Thursday, April 10, 2014

Guest Post by John Mondragon: Keeping Up with the Joneses and Household Debt

This guest post was contributed by John Mondragon, an economics PhD candidate at Berkeley. He is the coauthor of a working paper that is closely related to my recent post on consumption contagion and income inequality. I'm very excited that he has agreed to contribute this post about the working paper. John is on Twitter @Mondragon_John

Since the 1980s U.S. households have dramatically increased the amount of debt they hold. One frequent explanation for this trend is that the large increase in income inequality over this same period caused households to borrow more (see Figure 1). The intuition is that low-income households attempted to “keep up” with the increasing consumption of their high-income neighbors. This could affect debt levels if the low-income household decides to fund its consumption by leveraging with debt (as opposed to increasing labor supply or drawing down assets). This type of behavior is often referred to as “keeping up with the Joneses”, consumption cascades, consumption spillovers, or external habit.

In a working paper I have with Olivier Coibion, Yuriy Gorodnichenko, and Marianna Kudlyak we look at whether, in the years running up to the financial crisis as well as during the Great Recession, low-, middle-, and high-income households accumulated different amounts of debt (relative to their incomes)  depending on the level of income inequality in their region. Our main finding is that low-income households in high-inequality areas increased their leverage by less than similar households in low-inequality areas. Our non-parametric results in Figure 2 suggest that a household in the bottom third of the income distribution within their area and inequality distribution across areas increased their leverage by around 15 percentage points more than a similar household in the top third of the inequality distribution in the years immediately prior to the financial crisis. This is the exact opposite effect one would expect if “keeping up with the Joneses” was the primary cause of borrowing by low-income households.

Because our data (see Additional Details below) allow us to break debt into pieces, we can examine which types of debt are driving these differences. While we find similar patterns for mortgage debt, auto debt, and credit card limits as those documented for total debt accumulation, we find no systematic differences across households and inequality regions in terms of their credit card balances. Since credit card limits primarily reflect credit supply conditions whereas credit card balances reflect households’ demand for credit, we interpret the difference in results across credit card limits and balances as pointing toward credit supply factors as the root cause of the link between inequality and borrowing.

The intuition is simple. First, lenders confront asymmetric information as they try to infer which borrowers are less likely to default. Second, high-income borrowers are less likely to default so lenders use income as a way to infer borrower type. In a perfectly equal income distribution all borrowers are equally likely to be a high or low default risk. But as inequality increases and the income difference between low- and high-income borrowers becomes larger, high-risk and low-risk borrowers are easier to tell apart when they reveal their incomes to banks. Lenders will then be able to offer cheaper and more readily accessible credit to high-income/low-risk borrowers as well as more likely to deny loans to low-income/high-risk borrowers. To test these predictions we use data from the Home Mortgage Disclosure Act (HMDA) which requires mortgage lenders to report details on applications including whether a loan was denied, the size of the loan, income of the applicant, and other characteristics. We find that low-income applicants are more likely to be denied mortgages and to be charged a high interest rate in high-inequality areas relative to similar applicants in low-inequality areas. Thus, this evidence also supports a credit supply interpretation of the link between local income inequality and differential borrowing patterns across income groups that is at odds with the “keeping up with the Joneses” interpretation.

Part of the reason I was invited to write here was to discuss the differences between our results and those in a recent paper by Bertrand and Morse, because their empirical findings do provide evidence of “keeping up with the Joneses” forces. There are at least two important differences. First, their outcome is consumption while ours is debt. It is possible that low-income households funded their consumption with changes in labor supply, savings, or even some debt. But our results tell us that any use of debt in this way cannot be the primary story of inequality and debt accumulation during this period. This is important to note because debt accumulation was central to the creation of many of the financial assets behind the financial crisis. Second, Bertrand and Morse use changes in consumption among the wealthy as their explanatory variable while we use inequality. It is possible that in some areas the consumption differences between households are not as large as in other areas even though both have the same measured inequality. This can occur if there is variation in precautionary savings, the “visibility” of consumption bundles, or the proximity of high- and low-income households. As the relationship between high-income household consumption and measured inequality becomes more complex our results become less directly comparable.

Thanks very much to Carola for having us!

