The beauty of science II. Predicting the rate of unemployment in Australia

A few hours ago, I reported that Canada gives the best example of accurate quantitative prediction of unemployment in developed countries and therefore extreme satisfaction for a researcher. I changed my mind when revisited the case of Australia with new data - real GDP (GK per capita) data from the Total Economic Database and the rate of unemployment from the OECD. Two years ago, I presented a model based on data from the same sources and found relatively big discrepancy after 2000. In the new revision of the same data, this discrepancy have evaporated.

Historically, we published a paper in the Journal of Theoretical and Practical Research in Economic Fields in 2012. We presented the first version of the modified Okun’s law for developed countries including Australia. The model was estimated till 2010 and used the data available in 2011. Briefly, the model is estimated by the LSQ technique applied to the integral version of Okun’s law:

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

where u(t) is the predicted rate of unemployment at time t, G is the level of real GDP per capita, a and b are empirical coefficients. For Australia, we estimated the model with a structural break allowed by data somewhere between 1980 and 2000. The best-fit (dynamic) model minimizing the RMS error of the cumulative model (1) with the new data revision is as follows:

du = -0.69dlnG + 1.50, t before 1992

du = -0.45dlnG + 0.75, t after 1991 (2)

Originally, the model included the structural break neat 1995. With the new data the overall fit is better and the year of break moved to 1991, which is related to major revision of unemployment definition. The new model suggests a drop in slope and a big change in the intercept around 1991. Figure 1 depicts the observed and predicted curves of the unemployment rate. The agreement is very good. Figure 2 shows that when the observed time series is regressed against the predicted one, R²=0.86 (0.84 in 2011).  The integral form of the dynamic Okun’s law (1) is characterized by a standard error of 0.72% for the period between 1971 and 2012. The average rate of unemployment for the same period is 6.9% with a standard deviation of the annual increment of 1.9%.  This is an extremely accurate prediction considering the accuracy of GDP (~1% per year) and unemployment (0.3% to 0.4%) estimates. The whole discrepancy is related to the measurement errors and thus the residual error shown in Figure 3 is an I(0) random process.  

The rate of unemployment depends on the cumulative change in real GDP per capita, as relationship (1) implies. To reduce the rate of unemployment in Australia, the rate of GDP (real per capita) growth must be above 1.7% per year.  

 

Figure 1. The observed and predicted rate of unemployment in Australia between 1971 and 2012. 

 

Figure 2. The measured time series is regressed against the predicted one. R²=0.86 with both time series likely to be stationary.

Figure 3. The residual error of the unemployment model.

So, I have to repeat. The beauty of science is the accuracy of prediction. It is difficult to express the feelings of a researcher than new observations fit his predictions based on a simple concept.  It is especially sweet when this concept is different from the mainstream one.

The beauty of science. Unemployment in Canada

The beauty of science is the accuracy of prediction. It is difficult to express the feelings of a researcher than new observations fit his predictions based on a simple concept.  It is especially sweet when this concept is different from the mainstream one. I am sure that economists never feel like that with all models flawed. Here, I present one of many cases of accurate predictions based on the link between GDP and unemployment, which is a modified Okun’s law in an integral form.

 

Canada provides an excellent set of macroeconomic data which can be described by a few deterministic links with a high level of reliability and confidence. We have retrieved real GDP (GK per capita) data from the Total Economic Database and the rate of unemployment from the OECD. In 2012, we published a paper in the Journal of Theoretical and Practical Research in Economic Fields, where presented the first version of the modified Okun’s law for developed countries including Canada. The model was estimated till 2010 and used the data available in 2011. The original model for Canada was also presented in this blog in 2011. It’s time to revisit the model and its predictions.

Overall, the model is estimated using the 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 predicted rate of unemployment at time t, G is the level of real GDP per capita, a and b are empirical coefficients. For Canada, we estimated the model with a structural break allowed by data somewhere between 1980 and 1990. The best-fit (dynamic) model minimizing the RMS error of the cumulative model (1) is as follows:

du = -0.28dlnG + 1.16, t<1983
du = -0.28dlnG + 0.30, t>1982 (2)

 

 
This model suggests no shift in the slope and a bigger change in the intercept around 1983. Figure 1 depicts the observed and predicted curves of the unemployment rate. Considering the accuracy of measurements for both involved variable the fit is excellent. The integral form of the dynamic Okun’s law (1) is characterized by a standard error of 0.67% for the period between 1971 and 2012. The average rate of unemployment for the same period is 8.12% with a standard deviation of the annual increment of 0.92%.  Figure 2 shows that when the observed time series is regressed against the predicted one, R²=0.87.  Here we do not test both time series for stationarity but presume that the rate of unemployment has to be a stationary time series in the long run.
One can suggest that the rate of unemployment has been driven by real economic growth and there is no much room for other macroeconomic variable to intervene. Personally, I admire the performance of this simple model and will keep reporting on it for Canada, but also for Spain, France, etc.

