Checkerboard Puzzle, Moore's Law, and Growth Prospects

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My father the mathematician first posed the checkerboard puzzle to me back in grade-school, perhaps on some rainy Saturday. His version of the story went something like this:

The jester performs a great deed, and the king asks him how he would like to be rewarded. The jester is aware that the king is a highly volatile individual, and if the jester asks for too much, the king might just kill him then and there. The jester also knows that the king views his promise as sacred, so if the king says "yes" to the jester's proposal, then the king will honor that promise. So in a way, the jester's problem is how to ask for a lot, but have the king at least initially think it's not very much, so that the king will give his consent.

So the jester clowns around a bit and then says: "Here's all I want. Take this checkerboard. On the first square, but one piece of gold. On the second square, two pieces. On the third square, four pieces, and on the fourth square, 8 pieces. Double the amount on each square until you reach the end of the checkerboard."

In the story, the king laughs at this comic proposal and says,  "Your great deed was so wonderful, I would have happily done much more than this! I grant your request!"

But of course, when the king starts hauling up gold pieces from the treasury, he will discover that 2 raised to the 63rd power, the final spot on the checkerboard requires about 9 quintillion gold pieces (that is, 9 followed by 18 zeros). 

I've had some sense of the power of exponential growth ever since.  But what I hadn't thought about is the interaction of Moore's Law and economic growth. Moore's Law is of course named for Gordon Moore, one of the founders of Intel, who noticed this pattern back in 1965. Back in the 1970s, he wrote a paper that contained the following graph showing how much it cost to produce a computer chip with a certain number of components. Here's his figure. Notice that the numbers of component on the horizontal axis and the cost figures on the vertical axis are both graphed as logarithm (specifically, each step up the axis is a change by a factor of 10). The key takeaway was that the number of transistors ("components") on an integrated circuit was doubling about every two years, making computing power much cheaper and faster.


Ever since I started reading up on Moore's law in the early 1980s, there have been predictions in the trade press that it will soon reach technological limits and come to and end. But Moore's law marches on: indeed, the research and innovation targets at Intel and other chip-makers are defined in terms of making sure that Moore's law continues to hold for at least awhile longer. Stephen Shankland offers a nice accessible overview of the current situation in an October 15, 2012, essay on CNET: ""Moore's Law: The rule that really matters in tech"  (The Gordon Moore graph above is copied from Shankland's essay.)

As Shankland writes: "To keep up with Moore's Law, engineers must keep shrinking the size of transistors. Intel, the leader in the race, currently uses a manufacturing process with 22-nanometer features. That's 22 billionths of a meter, or roughly a 4,000th the width of a human hair." He cites a variety of industry and research experts to the effect that Moore's law has at least another decade to run--and remember, a decade of doubling every two years means five more doublings!

It's hard to wrap one's mind around what it means to say that the power of microchipo technology will increase by a factor of 32 (doubling five times) in the next 10 years. A characteristically intriguing survey essay  from the January 10 issue of the Economist on the future of innovation uses the checkerboard analogy to think about the potential effects of Moore's law. Here's a comment from the Economist essay:

Ray Kurzweil, a pioneer of computer science and a devotee of exponential technological extrapolation, likes to talk of “the second half of the chess board”. There is an old fable in which a gullible king is tricked into paying an obligation in grains of rice, one on the first square of a chessboard, two on the second, four on the third, the payment doubling with every square. Along the first row, the obligation is minuscule. With half the chessboard covered, the king is out only about 100 tonnes of rice. But a square before reaching the end of the seventh row he has laid out 500m tonnes in total—the whole world’s annual rice production. He will have to put more or less the same amount again on the next square. And there will still be a row to go.

Erik Brynjolfsson and Andrew McAfee of MIT make use of this image in their e-book “Race Against the Machine”. By the measure known as Moore’s law, the ability to get calculations out of a piece of silicon doubles every 18 months. That growth rate will not last for ever; but other aspects of computation, such as the capacity of algorithms to handle data, are also growing exponentially. When such a capacity is low, that doubling does not matter. As soon as it matters at all, though, it can quickly start to matter a lot. On the second half of the chessboard not only has the cumulative effect of innovations become large, but each new iteration of innovation delivers a technological jolt as powerful as all previous rounds combined."

