30/4/19: Journal of Financial Transformation paper on cryptocurrencies pricing

Our paper with O’Loughlin, Daniel and Chlebowski, Bartosz, titled "Behavioral Basis of Cryptocurrencies Markets: Examining Effects of Public Sentiment, Fear and Uncertainty on Price Formation" is out in the new edition of the Journal of Financial Transformation Volume 49, April 2019. Available at SSRN: https://ssrn.com/abstract=3328205 or https://www.capco.com/Capco-Institute/Journal-49-Alternative-Capital-Markets.

23/4/19: Income per Capita and Middle Class

New research reported by the Deutsche Bank Research shows that, on average, there is a positive (albeit non-linear) relationship between the per capita income and the share of middle class in total population:

Source: https://pbs.twimg.com/media/D42GiWNXkAMpID2.png:large

There is an exception, however, although DB's data does not test formally for it being an outlier, and that exception is the U.S. Note, ignore daft comparative reported in chart, referencing 'levels' in the U.S. compared to Russia, Turkey and China: all three countries are much closer to the regression line than the U.S., which makes them 'normal', once the levels of income per capita are controlled for. In other words, it is the distance to the regression line that matters.

Another interesting aspect of the chart is the cluster of countries that appear to be statistically indistinguishable from Russia, aka Latvia, Estonia and Lithuania. All three are commonly presented as more viable success stories for economic development, contrasting, in popular media coverage, the 'underperforming' Russia. And yet, only Latvia (completely counter-intuitively to its relative standing to Estonia and Lithuania in popular perceptions) appears to be somewhat (weakly) better off than Russia in income per capita terms. None of the Baltic states compare favourably to Russia in size of the middle class (Latvia - statistically indifferent, Lithuania and Estonia - somewhat less favourably than Russia).

23/4/19: Property, Property and More Property: U.S. Household Wealth Bubble

According to the St. Luis Fed, U.S. household wealth has reached a historical high of 535% of the U.S. GDP (see: https://www.zerohedge.com/news/2019-04-16/where-inflation-hiding-asset-prices).

There is a problem, however, with the above data: it reflects some dodgy ways of counting 'household wealth'. For two primary reasons: firstly, it ignores concentration risk arising from wealth inequality, and secondly, it ignores concentration risk arising from households' exposure to property markets. A good measure of liquidity risk controlled allocation of wealth is ownership of liquid equities (note: equities, of course, and are subject to Fed-funded bubble dynamics). The chart below - via https://www.topdowncharts.com/single-post/2019/04/22/Weekly-SP-500-ChartStorm---21-April-2019 shows a pretty dire state of equity markets (the source of returns on asset demand side being swamped over the last decade by shares buybacks and M&As), but it also shows that households did not benefit materially from the equities bubble.

In other words, controlling for liquidity risk, the Fed's meme of historically high household wealth is seriously challenged. And controlling for wealth inequality (distributional features of wealth), it is probably dubious overall.

So here's the chart showing just how absurdly property-dependent (households' home equity valuations in red line, index starting at 100 at the end of the Global Financial Crisis) the Fed 'wealth' figures (blue line, same starting index) are:

In fact, dynamically, rates of growth in household home equity have been far in excess of the rates of growth in other assets since 2012.  In that, the dynamics of the current 'sound economy' are identical (and actually more dramatic) to the 2000-2006 bubble: property, property and more property.

22/4/19: At the end of QE line... there is nothing but QE left...

Monetary policy 'normalization' is over, folks. The idea that the Central Banks can end - cautiously or not - the spread of negative or ultra-low (near-zero) interest rates is about as balmy as the idea that the said negative or near-zero rates do anything materially distinct from simply inflating the assets bubbles.

Behold the numbers: the stock of negative yielding Government bonds traded in the markets is now in excess of USD10 trillion, once again, for the first time since September 2017

Over the last three months, the number of European economies with negative Government yields out to 2 years maturity has ranged between 15 and 16:

More than 20 percent of total outstanding Sovereign debt traded on the global Government bond markets is now yielding less than zero.

