USA:OUTPUT GAP, L or U?

Measuring Potential Economic Recoveries

Antonio Carlos Lemgruber | Apr 28, 2009

Nouriel Roubini said recently the following: I am not Dr. Doom. I am Dr. Realist. I don't believe we are going to end up in a near-depression. Six months ago I was more worried about an L-shaped near-depression. Today, after the very aggressive policy actions taken by the U.S. and other countries . . . we are, instead, in the middle of a U.

The purpose of this article to bring the concept of output gap to the debate about economic recovery. We believe there is a serious flaw in the analysis when we deal with the concept of real GDP growth as opposed to output gap changes. Just as an example: a country may grow by 8% in one year and still maintain high unemployment if such 8% growth comes after a huge recession. After all, neither unemployment nor inflation are correlated to GDP growth; they are in fact correlated to the LEVEL of the output gap in a given year.

Let us assume that the potential rate of growth of the EUA (full employment, no inflationary pressures) is 2.5% per year. And for Brazil: 4% per year. Using logarithmic concepts in the same fashion as percentual changes, we have the following identity: Output Gap in Year T = Output Gap in Year T-1 less rate of real economic growth plus 4% (or 2.5%). Or: Output Gap in year T = (Potential Output less Effective Output)/Effective Output x 100 = Output Gap in Year T-1 plus 4% less effective rate of economic growth.

In other words, whenever the US economy grows by less than 2.5%, the output gap increases together with unemployment ( and 4% for Brazil). And vice-versa when these countries grow more than 2.5% and 4%, respectively. There is nothing to prevent such countries to grow for a certain period of time ( the "recovery" ) more than the potential rates, that is, more than 2.5% or 4%.

The whole discussion about recession and depression is missing something. One should follow if the US is growing 2.5% (not zero) and in the case of Brazil (4% not zero). If Brazil grows less than 4%, unemployment increases.

The major instrument of economic policy to influence the output gap used to be the interest rates and more recently we have the old-fashioned money base and government deficit acting in the same direction. For example, in Brazil, for the next meeting of the Copom, we begin to perceive that the Central Bank is becoming more comfortable with the output gap and less ready to bring interest rates down. It would not be a surprise to me a move of less than 1%, but the more likely change will be 1%.

But the true formula (although an identity for me) is the following: growth of GDP = 4% (or 2.5%) plus the LEVEL of output gap in T less the level in T-1.

What does it say? After the great recession of 2008-2009, even if both countries were facing zero output gaps in 2007, there is again a huge output gap both in the United States and in Brazil. Let us say: 10% in the US and 5% in Brazil because of the recession of 2008 and mainly 2009.

At the extreme, this opens a possibility for both these countries to grow at 10% in 2010 - a major recovery of the V type 9 (as opposed to the L or U types mentioned by Roubini). This does not seem plausible, although the Brazilian Miracle of 1968-1973 and the US miracle of 1992-2006 reflect probably some amazing recoveries after the recessions of 1962-66 (Brazil) and 1981-82 (US) followed by 1991 (US).

More than that, depending on the previous output gap (see the formula), growth theoretically could be even higher. There are good reasons to believe that in 2007 output gap was zero in the US and still "high" in Brazil, perhaps 2 or 3%. Therefore, given the formula, Brazil could grow in 2o10 even more than 5%.

One of the big question marks in this potential output analysis is the "distribution" of the recovery bonus created by the output gap along the years. Supposedly, in 2010, the United States will have lost 10% of GDP (a dramatic number) and Brazil will have lost 5% of GDP (also a relevant number). According to the "theory" behind potential output analysis, there is no L, that is, there is also a return to the trend growth rate. So these countries will grow more than potential growth for a certain period. The question is: 1 year or 10 years?

What is the evidence? There are Vs and Us, but very few Ls. The case of Japan is an exception: it never returned to the trend levels of the previous century. Something terrible happened with the Japanese economy. Even Brazil had a still enigmatic decline in potential output from 6& in the last century to 4% now.

Following up on the expectations of Mr. Roubini, one should approach a middle-of-the road expectations, which means that for a few years (one to three) countries like Brazil and the United States should grow well above potential until they return to their long-term trends and to zero output gaps, recovering partially the dramatic loss of output of 2008/2009 only similar to 1981/82 or 1929/1933