Now, it's of course true that doubling the capacity of computer chips doesn't translate in a direct way into a higher standard of living: there are many steps from one to the other. But my point here is to note that many of us (myself included) have been thinking about the changes in electronics technology a little too much like the king in the checkerboard story: that is, we think of something doubling a few times, even 10 or 20 times, and we know it's a big change, but it somehow seems within our range of comprehension.

But when something has already been doubling every 18 months or two years for a half-century--it is continuing to double!--the absolute size of each additional doubling is starting to get very large. I lack the imagination to conceive of what will be done with all this cheap computing power in terms of health care, education, industrial process, communication, transportation, entertainment, food, travel, design, and more. But I suspect that these enormous repeated doublings, as Moore's law marches forward in the next decade and drives computing speeds up and prices down, will transform lives and industries in ways that we are only just starting to imagine.

Checkerboard Puzzle, Moore's Law, and Growth Prospects

To contact us Click HERE
My father the mathematician first posed the checkerboard puzzle to me back in grade-school, perhaps on some rainy Saturday. His version of the story went something like this:

The jester performs a great deed, and the king asks him how he would like to be rewarded. The jester is aware that the king is a highly volatile individual, and if the jester asks for too much, the king might just kill him then and there. The jester also knows that the king views his promise as sacred, so if the king says "yes" to the jester's proposal, then the king will honor that promise. So in a way, the jester's problem is how to ask for a lot, but have the king at least initially think it's not very much, so that the king will give his consent.

So the jester clowns around a bit and then says: "Here's all I want. Take this checkerboard. On the first square, but one piece of gold. On the second square, two pieces. On the third square, four pieces, and on the fourth square, 8 pieces. Double the amount on each square until you reach the end of the checkerboard."

In the story, the king laughs at this comic proposal and says,  "Your great deed was so wonderful, I would have happily done much more than this! I grant your request!"

But of course, when the king starts hauling up gold pieces from the treasury, he will discover that 2 raised to the 63rd power, the final spot on the checkerboard requires about 9 quintillion gold pieces (that is, 9 followed by 18 zeros). 

I've had some sense of the power of exponential growth ever since.  But what I hadn't thought about is the interaction of Moore's Law and economic growth. Moore's Law is of course named for Gordon Moore, one of the founders of Intel, who noticed this pattern back in 1965. Back in the 1970s, he wrote a paper that contained the following graph showing how much it cost to produce a computer chip with a certain number of components. Here's his figure. Notice that the numbers of component on the horizontal axis and the cost figures on the vertical axis are both graphed as logarithm (specifically, each step up the axis is a change by a factor of 10). The key takeaway was that the number of transistors ("components") on an integrated circuit was doubling about every two years, making computing power much cheaper and faster.


Ever since I started reading up on Moore's law in the early 1980s, there have been predictions in the trade press that it will soon reach technological limits and come to and end. But Moore's law marches on: indeed, the research and innovation targets at Intel and other chip-makers are defined in terms of making sure that Moore's law continues to hold for at least awhile longer. Stephen Shankland offers a nice accessible overview of the current situation in an October 15, 2012, essay on CNET: ""Moore's Law: The rule that really matters in tech"  (The Gordon Moore graph above is copied from Shankland's essay.)

As Shankland writes: "To keep up with Moore's Law, engineers must keep shrinking the size of transistors. Intel, the leader in the race, currently uses a manufacturing process with 22-nanometer features. That's 22 billionths of a meter, or roughly a 4,000th the width of a human hair." He cites a variety of industry and research experts to the effect that Moore's law has at least another decade to run--and remember, a decade of doubling every two years means five more doublings!

It's hard to wrap one's mind around what it means to say that the power of microchipo technology will increase by a factor of 32 (doubling five times) in the next 10 years. A characteristically intriguing survey essay  from the January 10 issue of the Economist on the future of innovation uses the checkerboard analogy to think about the potential effects of Moore's law. Here's a comment from the Economist essay:

Ray Kurzweil, a pioneer of computer science and a devotee of exponential technological extrapolation, likes to talk of “the second half of the chess board”. There is an old fable in which a gullible king is tricked into paying an obligation in grains of rice, one on the first square of a chessboard, two on the second, four on the third, the payment doubling with every square. Along the first row, the obligation is minuscule. With half the chessboard covered, the king is out only about 100 tonnes of rice. But a square before reaching the end of the seventh row he has laid out 500m tonnes in total—the whole world’s annual rice production. He will have to put more or less the same amount again on the next square. And there will still be a row to go.

