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A 130-year long argument against the Solow growth model

Staff and Wire Reports — Fri, 10 Feb 2012 21:03:00 +0000

We have already presented strong quantitative arguments against the Solow growth model, which presumes that the rate of change in real GDP per capita must approach some constant level. In developed countries, the annual increments of real GDP per capita have been rather oscillating around constant level since 1955. We use the estimates of real GDP per capita published by the Conference Board’s total economy database. Since the late 1990s this database has been developed and maintained in conjunction with the Groningen Growth and Development Centre (University of Groningen, The Netherlands). As of the summer of 2007 the database has been transferred from the University of Groningen to The Conference Board and is maintained there. The GGDC also provides historical estimates of real GDP developed by Angus Maddison. It is instructive to use these historical estimates in order to reject the Solow model by empirical data.

Under our empirical framework [1,2,3], real GDP per capita in developed countries grows as a linear function of time, we call it inertial growth, when population pyramid does not change much in the long run:

G(t) = At + C (1)

Relationship (1) defines the linear trajectory of the GDP per capita, where C=G_i(t₀)=G(t₀) and t₀ is the starting time. In the regime of inertial growth, the real GDP per capita increases by the constant value A per time unit. The relative rate of growth along the inertial linear growth trend, g(t), is the reciprocal function of G:

g(t) = A/G(t) (2)

Relationship (2) implies that the rate of GDP growth will be asymptotically approaching zero, but the annual increment A will always be constant. This is different from the Solow model where the rate of growth is a positive (nonzero) value. Moreover, the absolute rate of GDP growth is constant and is equal to A [$/y]. This constant annual increment thus defines the constant “speed” of economic growth in a one-to-one analogy with Newton’s first law. Hence, one can consider the property of constant speed of real economic growth as “inertia of economic growth” or simply “inertia”.

In Figure 1, we present the estimates of annual increments of real GDP per capita in the USA since 1870. At first glance, these data support the Solow model, i.e. annual increments increase with time. However, we know that since 1955 the increment has been oscillating around constant level of $423 (2011 US dollars) and the accuracy of GDP measurements (actually obtained by reconstruction) before 1950 can hardly be characterized as a high one. In Figure 2, we display the estimates of annual increment since 1955 as measured by the Bureau of Economic Analysis. There is no linear time trend in the curve and thus the Solow model does not work well.

The period between 1940 and 1955 is characterized by extremely large oscillations. This period corresponds to the Second World War and the development of the concept of Gross Domestic Product (Simon Kuznets introduced this idea in 1934). Therefore, the war and the development of measurement procedure may introduce significant structural breaks in the time series and we remove the years between 1940 and 1955 from our consideration as a mixture of an artificial step in measurements (say, the transition from mph to km/h) and the effects of noneconomic factors in economic evolution. Figure 3 shows the period between 1871 and 1940 (70 years). Not surprisingly, there is no linear time trend and the overall length of the period when the Solow model is not applicable is now ~130 years.

All in all, the Solow model of economic growth (and all its branches and versions) contradicts hundred and fifty years of observations. We are going to report the evolution of real GDP per capita in other developed countries.

Figure 1. The estimates of annual increment of real GDP per capita in the USA since 1970.

Figure 2. Annual increments since 1955 as reported by the BEA. There is practically no linear trend.

Figure 3. The annual increment between 1871 and 1940. The mean value is $65.

Crude and steel – an unbreakable pair

Staff and Wire Reports — Fri, 10 Feb 2012 08:58:00 +0000

We have been reporting on the trade-off between the producer price index of crude oil (domestic production) and the PPI of iron&steel since 2009. It has been always a linear and lagged link between them. Our previous update included PPI data through July 2011. Here we present an annual wrap-up.

We reported that the PPI of crude oil had been likely evolving in sync with that of iron and steel, but with a lag of two months in September 2009. In order to present both indices in a comparable form, the difference between a given index, iPPI (i.e. iron&steel and crude), and the overall PPI was normalized to the PPI: (iPPI(t)-PPI(t))/PPI(t). These normalized differences represent the evolution of the rate of deviation from the PPI over years.