Additional Details

The data we use for our primary results are from the New York Federal Reserve Bank Consumer Credit Panel/Equifax (referred to as the CCP), which provides comprehensive debt measures for millions of U.S. households since 1999. Because these data do not include income we impute incomes using the relationship between common observables in the Survey of Consumer Finances. Using these imputed incomes we construct measures of local inequality, household positions in the income distribution, and household debt-to-income ratios. We are able to check our measures of inequality and rank against various external measures and find they are very highly correlated.

Our results are robust to the level at which we measure inequality (zip, county, state), the measure of inequality we use (ratio of log incomes at the 90th and 10th percentile from the CCP, Gini coefficients from the IRS and Census data), an extensive set of household and area controls, and numerous splits of our sample. In particular our results hold within subsamples defined according to house price appreciation, average credit scores, income levels, initial debt ratios, and geographic regions.

Monday, March 31, 2014

Consumption Contagion and Income Inequality

The trends of rising income inequality and the declining national savings rate since the early 1980s may be related, according to a paper by Marianne Bertrand and Adair Morse. The authors find that higher levels of visible consumption by increasingly better-off households at the top of the income distribution induces consumers in the lower parts of the income distribution to spend a higher share of their disposable income. From "Consumption Contagion: Does the Consumption of the Rich Drive the Consumption of the Less Rich?":
"Our empirical strategy exploits variation across geographic markets and over time to identify the effect of expenditures by the rich on that of the non-rich. We ask whether, everything else held constant, higher levels of consumption by the rich living in a household’s relevant market (which we define to be either a state or an MSA in a given year) predicts a higher propensity to consume out of disposable income for the non-rich household. After establishing that such vertical consumption correlations occur, we then explore possible mechanisms. Our results are most consistent with the view that visible increased consumption by the rich induces status-seeking or status-maintaining consumption by the less rich."
Bertrand and Morse define the rich households in each state as those with above the 80th percentile of income in that state. Their baseline regression shows that a 1 percent increase in consumption (excluding housing) among the rich in a particular state translates into a 0.07 percent increase in consumption among the less-rich. They find no evidence that this could be explained by the permanent income hypothesis; rising consumption by the rich in a particular state is not predictive of faster future income growth by the state's less-rich. Thus, they conclude that "Our preferred explanation for the vertical consumption spillovers we observed in our basic results is that low and middle income households witness the higher consumption levels by the rich and are tempted to also consume more."

To test this explanation further, they use data from the Consumer Expenditure Survey and use the Ori Heffetz (2011) index to rank goods into seven categories of increasing visibility. Highly visible consumption items include cars, clothing (except underwear!), shoes, and cigarettes; minimally visible consumption items include health or legal accounting services and, yes, underwear. They replicate the analysis by goods category, and find strongest effects in the most visible consumption categories, consistent with a "consumption contagion" explanation.

As another test, they replicate the analysis using Census Metropolitan Statistical Areas (MSAs) instead of states. They use a measure of community segregation, indicating how closely the rich live to the less-rich in each MSA. In MSAs where the rich and less-rich live closer together, there is more consumption contagion.

Overall, the authors estimate that the savings rate of median-income households would be one to two percentage points higher in the absence of this "consumption contagion" effect. This is non-trivial but also not huge. What is most important is the empirical support of a particular type of departure from the Permanent Income Hypothesis. Many types of departures have been hypothesized, but quantifying their relative importance and carefully tracing out their implications for macro models is an ongoing task.

Tuesday, March 25, 2014

Guest Post: The Second Machine Age Book Review Part I

This guest post was contributed by Richard Serlin, who teaches personal finance at the University of Arizona and is president and co-founder of National Personal Finance Education. Serlin blogs at Serlin will be reviewing The Second Machine Age: Work, Progress, and Prosperity in a Time of Brilliant Technologies by Erik Brynjolfsson and Andrew MacAfee in a series of guest posts.

I will right away get to the crux of the book, for me, and perhaps most people, and then do a beginning-to-end review over multiple posts that will refer back to this crux again and again.

The crux is, Will the explosion in computer/robot/machine ability result in mass unemployment this time, even though previous technological revolutions haven't? If yes, why? If no, why?

With my primary career in personal finance, this an issue I've worked hard to understand. Because there is a very real possibility of massive unemployment, and/or non-livable market wages. And I really do mean non-livable, like not even enough money to buy enough food to stay alive. There potentially are a huge number of jobs today that computers/robots will be able to do over the next generation at a comparative cost of pennies per hour, or less.

