The Okun's integral law for Australia revisited

Three and a half years ago, I reported that Australia gives the best example of accurate quantitative prediction of unemployment in developed countries and therefore I felt satisfaction. Historically, we published a paper on Okun's in developed countries 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 before 2010 and we used only 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. Essentially, our model says that the current level of unemployment is the integral effect of the historical growth in GDP per capita. Then the change in unemployment, du, is proportional to the growth rate in GDP per capita, whcih can be expressed as dlnG. This is the differential (dynamic) form of the Okun's law.

For Australia, we estimated an integral model with one 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 1991

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

This is an update with new data for the years between 2012 and 2016 obtained from:  real GDP (GK per capita)  from the Total Economic Database, and the rate of unemployment from the OECD. 

Figure 1 depicts the observed and predicted curves of the unemployment rate. Statistically, the agreement is better than three years ago, when it was excellent. Figure 2 shows that when the observed time series is regressed against the predicted one, R²=0.88 (0.86 in 2013 and 0.84 in 2011).  The integral form of the dynamic Okun’s law (1) is characterized by a standard error of 0.7% for the period between 1975 and 2016. The average rate of unemployment for the same period is 7.0% with a standard deviation of the annual increment of 1.4%.  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.

I have to repeat it again and again. 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 exiting when this concept is different from the mainstream one. 

Figure 1. The observed and predicted rate of unemployment in Australia between 1975 and 2015. The regression line is red.

Figure 2. The measured time series is regressed against the predicted one. R²=0.88 with both time series likely to be stationary.

  

Figure 3. The residual error of the unemployment model. 

In 2008, we accurately predicted the evolution of unemployment rate in Italy!

In this blog, three and a half years ago we revisited our prediction of the rate of unemployment in Italy, which had been made in our 2008 paper.  Five years after this publication, we found that the accuracy of prediction was excellent. We decided that our  model works well. Since the model has a natural 11-year horizon, in this post we check our original (2008!) prediction for 2013 and 2016 (preliminary) using new estimates.  According to the OECD, the unemployment rate in 2015 is 12.0%. For 2016, the rate is 11.6%.  There is no doubt; these values again fully validate our model of unemployment as a function of the change in labour force. Moreover, our model has predicted two pivot points in the unemployment rate – in 2008 and 2014. There was a peak observed in 2014 and currently the rate of unemployment is falling.  

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 overall 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 2016 was predicted almost exactly. (If anybody knows a better prediction in 2008 of the 2016 unemployment rate, please give us the link.)  

The fit between predictions and observations is the best validation of any quantitative model. No other macroeconomic model is capable to describe such dramatic turns many years ahead. 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 in order to reduce unemployment in the second half of 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. 

Comprehensive recovery of a weak aftershock sequence in the North Atlantic using waveform cross correlation

Full text of this paper is available on arxiv.org

Abstract
We apply cross correlation between multichannel seismic waveforms as a technique for signal detection and automatic event building at the International Data Centre (IDC). This technique allows detecting signals with amplitudes by at least a factor of two lower than those found in the current version of IDC processing. Previously, we processed with a cross correlation detector aftershock sequences of a large earthquake with thousands of aftershocks detected by the International Monitoring System (IMS) and a middle-size earthquake (hundreds of aftershocks). Our study has revealed that the official Reviewed Event Bulletin (REB) of the IDC misses from 50% to 70% valid seismic events. Since the IDC is a major contributor to the International Seismological Centre (ISC) these extra events together with the associated arrivals are missing from the ISC bulletin which is an open data source for the broader seismological and geophysical community.Here, we assess the ultimate resolution of the cross correlation technique with specific IDC constraints. The aftershock sequence of the October 5, 2011 mb(IDC)4.2 earthquake in the North Atlantic is an example of a weak sequence and includes only 38 REB events. The number and quality of these REB events, which are used as master events, allow conducting a comprehensive interactive review by experienced analysts of all event hypotheses obtained by the cross correlation technique. In an iterative procedure starting from the main shock, all 38 REB events were found and analysts added 26 REB events. Therefore, the cross correlation pipeline reduces the detection threshold by a factor of 2 to 3 and approximately doubles the number of events in the REB, and thus, in the ISC bulletin for the North Atlantic.

have a happy 2017 recession

Approximately 10 years ago we presented our macroeconomic model explaining the evolution of real GDP per capita in the USA [1, 2, 3] and other developed countries [4]. This model was formally tested by econometric tools for cointegration [5]. Standard tests have proven that the underlying concept is valid. 

Our model does explain the past measurements of real GDP as driven by the only population related variable – the influx of fresh blood - young people. Variations in the rate of growth for a given economy is fully defined by the change in the number of youngsters entering this economy with all their input to the future, including future credits.  Some of major results were presented in this blog (e.g., here and here). 

