Wednesday, December 4, 2013

The President's Speach on the Economy: a Review



Let's critique the President's speech and see what it tells us.

"Nevertheless, during the post-World War II years, the economic ground felt stable and secure for most Americans, and the future looked brighter than the past. "  - Yes, he's got the right idea.  We had good policies and programs that supported the middle class and a prosperous future for all.

"But starting in the late ‘70s, this social compact began to unravel." - Actually, it started in the early '70s, but no one noticed.

“Technology made it easier for companies to do more with less, eliminating certain job occupations. “ – NO.  This is always true, but not a cause of long term unemployment or dwindling prospects.  A common mistake made today.

“A more competitive world lets companies ship jobs anywhere. “  - NO.  Again, a common misconception.  The world has always been competitive, and globalized.  It was changing trade policies that allowed US corporations to ship jobs overseas, at least for now.

“And as good manufacturing jobs automated or headed offshore, workers lost their leverage, jobs paid less and offered fewer benefits.”  - Yep.
“As values of community broke down,…”  - He hits it on the head here.  We are no longer “One Nation”.  We have become “us” and “them”.

“As a trickle-down ideology became more prominent, taxes were slashed for the wealthiest, while investments in things that make us all richer, like schools and infrastructure, were allowed to wither.  And for a certain period of time, we could ignore this weakening economic foundation, in part because more families were relying on two earners as women entered the workforce.  We took on more debt financed by a juiced-up housing market.  But when the music stopped, and the crisis hit, millions of families were stripped of whatever cushion they had left.”  - So true.  Investment in future productivity makes us richer.

“Since 1979, when I graduated from high school, our productivity is up by more than 90 percent, but the income of the typical family has increased by less than eight percent.” – So true, so sad.

“The combined trends of increased inequality and decreasing mobility pose a fundamental threat to the American Dream, our way of life, and what we stand for around the globe. “  - Yes.  This is what being American is all about.  The current challenges being brought onto America are an existential threat.

“…and together with lax regulation, may contribute to risky speculative bubbles.” – The lax regulations, rather than the concentration of wealth itself, are the chief culprit.  Bring back Glass-Steagall.

“The opportunity gap in America is now as much about class as it is about race, and that gap is growing.”  - Yes, this is class issue and always has been.

“Second, we need to dispel the myth that the goals of growing the economy and reducing inequality are necessarily in conflict, when they should actually work in concert.  We know from our history that our economy grows best from the middle out, when growth is more widely shared.  And we know that beyond a certain level of inequality, growth actually slows altogether.”  - Absolutely.  Spot on.

“Third, we need to set aside the belief that government cannot do anything about reducing inequality.” – Again, right on.

“To begin with, we have to continue to relentlessly push a growth agenda.” – Good, but the devil is in the details as they say.

” And that means simplifying our corporate tax code in a way that closes wasteful loopholes and ends incentives to ship jobs overseas.” – Yes to ending the incentives to move jobs overseas, but too much emphasis on corporate taxes which have little impact on hiring.  This is just a cave in to special interests, and ignores the problems of trade imbalances and more appropriate mechanisms to remedy this such as tariffs.

“It means a trade agenda that grows exports and works for the middle class.  It means streamlining regulations that are outdated or unnecessary or too costly.”  - yes, but the problem is not regulations!!  It’s the trade imbalance caused by a lack of protective measures like tariffs which are traditionally used by all advanced countries.
Overall, the President ignores the trade deficit and does not tackle financial regulation that is needed for any meaningful recovery.

“Step two is making sure we empower more Americans with the skills and education they need to compete in a highly competitive global economy.”  - Good, we all need education to get good jobs.

“so we’ve helped more students go to college with grants and loans that go farther than before.  We’ve made it more practical to repay those loans.  And today, more students are graduating from college than ever before.” – Umm, I’m not sure what he’s talking about as grants are almost non-existent for the middle class and the costs of college are more burdensome than ever.  Also, more college graduates aren’t necessarily a good thing.  We need the proper education for kids as not everyone should go to college; sometimes vocational training is what is more useful.

“So we should offer our people the best technical education in the world.  That’s why we’ve worked to connect local businesses with community colleges, so that workers young and old can earn the new skills that earn them more money.” – As long as he’s not referring to ‘STEM’ because we have plenty of computer people.  We need more broad based skills for a wide variety of jobs.

