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).

Okun’s law revisited. Is there structural unemployment in developed countries?

Abstract

Okun’s law for the biggest developed countries is re-estimated using the most recent data on real GDP per capita and the rate of unemployment. Our results show that the change in unemployment rate can be predicted with a high accuracy. The link needs the introduction of a structural break which might be caused by the change in monetary policy or/and in measurement units. Statistically, the link between the studied variables is characterized by the coefficient of determination between 0.40 (Australia) and 0.84 (the USA). The residual errors can be associated with measurement errors. The obtained results suggest the absence of structural unemployment in the studied developed countries.

Key words: unemployment, GDP, modelling, Okun’s law

JEL classification: J65 

Introduction

The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2010 was awarded to P. Diamond, D. Mortensen and C. Pissarides ”for their analysis of markets with search frictions”. The core result of their study was an explanation of labour market dynamics including unemployment (e.g. Diamond, 2011; Mortensen and Nagypal, 2007; Pissarides, 2000). Hence, the dynamics of unemployment is a very important and actual problem for the modern economics.

One of the most actively discussed topics related to unemployment is its high persistence since the start of the financial crisis. In the United States, the current rate unemployment is above 9% and it does not show any sign of reduction in the future. There is an opinion that the current situation might manifest tangible structural changes in the labour market. This implies some major changes in the overall organization of the economy when significant parts of it become unnecessary.

We address the problem of structural unemployment by modelling the rate of unemployment using the relationship explaining the dynamics of unemployment by its negative correlation with the growth in GDP – Okun’s law (1962). This relation was revisited many times in the past (e.g. Altig, Fitzgerald and P. Rupert, 1997; Knotek, 2007; Tillman, 2010).

We also revisit Okun’s law using the most recent data on GDP per capita provided by the Conference Board (2011) and data on unemployment from the OECD (2011). To improve the agreement between the change in unemployment rate and real GDP per capita we introduce structural breaks in Okun’s law. Such breaks might manifest artificial changes in definitions of unemployment and real GDP as well as actual shifts in the linear relationship.

We have assessed Okun’s law in the biggest developed countries: the United States, France, the United Kingdom, Australia, Canada and Spain. Our results suggest the absence of structural unemployment in the studied developed countries. The persistence of high unemployment is completely related to low rate of real economic growth. In all studied countries, the rate of growth above 2% per year will result in a fall of the unemployment rate.

Okun’s law and empirical results

According to the original form of Okun’s law, there exists a negative relation between the growth rate of real GDP and the change in unemployment rate, du=u_i-u_i-1. The overall GDP includes the change in population as an extensive component which is not necessary dependent on other macroeconomic variables. Econometrically, it is mandatory to use macroeconomic variables of the same origin and we use real GDP per capita, G. It is better related to the portion of labor force without job, i.e. the rate of unemployment. Therefore, we rewrite Okun’s law in the following form:

            du = a + bdlnG      (1)

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

We start with the United States and have to introduce a structural break in 1984 into the link. The following relationship was obtained:  

 du = -0.42dlnG + 1.07, t<1985

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

where dlnG in the annual growth rate of real GDP per capita, du is the annual increment in the rate of unemployment, u. Figure 1 displays the observed and predicted du between 1958 and 2010. The agreement is excellent. Figure 2 presents some regression results for the curves in Figure 1 with the coefficient of determination R²=0.84. Therefore, more than 84% of the variability in the change of unemployment rate in the U.S. is explained by the change in real GDP per capita. Considering the fact that both macroeconomic variables are measured with an accuracy of approximately 1 percentage point the residual 16% of the variability can be easily associated with the uncertainty in their measurements. Figure 3 demonstrates that the residual error is rather random and does not contain a unit root and has no significant autocorrelation.

Relationship (2) shows that the sensitivity of the du to dlnG becomes higher after 1984 with the slope of -0.62 and the intercept +1.09. There are two assumptions on the reasons behind this structural break. One is related to the changes in monetary policy in the early 1980s to overcome extremely high inflation. On the other hand, the measures of the GDP deflator and CPI start to deviate around 1980 and the rate of unemployment obtained a new definition in 1984. Thus, the shift in 1984 might also be associated with new units of measurements. In any case, the period after 1984 is described with a very high accuracy including three episodes of unemployment surge in 1991, 2001 and 2009. Moreover, relationship (2) provides a smooth transition through 1984 and describes the fall in unemployment in 1984.

We have also checked several macroeconomic variables as a predictor variable in Okun’s law: the overall GDP, GDP per capita corrected for the difference between the whole population and working age population, and productivity as expressed by real GDP per worker.  All these variables are inferior to real GDP per capita and thus we use this variable for other countries.

The next country to model is France. We have reversed (1) and obtained the following relationship for dlnG:  

 dlnG = -5.0du + 4.6, t<1987

 dlnG = -1.5du + 1.4, t>1986                      (3)

Figure 4 present the observed and predicted curves. There is a shift in the dependence around 1987 and the slope in (3) fell from -5.0 to -1.5.  Correspondingly, the sensitivity of the unemployment rate to real GDP growth (the reciprocal value of the slope in (3)) increased from -0.2 to -0.67. In order to decrease the rate of unemployment in France, real GDP per capita has to grow by 1.5% per year. When the growth rate is lower, the rate of unemployment increases. 