Erik Brynjolfsson and Andrew McAfee of MIT make use of this image in their e-book “Race Against the Machine”. By the measure known as Moore’s law, the ability to get calculations out of a piece of silicon doubles every 18 months. That growth rate will not last for ever; but other aspects of computation, such as the capacity of algorithms to handle data, are also growing exponentially. When such a capacity is low, that doubling does not matter. As soon as it matters at all, though, it can quickly start to matter a lot. On the second half of the chessboard not only has the cumulative effect of innovations become large, but each new iteration of innovation delivers a technological jolt as powerful as all previous rounds combined."

Now, it's of course true that doubling the capacity of computer chips doesn't translate in a direct way into a higher standard of living: there are many steps from one to the other. But my point here is to note that many of us (myself included) have been thinking about the changes in electronics technology a little too much like the king in the checkerboard story: that is, we think of something doubling a few times, even 10 or 20 times, and we know it's a big change, but it somehow seems within our range of comprehension.

But when something has already been doubling every 18 months or two years for a half-century--it is continuing to double!--the absolute size of each additional doubling is starting to get very large. I lack the imagination to conceive of what will be done with all this cheap computing power in terms of health care, education, industrial process, communication, transportation, entertainment, food, travel, design, and more. But I suspect that these enormous repeated doublings, as Moore's law marches forward in the next decade and drives computing speeds up and prices down, will transform lives and industries in ways that we are only just starting to imagine.

Checkerboard Puzzle, Moore's Law, and Growth Prospects

To contact us Click HERE
My father the mathematician first posed the checkerboard puzzle to me back in grade-school, perhaps on some rainy Saturday. His version of the story went something like this:

The jester performs a great deed, and the king asks him how he would like to be rewarded. The jester is aware that the king is a highly volatile individual, and if the jester asks for too much, the king might just kill him then and there. The jester also knows that the king views his promise as sacred, so if the king says "yes" to the jester's proposal, then the king will honor that promise. So in a way, the jester's problem is how to ask for a lot, but have the king at least initially think it's not very much, so that the king will give his consent.

So the jester clowns around a bit and then says: "Here's all I want. Take this checkerboard. On the first square, but one piece of gold. On the second square, two pieces. On the third square, four pieces, and on the fourth square, 8 pieces. Double the amount on each square until you reach the end of the checkerboard."

In the story, the king laughs at this comic proposal and says,  "Your great deed was so wonderful, I would have happily done much more than this! I grant your request!"

But of course, when the king starts hauling up gold pieces from the treasury, he will discover that 2 raised to the 63rd power, the final spot on the checkerboard requires about 9 quintillion gold pieces (that is, 9 followed by 18 zeros). 

I've had some sense of the power of exponential growth ever since.  But what I hadn't thought about is the interaction of Moore's Law and economic growth. Moore's Law is of course named for Gordon Moore, one of the founders of Intel, who noticed this pattern back in 1965. Back in the 1970s, he wrote a paper that contained the following graph showing how much it cost to produce a computer chip with a certain number of components. Here's his figure. Notice that the numbers of component on the horizontal axis and the cost figures on the vertical axis are both graphed as logarithm (specifically, each step up the axis is a change by a factor of 10). The key takeaway was that the number of transistors ("components") on an integrated circuit was doubling about every two years, making computing power much cheaper and faster.


Ever since I started reading up on Moore's law in the early 1980s, there have been predictions in the trade press that it will soon reach technological limits and come to and end. But Moore's law marches on: indeed, the research and innovation targets at Intel and other chip-makers are defined in terms of making sure that Moore's law continues to hold for at least awhile longer. Stephen Shankland offers a nice accessible overview of the current situation in an October 15, 2012, essay on CNET: ""Moore's Law: The rule that really matters in tech"  (The Gordon Moore graph above is copied from Shankland's essay.)

As Shankland writes: "To keep up with Moore's Law, engineers must keep shrinking the size of transistors. Intel, the leader in the race, currently uses a manufacturing process with 22-nanometer features. That's 22 billionths of a meter, or roughly a 4,000th the width of a human hair." He cites a variety of industry and research experts to the effect that Moore's law has at least another decade to run--and remember, a decade of doubling every two years means five more doublings!