So, I will attempt to answer this big question, using much of what Brynjolfsson and MacAfee say in The Second Machine Age, as well as in their first book on these issues, Race with the Machine, which I also carefully read cover-to-cover. The authors don't directly say what will follow. This is my interpretation, or my interpretation of what they are saying combined with some of my own thinking.

We start with the classical L-shaped production function, which I think is especially instructive. Anyone who's taken beginning, or perhaps intermediate, microeconomics has seen this:

The graph has two inputs of production, labeled Z1 and Z2. I'm going to consider Z1 to be units of labor, specifically unskilled (or low skilled) workers, and Z2 to be a package of other – complementary – inputs. This package includes machines, buildings, and other physical capital, but also skilled labor.

So, for example, one unit of Z1 might be 1,000 unskilled workers. One unit of Z2 might be 800,000 square feet of facility, 400 machines, 500 robots,…, and 300 skilled workers: engineers, advanced technicians, MBA's, CPA's, etc.

Now, let's assume that there are two choices of production processes in the world to make use of raw materials. There's the one above – the ultra-high output one. And, there's using only unskilled labor (or unskilled labor with relatively low-tech tools). This can make the end products too, but at 1/1,000th the output per hour worked. As a result, if workers were forced to resort to this kind of work, they would have a subsistence wage (or might not even be able to subsist). The technology is just too primitive, too ancient.

Of course, even in prehistoric times, with the most primitive technology, people were usually able to produce enough to eat, usually at least to live into their 20's. But, they had more than just the value of their labor. They had access to free raw materials, basically by just taking them from whatever land they came across, or could fight to get. Today's unskilled would have little in the way of free, or owned, raw materials, or wealth of any kind. Already just 85 people have more wealth than the poorest 3.5 billion. To get raw materials they'd have to sell some of their labor endowment, and if that was worth too little, they would not be able to get enough raw materials to subsist.

The key feature of L-shaped isoquants is that without adding more L2, you're not going to get any more production no matter how many units of L1 you add. So, here, you're just not going to employ any more unskilled workers (L1), unless you can get more building space, machines, computers, robots, and – crucial to the argument I'm going to make – skilled workers: engineers, advanced technicians, college degreed business people (and not just a paper degree, one with the skills, knowledge, and analytical abilities to go with it), etc.

The skilled workers are just useless productivity-wise without complementary units of L2. Otherwise, all they can do is the primitive production method which produces so little that they starve. People will pay very little in the needed raw materials to the unskilled for the primitive production method, because for just a relatively tiny expenditure on high tech production they can produce the same as with all of the billions of unskilled laborers in the world working with primitive tools. Not only that, there are so many products today that the wealthy and middle class want that are simply impossible for the unskilled alone to produce at all, in any quantity, without the skilled, and the high-tech production method.

The unskilled only become valuable if the units of L2 get so large that complementary units of L1, unskilled laborers, start to get relatively scarce.

Now, what's happened historically. Metal stamping machines started replacing blacksmiths, but then we just started producing more and more metal stamping, and other, machines until all of the initial unemployed were countered with an equal number of jobs running, maintaining, and working with, the metal stamping and other machines. In other words, we just kept building more and more L2 until we pretty much soaked up all of the unemployed L1.

The initial building of the L2 made some lose their jobs, but every unit of L2 that you built required some units of L1 to complement it. When there was tons of unemployed L1, the L1 was cheap, and it made sense to just keep building tons of L2 to take advantage of that cheap L1 until the price (wage) of L2 (unskilled, or low skilled, workers) got extremely high by historical standards. And this was also because the combination of L1 and L2 produced so vastly much more than before using the primitive production function.

In other words, maybe blacksmiths and such forever lost those jobs, but we kept producing so many metal stamping machines, and other machines, and assembly lines, and blast furnaces,…, that eventually we replaced all of those jobs with jobs that were necessary for the new high-tech production method, assisting, maintaining, and complementing the new machines. And we produced so many of these new machines that the unskilled became relatively scarce enough, compared to the new productive capacity, to drive their wages far higher than ever in history.

So, you could just say, That's the solution today! The computers and robots won't 100% not need humans for a very long time, if ever. Just keep building more and more computers, and more and more robots, then you'll need more and more people to attend to, work with, and complement those computers and robots, until every unemployed human is now employed! They're all maintaining, assisting, and otherwise working with the robots and computers that took so many jobs originally!

