Income inequality raised! Blame the Census Bureau

The Census Bureau has reported income distribution in the USA for 2011. There is a number of posts and comments on increasing income inequality. Before writing writing on inequality one should first learn some definitions and measuring procedures. The reason behind the reported rise in (household) Gini ratio is not the change in income inequality per ce, but new population controls introduced after the 2010 census. All statistical agencies in the US (and supposedly in other countries as well) are famous for producing time series incompatible in time. Due to change in definitions, survey procedures and coverage the time series for inflation (and thus real GDP), unemployment, productivity, and so on, are not continuous. This is like to change from mph to km/h and back every five to ten years and then average the speed. Interestingly, all  these agencies are not guilty since they openly describe this incompatibility in their documents. These are the commenters who are careless.

In the CB's report for 2011, the Gini ratio for individuals has jumped to 0.510 in 2011 from 0.503 in 2010. (  It was near 0.503 through the 2000s. ) This would be the most dramatic jump in income inequality in the USA since  the start of measurement in 1947, if a not a  pure artifact.
If you would like to know the truth do not trust experts! Dig into raw data and documentation.

The use of “grand master” events for waveform cross correlation

This is for the 2012 AGU Fall Meeting.

Abstract
More than 90% of seismic events recorded at teleseismic and regional distances are from a few relatively small geographic regions, causing the distribution of seismic events in the Reviewed Event Bulletin (REB) of the International Data Centre (IDC) to be inhomogeneous. When considering the waveform cross correlation technique for the detection, phase association and event building processes that are performed as part of monitoring compliance of the Comprehensive Nuclear-Test-Ban Treaty one is confined to the areas with historical seismicity. The backbone of the waveform cross correlation method is the set of master events (earthquakes or explosions) with high quality waveform templates that have been recorded at array stations of the International Monitoring System (IMS). These master events have to be evenly distributed and their template waveforms should be representative and pure (ie., with negligible noise input). The coverage and characteristic of historical seismicity observed by the IMS seismic network since 2001 does not match these requirements. The current REB allows selection of a number of master events in seismically active areas but even in these areas the quality of templates varies from master to master. In this study, we propose to replicate waveforms from the best master event over a regular grid expanding several hundred kilometers from its epicenter. We call this master event the “grand master”. For each grid point, i.e. replicated grand master event, the template has the relevant theoretical time delays between individual sensors at the involved array stations. Since the empirical deviations from the theoretical arrival times at these sensors are inherently related to seismic velocity structure beneath the station, they are fully retained for all replicated master events within several hundred kilometers. These empirical travel time residuals are small but play a key role in the waveform cross correlation method for weak signals. They define a higher sensitivity for the cross correlation method relative to beam forming method where the channels are stacked with the theoretical delays. As a result, the waveform cross correlation technique detects more valid signals at local, regional, and global levels.

In assessing the performance of the grand master approach the aftershock sequence of the April 11, 2012 Sumatra earthquake (Ms(IDC)=8.2) was used, with16 master events (actual aftershocks) distributed over an area of 500x500 km. Waveform templates from the best master event over a regular grid with 1o spacing have been replicated. There are two principal procedures in comparing the performance of actual and replicated master events as associated with various characteristics/distributions of detections, as well as with the number of event hypotheses built with the varying sets of stations and locations. Both methods have shown the superiority of the replicated events distributed over a regular grid. Such distributions also reduce the volume of calculations by two orders of magnitude. When appropriately chosen, the grand master allows a reduction in the magnitude threshold of seismic monitoring and improving the accuracy and uncertainty of event locations at the IDC to the level of the best located events. When a ground truth event is available, one can expand its influence over hundreds of kilometers.



Key words: array seismology, waveform cross correlation, seismicity, master events, IDC, CTBT

Sumatera 2012 aftershocks: REB vs. waveform cross-correlation bulletin

I am working on an exiting problem associated with my professional duties - waveform cross correlation. Unfortunately, have no time to blog on economics. This post is to attract attention to our poster to be presented at the Monitoring Research Review 2012.

