V- vs L-shaped recovery: Is CBO’s economic projection wrong?

CBO has recently published a new economic projection covering the period between 2011 and 2021. It explicitly defines the rate of real economic growth (GDP) and inflation for several segments: forecasts for 2011 and 2012, and projections for 2013 -2016 and 2017-2021. Overall, after two years of slow growth in 2011 and 2012, CBO expects a dramatic increase to the rate of 3.6% per year between 2013 and 2016 with the next five years of slow economy with the rate of 2.4% per year on average. Inflation is low over the entire period: the rate of PCE inflation varies between 2.4% and 1.3% per year and that of CPI inflation will be in the range 1.3% to 2.8% per year. Considering these figures one can conclude that CBO expects a slow version of a V-shaped recovery in the 2010s.  There is no double dip.   

We have also projected the rate of inflation and real economic growth in this blog and academic papers. Our GDP (per capita) model is based on the change in demographic characteristics (the age pyramid). Another model describes price inflation as a function of the change rate of labor force. Skipping all mathematical details, we expect the rate of real economic growth (GDP per capita) to fall slightly below zero between 2012 and 2014 (recession) and hovering around 1%  per year after 2015. The rate of price inflation (the GDP deflator and CPI) in the 2010s has to be slightly negative on average with some years of formal deflation. All in all, we expect an L-shaped recovery, i.e. no actual recovery during the 2010s.

Don't trust seasonal adjustment in July

The U.S. Bureau of Labor Statistics has reported the estimates of various consumer price indices for July 2011. Unexpectedly, the difference between the core and headline CPI has fallen to zero after a crucial turn to growth in June. There are many factors which allow us to consider the difference for July a blip.

The difference between the core and headline CPI, as shown in Figure 1, is for seasonally adjusted, SA, values. As a rule, seasonal adjustment allows to separate trend and fluctuations for a given month. For example, it is good to know that temperature in January and July is two degrees above their normal climatic values, but these values are different for January and July. Same is with the seasonally adjusted consumer prices – they depend on previous years. When seasonal factors are correlated over years the seasonally adjusted values are informative and help the broader audience to ignore constants.

However, when one value used in the adjustment for a given month is a spike then all further values are biased. This is the case for the headline CPI in July 2011. Figure 2 compares the seasonally adjusted headline CPI and not seasonally adjusted CPI, NSA, between 2001 and 2011. The NSA curve shows a small increase in July 2011. The large difference between the SA and NSA curves from May to July 2011 (also clearly seen in 2010) is driven by the turbulence in consumer prices in the same months in 2008 and 2009. Since August, the effect of 2008 and is opposite and the SA values will be below the NSA ones. Specifically, the SA-NSA effect is a major contributor to the fall in the difference between the core and headline CPI in July 2011.  Hence, do not trust the seasonally adjusted CPIs in July.

Figure 1. The evolution of the difference between the core and headline CPI since 2002.

Figure 2. The evolution of the difference between the core and headline CPI, both SA and NSA, since 2001.

Other factors implying a blip in the July’s difference between the core and headline CPI are related to actual changes in consumer prices. In August 2011, the price index of energy has to fall by approximately 10% as one can see from the price evolution during the past 20 days. Technically, this fall will reduce the headline CPI by at least 1% with the core CPI intact. Apparently, the fall in energy prices will indirectly affect other consumer prices which might result in a slightly larger change in the core CPI. A heavy crop in 2011 is also foreseen in the U.S. and Europe what will likely suppress the current growth in the price index of food in 2011-2012.

All in all, we foresee the difference between the core and headline CPI to grow through rest of the year. Since the core CPI will be growing at its current pace between 1% and 2% per year the headline CPI will sink below zero.

Figure 3 briefly repeats our concept of sustainable (quasi-linear) long-term trends in the difference between the headline and core CPI in the U.S. There were two clear periods of linear behaviour: between 1981 and 1999 and between 2002 and 2009. A natural assumption of the future evolution of the difference was that a new trend has to emerge around 2010 after a short period of very high volatility (see Figure 1). However, the difference is very volatile also in 2011.  There is no sign that the higher volatility will calm down any time soon.

Figure 3. Linear regression of the difference between the core CPI and CPI for the period from 1981 to 1999 (R²=0.96, the slope is 0.67) and a regression of the difference between the core CPI and CPI between 2002 and 2009 (R²=0.91 and the slope is -1.59). 