“the third part of this middle-class economics is empowering our workers.  It’s time to ensure our collective bargaining laws function as they’re supposed to so unions have a level playing field to organize for a better deal for workers and better wages for the middle class.” – Good, this is how it’s supposed to work.  Unions have lost most of the clout that they had acquired by the 1950’s.  They need to organize and act more vigorously than ever.

“And that’s why it’s well past the time to raise a minimum wage that in real terms right now is below where it was when Harry Truman was in office. “  - Yes, the free market needs a bottom so people don’t drop right through.

“But there’s no solid evidence that a higher minimum wage costs jobs, and research shows it raises incomes for low-wage workers and boosts short-term economic growth. “ – Correct.

“Number four, as I alluded to earlier, we still need targeted programs for the communities and workers that have been hit hardest by economic change and the Great Recession… Promise Zones, urban and rural communities where we’re going to support local efforts focused on a national goal -- and that is a child’s course in life should not be determined by the zip code he’s born in, but by the strength of his work ethic and the scope of his dreams. “  - This is misguided and does not help the middle class which he so touted through the speech.  This will not help the structural problems of the economy or financial system.

“So we’re going to have to do more to encourage private savings and shore up the promise of Social Security for future generations.  And remember, these are promises we make to one another.  We don’t do it to replace the free market, but we do it to reduce risk in our society by giving people the ability to take a chance and catch them if they fall.” – Yes.  The name says it all: Social Security.  Only the Federal government has the ability to guarantee income in spite of the vagaries of life that befall all of us.

“…SNAP…unemployment insurance… These programs are almost always temporary means for hardworking people to stay afloat while they try to find a new job or go into school to retrain themselves for the jobs that are out there, or sometimes just to cope with a bout of bad luck. “  - Yes, the idea is that the normal state is for people to have good, well-paying jobs, that the government supplies support when those good jobs become unavailable for a time.

“That’s why we fought for the Affordable Care Act -- (applause) -- because 14,000 Americans lost their health insurance every single day, and even more died each year because they didn’t have health insurance at all.  We did it because millions of families who thought they had coverage were driven into bankruptcy by out-of-pocket costs that they didn't realize would be there.  Tens of millions of our fellow citizens couldn’t get any coverage at all.  And Dr. King once said, "Of all the forms of inequality, injustice in health care is the most shocking and inhumane.” – Yes, the American people, acting through their government, has a responsibility to see that all Americans get needed health care.  Is the ACA it, probably not, but it might be better than what existed before.

The President has some idea of the forces acting against the middle class, but does not seem to comprehend the fundamental causes of these.  Those are: the lack of balanced trade, the lack of trade protections for industries which provide high value added, high wage jobs and the economic foundation of our country, the regulation of finance which separated depository institutions from investment and speculation, the control over the money creation process, and the restoration of a trade settlement system like Bretton Woods.  All the good intentions and laudable goals will do nothing if these fundamental issues are not addressed.




What can we learn about trade from Germany???

The Germans are taking a lot of heat lately for their large trade surplus of nearly $250B this year.  This kind of criticism is par for the course from the talking heads, but what really stunned me is that nobody asked "how did Germany manage to have such a large trade surplus when they have such high labor and structural costs?"  This to me is the key issue here, so I did a little searching around and found this great article from 2010 about just this issue.  Ian Fletcher has written an interesting piece about what the Germans are doing right and how they do it.  You can find it here:

http://www.huffingtonpost.com/ian-fletcher/how-do-other-nations-bala_b_628157.html

The principle reason for the German trade surplus is the underlying philosophy of the Germans which Ian describes as: "Germany, like the U.S., is nominally a free-trading country. The difference is that while the U.S. genuinely believes in free trade, Germany quietly follows a contrary tradition that goes back to the 19th-century German economist Friedrich List (who was, ironically, a student of our own Alexander Hamilton, the man on the $10 bill). So despite Germany's nominal policy of free trade, in reality, a huge key to its trading success is a vast and half-hidden thicket of de facto non-tariff trade barriers."  They, being disciples of List, understand the importance of protecting their high value added, high wage, high tech industries and never running trade deficits as the path to prosperity.  List wrote the brilliant critique of Adam Smith in "The National System of Political Economy", which I highly recommend to all.