Figure 1. The observed and predicted rate of unemployment in the Canada between 1970 and 2010. 

Figure 2. The measured time series is regressed against the predicted one. R²=0.87 with both time series likely to be stationary.

CPI inflation in the UK will not fall below 2.5% to 3% per year till 2020

Two years ago we presented a model for the rate of inflation in the UK and a prediction for 2010-2020. Actual rate in 2011 and 2012 was very close to the predicted one as Figure 1 demonstrates. There is no change to the model and we foresee another ten years of a reactively large (CPI) inflation rate in the UK – nearly 3% per year. In 2013, the predicted rate is 2.9%.  

According to our concept, the original paper was published by  the Euro Area Business Cycle Network, there exists a long-term equilibrium link between price inflation, CPI_t, unemployment, u_t, and the rate of change of labour force, l_t=dLF/LFdt. We follow up our predictions for many counties in this blog.  The UK is one of the world biggest economies with a relatively good statistics started chiefly from 1973.  It is a major challenge to model inflation in the UK using our approach.

There is a structural break in the link between three defining variables in 1985, which is purely artificial and induced by the change in measurement units and definitions. Accordingly, we have to distinguish two periods to fit observations: before and after 1985:  

CPI_t = 1.0l_t  + u_t  - 0.046; t>1985

CPI_t = -1.0l_t -1.7 u_t + .025; t<1985               (1) 

For both periods, inflation does not lag behind unemployment and l_t. Figure 1 presents the observed and predicted CPI curves, all variables were obtained from the OECD database in 2013. All in all, the predictive power of the model is good and timely fits major peaks and troughs. The change from negative to positive linear coefficient in 1985 needs a special explanation. But such effects were observed in other developed countries as well. 

The NSO's labour force projection helps to predict the future inflation. Since the inflow of new employees is still positive,  l_t >0, and the rate of unemployment does not foresees any dramatic decline in the long run one can be sure that inflation will be positive in the near future, as Figure 2 predicts. 

 

Figure 1. The predicted and measured rate of consumer price inflation (CPI) in the UK.

 

 

Figure 2. The predicted rate of CPI inflation in the UK between 2008 and 2020 estimated from the labour force projection by the NSO.

The rate of participation in labor force in the U.S. will regain 0.7% in 2013-2014

Five years ago we published a paper 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. We used the change in a younger population cohort and foresaw the fall by 1.5% in 2010.  Figure 1 reproduces Figure 8 from the paper. This dramatic fall happened on time. It was a success of the model.

Figure 1. Prediction of the LFP evolution in the USA between 2000 and 2014 from the number of 3-year-olds. Flat segment between 2004 and 2009 will end up in a rapid drop by 1.3% after 2010. This is the effect of an elevated (above potential) real economic growth.

 The predicted curve in Figure 2 was obtained from real GDP per capita as a proxy to the population change (see the article for details). Both curves in Figure 2 almost coincide between 1960 and 2012. The largest deviations are observed in the years of biggest revisions to the LFP after decennial censuses and changes to GDP definitions. Therefore, they can be neglected as having artificial character.  

The model predicts the secular change in the LFP!

In 2011 and 2012, the rate of participation is expected to hover near 64.5%, but actually fell to 63.7%. As an option explaining the observed deviation, the rate of GDP growth in 2011 and 2012 could be overestimated. As an alternative, the rate of participation in labor force may rise by 0.7%. This is in line with the predicted fall in the rate of unemployment to 6% by the end of 2013.

Figure 2. Observed and predicted LFP in the U.S.

We accurately predicted the current rate of unemployment in Italy in 2008 !

A year ago, we revisited our prediction of the rate of unemployment in Italy made in 2008 and found that it was excellent. The model worked well. As it has an 11-year horizon, we can check our old prediction for 2012 and 2013 (preliminary). A new estimate of unemployment rate in 2012 is 10.6%. For 2013, the rate is 11.5 in March.  There is no doubt, these values fully validate our model of unemployment as a function of the change in labour force.    

We introduced the model of unemployment in Italy in 2008 with data available only for 2006. The rate of unemployment was near its bottom at the level of 6%. The model predicted a long-term growth in the rate unemployment to the level of 11% in 2013-2014. 

The agreement between the measured and predicted unemployment estimates in Italy validates our concept which states that there exists a long-term equilibrium link between unemployment, u_t, and the rate of change of labour force, l_t=dLF/LFdt. Italy is a unique economy to validate this link because the time lag of unemployment behind l_t  is eleven (!) years.   

The estimation method is standard – we seek for the best overall fit between observed and predicted curves by the LSQR method. All in all, the best-fit equation is as follows: 

u_t = 5.0l_t-11  + 0.07    (1) 

As mentioned above, the lead of l_t is eleven years. This defines the rate of unemployment many years ahead of the current change in labour force.  