I have covered the signals that are being sent to us by the bond markets in my most recent column at the Cayman Financial Review (https://www.caymanfinancialreview.com/2019/02/04/leveraging-up-the-global-economy/).

15/4/19: One order of "Bull & Sh*t" for the U.S. Labor Market, please

The 'strongest economy, ever'...

Despite a decade-long experiment with record-low interest rates, despite trillions of dollars in deficit financing, and despite headline unemployment numbers staying at/near record lows, the U.S. economy is not in a rude health. In fact, by two key metrics of the labor force conditions, it is not even in a decent health.

As the chart above clearly shows, both in terms of period averages and in terms of current level readings, Employment to Population Ratio (for civilian population) has remained at abysmally low levels, comparable only to the readings attained back in 1986. Meanwhile, labor force participation rate is trending at the levels consistent with those observed in 1978.

Dire stuff.

Update: Here is a chart showing how the current recovery compares to past recoveries (hint: poorly):

10/4/19: Rewarding Reckless Risk Pricing, Again

Markets are supposed to be efficient. At least, on the timeline that allows to price in probabilistically plausible valuations of the firms. Markets failed to be efficient at the time of the dot.com bubble. And, it appears, they are back at the same game:

As the chart above shows, share of IPOs issued at negative earnings (companies losing money) is now at the levels last seen during the height of the dot.com bubble. What can possibly go wrong?

10/4/19: Russian Foreign Exchange Reserves and External Debt

As recently posted by me on Twitter, here are three charts showing the evolution of Russian foreign reserves and external debt:

Remember the incessant meme in the Western media about Russia eminently in danger of running out of sovereign wealth funds back at the start of the Western sanctions in late 2014? Well, the chart above puts that to rest. It turns out, Russia did not run out of the reserves, and instead quite prudentially used funds available to carefully support some economic adjustments (especially in agriculture and food sector), while simultaneously balancing out its fiscal deficits.

Do note that the reserves above exclude over USD 91 billion worth of Gold that Russia holds and continues to buy at rising clips.

The result of the prudentially balanced management of the reserves and the economy was deleveraging out of debt (a lot of this was done via restructuring of intracompany loans and affiliated enterprises refinancing), with a reduction in the external debt (chart below), without use of sovereign funds:

As of current, Russian foreign exchange reserves ex-gold are more than sufficient to cover the entirety of the country public and private sectors external debts.

If the above chart is not dramatic enough, here is a contrasting experience over the same years for the U.S. economy:

Nothing that CNN and the rest of the Western media pack ever managed to capture.

10/4/19: How US Tax Inversions Affect Shareholder Wealth

Our article on how corporate tax inversions impact shareholders' wealth is now available on Columbia Law School blog: http://clsbluesky.law.columbia.edu/2019/04/10/how-u-s-tax-inversions-affect-shareholder-wealth/.

6/4/19: Industrial Production and Global Trade are Tanking

The great convergence of simultaneously declining global trade flows and industrial production:

Via topdowncharts.com

The trend is also evident from the global manufacturing and composite PMIs (see https://trueeconomics.blogspot.com/2019/04/4419-bric-manufacturing-pmis-for-1q.html and https://trueeconomics.blogspot.com/2019/04/6419-bric-services-lead-manufacturing.html).

Note the range bounds for two periods (pr-GFC and post-GFC) in the first chart above.

6/4/19: Student Loans: The Bubble Is Still Inflating

A neat chart from Bloomberg summarizing the plight of student debt overhang in the U.S. economy:

In effect, education is the most leveraged, over the recent cycle, form of household investment out there. Second to it, is only investment in health. Via https://www.healthsystemtracker.org/chart-collection/u-s-spending-healthcare-changed-time/#item-total-health-expenditures-have-increased-substantially-over-the-past-several-decades_2017:

6/4/19: BRIC Services Lead, Manufacturing Lag Global Growth Momentum

I have blogged recently on BRIC and global PMIs for manufacturing and services, covering the data for 1Q 2019, as well as monthly PMIs for BRIC economies. Here are the 1Q 2019 PMIs for composite economic activity across the same:

In 1Q 2019, only Brazil posted improving Composite PMI reading, with the rest of BRIC economies showing deteriorating growth conditions, in line with continued drop in Global Composite PMI. Over the last 5 quarters, Global Composite PMI has dropped from its peak of 54.23 in 1Q 2018 to 52.5 in 1Q 2019, with current reading at its lowest in 10 quarters.