What is unfortunate about the German trade policy is that they must maintain the pretense of "free trade" while they nonetheless go about instituting obscure policies which provide protections.  Wouldn't it be easier, clearer, fairer, and more straightforward to simply replace many of these rules and regulations with tariffs?  Let's just state again that all nations have the right to balanced trade, and that tariffs are a legitimate mechanism for achieving this balanced condition.  Indeed tariffs should be the preferred mechanism due to the reasons above.  Certainly, the need for balanced trade is self evident as in the long run trade deficits are unsustainable and trade will come back into balance as the "free trade" crowd insists, but this will likely be accomplished through a variety of shocks that will inflict more suffering on the public.

Now List goes beyond balanced trade to requiring protection of key industries that provide for high value, high wage jobs be protected and promoted above  that necessary for domestic consumption, with the surplus being exported in exchange for low value commodities produced at low wages.  This policy, will as List adequately shows, create prosperity at home, but at the cost of prosperity for other nations.  A balance of trade with all providing roughly for their own needs, or trading for similarly value added goods will likely be more palatable to all.

As to the current criticism that the Germans are suffering?  Well, there is some merit in that, as we'll say again, all nations have the right to balanced trade, including the Germans.  They will eventually have to spend what they are saving from running a trade surplus so they might as well do it now and give a demand boost to production in other EU countries, such as Spain and Greece, which are running far below their production potential.  This may induce some inflation in the Eurozone, but maybe that will provide the impetus that the Germans need to exit the EU.


Saturday, November 16, 2013

In praise of wage inflation!!!!

"Wage inflation". The very words strike terror into the hearts of economists and financiers everywhere. We are taught that wage inflation is categorically evil, as if some comprehensive set of data proved this beyond any doubt. But, maybe there is a time and place for wage inflation, and maybe that time is now and that place is here.

A primary goal of the government today should be to stimulate the economy to, in principle, cause hiring to create additional GDP. US companies are sitting on record balances of cash, so they have no problem funding capital expansion and hiring. The low interest rates may help them on current interest payments by some refinancing, but otherwise makes not difference to them. They see no demand for more goods and services beyond what they currently plan to produce, so they sit and wait. They are waiting to be signaled by consumers to increase production by consumers buying more goods and services than these companies are currently planning for. This is the demand signal that moves companies to hire workers and invest in capital expansion.

Consumers, seeing their pay stagnate or shrink, and being up to their ears in debt, are in no position to increase their spending to create the demand needed to signal companies. So, they muddle through hoping not to loose the jobs they have and become one of the tens of millions of unemployed.

The long-term unemployed try to find work, but are unable. Neither are they in much of a position to start businesses of their own. I suppose some try to do odd jobs or deal things at flea market and on line. But they just hope to find some decent job before their unemployment runs out. BTW, unemployment insurance payment is the one fiscal stimulus that is actually in effect to boost demand.

I believe this whole line of argument is the one Keynes made to justify government intervention in the first place. And that fiscal policy is needed during recessions.

Consumers are spending all they can afford to, but that level is below the amount that the businesses in the economy are structured to produce. The lack of growth in the economy is because the consumer isn't buying more. And the consumer isn't buying more because they lack the income to do so. In other words, incomes have not kept up with expectations of producers. So, production is cut back to a level that consumers can currently afford. This means the supply and demand curve is moved to lower demand and thus lower supply at a lower price. This is source of the lack of inflation that we've been seeing.

What is needed is for consumers incomes to grow, which would spur purchasing, which would spur increased production, which would spur hiring and capital expansion. Which would...increase incomes. This is, in fact, wage inflation. Prices would necessarily rise as demand is bid up by rising incomes, and rising supply would only happen if prices were bid up to motivate the increase in production.

The happy side effects of this wage inflation are: lowered unemployment, raised taxes, and likely increases in long term profits for companies as those sales increases accrue over the years. This is a much better situation for all then if those unemployed stay idle, government deficits continue at the current pace, and production at companies remain below the potential output.

