Food price. Quarterly update

This is a quarterly update. We continue reporting on the evolution of the difference between core CPI and the index for food (beverages not included). In several previous posts we confirmed that this difference had been following a long-term (negative) quasi-linear trend since 2001.  There is no important change so far.

In 2008, the trend line was much steeper than predicted and crossed the zero line. In the beginning of 2009, the trend reached the bottom and turned to a positive one, although not for long. The growth in food prices restarted in 2010 and has been in place since.

In June 2011, the trend (black) line crosses the zero line in the end of 2010. Therefore, Figure 1 demonstrates that the difference between the core CPI and the index of food has been slowly approaching to its original trend (red line) since 2009.

Here we suggest that the intercept with the zero line and the pivot to the decreasing food price may start any time in 2011 or 2012 depending on the bottom (resistance) level. Since the previous negative/positive pivot was at the level of -10, as displayed in Figure 2, one cannot exclude that the negative trend may change only after 2016. This case is less likely, however.

Figure 1. The difference between the core CPI and the price index of food. The pivot point to a positive trend is likely in 2011 or 2012.

Figure 2. The difference between the core CPI and the price index of food between 1960 and June 2011.

Housing price index. Quarterly update

This is a quarterly update. The housing index comprises approximately a half of the headline CPI. Three months ago we reported that the price index of housing had been decreasing since the end of 2008 relative to the overall CPI. In May 2011, the difference reached its peak and showed a slight decrease. In June, the difference fell by 0.6 points. This makes May 2011 a pivot point in the behavior of the housing index relative to the CPI. The latter fell by 0.5 in June while the housing index grew by 0.13, with the average increment during the past 12 months of 0.23.  Therefore, the housing index is not accelerating and the turn in the difference is caused by the fall in energy price and in the headline CPI, as we predicted in April 2011.  

The Figure 1 displays the difference between the CPI and the housing index (both are seasonally adjusted) as reported by the BLS on July 15, 2011.  The current trend is negative, i.e. the CPI grows slower than the index of housing. Due to the leading role of energy in the current decrease of the CPI, the housing index will demonstrate a faster growth (or slower fall) than the CPI through 2011 and the difference in Figure 1 will likely approach the zero line.

Figure 1. The change in the trend started in 2009.  After the turn in May 2011, the current trend is negative, i.e. the CPI grows slower than the index of housing.

CPI and core CPI. Quarterly update

The U.S. Bureau of Labor Statistics has reported the estimates of various consumer price indices for June 2011. According to our quarterly schedule, we have to revisit the difference between the headline and core CPI in July 2011. As expected, these new estimates reveal a crucial turn in the difference. After 10 consecutive months of fall, the difference started to grow.  This turn manifests the beginning of a new period leading to price deflation in 2012. We expect the rate of consumer price inflation to fall below zero somewhere in 2012.  

Figures 1 and 2 briefly repeat 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. (However, the difference is very volatile also in 2011.  There is no sign that the higher volatility will calm down any time soon.)

Figure 1. 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). 

Accordingly, Figure 2 illustrates this hypothesis with the reversion (like mirror reflection) of the trend between 2002 and 2009. We expected this new trend with a positive slope to be developed between 2008 and 2011, as shown by the solid red line. Against our early expectations, after a year of “right” evolution in 2010 the difference fell to the zero line again in 2011. After a slight growth in May 2011, which we discussed a month ago, the difference made a large step up in June 2011. Hence, May 2011 was a pivot point for the difference and it will likely be approaching the trend through the end of 2011.

Figure 2. The evolution of the difference between the core and headline CPI since 2002.

Figure 3 depicts the most recent period with the turn in May 2011. It is not excluded that the difference will return to the long-term trend by the end of 2011. This return should be accompanied by a remarkable drop in the index price of energy which was the driver of the headline CPI in the first quarter of 2011.  As a result, oil price will be falling in 2011 and food price will likely grow at a very low pace if grow at all. We are preparing some updates for the difference between the price index of energy and the core CPI.

Figure 3. The evolution of the difference between the core and headline CPI since 2010.

U.S. collapse?

This is to summarize some recent and older posts. In 2012, our models show:

1.     Recession
2.     Deflation
3.     Low employment/population rate
4.     High unemployment rate
5.     Increasing income inequality

Without hesitation one can add:
1.     Three wars for the Nobel Peace Prize Laureate
2.     Threat of  new wars
3.     Budget deficit and the possibility of a technical default
4     Presidential election

Okun's law integrated: Spain

We have estimated a version of Okun’s law for the USA and France. We have applied a LSQ technique to the integral version of Okun’s law: 

u(t) = u(t₀) + bln[G/G₀] + a(t-t₀)  (1)  

where u(t) is the rate of unemployment at time t, G is the level of real GDP per capita, a and b are empirical coefficients. 