The performance of 10-year T-notes during deflation

In our previous article we presented a prediction of an extended period of price deflation in the U.S. since 2012. Our projection was made in 2006 and covers the period between 2006 and 2016. At least five years are characterized by negative inflation. The underlying model can also foresee beyond 2016 when some updated labour force projections are used (see Appendix). There is no expectation of a positive inflation rate at least in the 2010s. Deflation is a major risk for the U.S. economy and stock market. Therefore, one can consider a safer investment in Treasuries. Let us check various options. 

Currently (August 18, 2:15), T-notes and T-bonds have very low yields between 0.19% for 2-year T-notes and 3.55% for 30-year T-bonds. Since the predicted deflationary period will last at least 8-years one can choose between 7-year and 10-year T-notes. The former has the yield of 1.45% and the latter 2.15% (coupon 2.125%). Taking into account the predicted rate of inflation below -0.5% per year in the near future, one can evaluate the real yield as 3% in the next few years. This is a safe and relatively profitable investment during the poor years to come. The stock market will likely be stangnant if not  decaying.

 Appendix

The BLS has projected the level of labour force to increase from 154.300.00 in 2008 to 167.000.00 in 2018, i.e. by 0.8% per year on average. Considering the current fall in the rate of participation down to 64.5% (instead of 66%) which was expected only in 2018, we should decrease the projected level in 2018 by approximately 1.2%, i.e. to 165.000.000. Then, the rate of labour force growth is 0.66% on average between 2008 and 2018. According to our model the rate of consumer price inflation is driven by the change rate in labour force: 

CPI(t)=4.5dlnLF(t-3)/dt - 0.032 (1) 

where CPI(t) is the rate of consumer price inflation at time t, LF(t-3) is the level of labour force three years before the predicted rate of inflation. Using the average rate of labour force change between 2008 and 2018 one can estimate the average consumer price inflation between 2008 and 2018 as -0.3% per year. Since the years between 2008 and 2011 have a positive inflation rate the years after 2012 will have evens a smaller average inflation rate.  On average, I would estimate the future rate of inflation as -0.5% per year since 2012. However, during 2012 and 2013 it can be as low as -3%.  

Producer price of iron has to fall

This is a quarterly update of producer prices of crude petroleum and iron. We have been following the link between these price indices since 2009. Our previous update included PPI data for March 2011. Here we extend this set by data available for July. Otherwise, we retain the form of the report untouched.

Historically, we first reported that the price index of crude oil had been likely evolving in sync with that of iron and steel, but with a lag of two months in September 2009.  In order to present both indices in a comparable form, the difference between a given index, iPPI (i.e. iron&steel and crude), and the overall PPI was normalized to the PPI: (iPPI(t)-PPI(t))/PPI(t). These normalized differences represent the evolution of the rate of deviation from the PPI over years.

Figure 1 depicts the corresponding time histories of the normalized deviations from the PPI, including the most recent period since March 2011.  Even a simple visual inspection reveals the following feature: the (normalized deviation from the PPI of the) index of iron and steel lags by approximately two months behind the (normalized) index of crude oil.

Figure 1. The deviation of the iron and steel price index and the index of crude oil from the PPI, normalized to the PPI.

In order to reduce both deviations to the same scale we additionally normalized the curves in Figure 1 to their peak values between 2005 and 2011

(iPPI(t)-PPI(t))/[PPI(t)*max{iPPI-PPI)}]

This scaling allows a direct comparison of corresponding shapes. In Figure 2, we display the normalized index of iron and steel shifted by two months ahead to synchronize its peak with that observed in the normalized index for crude petroleum. The scaled index of crude demonstrates just short-term deviations from the index of iron and steel in the overall shape and timing of the peak and trough. Simple smoothing with MA(3) makes the curves resemblance even better. As an invaluable benefit of the resemblance, one can use the two-month lag to predict the future of the iron and steel price index.

Figure 2. Deviation of the iron and steel price index from the PPI, normalized to the PPI and the peak value after 2005 as compared to the deviations of the index for crude petroleum normalized in the same way. The normalized index for iron and steel is shifted two months ahead. 