Going back to Keynes, this is where the government needs to step in. How to achieve wage inflation? By cutting taxes on wage earners. I.e. those folks who make their incomes through work producing real goods and services. Also known as the middle class and the working class. The groups who have been taking the brunt of the economic crisis. One which they largely didn't create. How to pay for this? By increasing taxes on those who benefit by increased incomes from unproductive activities. I.e. Wall St types and those who's incomes come from rents and capital gains. This isn't a punitive suggestion, merely a recognition that the wealth is flowing to those groups and they are not spending it to produce increased demand for the goods and services that the nation's companies are set up to produce. Such a trade off of taxes would be essentially revenue neutral, but would increase demand in the economy and send it back to full production and employment.

Such a suggestion goes against the entire "cut taxes on job creators and the wealthy" arguments.  But, I think that those arguments were weak to begin with, and have now been largely discredited by the current economic and financial crisis.  Will government have the will to make these changes?  Will the economics profession have the will to acknowledge these new policies are the correct ones to make?  Only time will tell.


Tuesday, November 5, 2013

Should America remain a sovereign nation??

The modern nation-state is a political entity that was created at the end of the thirty years war by the Peace of Westphalia.  This new concept recognized geographic boundaries of a nation and that nations should largely be free of outside influence.  Also, that the nation was the primary, cohesive entity with common internal interest that negotiated with other nation states that have their own interests.  The idea of empire became passe', particularly as related to a single sovereign person (king, emperor) or one of a religious state that ailed with a particular religious sect.

The essential properties of a nation-state are:
Sovereignty:  being independent from other nations.
Independence of the influence of external agents, either other nations or others.
Have relations with other nations.  The nation is the primary negotiating entity.
Has a population of citizens.  These folks have rights and responsibilities to the nation.
Has a geographic boundary.  The nation controls the land within its boundaries.
Has a national currency.  Controls and regulates the values of the currency used by the nation.
Has a common culture.  Common values, rituals, symbols, mythology, and history.
System of laws aligned with the culture.
A national defense to defend against other nations which could be hostile.

The United States of America, one could argue, became by the mid-twentieth century, the purest realization of the ideal of the nation-state.  It kicked out the british king and became sovereign.  It kicked out the british to get rid of external agents (at least they tried).  It formed relations with other nations, e.g. France.  Americans then thought of themselves as, well, Americans rather than brits.  The borders were the combination of the state boarders.  They eventually created a national currency, but that took some time.  By mid-twentieth century the US had a culture that bound its citizens (most of them at least) together with a common identity.  It had laws which reflected this culture and the founding principles of the rights of man.  And it developed a military in WWII that was able to overwhelm fascism.  So, the USA became truly a nation-state.

But how does a nation cause those properties to come into being and continue into the future?  That is what actions does a nation-state take and what structures does it put in place to actually be a nation-state?  Looking back at the list we see that the essential feature of a nation-state is controlling what transits boarders.  That is, what leaves and enters the geographic boundary of the nation.  Control over boarders is how the nation-state puts into effect the properties to be a nation-state.  In a sense, a nation is defined by its borders and the control thereof.  Well, what transits borders?  People, goods, services, money, communications, ideas.  These elements that transit borders are mostly economic and financial in nature.  So, being a nation entails border concerns with economic and finance issues as well as political issues.  So the opposite must also be true.  That is, nations which don't control their borders are no longer sovereign.

The US used to control these boarder crossing entities quite strictly, as do all sovereign nations.  Entering and leaving the country was controlled by strict visas on how long one could visit.  And for work, relatively few could enter and stay on a temporary basis.  Entry for work was predicate upon intent to immigrate and become a citizen.  And the right to immigrate was relatively difficult to secure.  The currency, i.e. the US dollar, was backed by gold and then by the gold exchange mechanism of Bretton Woods, which ensured its value and stability.  Trade was regulated to prevent deficits and protect key national industries by means of tariffs and quotas.  Even ideas were regulated to some extent as certain books and publications were prohibited from import.

Today the situation for the US is much different.  No longer are borders so controlled.  People flow over the border relatively unimpeded as illegals aliens to work in agriculture and construction.  H1-B visa workers come by the tens of thousands for years to fill technology positions because of a supposed shortage of domestic talent.  Trade is now almost totally unregulated, so massive deficits accrue year after year.  Financial transactions across the border are similarly almost unregulated with foreigners able to buy up property and businesses unimpeded.  National defense has become world policing for someone's interests.  However, who's interests that is remains a bit unclear.