The power of our model is not in explanation of the past, but in prediction of the future. We can predict at a 9-year horizon for the USA using population measurements and at a longer horizon with population projections. In this blog, we have not been reporting on this model since 2011, however, because of no changes predicted after the 2009 recession. Today, we present a forecast of a dramatic fall in real GDP per capita in 2017. Figure 1 compares the measured rate of growth in real GDP per capita  (dGDPpc/GDPpc), as obtained from the BEA’s quarterly tables,  and that  predicted by the change rate of the number of 9-year-olds, dN9/N9, as projected by the Census Bureau. Since the 2009 recession is well explained (actually predicted) by the same data we consider the probability of the 2017 recession as very high. In essence, it might be even deeper than in 2009. 

Figure 1. The measured change in the number of 9-year-olds, dN9/N9, and that predicted from the change in real GDP per capita (0.5dGDPpc/GDPpc). 

Food will be getting cheaper during the next decade

We did not report on the difference between the core consumer price index (cCPI) and the index for food (less beverages) since 2013, when we reported the overall fall in food price in the USA. This update is a bit late considering our promise to update at an annual rate, but the current trend in the discussed difference is so strong and indicative that we could not miss the opportunity to praise the success of our 8-year-old prediction.

So we continue reporting on and predicting the evolution of the difference between the core consumer price index (cCPI) and the index for food (less beverages).  Previously, we confirmed in many posts (see this blog) and papers [1, 2] that this difference had been following a long-term negative and linear (time) trend since 2001.  Originally, we predicted a turn to a positive trend in 2014. Five years ago, we expected the turn to a positive trend in 2012. In Figure 1, one can observe that the turn actually occurred in November 2014 and the current trend is positive – the price index of food grows at a lower rate than that of the core CPI.

For an investor dealing with commodities, the index of food, which is growing at a rate lower than the core CPI, is an important reference for any action. Food price affects not only economic but also social and political processes.

Figure 1 depict the most recent period. In 2008, when we first addressed the issue of sustainable trends in CPIs, the trend line was much steeper than now and intersected the zero line in 2014.  This was our initial estimate of the turning point for the negative trend. The zero line was considered as a natural level of reflection.  In the beginning of 2009, the difference reached the bottom and turned to a positive one, although not for long. The growth in food prices restarted in 2010. In the end of 2011, the difference had a short stop which we likely misinterpreted as a manifestation of the transition to a positive trend. Since October 2011, the difference has not been changing much with just a slight positive trend. In 2014, the studied difference began to grow and will likely grow another decade.

Food is getting cheaper in relative terms.

Figure 1. The difference between the core CPI and the price index of food since 2002. 

Oil price will not grow during the next 15 years

In 2008, we published a paper on the presence of long-term sustainable trends in the differences between various components of the CPI in the USA. We started with the difference between the core CPI (i.e. CPI less food and energy) and the overall CPI. Two Figures below are borrowed from the paper:

Figure 1. Linear regression of the difference between the core CPI and CPI for the period from 1981 to 1999.  The goodness-of-fit is 0.96, and the slope is 0.67.

Figure 2. Linear regression of the difference between the core CPI and CPI after 2002.  The goodness-of-fit is 0.86, and the tangent is -1.57.  An elevated volatility has been observed from 2005.

In this eight-year-old paper as well as in later papers on the sustainable trends in the CPI and PPI (see here), we suggested that the negative trend shown in Figure 2 should reach some bottom point and then turn to a positive trend. It was also mentioned that such processes in the past had been accompanied by an elevated volatility in the difference, i.e. high amplitude fluctuations.

Eight years later, we are happy to state that our predictions were accurate - the trend now positive and is likely approaching the mid-point of the linear segment. Since the very beginning, we have been reporting on the evolution of the difference between the headline CPI and core CPI many times.

Our concept of cyclic evolution was formulated in 2007. Essentially, this concept says that the future trajectory has to repeat the path observed thirty years ago, i.e. the cycle has a 30 years period. Figure 3 presents the state of the CPI difference normalized to the headline CPI as observed since the late 1950s (dotted red line) and the predicted trajectory (blue dotted line), which is the current curve shifted by 30 years ahead. Figure 4 presents corresponding linear trends with all volatile periods removed.

We can say that eight years ago we successfully predicted the era of low energy+food prices (core CPI is the headline CPI less food and energy) since 2014 and for the following 20 years. For energy companies, Figure 4 implies that oil/energy prices will be on a negative trend until 2030. We are just in the middle of the fall, which is supposed to be dramatic in the next two to four years. All measured taken by oil-producing countries are worthless  -

 actual economic forces are beyond simple control. 

Figure 3. The difference between core (cCPI) and headline (CPI) CPI normalized to CPI. The period of cycle is 30 years and dotted  blue line presents the future of the normalized difference before 2044.

Figure 4. The current state of our prediction. Red line follows up the blue line.

Tahiti hemisphere

The International monitoring system of the CTBTO includes seismic station PPT, which is situated near Papeete, Tahiti. This station is a rather isolated one. Working with its data at an everyday basis I could not imagine  how beautiful is the Earth for a space traveler flying directly to PPT. Google Earth gave me a striking view on the Papeete hemisphere.