Figure 1 depicts the corresponding time histories of the normalized deviations from the PPI, including the most recent period through December 2011. Even a simple visual inspection reveals the following feature: the (normalized deviation from the PPI of the) index of iron and steel lags by approximately two months behind the (normalized) index of crude oil.

Figure 1. The deviation of the iron and steel price index and the index of crude oil from the PPI, normalized to the PPI.

In order to reduce both deviations to the same scale we additionally normalized the curves in Figure 1 to their peak values between 2005 and 2011.

(iPPI(t)-PPI(t))/[PPI(t)*max{iPPI-PPI)}]

This scaling allows a direct comparison of corresponding shapes. In Figure 2, we display the normalized index of iron and steel shifted by two months ahead to synchronize its peak with that observed in the normalized index for crude petroleum. The scaled index of crude demonstrates just short-term deviations from the index of iron and steel in the overall shape and timing of the peak and trough. Simple smoothing with MA(3) makes the curves resemblance even better. As an extra benefit of the resemblance, one can use the two-month lag to predict the future of the iron and steel price index.

Figure 2. Deviation of the iron and steel price index from the PPI, normalized to the PPI and the peak value after 2005 as compared to the deviations of the index for crude petroleum normalized in the same way. The normalized index for iron and steel is shifted two months ahead.

Conclusion

The link between oil and iron seems to be unbreakable. Between 2006 and 2012, the deviation of the price index of iron and steel from the PPI in the USA repeats the trajectory of the deviation of the index of crude petroleum (domestic production) with a two-month lag. Therefore, the prediction of iron and steel price for at this horizon is a straightforward one.

Implications of a Positively Correlated SPX and VIX

Staff and Wire Reports — Fri, 10 Feb 2012 07:28:00 +0000

For those who missed today’s market action and just looked at the post-mortem reports, today probably looked like just another in a series of uneventful days. For those who were paying attention to the likes of the VIX futures and ETPs based on VIX futures such as TVIX (+10.7%) and VXX (+5.2%), however, the tension in the air was obvious.

But the SPX, DJIA and NASDAQ composite indices were all up today, so what’s the big deal? It turns out that investors are easily spooked if the VIX (+2.6%) and the SPX (+0.1%) both move in the same direction. As the graphic below shows, the VIX and the SPX move in the same direction about 22% of all trading days. I think the real issue behind the concern about the direction of the VIX and the SPX is related to a hypothesis I laid out yesterday in What the VIX Kitchen Sink Chart Says:

“…the general consensus seems to be that stocks just do not deserve their current lofty valuation. In this type of environment, many investors become particularly susceptible to confirmation bias and scramble to find one or more indicators which will tell them what they have already begun to believe: that a major correction is likely just around the corner.”

The last time I crunched the numbers for VIX and SPX daily correlations, was in May 2007 and in looking at data from 1990, I concluded that a High Positive Correlation Between VIX and SPX Often Signals Market Weakness. Interestingly, when I ran the numbers today, the data from the last five years had completely reversed the conclusions. Thanks to some particularly strong results from 2009 and 2010, the full data set (1990-2012) now shows that when both the VIX and SPX are up on the same day, the mean returns for the next 1-100 trading days far exceed the typical returns for the full data set.

In terms of key takeaways, it now appears that stocks perform best following days when the SPX is up and the VIX is down (the ROI +1 column refers to the performance of the SPX one day hence) and worst on days when the SPX is down and the VIX is up. Interestingly, if one combines the up/down and down/up days, as I have done in the “split up/down” row, the aggregate data set of the SPX and VIX going in different directions looks almost exactly the same as the full data set in terms of future performance.

Getting back to the up/up phenomenon of today and yesterday, this bodes quite well for stocks going forward, based on historical data. By the same token, down/down days correspond to future performance that is, on average, well below the full data set.

Of course another key takeaway is that no matter what the data says today – for this study or any study – future events may overwhelm the current historical data and invalidate the generally accepted conclusions, even with a large sample size.

Now I will be the first to admit that stocks are overdue for a pullback, but just because the VIX and SPX both advanced on two consecutive days does not necessarily mean the planets are aligning for an Aquarian selloff. If investors are looking for that market reversal silver bullet, the SPX-VIX correlation data are not going to make them happy.