It's hard to wrap one's mind around what it means to say that the power of microchipo technology will increase by a factor of 32 (doubling five times) in the next 10 years. A characteristically intriguing survey essay  from the January 10 issue of the Economist on the future of innovation uses the checkerboard analogy to think about the potential effects of Moore's law. Here's a comment from the Economist essay:

Ray Kurzweil, a pioneer of computer science and a devotee of exponential technological extrapolation, likes to talk of “the second half of the chess board”. There is an old fable in which a gullible king is tricked into paying an obligation in grains of rice, one on the first square of a chessboard, two on the second, four on the third, the payment doubling with every square. Along the first row, the obligation is minuscule. With half the chessboard covered, the king is out only about 100 tonnes of rice. But a square before reaching the end of the seventh row he has laid out 500m tonnes in total—the whole world’s annual rice production. He will have to put more or less the same amount again on the next square. And there will still be a row to go.

Erik Brynjolfsson and Andrew McAfee of MIT make use of this image in their e-book “Race Against the Machine”. By the measure known as Moore’s law, the ability to get calculations out of a piece of silicon doubles every 18 months. That growth rate will not last for ever; but other aspects of computation, such as the capacity of algorithms to handle data, are also growing exponentially. When such a capacity is low, that doubling does not matter. As soon as it matters at all, though, it can quickly start to matter a lot. On the second half of the chessboard not only has the cumulative effect of innovations become large, but each new iteration of innovation delivers a technological jolt as powerful as all previous rounds combined."

Now, it's of course true that doubling the capacity of computer chips doesn't translate in a direct way into a higher standard of living: there are many steps from one to the other. But my point here is to note that many of us (myself included) have been thinking about the changes in electronics technology a little too much like the king in the checkerboard story: that is, we think of something doubling a few times, even 10 or 20 times, and we know it's a big change, but it somehow seems within our range of comprehension.

But when something has already been doubling every 18 months or two years for a half-century--it is continuing to double!--the absolute size of each additional doubling is starting to get very large. I lack the imagination to conceive of what will be done with all this cheap computing power in terms of health care, education, industrial process, communication, transportation, entertainment, food, travel, design, and more. But I suspect that these enormous repeated doublings, as Moore's law marches forward in the next decade and drives computing speeds up and prices down, will transform lives and industries in ways that we are only just starting to imagine.

The Financial Cycle: Theory and Implications

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In the aftermath of the Great Recession, mainstream macroeconomists have been seeking in various ways to bring the financial sector into their models. As that activity implies, the financial sector had not previously been playing much of a role mainstream models. Claudio Borio lays out a perspective on treating cycles in the financial sector as having a life of their own in "The financial cycle andmacroeconomics: What have we learnt?", published in December 2012  as working paper #395 for the Bank of International Settlements. I should note that Borio's view of how the financial sector interrelates with the real economy is not conventional macroeconomic wisdom, but I should also note that conventional macroeconomics hasn't exactly covered itself with glory in the last few years.


Borio begins by point out that conventional macroeconomics was paying little attention to the financial sector in the years before the Great Recession, and argues that the strategies for trying to add a  financial sector to existing models doesn't go nearly far enough. (Citations and footnote are omitted from quotations throughout.)  Here's Borio: "The financial crisis that engulfed mature economies in the late 2000s has prompted much soul searching. Economists are now trying hard to
incorporate financial factors into standard macroeconomic models. However, the prevailing,
in fact almost exclusive, strategy is a conservative one. It is to graft additional so-called
financial “frictions” on otherwise fully well behaved equilibrium macroeconomic models ... The main thesis is that macroeconomics without the financial cycle is like Hamlet without the Prince. In the environment that has prevailed for at least three decades now, just as in the one that prevailed in the pre-WW2 years, it is simply not possible to understand business fluctuations and their policy challenges without understanding the financial cycle."

Borio argues that there is a "financial cycle" with its own dynamics. Here's a figure with U.S. data showing the regular business cycle, measured by variations in GDP, compared with the "financial cycle," based on estimates of credit, the credit/GDP ratio, and property prices. He argues that while business cycles are usually in the range of 1-8 years, "the average length of the financial cycle in a sample of seven industrialised countries since the 1960s has been around 16 years."

Borio argues that the peaks of the financial cycle are associated with financial crises. When a business cycle recession happens at the same time as the contraction part of a financial cycle, the recession is about 50% deeper.