 Our objective is to assess the performance of waveform cross-correlation technique, as applied to automatic processing of the aftershock sequence of the 2012 Sumatera (Mw=8.6) earthquake, relative to the Reviewed Event Bulletin (REB) issued by the International Data Centre. The REB includes ~1150 aftershocks between April 11 and May 23 with (IDC) body wave magnitudes from 3.05 to 6.19. The aftershocks cover a slightly unusual V-shaped area. The cross correlation technique allows a flexible approach to signal detection, phase association and event building. To automatically recover the sequence, we selected sixteen aftershocks with mb(IDC) between 4.5 and 5.0 from the IDC Standard Event List (SEL3) available on April 13. These events evenly but sparsely cover the whole area. After a superficial manual review these aftershocks were designated as master events. Waveform templates from only seven array stations with the largest SNR for the signals from the main shock were used to calculate cross-correlation coefficients. All detections obtained by cross-correlation were then used to build events according to the IDC definition, i.e. at least three primary stations with accurate arrival times, azimuth and slowness estimates. The qualified events populated the cross-correlation Standard Event List (XSEL). The XSEL was compared with two IDC products: the final automatic bulletin (SEL3) and the interactive bulletin (REB). There are some valid events missed in the REB but found in the XSEL. As a bootstrap exercise to confirm the significance of the XSEL findings, a large portion of the newly built events was reviewed interactively by experienced analysts. In order to investigate the influence of all defining parameters (cross correlation coefficient threshold and SNR, F-statistics and F-K analysis, azimuth and slowness estimates, relative magnitude, etc.) on the final XSEL we have constructed relevant frequency distributions for all detections and only for those which were associated with the XSEL events. These distributions are also station and master dependent. This allows the introduction of accurate threshold for all defining parameters.


Key words: cross-correlation, IDC, REB, Sumatera

Why price inflation in developed countries is systematically underestimated

Following several posts in this blog, I've compiled a paper (link to a complete pdf version):

 Why price inflation in developed countries is systematically underestimated

Abstract
There is an extensive historical dataset on real GDP per capita prepared by Angus Maddison. This dataset covers the period since 1870 with continuous annual estimates in developed countries. All time series for individual economies have a clear structural break between 1940 and 1950. The behavior before 1940 and after 1950 can be accurately (R2 from 0.7 to 0.99) approximated by linear time trends. The corresponding slopes of regressions lines before and after the break differ by a factor of 4 (Switzerland) to 19 (Spain). We have extrapolated the early trends into the second interval and obtained much lower estimates of real GDP per capita in 2011: from 2.4 (Switzerland) to 5.0 (Japan) times smaller than the current levels. When the current linear trends are extrapolated into the past, they intercept the zero line between 1908 (Switzerland) and 1944 (Japan). There is likely an internal conflict between the estimating procedures before 1940 and after 1950. A reasonable explanation of the discrepancy is that the GDP deflator in developed countries has been highly underestimated since 1950. In the USA, the GDP deflator is underestimated by a factor of 1.4. This is exactly the ratio of the interest rate controlled by the Federal Reserve and the rate of inflation. Hence, the Federal Reserve actually retains its interest rate at the level of true price inflation when corrected for the bias in the GDP deflator.

Real GDP per capita since 1870

We've just finished and published a working paper. The reader may want to download it from the MPRA: Real GDP per capita since 1870

Abstract

The growth rate of real GDP per capita in the biggest OECD countries is represented as a sum of two components – a steadily decreasing trend and fluctuations related to the change in some specific age population. The long term trend in the growth rate is modelled by an inverse function of real GDP per capita with a constant numerator. This numerator is equivalent to a constant annual increment of real GDP per capita. For the most advanced economies, the GDP estimates between 1950 and 2007 have shown very weak and statistically insignificant linear trends (both positive and negative) in the annual increment. The fluctuations around relevant mean increments are characterized by practically normal distribution. For many countries, there exist historical estimates of real GDP since 1870. These estimates extend the time span of our analysis together with a few new estimates from 2008 to 2011.  There are severe structural breaks in the corresponding time series between 1940 and 1950, with the slope of linear regression increasing by a factor of 4.0 (Switzerland) to 22.1 (Spain). Therefore, the GDP estimates before 1940 and after 1950 have been analysed separately. All findings of the original study are validated by the newly available data. The most important is that all slopes (except that for Australia after 1950)  of the regression lines obtained for the annual increments of real GDP per capita are small and statistically insignificant, i.e. one cannot reject the null hypothesis of a zero slope and thus constant increment. Hence the growth in real GDP per capita is a linear one since 1870 with a break in slope between 1940 and 1950.  

Key words: GDP, model, economic growth, inertia, trend, OECD

Time to buy SPY

A month ago, we predicted a drop in the S&P 500 to the level of 1300 by the end of May. We also suggested buying the index when it is 1300.  Both are done by now. We are waiting the level 1500 in October 2013 to sell and fix profit. The explanation from April is fully repeated below. The red segment in Figure 2 is now black since the prediction is realized.

We also expect oil price to drop further and force deflation by the end of 2012.

This repeats our previous postSeveral days ago we predicted the current fall in the S&P 500 index. For this reason, we did not enter the stock market and instead invested in a defensive portfolio. We are waiting the level of 1350.  The reason is explained below.

Figure 1 shows the evolution of the S&P 500 index since 1980. After 1995, the index behavior reveals some saw teeth with peaks in 2000 and 2007. The current growth resembles those between 1997 and 2000 and from 2003 and 2007.  There are two deep troughs in 2002 and 2009 which are marked by red and green lines, respectively.  For the current analysis we assume that the repeated shape of the teeth is likely induced by a degree of similarity in the evolution of macroeconomic variables. The intuition behind such an assumption is obvious – in the long run the market depends on the overall economic growth.