[For the record, the data in the table below includes Fridays and Mondays, so it is possible that calendar reversion may have had an impact on the results.]

Below is a larger than usual set of links for those who may be interested in digging into the history of some of the SPX-VIX correlation themes in this space.

[source(s): CBOE, Yahoo]

Disclosure(s): short TVIX and VXX at time of writing

Hard read tonight but I think I got it

Staff and Wire Reports — Fri, 10 Feb 2012 03:16:00 +0000

This one wasn't as easy to see as the others (may have yet to be valid too, since its still forming as I write). The W is a bearish crab, the white dash. The yellow is a bearish 3 drives pattern with .127 fib on the first dip and .161 on the second. Not sure if the two dips have to have the same fib levels but it seems to work since at about the same place where the two bear patterns met there was a red candle. Was looking for a longer one, but like I said, this thing is still forming as I type. The blue line is a projection, with the guess being a formation of an M (XA is CD of the W, with the blue line being the AB of the M that's forming--got it??). So far I've been pretty decent with natgas futures and these patterns. Wish I was able to do the same thing with S&P daily futures so I can jump in the top calling festivities but be correct for once. But like I say, give me enough time and I'll be right, eventually.

Last night's pattern took longer than expected to complete, but it looked like my second higher target was hit before the open:
https://twitter.com/#!/BNGESG/status/167464209716740096

Follow the rules: Cut losses quickly; Don't overtrade; Take profits/sell into strength; Don't chase, watch for the pullback; Have a plan and stick to it

View my other posts/give me some advice at http://part-timepennystocktrader.blogspot.com/. Follow me on twitter @BNGESG.

Putin and crisis – lie again

Staff and Wire Reports — Thu, 09 Feb 2012 18:27:00 +0000

Another lie from Putin is that Russia was very successful during the last crisis and has recovered to the healthy pace of growth. And we know the name of the hero who led us though these dark years. Unfortunately for Russia, it had hardest problems between the BRICS countries. Figure 1 shows that Russia was the only country in BRICS who had a dramatic fall in real GDP per capita – the best variable describing real economic growth independent on the change in population.

The years of Putin as the Prime Minister are characterized by a deep fall in economic growth and there is nothing to be proud of. As shown in our previous post, the pace of economic growth between 2001 and 2008 was just an extension of the push given in 1998 and not by Putin.

Figure 1. The evolution of real GDP per capita in BRICS.

Tried to post this chart on twitter, didn’t work for some reason

Staff and Wire Reports — Thu, 09 Feb 2012 04:22:00 +0000

You think its going one way and then it fails to pass a certain fib level and another pattern emerges, making the previous one invalid. M was the white pattern, W the smaller yellow. W still valid, target 2.465, b/o then 2.476. If it doesn't break out of the last, smaller gray circle (if it breaks down inside that circle) then it'll make the yellow W invalid, create a possible smaller M, and, interestingly, the larger white M can still be in play.

Follow the rules: Cut losses quickly; Don't overtrade; Take profits/sell into strength; Don't chase, watch for the pullback; Have a plan and stick to it

View my other posts/give me some advice at http://part-timepennystocktrader.blogspot.com/. Follow me on twitter @BNGESG.

Why Putin lies about his input to economic growth in Russia?

Staff and Wire Reports — Wed, 08 Feb 2012 20:27:00 +0000

One of the biggest lies from Putin is that he has pulled out the Russian economy from ruins and given it a big push. It is not true because the evolution of real GDP per capita in Russia follows the same path since 1998, i.e. the push to the economy had been given by President Yeltsin. Figure 1 presents the measured real GDP per capita in Russia since the start of transition in 1991. We have also plotted our prediction as based on a physical model of transition from socialism to capitalism.

The years of Putin’s presidency are characterized by inertial economic growth, which is not different from the previous years. There is no chance that Putin could make any difference. On average, the rate of real economic growth in Russia was of 4.0% per year since 1998. According to our model, the rate should be around 5% per year for the level of GDP per capita in 1998-2007. This means that the Russian economy has been lagging behind its potential output.