Figure 1 presents the observed unemployment curve and that predicted using the rate of labour force change 11 years ago and equation (1). Since the estimates of labour force in Italy are very noisy we have smoothed the annual predicted curve with MA(5). All in all, the predictive power of the model is excellent and timely fits major peaks and troughs after 1988. The period between 2006 and 2013 was predicted almost exactly. (If anybody knows a better prediction in 2008 of 2013 unemployment rate please give us the link.)  This is the best validation of the model – it has successfully described a major turn in the evolution of unemployment near its bottom. No other macroeconomic model is capable to describe such dramatic turns many years ahead. Four years ago, we expected the peak in the rate of unemployment in 2013-2014 at the level of 11% (+5% from the level in 2008) and it has come! 

The evolution of the rate of unemployment in Italy is completely defined ten year ahead.  Since the linear coefficient in (1) is positive one needs to reduce the growth in labour force (see Figure 3) in order to reduce unemployment in the 2020s. For the 2010s everything is predefined already and the rate of unemployment will be high, i.e.  above 9%.

Figure 1. Observed and predicted rate of unemployment in Italy.

 

Figure 2. The rate of growth in labour force.

Waveform cross correlation at the International Data Centre: comparison with Reviewed Event Bulletin and regional catalogues

Another poster at the EGU 2013.

Abstract

Waveform cross correlation substantially  improves detection, phase association, and event building procedures at the International Data Centre (IDC) of the Comprehensive Nuclear-Test-Ban Treaty Organization. There were 50% to 100% events extra to the official Reviewed Event Bulletin  (REB) were found in the aftershock sequences of small, middle size, and very big earthquakes. Several per cent of the events reported in the REB were not found with cross correlation even when all aftershocks were used as master events. These REB events are scrutinized in interactive analysis in order to reveal the reason of the cross correlation failure. As a corroborative method, we use detailed regional catalogues, which often include aftershocks with magnitudes between 2.0 and 3.0. Since the resolution of regional networks is by at least one unit of magnitude higher, the REB events missed from the relevant regional catalogues are considered as bogus. We compare events by origin time and location because the regional networks and the International Monitoring System are based on different sets of seismic stations and phase comparison is not possible.   Three intracontinental sequences have been studied: after the March 20, 2008 earthquake in China (m_b(IDC)=5.4), the May 20, 2012 event in Italy (m_b(IDC)=5.3), and one earthquake (m_b(IDC)=5.6) in Virginia, USA (August 23, 2011).  Overall, most of the events not found by cross correlation are missing from the relevant regional catalogues. At the same time, these catalogues confirm most of additional REB events found only by cross correlation. This observation supports all previous findings of the improved quality of events built by cross correlation. 

Seismicity of the North Atlantic as measured by the International Data

I have uploaded a poster presented at the EGU 2013.

Abstract

The Technical Secretariat (TS) of the Comprehensive Nuclear Test-Ban Treaty Organization (CTBTO) will carry out the verification of the CTBT which obligates each State Party not to carry out nuclear explosions. The International Data Centre (IDC) receives, collects, processes, analyses, reports on and archives data from the International Monitoring System. The IDC is responsible for automatic and interactive processing of the International Monitoring  System (IMS) data and for standard IDC products. The IDC is also required by the Treaty to progressively enhance its technical capabilities. In this study, we use waveform cross correlation as a technique to improve the detection capability and reliability of the seismic part of the IMS. In order to quantitatively estimate the gain obtained  by cross correlation on the current sensitivity of automatic and interactive processing we compared seismic bulletins built for the North Atlantic (NA), which is a seismically isolated region with earthquakes concentrating around the Mid-Atlantic Ridge. This allows avoiding the spill-over of mislocated events between adjacent seismic regions and biases in the final bulletins: the Reviewed Event Bulletin (REB) issued by the IDC and the cross correlation Standard Event List (XSEL). To begin with, we cross correlated waveforms recorded at 18 IMS array stations from 1500 events reported in the REB between 2009 and 2011. The resulting cross correlation matrix revealed the best candidates for master events. We have selected 60 master events evenly distributed over the seismically active zone in the NA. High-quality signals (SNR>5.0) recorded by 10 most sensitive array stations were  used as waveform templates. These templates are used for a continuous calculation of cross correlation coefficients  in the first half of 2012. All detections obtained by cross-correlation are then used to build events according to the current IDC definition: at least three primary stations with accurate arrival times, azimuth and slowness estimates. The qualified event hypotheses populated the XSEL. In order to confirm the XSEL events not found in the REB, a portion of the newly built events was reviewed interactively by experienced analysts. The influence of all defining parameters (cross correlation coefficient threshold and SNR, fk-analysis, azimuth and slowness estimates, relative magnitude, etc.) on the final XSEL has been studied using the relevant frequency distributions for all detections vs. only for those which were associated with the XSEL events. These distributions are also station and master dependent. This allows estimating the thresholds for all defining parameters, which may be adjusted to balance the rate of missed events and false alarms.