The biggest current problem with this is there's a bottleneck. And it's a very serious one – skilled workers. It's relatively easy to keep building more and more and more robots, and computers, and facilities, and high-tech machines (at least if you have the skilled workers), but to produce enough trained engineers, and business managers, and skilled technicians, etc. to complement, and keep employed, all of the billions of unskilled workers globally, that's what we're not nearly up to the task for. That's the bottleneck, or at least the biggest and hardest one.

Without far more skilled workers – many highly skilled – there will not be nearly enough need for the masses of unskilled workers. There just won't be anything for them to do that's a high-tech production method like we've discussed without more skilled workers. All you'll be able to do with them is the primitive production method that employs only unskilled workers. And that production method is so relatively low output, it will be paid too little in raw materials to create non-poverty, or perhaps even subsistence, wages for most of the workers.

So it looks like to me the solution depends most on attacking this bottleneck, skilled labor – and the right skills needed for an L2 package. You do this, and you keep employing more and more of a smaller and smaller number of remaining unskilled workers, until their unutilized numbers get small enough to push their wages to a middle class, or at least non-destitute, level.

Of course, this is easier said than done. It would require a massive investment in education and training – starting prenatal; see the work of Nobel Prize winning economist James Heckman – but that effort, in of itself, would create an enormous number of jobs. And it would be hugely high-social-return and positive-social-NPV. If your goal is to maximize total societal utils, or if this is an important goal for you, then this is enormously efficient. 

The authors of The Second Machine Age recognize the crucial point of the importance of high public investment in education to prevent massive technological unemployment. And they also note that they are far from the first prominent economists to do so. On pages 208-10 they write:

The United States was the clear leader in primary education in the first half of the twentieth century, having realized that inequality was a "race between education and technology", to use a phrase coined by Jan Tinbergen (winner of the first Nobel Prize in Economic Sciences) and used by the economists Claudia Goldin and Lawrence Katz as the title of their influential 2010 book…Over the past half century that strong U.S. advantage in primary education has vanished…It's been said that America's greatest idea was mass education. It's still a great idea that applies at all levels, not just K-12 and university education, but also preschool, vocational, and lifelong learning.

I'll add too, that it's not just a bottleneck of insufficient skilled workers to utilize all of the unskilled in the high-output production method. On top of this, to make education even more important, we're also looking at a potentially profound shrinking in the proportion of workers needed in high-output production that are unskilled.

In other words, those L-shaped isoquants may shift 50%, or much more, to the left within a decade or two. Brynjolfsson and McAfee present dramatic evidence that long-vexing stumbling blocks in human-like robotics and computers are finally being overcome, with dramatic recent progress, after decades of slow frustration. And this is what you typically see with exponential growth of the kind we have with Moore's Law. At first the progress, the slope, is not so steep, but suddenly it takes off skyward, as each new doubling now doubles an enormous number.

I'll review this in detail in a later post, but for now I'll quote the authors on pages 31-2:

After revisiting Rethink and seeing Baxter in action we understood why Texas Instruments Vice President Remi El-Quazzane said in early 2012, "We have a firm belief that the robotics market is on the cusp of exploding." There's a lot of evidence to support his view. The volume and variety of robots in use at companies is expanding rapidly, and innovators and entrepreneurs have made deep inroads against Moravec's paradox.

It may not for long be that computers can beat Garry Kasparov, but they can't flip a burger, or oil machines spread across the factory floor. There's recently been breakthrough progress; long intractable walls have fallen in machine pattern recognition, sensation, and dexterity, and it's showing up in a lot more than just the Google Car.

Now, most of my economic analysis so far comes from The Second Machine Age, or I think is implied by it. In particular, I've bolded the terms complementary and bottleneck. Brynjolfsson and McAfee's use of these terms was important in leading me to my analysis. And I think it's possible that given how they use these terms they were also thinking in terms of L-shaped production functions, or something similar.

For example, starting on page 181-2, they write:

The better machines can substitute for human workers, the more likely it is they'll drive down the wages of humans with similar skills…But in principle, machines can have very different strengths and weaknesses than humans. When engineers work to amplify these differences, building on the areas where machines are strong and humans are weak, then the machines are more likely to complement humans, rather than substitute for them. Effective production is more likely to require both human and machine inputs, and the value of the human inputs will grow, not shrink, as the power of machines increases. A second lesson of economics and business strategy is that it's great to be a complement to something that's increasingly plentiful.