Of all BRIC economies, India and Russia are outperforming the Global Composite PMI, with Russia posting the fastest growth at 54.1 of all BRIC economies in 1Q 2019. Brazil is statistically in line with Global Composite PMI, while China is a clear under-performer.

Sectorally, the main weakness amongst the BRICs is in Manufacturing, with Services outperforming Global Composite index:

6/4/19: U.S. Tax Compliance Costs and Lobbying

Not a fan of The Atlantic on a range of topics, especially geo-politics, but a great write up on the relationship between tax accounting industry, lobbying and U.S. tax codes (painfully and daftly complex) here: https://www.theatlantic.com/ideas/archive/2019/04/american-tax-returns-dont-need-be-painful/586369/. Worth a read:

Of course, the solution is to make tax filing for ordinary income taxes simple, and to make tax codes more streamlined. A flat tax would work. Charged across all income at one rate. Or a flatter tax, with a schedule of just two or three bands, applying, again, across all income.

5/4/19: Does Government Debt Matter? The Reality of Fiscal Multipliers

There has always been a lot of debate in economics about the effects of debt (especially sovereign debt) on growth and fiscal dynamics. And, despite numerous papers on the subject, the debate is far from settled.

Here is an interesting new study that looks at the effect high levels of government indebtedness have on the effectiveness of fiscal policy stimulus. The reason this topic is important is simple: fiscal policy can and is used to offset or smooth out recessionary shocks. The extent to which fiscal policy is effective in doing so (the impact expansionary fiscal policy may have on unemployment and output) can be varied across different economies and under different crises conditions. But, does this extent vary under different debt conditions?

In theory, the debt levels carried by a given sovereign can impact the size of fiscal multipliers (the effectiveness of fiscal policy) through two main channels:

1. The so-called Ricardian channel: a government with a weak fiscal position (high debt) deploying fiscal stimulus (an increase in public spending) can cause households to expect future tax increases. The result is that in economies with high public debt levels, deploying fiscal stimulus can trigger increased savings by households, reducing consumption, and lowering the size of fiscal policy multiplier.
2. An interest rate channel: when the government debt is high, so that the government fiscal position is weak, fiscal stimulus can increase concerns about sovereign credit risk amongst government bond holders and buyers. This can increase bond yields, raise borrowing costs, lower liquidity of bonds for the sovereign, but also increase cost of capital across the private sector. The result is the crowding out effect, whereby public spending crowds out private investment and credit-finance consumption.

In theory, both channels imply that fiscal policy is less effective when fiscal stimulus is implemented from a weak initial fiscal position (position of high starting government debt levels).

A new World Bank paper, authored by Huidrom, Raju and Kose, M. Ayhan and Lim, Jamus Jerome and Ohnsorge, Franziska, and titled "Why Do Fiscal Multipliers Depend on Fiscal Positions?" (March 2019, World Bank Policy Research Working Paper No. 8784: https://ssrn.com/abstract=3360142) considers the two theoretical channels operating simultaneously. Using data for 34 countries (19 advanced economies and 15 developing economies),  over 1Q 1980 through 1Q 2014, the authors show that "the fiscal position helps determine the size of the fiscal multipliers: estimated multipliers are systematically smaller when the fiscal position is weak (i.e. government debt is high).

Looking at the longer run panel in the chart above, fiscal multipliers rapidly reach into negative territory as Government debt rises to around 37-40 percent of GDP. Over a medium term horizon, of 2 years, multipliers hit negative values for debt levels above 75 percent of GDP.