Having two peaks and troughs between 1995 and 2009, what can we say about the current growth in the S&P 500? Before making any statistical estimates, in Figure 2 we have shifted forward the original curve in Figure 1 in order to match the 2009 trough (blue line).  When the 2002 and 2009 troughs are matched, one can see that the current growth path closely repeats that after 2002. The first big deviation from the blues curve in Figure 2 started in 2011 and had amplitude of 150 units (from 1210 to 1360).  The black curve returned to the blue one in August/September 2011. A month ago, we observed a middle-size deviation of about 100 units and predicted that the index will have a negative correction down to the level of 1300 any time soon.  If the index will repeat the path of the previous rally one-to-one, one may expect the peak level of 1500 in the end of 2013.  In two to four weeks it might be a good time to invest for a 15% return cumulated to October 2013 (but not more than two months), when the negative correction is over. 

With the S&P 500 falling down to 1350, the prediction does not seem inappropriate. The next several weeks should decide on the new level. In Figure 2, we have drawn the fall we expect by the end of May 2012. We would wait by the end of April to decide on the following move in the S&P 500. If the current fall will reach 1300, it’s likely a good time to buy. Otherwise, the end of May is the horizon to wait the bottom.

Figure 1. The evolution of the S&P 500 market index between 1980 and 2012. 

Figure 2. The curve in Figure 1 peak is shifted forward to match the 2009 trough (blue line). Red line – expected fall in the S&P 500: from 1400 in Mach to 1300 in May.

On comprehensive recovery of an aftershock sequence with cross correlation

The name of this blog suggests that I am a physicist trying to introduce some principal rules of  mechanics into economics. Economics is a hobby rather than every day activity. At some point, it's worth  to present my professional work. Here is our poster from the 2012  General Assembly  of the European Geophysical Union.  

Abstract and Poster

I. Kitov, D. Bobrov, J. Coyne, and G. Turyomurugyendo

CTBTO, IDC, Vienna, Austria (Ivan.Kitov@ctbto.org)

We have introduced cross correlation between seismic waveforms as a technique for signal detection and automatic event building at the International Data Centre (IDC) of the Comprehensive Nuclear-Test-Ban Treaty Organization. The intuition behind signal detection is simple – small and mid-sized seismic events close in space should produce similar signals at the same seismic stations. Equivalently, these signals have to be characterized by a high cross correlation coefficient. For array stations with many individual sensors distributed over a large area, signals from events at distances beyond, say, 50 km, are subject to destructive interference when cross correlated due to changing time delays between various channels. Thus, any cross correlation coefficient above some predefined threshold can be considered as a signature of a valid signal. With a dense grid of master events (spacing between adjacent masters between 20 km and 50 km corresponds to the statistically estimated correlation distance) with high quality (signal-to-noise ratio above 10) template waveforms at primary array stations of the International Monitoring System one can detect signals from and then build natural and manmade seismic events close to the master ones. The use of cross correlation allows detecting smaller signals (sometimes below noise level) than provided by the current IDC detecting techniques. As a result it is possible to automatically build from 50% to 100% more valid seismic events than included in the Reviewed Event Bulletin (REB).We have developed a tentative pipeline for automatic processing at the IDC. It includes three major stages. Firstly, we calculate cross correlation coefficient for a given master and continuous waveforms at the same stations and carry out signal detection as based on the statistical behavior of signal-to-noise ratio of the cross correlation coefficient. Secondly, a thorough screening is performed for all obtained signals using f-k analysis and F-statistics as applied to the cross-correlation traces at individual channels of all included array stations. Thirdly, local (i.e. confined to the correlation distance around the master event) association of origin times of all qualified signals is fulfilled. These origin times are calculated from the arrival times of these signals, which are reduced to the origin times by the travel times from the master event. An aftershock sequence of a mid-size earthquake is an ideal case to test cross correlation techniques for autiomatic event building. All events should be close to the mainshock and occur within several days. Here we analyse the aftershock sequence of an earthquake in the North Atlantic Ocean with mb(IDC)=4.79. The REB includes 38 events at distances less than 150 km from the mainshock. Our ultimate goal is to excersice the complete iterative procedure to find all possible aftershocks.We start with the mainshock and recover ten aftershocks with the largest number of stations to produce an initial set of master events with the highest quality templates. Then we find all aftershocks in the REB and many additional events, which were not originally found by the IDC. Using all events found after the first iteration as master events we find new events, which are also used in the next iteration. The iterative process stops when no new events can be found. In that sense the final set of aftershocks obtained with cross correlation is a comprehensive one.