For Spain, we have a model estimated by a simple eye-fit. Here we re-estimate the model with a structural break  somewhere between 1980 and 2000.  The best-fit (dynamic) model minimizing the RMS error of the cumulative model (1) is as follows:

du = -0.406dlnG + 2.00, t<1995
du = -1.11dlnG + 1.54, t>1994    (2)

This model suggests a big shift in the slope and a smaller change in the intercept around 1995. Figure 1 depicts the observed and predicted curves. The agreement is very good, especially after 1995. 

The cumulative form of the dynamic Okun’s law is characterized by standard error of 1.71% for the period between 1971 and 2010 (0.96% after 1995). The average rate of unemployment for the same period is 13.6% (14.6% after 1995) with a standard deviation of the annual increment of 2.12%.

Figure 1.  The observed and predicted rate of unemployment in the Spain between 1971 and 2010. 

Okun's law integrated: France

We have just estimated a version of Okun’s law for the USA. We have applied a LSQ technique to the integral version of Okun’s law:

u(t) = u(t0) + bln[G/G0] + a(t-t0) (1)

where u(t) is the rate of unemployment at time t, G is the level of real GDP per capita, a and b are empirical coefficients.

For France, we have a model estimated by a simple eye-fit. Here we re-estimate the model  with a structural break somewhere between 1980 and 1990. The best-fit (dynamic) model minimizing the RMS error of the cumulative model (1) is as follows:

du = -0.155dlnG + 0.805, t<1987

du = -0.508dlnG + 0.710, t>1986 (2)

This model suggests a big shift in the slope and a smaller change in the intercept around 1986. Figure 1 depicts the observed and predicted curves. The agreement is very good, with the highest difference since 1995 which might be associated with the change in monetary policy.

The cumulative form of the dynamic Okun’s law is characterized by standard error of 0.60% for the period between 1958 and 2010. The average rate of unemployment for the same period is 3.3% with an average annual increment of 0.59%. Figure 2 displays the cumulative model error.

Figure 1. The observed and predicted rate of unemployment in the France between 1962 and 2010.

Figure 2. The residual error or the cumulative model.

Okun's law integrated

In our previous post, we have estimated Okun’s law for the USA and several develop countries. This law links real economic growth and the change in unemployment rate. Here we integrate this relationship and obtain the dependence of the unemployment rate on real GDP. It allows modeling the rate of unemployment over time.

We have rewritten Okun’s law using the growth rate of real GDP per capita instead of GDP itself:

du = a + bdlnG (1)

where du is the annual increment in the rate of unemployment, dlnG=dG/G is the relative change rate of real GDP per capita per one year, a and b are empirical coefficients. Okun’s law suggests that b<0.

The reason to use per head values is obvious – the rate of unemployment is a population independent characteristic (i.e. normalized to total population) and GDP implicitly includes the change in population. When the change in population is fluctuating, relationship (1) is biased.

For the United States we have obtained the following relationship:

du = -0.42dlnG + 1.07, t<1985

du = -0.62dlnG + 1.09, t>1984 (2)

with a structural break in 1984. This was a preliminary assessment of the links as based on an eye-fit between measured and predicted curves. No formal minimization was applied.

When integrated between t0 and t, equation (1) can be rewritten in the following form:

u(t) = u(t0) + bln[G/G0] +a(t-t0) + c (3)

Without loss of generality, we assume t0=0. The intercept c≡0, as is clear for t=t0. Instead of integrating (3), we calculate cumulative sums of the annual estimates of du and lnG with appropriate initial conditions. The cumulative sum of du’s is the time series of the unemployment rate. Figure 1 depicts the measured and observed curves. The agreement is excellent and has been obtained by a formal statistical method.

We have re-estimates all coefficients in (3), and thus in (2), using a LSQ technique. Since we have already introduced a structural break in (2), we have sought the best fit allowing the year of this break to vary between 1970 and 1990. The best-fit (dynamic) model minimizing the RMS error of the cumulative model (3) is as follows:

du = -0.406dlnG + 1.113, t<1979

du = -0.465dlnG + 0.866, t>1978 (4)

This model suggests a smaller shift in the slope and a larger change in the intercept around 1979. The break year has changed from 1984 to 1979. This is a very important finding because both relationships in (4) give very close predictions for the period between 1978 and 1985. Therefore, the shift in coefficients in (4) is likely not an abrupt one but actually a transition process between two different states of the US economy.

The cumulative form of the dynamic Okun’s law (4) is characterized by standard error of 0.53% for the period between 1958 and 2010. The average rate of unemployment for the same period is 5.6% with an average annual increment of 1.06%. Figure 2 displays the cumulative model error.

Figure 1. The observed and predicted rate of unemployment in the USA between 1958 and 2010.

Figure 2. The residual error or the cumulative model (4).