Figure 1. Observed and predicted evolution of real GDP per capita in Russia.

Why income inequality is very difficult to analyze?

Staff and Wire Reports — Wed, 08 Feb 2012 18:12:00 +0000

There are several major agencies reporting various measures of personal income. The Census Bureau, CB, measures personal incomes in household surveys (CPS ASEC) at an annual rate. This measure is called Money Income, MI, and includes various types of personal income. The CB provides these estimates to the Bureau of Labor Statistics in form of distributions over age/race/sex.

The Bureau of Economic Analysis also carries out annual estimates of gross personal income, GPI, as based on administrative records but does not provide any dependence on age/race/sex. In that sense the BEA reports only the cumulative number and does not allow inferring any evolution of personal income distribution in time. The most important similarities and differences of the CB and BEA measures are discussed in depth in this CB document.

The IRS also measures and reports personal incomes filed for tax purposes. Since 1996, the IRS has been publishing detailed tables of personal incomes distribution is various income bins. This is similar to the CB reports but includes capital gains as income source.

Unfortunately, multiple purposes and multiple agencies reporting personal incomes make it difficult to follow up actual evolution of income distribution and income inequality in the US. There is no unique way to merge all data in one consistent table and to estimate the distribution of income over age/race/sex and to calculate any quantitative measure of inequality like Gini coefficient or Thile index. We illustrate the difficulties with two plots. Figure 1 shows the portion of personal income reported by three agencies in nominal GDP. The BEA reports around 85% of GDP as personal incomes but does not include capital gains. The CB and IRS both report only 55% to 62% of GDP as personal incomes with a very large difference in sources of income.

Figure 2 shows the portion of population with income as defined by the CB and IRS. There is a dramatic difference of 30% between these agencies. In other word, the IRS does not count as personal income what approximately 30% of the total population define as money income. This might be not a big difference in total income when all personal incomes are summarized over this 30 per cent of population.

One may conclude that the way these three major agencies consider and resolve the problem of personal income and income inequality is counterproductive and confusing for any quantitative analysis. This also means that the speculations about income inequality are mostly qualitative and thus emotional.

Figure 1. Portion of personal income in GDP.

Figure 2. Portion of people with personal income in total population.

What the VIX Kitchen Sink Chart Says

Staff and Wire Reports — Wed, 08 Feb 2012 16:08:00 +0000

One of the more interesting developments of 2012 has been to watch the diminution of the strident bearish narrative that has been focused largely on the collision course between a preponderance of debt and low or negative growth. The bullish beginning to 2012, however, has not prompted many in the way of converts to the bullish camp. Instead, there have been whispers of “…overbought…” that have turned into a soft murmur and are now verging on becoming a loud chorus. Suddenly the general consensus seems to be that stocks just do not deserve their current lofty valuation.

In this type of environment, many investors become particularly susceptible to confirmation bias and scramble to find one or more indicators which will tell them what they have already begun to believe: that a major correction is likely just around the corner.

For better or for worse, a look at the VIX is often one of the first stops for those who are looking for evidence of a market reversal.

In the chart below, I have updated and extended a chart from three years ago that I call my “VIX kitchen sink chart” – as it pokes and prods the VIX in a number of different ways. Standard VIX analysis attempts to determine whether the VIX has strayed too far from historical norms, whether this be in the form of moving averages, Bollinger bands or other mechanisms. I have even included a separate rate of change study (with its own Bollinger bands) and a Bollinger band width study below the main chart in order to provide a couple of additional analytical twists.

The bottom line, however, is this: if stocks are overbought and a correction is indeed just around the corner, the VIX does not appear to be aware of any such inevitability. Instead, it looks a lot more like business as usual in the land of the CBOE Volatility Index.

[source(s): StockCharts.com]

Disclosure(s): none

What the VIX Kitchen Sink Chart Says

Staff and Wire Reports — Wed, 08 Feb 2012 16:08:00 +0000

For better or for worse, a look at the VIX is often one of the first stops for those who are looking for evidence of a market reversal.

[source(s): StockCharts.com]

Disclosure(s): none