Conclusion

Between 2006 and July 2011, the deviation of the price index of iron and steel from the PPI in the USA repeats the trajectory of the deviation of the index of crude petroleum (domestic production) with a two-month lag. Therefore, the prediction of iron and steel price for at this horizon is a straightforward one.  We expect the index of iron&steel to fall in the near future in accordance with the currently observed fall in oil price.

Deflation is a long term threat for the stock market

Price deflation in the U.S. is an issue which attracts attention. For example, the FOMC statement implies very low inflation at a two year horizon. The two-year breakeven inflation rate is negative. As a result, economics blogs are also full of discussions around the near future of the overall price behaviour.  (Despite the explicit FOMC statement many experts expect a period of hyperinflation after two sessions of quantitative easing.) The danger of deflation has been demonstrated by Japan where the quantitative easing did not show any positive results.  

We predicted an extended deflationary period since 2012 five years ago. This prediction was based on a model describing inflation in developed countries as a linear and lagged function of labour force. In 2006, we published a forecast for the U.S. a ten year horizon using the following relationship:  

DGDP(t) = 4.0dlnLF(t-2)/dt – 0.03              (1)                       

 where DGDP is the GDP deflator at time t, and dlnLF(t-2)/dt  is the rate of growth in the level of labour force two years before, t-2. In equation (1), the slope is 4.0 and intercept is -0.03. Using (1) and various projections of labour force we estimated the rate of inflation between 2006 and 2016. Figure 1 compares the predicted rate of inflation with that observed between 2006 and 2010.  The agreement is very good considering the precision of inflation measurements and the labour force projection published by the CBO in 2004.  

For 2011, the model predicts the rate of inflation near 0.4%. The current fall in commodity prices and the deceleration in real economic growth both imply no price inflation in the second half of 2011. Hence, our prediction for 2011 from 2006 seems to be right.   

Between 2012 and 2016, the rate of inflation (as expressed by the GDP deflator) will be negative at the level between -0.5% and -1.2% (2013).  Obviously, the CBO labour force projection at a ten year horizon could not be too precise and actual values of the future inflation rate may differ from the predicted ones. However, the negative inflation trend is a serious and long term danger for the U.S. economy.

Figure 1. Predicted inflation rate for the period between 2006 and 2016 according to the CBO’s (2004) labour force projection.  A deflationary period starts in 2012.  

Deflation in consumer prices is also predicted by the current measurements of labour force. We estimated a similar relationship for the headline CPI. Five years ago the following relationship was obtained: 

CPI(t) = 4.5dlnLF(t-3)/dt – 0.032                (2) 

The time lag of three years (actually 2.5 years) provides the best fit between observed and predicted values.  In (2), the slope is larger than in (1). This difference expresses a larger volatility in consumer prices.  Figure 2 illustrates the agreement between the observed and predicted rate of consumer price inflation between 1960 and 2010.  At a three year horizon one can expect a significant fall in the rate of inflation, down to -4% per year.  This is a great threat for producers, consumers and the U.S. economy as a whole. 

The uncertainty in labour force measurements is directly mapped into high-amplitude fluctuations. These fluctuations represent banal measurement noise and can not be removed without improvements in the relevant BLS methodology and procedures. It is instructive that the largest fluctuations correspond to the years of decennial censuses. The Census Bureau has to smooth the difference between counted and projected population values (so called population controls) and the BLS ignores these steps. As usually, the most reliable readings correspond to the changes with the largest amplitude.

The best way to suppress this measurement noise is to use integral (cumulative) values.  Figure 3 displays the observed and predicted cumulative inflation curves starting from 1965. The predicted cumulative curve is obtained by a progressive summation of values from 1963 and is also shifted ahead by 2 years. There is an almost complete agreement between the cumulative curves for the whole period. The only small deviation occurred around 1993 and corresponds to a sharp drop of the rate of labour force growth as induced by the baseline working age population correction.

Figure 2. Measured inflation and that predicted from the dLF/LF (shifted 2 years ahead). An agreement is observed throughout the whole period with some short fluctuations in labour force potentially induced by the population corrections implemented by the Census Bureau in the census years. 

The predicted cumulative curve is very sensitive to free term in (2). Even the initial difference of 0.0001 results in a tangible deviation from the measured curve after 50 years. Therefore, the value of free term in (2) can be estimated with a good accuracy. It is important that the cumulative curves represent actually measured macroeconomic variables: labour force and price. Inflation and change rate are based on first differences of the original values and thus are much more sensitive to measurement errors.  