Similar dynamics are confirmed in the chart below:

The authors subsequently "show that when a government with weak public finances conducts expansionary fiscal policy, the private sector scales back on consumption in anticipation of future tax pressures (Ricardian channel) and risk premia rise on mounting concerns about sovereign risk (interest rate channel)." In other words, high starting debt position does trigger both theoretical effects to reinforce each other.

This is an unpleasant arithmetic for uber-Keynesians who hold that fiscal policy is always effective in stimulating economic growth during periods of economic crises. The findings also support the view that the 'fiscal policy space' is indeed bounded by the reality of pre-crisis fiscal policy paths: there is no free lunch when it comes even to sovereign financing.

4/4/2019: Debt Relief for Households: It Turns Out to be a Great Idea, Folks

The question of debt relief for households during the periods of financial crises has been a pressing one in the aftermath of the 2008 Global Financial Crisis. I have written a lot on the topic in topic in the past, but to sum the arguments here in a brief format:

• Argument in favour of debt relief: households carrying unsustainable debt burden during the crisis are likely to substantially reduce current and future consumption and investment, including long term investment in education, health and other activities. The resulting decline in the aggregate demand is likely to be prolonged and extensive, with a positive correlation to the crisis-triggered recession. Thus, debt relief via direct debt forgiveness and/or generous bankruptcy writedowns can help ameliorate adverse shocks to employment, demand and investment during large scale crises;
• Argument against debt relief: debt relief can lead to the emergence of moral hazard (inducing greater leveraging by households post-crises), and adversely impact balancesheets of the lending institutions.

I favour the first argument, based on my view that the economy is crucially dependent on households' financial health, and that moral hazard consideration does not apply ex post the crisis, but only ex ante, which means that policymakers can tackle adverse effects of moral hazard after debt forgiveness in the wake of the structural crises.

A new paper by Auclert, Adrien and Dobbie, Will and Goldsmith-Pinkham, Paul S., titled "Macroeconomic Effects of Debt Relief: Consumer Bankruptcy Protections in the Great Recession" (CEPR Discussion Paper No. DP13598: https://ssrn.com/abstract=3360065) tries to settle the debate.

The paper argues that "the debt forgiveness provided by the U.S. consumer bankruptcy system helped stabilize employment levels during the Great Recession." The authors "document that over this period, states with more generous bankruptcy exemptions had significantly smaller declines in non-tradable employment and larger increases in unsecured debt write-downs compared to states with less generous exemptions. We interpret these reduced form estimates as the relative effect of debt relief across states,... [showing that] the ex-post debt forgiveness provided by the consumer bankruptcy system during the Great Recession increased aggregate employment by almost two percent."

More specifically, the model of debt forgiveness effects developed by the authors "implies that ex-post debt relief had positive effects on employment in ...sectors and in ...regions. Ex-post debt relief directly increases spending and employment in both sectors [tradables and non-tradables] in the high--[debt]-exemption region, which increases tradable employment in the low-[debt]-exemption region through a demand spillover effect. The increase in tradable employment in the low-exemption
region then increases non-tradable spending and employment in that region. Calibrating the model
to the observed path of debt write-downs during the financial crisis, we find that average employment across regions in the second half of 2009 would have been almost 2 percent lower in both the
non-tradable and the tradable sector in the absence of the ex-post debt forgiveness provided by the
consumer bankruptcy system."

Furthermore, the authors "conclude by using the model to conduct three policy counterfactuals.

• First, we ask how the effect of ex-post debt relief changes in normal times when the zero lower bound does not bind. We find that even with a relatively aggressive monetary policy response, debt relief continues to have positive effects in both regions and in both sectors. 
• Second, we ask how the effect of debt relief changes with the size of the relief provided to borrowers. We find that the debt relief multiplier is initially invariant to the size of the relief provided to borrowers, but eventually falls as the size of debt relief grows large due to the concavity of borrowers’ consumption functions. [see chart]
• Finally, we ask how the effect of ex-post debt relief changes with the location of the savers that pay for the relief provided to borrowers. We find that the debt relief multiplier is invariant to the location of these savers, as savers smooth consumption in response to wealth transfers no matter where they are located."

