{0} is the NGDP for the base year and *N*_{t} is the NGDP occurring *t* years after the base year.

For consistency, assume that the CB’s target for NGDP (if it targets the NGDP *level*) would be *N*_{t}^{*} = *N*_{0} (1.05)^{t}. Hence, as long as the central bank meets its target, then NGDP will be the same whether the central bank targets the growth rate or the level of NGDP.

The difference between growth rate targeting and level target occurs when the central bank misses its target. Assume for example *N*_{0} = 10. Initially, both NT and ΔNT have the same intended NGDP trajectory of *N*_{t} = 10(1.05)^{t}; in particular, both NT and ΔNT aim for *N*_{1} to be 10.5. However, assume the central bank misses its target and *N*_{1} = 10.08, which is 4% below its targeted *level* of NGDP. We define NGAP_{t} as the percent deviation at time t of NGDP from its previous trend; hence in this example NGAP_{1} = -4%. Under NT, the central bank will try to make up for lost ground to reduce NGAP to zero and return NGDP back to its targeted path of *N*_{t} = 10(1.05)^{t}.

In contrast, under NGDP *growth* targeting, the central bank will only try to meet its targeted NGDP growth rate of 5% in the future. Hence, under NGDP *growth* targeting, the central bank will shift its NGDP trajectory to *N*_{t} = 10.08(1.05)^{t-1}, which is 4% below the initial NGDP trajectory of *N*_{t} = 10(1.05)^{t}. In other words, under NGDP growth targeting, the central bank would let the 4% NGAP continue indefinitely. NGDP* base drift* occurs when the central bank allows NGAP to continue rather than trying to eliminate that NGAP in the future.

**Price Level Targeting vs. Inflation Targeting**

The concept of NGDP base drift is related to the concept “price-level base drift,” which many economists such as Svensson (1996) and Kahn (2009) have long recognized to be the theoretical difference between price-level targeting (PLT) and inflation targeting (IT).

In particular, Mankiw (2006) states, *“The difference between price-level targeting and inflation-targeting is that price-level targeting requires making up for past mistakes,”* while Taylor (2006) states, *“Focusing on a numerical inflation rate tends to let bygones be bygones when there is a rise [or fall] in the price level”* [brackets added].

Also, Meh, et al (2008) state, *“Under IT, the central bank does not bring the price level back and therefore the price level will remain at its new path after the shock.”* They go on to say that under PLT,* “the central bank commits to bringing the price level back to its initial path after the shock.”*

To see the similarities and differences between PLT and IT, assume the central bank’s target for inflation (if it follows IT) would be 2%. Then the CB’s trajectory for the price level will be *P*_{t} = *P*_{0} (1.02)^{t} where *P*_{0} is the price level for the base year and *P*_{t} is the price level occurring *t* years after the base year. Similarly assume that the central bank’s price-level target (if it follows PLT) would be *P*_{t}^{*} = *P*_{0} (1.02)^{t}. Hence, when the central bank meets its target, the price level will be the same regardless if the central bank follows PLT or IT.

The difference between PLT and IT occurs when the central bank misses its target. For this example, assume *P*_{0} = 100. Initially, both PLT and IT have the same price-level trajectory of *P*_{t} = 100(1.02)^{t}. In particular, under both PLT and IT, the CB is aiming for *P*_{t} to be 102 at time *t*=1. However, assume that the central bank misses its target and *P*_{t} = 100.47, which is 1.5% less than its targeted price level of 102. We define PGAP_{t} to be the percent deviation of the price level at time *t* from its previous trend; hence, in this example; PGAP_{1} = ‑1.5%.

Under PLT, the central bank will try to return PGAP back to zero by increasing the price-level back up to its targeted price-level path of *P*_{t} = 100 (1.02)^{t}. Under IT, the central bank will *“let bygones be bygones”* and merely try to meet its inflation target of 2% in the future. Hence, under IT, the central bank shifts its price-level trajectory to *P*_{t} = 100.47 (1.02)^{t-1}, which is 1.5% below its initial trajectory. In other words, the central bank lets the -1.5% PGAP continue into the foreseeable future. Price-level base drift occurs when the central bank allows PGAP to continue rather than trying to eliminate that PGAP in the future.

**Price-level base drift implies NGDP base drift**

Because IT leads to price-level base drift, it also leads to NGDP base drift. To illustrate with an example, assume the long-run growth rate in *real* GDP (RGDP) is 3% and RGDP in the base year is *Y*_{0} = 10 trillion dollars. Therefore, when the central bank expects RGDP to grow at its long-run growth rate, it expects *Y*_{t} = 10(1.03)^{t}.

Initially in this example when the central bank has a 2% inflation target, the central bank’s trajectory for the price level under inflation targeting is *P*_{t} = 100 (1.02)^{t}. Since *N*_{t}=*P*_{t}*Y*_{t}/100 when we use 100 as the price level in the base year, this means that the CB’s trajectory for NGDP_{t} is *N*_{t} = 10 (1.02)^{t}(1.03)^{t}. When it turned out that *P*_{1} was 100.47 instead of 102, the central bank following IT would shift its price level trajectory to *P*_{t} = 100.47 (1.02)^{t-1} and its NGDP trajectory to *N*_{t} = 10.047 (1.02)^{t-1}(1.03)^{t}, which is 1.5% below its initial NGDP trajectory. Therefore, NGAP under this trajectory will be -1.5%, which means a negative NGDP base drift.

**“Inflation targeting” can be many things**

In practice, inflation targeting is not as simple as I described above or even as several of the economists I quoted described it. In practice, central banks following inflation targeting target a long-run rather than a short-run inflation rate. They also try to target “core inflation” rather than general inflation. Also, they do consider output gap and unemployment as well as inflation. Therefore, the question whether IT in practice leads to NGDP base drift is primarily an empirical one.

According to my empirical research that I plan to report in a later blog, past U.S. monetary policy has on average resulted in a significant negative NGDP base drift. Also, that research indicates that the primary reason for the prolonged high unemployment following a recession is this negative NGDP base drift.

*References:*

Kahn, George A. (2009). “Beyond Inflation Targeting: Should Central Banks Target the Price Level?” Federal Reserve Bank Of Kansas City *Economic Review* (Third quarter), http://www.kansascityfed.org/PUBLICAT/ECONREV/pdf/09q3kahn.pdf

Mankiw, Greg (2006). “Taylor on Inflation Targeting,” *Greg Mankiw’s Blog* (July 13) http://gregmankiw.blogspot.com/2006/07/taylor-on-inflation-targeting.html

McCallum, Bennett, “Nominal GDP Targeting” Shadow Open Market Committee, October 21, 2011, http://shadowfed.org/wp-content/uploads/2011/10/McCallum-SOMCOct2011.pdf

Meh, C. A., J.-V. Ríos-Rull, and Y. Terajima (2008). “Aggregate and Welfare Effects of Redistribution of Wealth under Inflation and Price-Level Targeting.” Bank of Canada Working Paper No. 2008-31, http://www.econ.umn.edu/~vr0j/papers/cvyjmoef.pdf

Svensson, Lars E. O. (1996). “Price Level Targeting vs. Inflation Targeting: A Free Lunch?” NBER Working Paper 5719, http://www.nber.org/papers/w5719.pdf, accessed on January 4, 2012.

Taylor, John (2006). “Don’t Talk the Talk: Focusing on a numerical inflation rate tends to let bygones be bygones when there is a rise in the price level.” *The Economist* (July 13), http://online.wsj.com/article/SB115275691231905351.html?mod=opinion_main_commentaries

© Copyright (2012) David Eagle

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