This perspective on the financial cycle also offers some policy advice. Central banks and financial regulators should pay attention to credit/GDP ratios and to property prices. Borio writes: "The idea is to build up buffers in good times, as financial vulnerabilities grow, so as to be able to draw them down in bad times, as financial stress materialises. There are many ways of doing so, through the appropriate design of tools such as capital and liquidity standards, provisioning, collateral and margining practices, and so on. ... In the case of monetary policy, it is necessary to adopt strategies that allow central banks to tighten so as to lean against the build-up of financial imbalances even if near-term inflation remains subdued – what might be called the “lean option”. Operationally, this calls for extending policy horizons beyond the roughly 2-year ones typical of inflation targeting regimes and for giving greater prominence to the balance of risks in the outlook, fully taking into account the slow build-up of vulnerabilities associated with the financial cycle. ... In the case of fiscal policy, there is a need for extra prudence during economic expansions associated with financial booms. ...  Financial booms are especially generous for the public coffers, because of the structure of revenues. And the sovereign inadvertently accumulates contingent liabilities, which crystallise as the
boom turns to bust and balance sheet problems emerge, especially in the financial sector."

However, once the double-whammy of a financial crisis and a business cycle recession has hit simultaneously, Borio also argues that conventional policy responses may not work well. In a "balance sheet recession," fiscal and monetary policy may not be very capable of stimulating demand, and instead may encourage financial firms and businesses to put off the necessary hard steps they need to take, leaving the economy too dependent on government stimulation rather than on the private sector moving forward. As he writes:  "On reflection, the basic reason for the limitations of monetary policy in a financial bust is not hard to find. Monetary policy typically operates by encouraging borrowing, boosting asset prices and risk-taking. But initial conditions already include too much debt, too-high asset prices (property) and too much risk-taking. There is an inevitable tension between how policy works and the direction the economy needs to take."

The concept of a "financial cycle" has a plausible back-story. When times are good, borrowers and investors of all kinds tend to let down their guard, worry less about risks, and gradually become overextended--which can then brings on a counterreaction, or even in some cases a financial crisis. It's easy to point to financial crises, but it's harder to show convincingly that an earlier financial boom is the cause of the crisis. The nice smooth curve of financial cycles above is created by using statistical tools ("filtering") to blend together tBorio is up front about this difficulty and others, and has some suggestions for how the appropriate modeling might proceed. But even if one doesn't buy into the notion of a self-perpetuating financial cycle, standing apart from the regular business cycle, one lesson that everyone seems to have learned from the Great Recession is that rapid expansions of credit and rapid rises in property values have real macroeconomic risks--and thus are an appropriate target for policy.


 

Checkerboard Puzzle, Moore's Law, and Growth Prospects

To contact us Click HERE
My father the mathematician first posed the checkerboard puzzle to me back in grade-school, perhaps on some rainy Saturday. His version of the story went something like this:

The jester performs a great deed, and the king asks him how he would like to be rewarded. The jester is aware that the king is a highly volatile individual, and if the jester asks for too much, the king might just kill him then and there. The jester also knows that the king views his promise as sacred, so if the king says "yes" to the jester's proposal, then the king will honor that promise. So in a way, the jester's problem is how to ask for a lot, but have the king at least initially think it's not very much, so that the king will give his consent.

So the jester clowns around a bit and then says: "Here's all I want. Take this checkerboard. On the first square, but one piece of gold. On the second square, two pieces. On the third square, four pieces, and on the fourth square, 8 pieces. Double the amount on each square until you reach the end of the checkerboard."

In the story, the king laughs at this comic proposal and says,  "Your great deed was so wonderful, I would have happily done much more than this! I grant your request!"

But of course, when the king starts hauling up gold pieces from the treasury, he will discover that 2 raised to the 63rd power, the final spot on the checkerboard requires about 9 quintillion gold pieces (that is, 9 followed by 18 zeros). 

I've had some sense of the power of exponential growth ever since.  But what I hadn't thought about is the interaction of Moore's Law and economic growth. Moore's Law is of course named for Gordon Moore, one of the founders of Intel, who noticed this pattern back in 1965. Back in the 1970s, he wrote a paper that contained the following graph showing how much it cost to produce a computer chip with a certain number of components. Here's his figure. Notice that the numbers of component on the horizontal axis and the cost figures on the vertical axis are both graphed as logarithm (specifically, each step up the axis is a change by a factor of 10). The key takeaway was that the number of transistors ("components") on an integrated circuit was doubling about every two years, making computing power much cheaper and faster.