4/4/19: BRIC Services PMIs for 1Q 2019: Converging to Global Growth Momentum

Q1 2019 Services PMIs for BRIC economies came in signaling no change on 4Q 2018 and converging to the Global Services PMI reading.

Brazil Services PMI averaged 52.3 in 1Q 2019, a gain on 51.2 in 4Q 2018, and the highest quarterly reading since 1Q 2013 when it stood at exactly the same reading. 

Russia Services PMI average for 1Q 2019 was at 54.9, down from 55.6 in 4Q 2018, singling moderating, but still fast pace of growth in the Services sectors of the economy. 

China Services PMI was at 53.0 in 1Q 2019, a marginal improvement on 52.8 reading in 4Q 2018, but still substantially down on 53.7 reading in 1Q 2018.

India Services PMI was at 52.2- a slip on 53.0 recorded in 4Q 2018. Given past weakness in Services sector in the Indian economy, 52.2 reading is still respectably tied to the second fastest growth for any quarter since 4Q 2016.

GDP-weighted BRIC Services PMI averaged 53.0 in 1Q 2019, the same reading as in 4Q 2018 and singling marginally faster growth than 52.7 reading for 1Q 2018.

Meanwhile, Global Services PMI averaged 53.2 in 1Q 2019, down marginally on 53.4 in 4Q 2018 and marking the third consecutive quarter of declining growth in global services economy. 

CHART

4/4/19: BRIC Manufacturing PMIs for 1Q 2019: In Line With Global Growth Slowdown

Q1 2019 Manufacturing PMIs for BRIC economies came in as effectively flat on 4Q 2018 and relatively in line with the collapsing Global Manufacturing PMI.

Brazil Manufacturing PMI averaged 53.0 in 1Q 2019, a gain on 52.1 in 4Q 2018, and the highest quarterly reading since 1Q 2011. 

Russia Manufacturing PMI average for 1Q 2019 was at 51.3, down from 51.9 in 4Q 2018, but still the second highest in 5 quarters. 

China Manufacturing PMI was at 49.7 in 1Q 2019, the first sub-50 reading for a quarterly average since 2Q 2016, and the fourth consecutive quarter of declining PMIs.

India Manufacturing PMI was at 53.6 - a gain on 53.4 in 4Q 2018, and the highest reading since 4Q 2012.

GDP-weighted BRIC Manufacturing PMI averaged 51.0 in 1Q 2019, marginally down on 51.2 in 4Q 2018 and singling slower growth than 51.5 reading for 1Q 2018.

Meanwhile, Global Manufacturing PMI averaged 50.7 in 1Q 2019, down significantly on 51.8 in 4Q 2018 and marking the fourth consecutive quarter of declining growth in global manufacturing. 

CHART

4/4/19: BRIC PMIs for March Show Improved Growth Conditions

With March PMIs reported by Markit in, here are the monthly frequency trends for the BRIC economies activity, based on composite PMIs:

Overall BRIC activity as signalled by PMIs remains range-bound in the tight, low activity range over the last 6 years (second chart above). However, the composite activity is running close to the upper bound of the range, implying overall stronger performance in the recent month. This is confirmed by the first chart above, showing that both Russia and ex-Russia BRIC economies activity is accelerating on trend since July 2018.

More analysis, based on smoother quarterly data forthcoming, so stay tuned.

2/4/19: Brain Drain Reversed or Inverted?

Generally, we associate skilled emigration with the phenomenon of 'brain drain' or a zero sum game - the loss of human capital from the country of origin and a corresponding gain to the recipient country. However, as common, the real nature of these effects is more complex than the first order analysis implies.