Figure 3. Comparison of the cumulative values of the observed and predicted inflation presented in Figure 2. The predicted curve starts from 1963 and is shifted by 2 years ahead. An agreement is observed with a notable change from convexity before 1980 to concavity one after 1980.

One can conclude that a deflationary period will likely start in 2012 and then may extend into the second half of the 2010s. Price deflation is a major risk for the stock market.  

Revised GDP estimates support the model of inertial growth

On July 29, the BEA revised real GDP estimates for the years after 2007. The most important news is:

For 2007-2010, real GDP decreased at an average annual rate of 0.3 percent; in the previously 

published estimates, real GDP had increased at an average annual rate of less than 0.1 percent. From the fourth quarter of 2007 to the first quarter of 2011, real GDP decreased at an average annual rate of 0.2 percent; in the previously published estimates, real GDP had increased at an average annual rate of 0.2 percent. 

These new BEA data strongly support our model of real economic growth. Previously in this blog, we found that real GDP per capita in developed countries grows as a linear function of time. Similarly to classical mechanics, we interpret this linear growth as “inertial” growth. When the population pyramid does not change over time one can write the following relationship for real GDP per capita, G(t):

G(t) = At + C           (1)

Relationship (1) defines the linear trajectory of the GDP per capita, where C=G_i(t₀)=G(t₀) and t₀ is the starting time. In the regime of inertial growth, the real GDP per capita increases by the constant value A per time unit. Figure 1 depicts the evolution of annual increment of real GDP per capita in the U.S. since 1950. The new GDP revision makes the slope of the linear regression line (trend) almost negligible (+$1.9 per year) and thus supports our concept. In 2011, the slope may become negative if the increment is below $432. After the two mediocre quarters in 2011, we would not expect real GDP per capita in 2011 to grow faster than in 2010.  

On June 5 we had a post on the current position of the U.S. economy relative to some long term trend. As a rule, economists consider real growth as an exponential process and see the U.S. economy far below its trend. We compared the trends in real GDP and GDP per capita. The latter should be a linear one. Figure 2 depicts the evolution of both variables between 1950 and 2010 with the new readings between 2007 and 2010.

The real GDP curve has an exponential shape as related to the growth in total population. One can easily observe the current deviation from the exponential trend and blame poor economic conditions after 2007. With the decelerating rate of total population growth we would not expect the observed curve to return to the exponential trend (exponential extrapolation of the previous growth.)  

The real GDP per capita evolves along a straight line. After the revision, the curve falls below the linear trend. It touched the trend with the previous set of GDP estimates. All in all, during the past four years the observed curve returned to the long-term trend and may stay below the trend for a while.   We also presented an exponential trend which has a small coefficient of 0.02. This coefficient effectively makes the line very close to a straight one between 1 and 60. However, the deviation from the (extrapolated) exponential trend will be growing and observations will contradict the hypothesis of exponential growth. 

Figure 1. Annual increment of real GDP per capita in the U.S. between 1950 and 2010.

Figure 2. The evolution of real GDP and real GDP per capita between 1950 and 2010. 

The rate of participation in labor force will not fall

Two years ago we published a post with a model describing the evolution of labor force participation rate, LFP, in developed countries. Among other countries, we presented a prediction for the U.S. Figure 1 reproduces the evolution of observed and predicted LFP in the United States as predicted in 2008. The predicted curve was obtained directly from real GDP per capita (see this article for details). Both curves in Figure 1 almost coincide between 1960 and 2007. The largest deviations are observed in the years of biggest revisions to the LFP after decennial censuses. Therefore, they can be neglected as having artificial character. The predicted curve shows that the LFP should decrease after 2006 - the last year with the LFP estimates available when the model was developed.

Figure 1. Observed and predicted LFP in the U.S. as described in 2008.  Notice the largest deviation between the curves is associated with the years of major revisions to the LFP - 1980 and 1990.

Using the same model we revisited the model and obtained a new prediction for the past four years and also two years ahead. Figure 2 compares the predicted and observed LFP curves in the U.S. The prediction for the years between 2007 and 2010 is excellent. In 2011 and 2012, the rate of participation is expected to stall near 64.5%.

Figure 2. Observed and predicted LFP in the U.S. The years between 2007 and 2010 are well predicted.