Many of the essential characteristics of a sovereign nation have been given up by the US over the last few decades.  The US really doesn't control its borders anymore.  Which makes me ask: is the US still a sovereign nation?  and should it even continue to try to be one?  Perhaps the globalists are right? or at least are getting their way?

Friday, October 25, 2013

Dealing with China

In 2012 the US had a trade deficit with China of $315.0B.  That is, the US exported $110.6 to China while importing $425.6B of goods and services[1].  This is an extraordinary imbalance and constitutes the largest single contributor to the total trade deficit of $735B that same year.

Why would China want to run such a huge trade surplus with the US? And why would the US allow such a situation to continue so long?  There has been much speculation about these reasons.  Mainly because in politics the announced reasons are often not the real reasons.  So, I will also speculate about these as well.

For the first question, the Chinese have been growing their economy at a furious rate of about 8-10%/year in a bid to become a technologically advanced, developed nation.


In order to do this they need to spur domestic development at a level that is much higher than in the developed countries.  To do so using only domestic resources and investment mechanisms would likely proceed at a slower rate simply due to the inherent difficulties in growing that quickly.  Instead, the Chinese are supplementing growth by exporting the excess production, mainly to the US.  Thus, the US provides the demand to spur growth that would not generally come at home in China so quickly.  The other reason, which may be the more important one, is that China wants to import advanced technology that is only available in the west, and in the US in particular.  Many of the deals China now makes are not to purchase goods and services from the US with its vast holdings of USD, but to buy US companies with technologies that they need.  Or, to enter into production agreements with US firms which requires the US company to share their technology with their Chinese counterpart.

Why the US would allow this?  From a national perspective this ongoing deficit is bad as it adds to the total deficit and reduces employment in manufacturing in the US.  Worse, it transfers important technology from US companies to Chinese ones, or transfers the whole company to China.  Who benefits from this situation?  Well, US companies that move manufacturing to China can reduce their manufacturing costs to generate larger profits, as long as the Chinese Yuan (CNY) remains low relative to the USD.  That's the key for US companies, a low Yuan.  If the Yuan rises in value relative to the USD then the advantages of manufacturing in China drop and will eventually disappear, and so will their out-sized profits.

China, it is well known, intervenes in the currency market to keep the Yuan low against the dollar.  This keeps their exports up and technology flowing in.  It also pleases US companies that import from China, as they can continue to generate large profits.  But this creates the trade imbalance that doesn't allow market forces to bring trade into balance, and continues all the dislocations to the economy that have occurred.  One would think that the advocates of free trade would be furious at this and vociferous in their demands for market exchange rates for the Yuan.  But, hardly a peep.  The US sends some trade delegates, and even the President, to ask for a floating Yuan, but nothing happens.  In response, Washington does nothing.  Why would the Chinese change anything if there are no consequences to their policies?

The traditional solution to this is again the tariff.  Imposing a tariff is the needed consequence to not allowing the Yuan to float.  To be clear, a tariff for this reason has nothing to do with trade imbalances that exist for reasons other than China's intervention in the Yuan currency market.  The sole reason is that the currency market is designed to work only when exchanges of currencies are due to market forces alone.  Intervention breaks this system, so either China needs to play by the rules or we need a new system.  Now, I'm not a fan of floating market currency systems, as they have many problems that have be previously discussed.  But, at a minimum, if we're going to use this system then all participants need to play by the rules.  Or else face consequences.

A significant tariff (in a previous post I suggested ~60% for general trade) should be applied to imports from China.  The Chinese might not like this, as it thwarts their plan for growth and technology acquisition, and US companies which import would certainly not like the immediate hit to their bottom line.  So, imposing a tariff would largely be a political fight.  But with such powerful foes like China and US corporations on one side, who will represent America's interests in this fight?


[1] http://en.wikipedia.org/wiki/List_of_the_largest_trading_partners_of_the_United_States#cite_note-2

Wednesday, October 16, 2013

Two kinds of growth

Much has been written about how China and other developing nations are growing much faster than the developed nations in general, and the US in particular.  The growth of China's GDP over the last decade has averaged nearly 10%, while that of the US has been below 3%. 



This difference, it is implied, is due to the superiority of the Chinese model over the US model, which is now seen as faltering.  I think this kind of comparison is unfounded.  There are really two kinds of growth which I will term: Innovative growth, and Catch-up growth.