Ever since I started reading up on Moore's law in the early 1980s, there have been predictions in the trade press that it will soon reach technological limits and come to and end. But Moore's law marches on: indeed, the research and innovation targets at Intel and other chip-makers are defined in terms of making sure that Moore's law continues to hold for at least awhile longer. Stephen Shankland offers a nice accessible overview of the current situation in an October 15, 2012, essay on CNET: ""Moore's Law: The rule that really matters in tech"  (The Gordon Moore graph above is copied from Shankland's essay.)

As Shankland writes: "To keep up with Moore's Law, engineers must keep shrinking the size of transistors. Intel, the leader in the race, currently uses a manufacturing process with 22-nanometer features. That's 22 billionths of a meter, or roughly a 4,000th the width of a human hair." He cites a variety of industry and research experts to the effect that Moore's law has at least another decade to run--and remember, a decade of doubling every two years means five more doublings!

It's hard to wrap one's mind around what it means to say that the power of microchipo technology will increase by a factor of 32 (doubling five times) in the next 10 years. A characteristically intriguing survey essay  from the January 10 issue of the Economist on the future of innovation uses the checkerboard analogy to think about the potential effects of Moore's law. Here's a comment from the Economist essay:

Ray Kurzweil, a pioneer of computer science and a devotee of exponential technological extrapolation, likes to talk of “the second half of the chess board”. There is an old fable in which a gullible king is tricked into paying an obligation in grains of rice, one on the first square of a chessboard, two on the second, four on the third, the payment doubling with every square. Along the first row, the obligation is minuscule. With half the chessboard covered, the king is out only about 100 tonnes of rice. But a square before reaching the end of the seventh row he has laid out 500m tonnes in total—the whole world’s annual rice production. He will have to put more or less the same amount again on the next square. And there will still be a row to go.

Erik Brynjolfsson and Andrew McAfee of MIT make use of this image in their e-book “Race Against the Machine”. By the measure known as Moore’s law, the ability to get calculations out of a piece of silicon doubles every 18 months. That growth rate will not last for ever; but other aspects of computation, such as the capacity of algorithms to handle data, are also growing exponentially. When such a capacity is low, that doubling does not matter. As soon as it matters at all, though, it can quickly start to matter a lot. On the second half of the chessboard not only has the cumulative effect of innovations become large, but each new iteration of innovation delivers a technological jolt as powerful as all previous rounds combined."

Now, it's of course true that doubling the capacity of computer chips doesn't translate in a direct way into a higher standard of living: there are many steps from one to the other. But my point here is to note that many of us (myself included) have been thinking about the changes in electronics technology a little too much like the king in the checkerboard story: that is, we think of something doubling a few times, even 10 or 20 times, and we know it's a big change, but it somehow seems within our range of comprehension.

But when something has already been doubling every 18 months or two years for a half-century--it is continuing to double!--the absolute size of each additional doubling is starting to get very large. I lack the imagination to conceive of what will be done with all this cheap computing power in terms of health care, education, industrial process, communication, transportation, entertainment, food, travel, design, and more. But I suspect that these enormous repeated doublings, as Moore's law marches forward in the next decade and drives computing speeds up and prices down, will transform lives and industries in ways that we are only just starting to imagine.

Rebuilding Unemployment Insurance

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In theory,  the federal government sets minimum guidelines for each state's unemployment insurance system, and then each state sets its own rules for what is paid in and and what benefits are offered. Each state has its own unemployment trust fund. The idea is that the the trust fund will build up in good economic times, and then be drawn down in recessions. But it hasn't actually worked that way for a long time, and the problem is getting worse.  Christopher J. O’Leary lays out the issue and possible solutions in "A Changing Federal-State Balance in Unemployment Insurance?" written for the January 2013 Employment Research Newsletter published by the Upjohn Institute.