For France, both variables are characterized by an elevated volatility and thus the coefficient of determination R²=0.53 is relatively low. To remove the measurement noise we have smoothed both curves with MA(3). The lower panel in Figure 4 shows that the agreement between the measured increase in real GDP per capita and that predicted from the change in unemployment rate became extremely good.  

The United Kingdom also shows an excellent result for Okun’s law. The following equation:

dlnG = -1.5du + 2.5, t<1987

dlnG = -2.0du + 1.7, t>1986                 (4) 

describes the period after 1972. Figure 5 illustrates the agreement between the observed and predicted time series. Before 1972, the OECD provides no unemployment estimates. The year of structural break is the same as in France but the change in the slope is much lower. In any case, to reduce the current rate of unemployment the UK needs to grow at a rate above 1.7% per year in term of real GDP per capita.  

For Canada, the following equation was estimated with a structural break around 1985:  

dlnG = -2.7du + 3.1, t<1985

dlnG = -2.7du + 1.2, t>1984       (5) 

Figure 6 depicts the measured and predicted curves for dlnG. For Canada, the rate of growth above 1.2% per year is enough to reduce the rate of unemployment from its current level of 8%. In 2009, dlnG=-0.033 y^-1 and the rate of unemployment rose by 4.7%. In 2010, the change rate of real GDP per capita was +0.021y^-1 and the rate of unemployment fell by 0.3%.   For Australia, the following equation was estimated with a structural break around 1995:  

dlnG = -1.7du + 2.4, t<1995

dlnG = -3.0du + 1.2, t>1994       (6) 

The timing of this break is different from those obtained before but the shift in the slope and intercept is big enough to consider it with confidence. It is likely that the structural break was induced by the introduction of a new monetary policy in 1994 (RBA, 1994).

 

Figure 1.  The link between the du and dlnG in the U.S. as described by relationship (2) with a structural break in 1984 

Figure 7 displays the measured and predicted curves for dlnG. The overall agreement is not good with R²=0.40 for the period between 1968 and 2010. This low correlation coefficient is associated with the high volatility in both time series. When smoothed with MA(3), the curves in Figure 7 show a much better resemblance. For Australia, the rate of growth above 1.2% per year is enough to reduce the rate of unemployment from its current level of 5.2% (2010). It is similar to Canada. 

Finally, the case of Spain is a decisive one. The rate of unemployment in Spain is extremely high and has been varying in a wider range since the 1960s. This is a big challenge for Okun’s law. We have obtained the following relationship with a structural break in 1987:  

dlnG = -2.0du + 5.0, t<1987

dlnG = -0.8du + 2.1, t>1986                     (7) 

The timing of this break practically coincides with those in other countries. The sensitivity of unemployment to real economic growth rose significantly in 1987. 

Figure 8 displays the measured and predicted curves for dlnG. The overall agreement is not good with R²=0.59 for the period between 1961 and 2010. When smoothed with MA(3), the curves in Figure 8 show an extraordinary agreement but one can also introduce another structural break near 1968.

Figure 2.  A scatter plot du against dlnG from Figure 1with a linear regression line. R²=0.84.

Figure 3. The model error for the U.S.

Figure 4.  Observed and predicted dlnG for France. The lower panel presents the curves smoothed with MA(3).

Figure 5.  Observed and predicted dlnG for the UK. The lower panel presents the curves smoothed with MA(3). 

Figure 6.  Observed and predicted dlnG in Canada. The lower panel presents the curves smoothed with MA(3).

Figure 7.  Observed and predicted dlnG in Australia. The lower panel presents the curves smoothed with MA(3).

Figure 8.  Observed and predicted dlnG in Spain. The lower panel presents the curves smoothed with MA(3).

Conclusion

With real GDP per capita instead of the overall GDP, Okun’s law demonstrates an extraordinary predictive power for the biggest developed countries. One can accurately describe the dynamics of unemployment since the 1960s. The currently high levels of unemployment in developed countries cannot be reduced without fast economic growth well above 2% per year. In that sense, there are no structural unemployment components in the currently high rates of unemployment in the studied countries. 

References

Altig, D., T. Fitzgerald, and P. Rupert. (1997). Okun’s Law Revisited: Should We Worry About Low Unemployment?” Federal Reserve Bank of Cleveland, Economic Commentary.

Conference Board. (2011).  Total economy database. http://www.conference-board.org/data/economydatabase/

Diamond, P. (2011). Unemployment, Vacancies, Wages. American Economic Review, 101(4): 1045–72.

Knotek, E. S. II. (2007). How Useful is Okun’s Law?, Federal Reserve Bank of Kansas City Economic Review, 4th Quarter, 73-103.

Mortensen, D. T. and E. Nagypal. (2007). More on Unemployment and Vacancy Fluctuations, Review of Economic Dynamics, 10 (3): 327{347.

Okun, A. M. (1962). Potential GNP: Its Measurement and Significance, American Statistical Association, Proceedings of the Business and Economics Statistics Section, 98–104.

Organization of Economic Cooperation and Development (2011). Original release data and revisions database. http://stats.oecd.org/mei/default.asp?rev=1

Pissarides, C. A. (2000). Equilibrium Unemployment Theory, Cambridge: MIT.

Reserve Bank of Australia. (1994). 1994 Report and Financial Statements. Reserve Bank of Australia. Sydney

Tillmann,  P. (2010). Do FOMC members believe in Okun's Law? Economics Bulletin,  30, No. 3, 2398-2404.