Developed nations, like the US, are operating near their potential production.  Although recently the recession has put a major dent in this.  What being near potential production means is that the economy is at full employment using state-of-the-art technology and is producing the maximum possible output.  More importantly the per capita production is maximal.  Any increase in production has to come from either increases in efficiency of current methods or innovations of new methods of production.  And, in any case, the former is usually a form of the latter.  So, for an advanced developed nation like the US to grow it has to innovate.  Innovation is risky, expensive, and time consuming.  Innovation forms a cost to current consumption that promises an increase in future growth, albeit at an uncertain rate.  The rate of growth in a developed country is mainly determined by the rate of investment in innovation.

In a developing country like China, the state of technology is generally far behind that of the developed countries.  That's pretty much the definition of developed and less-developed nations.  So, for that country to develop further it must first acquire existing technologies from the developed countries and implement them domestically.  The developing country must catch up technologically with the developed countries.  Importing technology is much simpler, cheaper, less risky, and less time consuming than creating new innovation themselves.  So, the developing country can grow much faster than the developed country.

The real issue for the US is that investment in innovation and new production has fallen, which limits the rate of growth of the economy.  But, even when those pick up again, a growth rate much above 3% is unlikely due to the need for massive investment in innovation to spur such high growth rates.  A massive level of investment does not seem likely without some government mandate for some great national cause.

The effects of imposing tarrifs on trade

Today tariffs average a mere 1.3% [1], which is quite low by historical levels, where tariffs have more typically been in the 10%-30% range.  What would be the effect of raising the average tariff to 10%?  The US imported $2299B of goods and services in 2012 [2], and exports of $1564B in the same year [3], so we'll use these number for a simple analysis.

What effect would that 10% tariff have on the balance of trade?  This is a complicated question but one for which we can make some simple estimates.  A recent study of the effects of trade barriers [4] finds that "The elasticity of imports to the domestic cost of importing is about 0.50, and that of exports to the domestic cost of exporting is about 0.48. That is, a 10% reduction in the cost associated with importing (exporting) would increase imports (exports) by about 5% (4.8%)."  Per country details vary but we can nonetheless use these values to estimate the effect of changes in tariffs on the level of imports and exports for the US.  An increase in tariffs acts the same way.  That is, for imports an increase in the tariff of 10% will decrease the amount of imports by 5%.  A tariff is just a percentage increase in price of an imported good.

Elasticity is a bit difficult for many people to understand.  But it basically says if I perturb one value a little bit, how much does the other value change?  In the case of imports a small change in price causes half as much change in imports.  A key concept here is that elasticity is only valid for small changes in values.  Even the change of 10% in price is probably a bit unrealistic, but it will nonetheless give us some idea of how imports are changing with price.

Balancing trade requires that the level of imports equals the level of exports.  So, to decrease the level of imports to that of the level of exports in 2012 is a drop from $2299B to $1564B, which is a large reduction of imports of 32%.  Given the elasticity factor of tariffs for imports of 0.50, this means the tariff increase needed on imports to achieve this goal is 32%/0.50 = 64%.  This is a large tariff by historical standards, and in practice this amount may not be needed as the actual adjusting of trade is not so simply defined by the elasticity.

The complexities of trade suggest that an incremental approach to tariff be taken.  Start by increasing the tariff to 10% one year and see the effects.  Perhaps increase the tariff again the next year and see the effects.  Continue increasing the tariff until trade comes to a balance.  Or in the case of the US, a surplus is generated, which is needed to pay down the years of accumulated trade deficits.

A second benefit of the tariff is raising revenue for the government.  A simple application of the tariff assuming no change in imports for a 10% tariff  to all of the new level of imports of $2184B it would produce $218.4B of revenue for the US government, which is $190B more than the government collected would have collected.  Tariffs reduce the tax burden on Americans and helps balance the budget as well as affecting trade.


Still using general references due to the government shutdown
[1] http://en.wikipedia.org/wiki/Tariffs_in_United_States_history
[2] https://www.cia.gov/library/publications/the-world-factbook/rankorder/2087rank.html
[3] https://www.cia.gov/library/publications/the-world-factbook/rankorder/2078rank.html
[4] Hoekman, Bernard & Nicita, Alessandro, 2011. "Trade Policy, Trade Costs, and Developing Country Trade," World Development, Elsevier, vol. 39(12), pages 2069-2079.