When a recession hits, the federal government has developed a habit of stepping in with extra unemployment insurance funds. For example, the feds stepped in with additional funding for extending unemployment benefits in 1958, 1961, 1971, 1974, 1982, 1991 and 2002--as well as during the most recent recession. With the feds stepping up, it has been easier and easier for the states to keep their unemployment taxes as low as possible. For example, average unemployment insurance taxes (adjusted for inflation) were $274/employee in 2008, lower than the $350/employee in 1994 and the $515/employee in 1984, according to Ronald Wilus of the U.S. Department of Labor.

As a result, over time the feds are paying for a larger share of unemployment insurance during recessions. Here's an illustrative figure from O'Leary.


For some perspective on the revenues coming into the unemployment trust funds from the regular unemployment tax, as opposed to how much money is going out, here's a table from a Congressional Research Service report on "Unemployment Insurance: Programs and Benefits," by Julie M. Whittaker and Katelin P. Isaacs, dated December 31, 2012. Notice that when unemployment rates were fairly low from 2005-2007, revenue exceeded outlays by about $10 billion per year. Then from 2009, 2010, and 2010, outlays exceeded revenue by something like $100 billion per year. The difference was made up by general taxpayer spending.

The intergovernmental incentives in the unemployment insurance system are clearly messed up. States have an incentive to keep unemployment insurance premiums fairly low, promise significant benefits, and then let the federal government pick up the tab when a recession occurs. What would be needed to get back to a system where states save up funds for unemployment insurance money in trust funds--even if some federal help might occasionally be needed?

One step suggested by O'Leary is to raise the "tax base." At present, the minimum federal standard requires that states collect unemployment insurance taxes on the first $7000 of taxable wages--a level that was established back in 1983. Just adjusting that $7,000 base for inflation would mean increasing it to about $16,000. O'Leary notes that 35 states currently have a taxable wage base at or below $15,000.

A second step would be to have a rule that unemployment insurance benefits would not kick in until after a waiting period. O'Leary writes: "A much neglected potential reform on the benefit side would be to institute waiting periods of 2–4 weeks, with the duration of the wait depending inversely on the aggregate level of unemployment. ... A somewhat longer waiting period will reduce program entry by those with ready reemployment options, and help to preserve the income security strength of the system for those who are involuntarily jobless for 4, 5, or 6 months."

Yet another step would be to use federal rules to discourage states from lowballing the funding of their unemployment insurance and relying on an influx of federal funding. Here's O'Leary: "[T]he federal partner should institute minimum standards on weekly benefit levels and durations, and also tie potential durations of any future federal emergency benefits to the existing state maximum durations. For example, a state providing up to 26 weeks would get 13 weeks of federal temporary benefits, but if the state maximum were 20 weeks the federal supplement would be 10 weeks."

It's worth pointing out that unemployment insurance has a number of problems other than whether it is pre-funded. You need to meet certain qualification tests for unemployment insurance, typically based on earnings in the previous year or so, and as a result, many of the unemployed do not receive unemployment insurance. In January 2013, about 3.5 million people were receiving unemployment insurance benefits, but about 12.3 million people were unemployed.


There are also a number of proposals that seek to adjust the incentives so that unemployment insurance can better co-exist with incentives to find a new job. Some proposals are that unemployment benefits should be larger, so as to soften the economic blow of unemployment, but for a shorter time, to hasten the incentive to find a new job. Some proposals would require or allow people to set up individual unemployment accounts, which they could keep at retirement, so that people would tap their own money before turning to the government fund. One proposal would offer a bonus to those receiving unemployment insurance if they found a job quickly, because it could be less costly for the unemployment insurance trust fund if they find a job faster rather than linger on receiving benefits.

The Great Recession and its aftermath have wrecked the premises of the existing unemployment insurance system. It's time to rebuild.

Checkerboard Puzzle, Moore's Law, and Growth Prospects

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My father the mathematician first posed the checkerboard puzzle to me back in grade-school, perhaps on some rainy Saturday. His version of the story went something like this:

The jester performs a great deed, and the king asks him how he would like to be rewarded. The jester is aware that the king is a highly volatile individual, and if the jester asks for too much, the king might just kill him then and there. The jester also knows that the king views his promise as sacred, so if the king says "yes" to the jester's proposal, then the king will honor that promise. So in a way, the jester's problem is how to ask for a lot, but have the king at least initially think it's not very much, so that the king will give his consent.

So the jester clowns around a bit and then says: "Here's all I want. Take this checkerboard. On the first square, but one piece of gold. On the second square, two pieces. On the third square, four pieces, and on the fourth square, 8 pieces. Double the amount on each square until you reach the end of the checkerboard."