A new paper by Fackler, Thomas, Giesing, Yvonne and Laurentsyeva, Nadzeya, titled "Knowledge Remittances: Does Emigration Foster Innovation?" (CESifo Working Paper No. 7420) accessible via https://ssrn.com/abstract=3338774, looks at the issue of knowledge flows relating to emigration. The authors find that based on "industry-level patenting and migration data from 32 European countries," "...emigration in fact positively contributes to innovation in source countries. ... While skilled migrants are not inventing in their home country anymore, they contribute to cross-border knowledge and technology diffusion and thus help less advanced countries to catch up to the technology frontier."

More specifically, authors show that "one percent increase in the number of emigrants increases patent applications by 0.64 percent in the following two years. This result is statistically significant at the one percent level and robust to controls, fixed effects, and varying lags. The effect is quantitatively more pronounced when we consider only the flows of migrants with patenting potential."

A picture worth a 1,000 words:

Notice, the above suggests that the positive effect of opening up migration channels on technological convergence is evident as early as two years prior to the EU Accession of 2004. The same is confirmed in the following chart:

In line with their findings, the authors suggest that

• The EU "could benefit from further facilitating migration within Europe", by focusing on reducing cultural and social barriers to migration, such as "language and administrative barriers, ...ensuring the recognition of foreign qualifications and the promotion of language courses at all age levels."
• "Another policy implication is to ease skilled migration to Europe from outside the European Union. This could be achieved by easing the access to European labour markets and the recruitment of highly qualified foreign workers. While the Blue Card has been a step in this direction, its scope could be increased to obtain a higher impact and administrative barriers should be reduced." 

Update: Similar findings are reported in Kim, Jisong and Lee, Nah Youn, High-Skilled Inventor Emigration as a Moderator for Increased Innovativeness and Growth in Sending Countries, East Asian Economic Review Vol. 23, No. 1 (March 2019) 3-26: https://ssrn.com/abstract=3360938. Their paper uses data from 154 countries to show that high-skilled inventor emigration rate has a positive growth effect on the country of origin (COO) by spurring "knowledge diffusion and technology transfer back to their COOs, which in turn affects innovation and growth in their home countries. The result indicates that the direct negative impact of the brain drain can be mitigated by the positive feedback effect generated by the high-skilled inventor emigrants abroad. When coupled with an active trade policy that reinforces growth, countries can partially recoup the direct effect of the human capital loss."

2/4/19: Capital Markets Union: An Action Plan of Unfinished Reforms

Our paper on the progress of the EU Capital Markets Union reforms is now available on SSRN:

Capital Markets Union: An Action Plan of Unfinished Reforms (March 21, 2019). with Tracy Lee Lyon, Alexandra Cohen, Margaret Poda and Matthew Salyer (Middlebury Institute of International Studies at Monterey (MIIS); GUE/NGL Group, European Parliament, Policy Analysis Paper, March 2019. Available at SSRN: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3357380.

2/4/19: World Economic Conditions and Yield Signals

Global divergence...

... until global convergence?

More likely, the latter: https://www.reuters.com/article/us-ecb-policy-rates-idUSKCN1R81B3. 

2/4/19: Spending your way into oblivion?

As Donald Trump talks about forcing UK NHS to pay higher prices for U.S. pharmaceutical companies' output, an amazing chart from the Our World in Data project (link to more interactive charts on health expenditure: https://ourworldindata.org/the-link-between-life-expectancy-and-health-spending-us-focus) plotting life expectancy against health expenditure for all OECD countries:

Source: https://ourworldindata.org/the-link-between-life-expectancy-and-health-spending-us-focus

This data is dire. The U.S. vastly outspends other countries in terms of health spending, yet it also vastly underperforms in terms of life expectancy. Yes, in part, the latter feature is down to violence (not ineffectiveness of healthcare), and in part it is down to horrific diets and sedentary life-styles of Americans. But controlling for all this, Americans still live shorter lives and get less preventative healthcare and lower quality medical interventions. All for a higher price.