In the story, the king laughs at this comic proposal and says,  "Your great deed was so wonderful, I would have happily done much more than this! I grant your request!"

But of course, when the king starts hauling up gold pieces from the treasury, he will discover that 2 raised to the 63rd power, the final spot on the checkerboard requires about 9 quintillion gold pieces (that is, 9 followed by 18 zeros). 

I've had some sense of the power of exponential growth ever since.  But what I hadn't thought about is the interaction of Moore's Law and economic growth. Moore's Law is of course named for Gordon Moore, one of the founders of Intel, who noticed this pattern back in 1965. Back in the 1970s, he wrote a paper that contained the following graph showing how much it cost to produce a computer chip with a certain number of components. Here's his figure. Notice that the numbers of component on the horizontal axis and the cost figures on the vertical axis are both graphed as logarithm (specifically, each step up the axis is a change by a factor of 10). The key takeaway was that the number of transistors ("components") on an integrated circuit was doubling about every two years, making computing power much cheaper and faster.


Ever since I started reading up on Moore's law in the early 1980s, there have been predictions in the trade press that it will soon reach technological limits and come to and end. But Moore's law marches on: indeed, the research and innovation targets at Intel and other chip-makers are defined in terms of making sure that Moore's law continues to hold for at least awhile longer. Stephen Shankland offers a nice accessible overview of the current situation in an October 15, 2012, essay on CNET: ""Moore's Law: The rule that really matters in tech"  (The Gordon Moore graph above is copied from Shankland's essay.)

As Shankland writes: "To keep up with Moore's Law, engineers must keep shrinking the size of transistors. Intel, the leader in the race, currently uses a manufacturing process with 22-nanometer features. That's 22 billionths of a meter, or roughly a 4,000th the width of a human hair." He cites a variety of industry and research experts to the effect that Moore's law has at least another decade to run--and remember, a decade of doubling every two years means five more doublings!

It's hard to wrap one's mind around what it means to say that the power of microchipo technology will increase by a factor of 32 (doubling five times) in the next 10 years. A characteristically intriguing survey essay  from the January 10 issue of the Economist on the future of innovation uses the checkerboard analogy to think about the potential effects of Moore's law. Here's a comment from the Economist essay:

Ray Kurzweil, a pioneer of computer science and a devotee of exponential technological extrapolation, likes to talk of “the second half of the chess board”. There is an old fable in which a gullible king is tricked into paying an obligation in grains of rice, one on the first square of a chessboard, two on the second, four on the third, the payment doubling with every square. Along the first row, the obligation is minuscule. With half the chessboard covered, the king is out only about 100 tonnes of rice. But a square before reaching the end of the seventh row he has laid out 500m tonnes in total—the whole world’s annual rice production. He will have to put more or less the same amount again on the next square. And there will still be a row to go.

Erik Brynjolfsson and Andrew McAfee of MIT make use of this image in their e-book “Race Against the Machine”. By the measure known as Moore’s law, the ability to get calculations out of a piece of silicon doubles every 18 months. That growth rate will not last for ever; but other aspects of computation, such as the capacity of algorithms to handle data, are also growing exponentially. When such a capacity is low, that doubling does not matter. As soon as it matters at all, though, it can quickly start to matter a lot. On the second half of the chessboard not only has the cumulative effect of innovations become large, but each new iteration of innovation delivers a technological jolt as powerful as all previous rounds combined."

Now, it's of course true that doubling the capacity of computer chips doesn't translate in a direct way into a higher standard of living: there are many steps from one to the other. But my point here is to note that many of us (myself included) have been thinking about the changes in electronics technology a little too much like the king in the checkerboard story: that is, we think of something doubling a few times, even 10 or 20 times, and we know it's a big change, but it somehow seems within our range of comprehension.

But when something has already been doubling every 18 months or two years for a half-century--it is continuing to double!--the absolute size of each additional doubling is starting to get very large. I lack the imagination to conceive of what will be done with all this cheap computing power in terms of health care, education, industrial process, communication, transportation, entertainment, food, travel, design, and more. But I suspect that these enormous repeated doublings, as Moore's law marches forward in the next decade and drives computing speeds up and prices down, will transform lives and industries in ways that we are only just starting to imagine.