1/4/19: Hollowing out of the American Middle Class: the High Earners, and the 1-percenters

An interesting and insightful 2016 paper from John Komlos of CESIfo, titled "Growth of Income and Welfare in the U.S. 1979-2011" (CESifo Working Paper No. 5880), paints the pretty dire picture of the post-1980s dynamics in the U.S. labor markets, that laid the foundations of the current acceleration and deepening of political populism and opportunism not only in the U.S., but also in Western Europe.

Kolmos estimated growth rates in real incomes in the U.S. from the Congressional Budget Office’s (CBO) post-tax, post-transfer data. Kolmos also adjusts the real income data to improve the accuracy of the measures. The result is striking: "... the major consistent findings include what in the colloquial is referred to as the “hollowing out” of the middle class. According to these estimates, the income of the middle class 2nd and 3rd quintiles increased at a rate of between 0.1% and 0.7% per annum, i.e., barely distinguishable from zero. Even that meager rate was achieved only through substantial transfer payments." Of course, given that we have experienced positive growth in the aggregate economy in excess of these figures and well above the demographic change, this "hollowing out" of the middle class had to be accompanied by the "fattening up" of some other income classes, either the rich or the poor or both. Per Kolmos, it was the former one: "the income of the top 1% grew at an astronomical rate of between 3.4% and 3.9% per annum during the 32-year period, reaching an average annual value of $918,000, up from $281,000 in 1979 (in 2011 dollars)." Predictably, "...the post-tax, post-transfer income of the 1% relative to the 1st quintile increased from a factor of 21 in 1979 to a factor of 51 in 2011."

But what about the poor? Again, per Kolmos, "...income of no other group increased substantially relative to that of the lowest quintile. Oddly, the income of even those in the 96-99 percentiles increased only from a multiple of 8.1 to a multiple of 11.3."

Kolmos id this exercise for 'high' and 'low' ranges of income (depending on specific assumptions that were less and more conservative ratline to the CBO's raw data.

The results of the two calculations are shown in the chart below

Source: Kolmos (2016: 14)

In simple terms, this chart shows two interesting things:
1) The dramatic growth differential between income estimates for all quintiles compared to the top quintile is fully accounted for by the massive growth in income of the top 5% of the populations and especially by the growth in income of the top 1%.
2) The gap between high and low estimates for income growth are massive for the second and third quintiles (the middle class), and are relatively comparable for the first (low income earners) and 4th quintile (upper middle class). The gap becomes much smaller for the 5th quintile (high earners) and turns negligible for top 1%.

Kolmos attempts to convert income into more meaningful 9albeit harder to pin down) measure of well-being. To do this, he estimates the logarithmic utility function for the quintiles (logarithmic utility function preserves the property of the diminishing marginal utility - the idea that as our incomes continue to increase, each percent increase in our income results in progressively smaller gains in satisfaction/utility). Here is what he finds: "A logarithmic utility function yields a growth in welfare for the middle class of roughly 0.01% to 0.07% per annum, which is indistinguishable from zero. With interdependent utility functions only the welfare of the 5th quintile experienced meaningful growth while those of the first four quintiles tend to be either negligible or even negative." Chart below shows these estimates.

Source: Kolmos (2016: 15)

Focusing on the Percentiles section, markers 6-9 disaggregate the last 5th quintile into the ranges of top 81-90%, 91-95%, 96-99% and top 1%. It is quite evident that only top 5% (segments 8 and 9) experienced welfare gains of more than the 4th quantile cohorts.

This strongly implies that, contrary to some left-leaning policymakers' proposals and preferences, the problem of 'hollowing out' of the American middle class is not driven by the incomes of the top 81-90th percentiles, nor even by those in 91st-95th percentiles. The real source of the problem starts somewhere within the 96-99th percentile and most certainly extends to the top 1%.

The same is confirmed by looking at each cohort income relative to that of the top quintile, shown in the chart below

Source: Kolmos (2016:27)

In summary, thus, the problem with the 'hollowing out' of the middle class is not within theta 20% earners, nor within the top 10% earners. It starts much higher than that.