And on page 213:

We have little doubt that improving education will boost the bounty by providing more of the complementary skills our economy needs to make effective use of new technologies.

For the term Bottleneck, on page 200:

The college premium exists in part because so many types of raw data are getting dramatically cheaper, and as data get cheaper, the bottleneck increasingly is the ability to interpret and use the data.

Another important term the authors use is inelasticity of demand, but that will have to wait until my part II post! There, I will begin a detailed chapter by chapter review.

Thursday, March 20, 2014

Vox Ukraine

Just wanted to point interested readers to a new blog that my advisor, Yuriy Gorodnichenko, is part of. VoxUkraine is described as "a portal set up to discuss developments in Ukraine. VoxUkraine aims to promote research-based policy analysis and commentary by leading scholars, policymakers and businessmen. The intended audience is people in governments, international organizations, academia and the private sector as well as journalists specializing in economics, politics, and business."

The other members of the VoxUkraine editorial board are Tymofiy Mylovanov (University of Pittsburgh) and Oleksandr Talavera (University of Sheffield). The board considers submissions of “research-based analysis and commentary” for possible publication on VoxUkraine.

Posts include "Crimean secession: self-determination with a false bottom," by Kateryna Dronova, and "Referendum in Crimea and sanctions on Russia," by Yuriy Gorodnichenko. 

You can also follow @voxukraine on twitter.

Monday, March 17, 2014

Who will Save Us from Inequality?

"Paul Krugman won't save us," writes Thomas Frank. (Neither, he adds for good measure, will Brad DeLong.) Frank is referring to economic inequality--in his opinion a "needlessly clinical" phrase and "a pleasant-sounding euphemism for the Appalachification of our world." Inequality, he believes, has gotten into the wrong hands:
"Who is called upon to speak on the subject [of inequality] today? Why, academics, of course. 'Inequality' is a matter for experts, a field for the playful jousting of rival economists, backed up by helpful professors of political science, and with maybe an occasional sociologist permitted into the games now and then...
The discovery of inequality has also compelled our leadership class to establish things like the Washington Center for Equitable Growth, which boasts a steering committee made up of six economists plus one Democratic foundation/policy type....But to look at its website, it’s just another platform for the trademark blog styling of the well-known economist Brad DeLong." 
Our ancestors, notes Frank, referred not to "inequality" but to "the social question." And they treated the question not with the "wonkery" and endless charts of today, but with wide and deep conviction. 
"'Inequality' is not some minor technical glitch for the experts to solve; this is the Big One. This is the very substance of American populism; this is what has brought together movements of average people throughout our history. Offering instruction on the subject in a classroom at Berkeley may be enlightening for the kids in attendance but it is fundamentally the wrong way to take on the problem...We owe the economists thanks for making the situation plain, but now matters must of necessity pass into other hands."
Whose hands? Frank isn't entirely explicit. His historical examples include an 1892 passage from the Omaha Platform of the Populist Party, a 1916 report of the Commission on Industrial Relations, and a 1932 testament of a socialist newspaper editor to a congressional committee. He highlights their "singing" language but not the fruits of their labors. He mentions that in the current day, a local union leader would be a more effective mouthpiece than a Nobel Laureate, and says that "This is a job we have to do ourselves." But how? 

Frank neglects any mention of religious figures and institutions that can speak to the social question. As I wrote in an earlier post, the Catholic Church has a very long history of teaching about economic justice. Pope Francis, thankfully, is bringing this tradition back into the forefront. Hopefully his words will influence not only Catholic believers who may have been unaware of the Church's position on inequality, but also members and leaders of other faiths who will see that economic and social justice are pressing moral issues. The moral issues involved in an economic system can be appreciated by thoughtful members of any religion, or of no religion, who share a concern for justice and for their neighbors. Ultimately, policy changes will be required, and these people can be the impetus.

Frank writes that "When President Obama declared in December that gross inequality is the `defining challenge of our time,' he was right, and resoundingly so. As is his habit, however, he quickly backed away from the idea at the urging of pollsters and various Democratic grandees." If Pope Francis' convictions were sufficiently widespread, maybe politicians wouldn't be able to back away.

Still, I don't think economists' work here is done. Economists are still learning new things about the causes and extent of inequality. They still disagree among themselves. (Minimum wage hikes, anyone?) Even if politicians and the public were 100% gung ho about reducing economic inequality, the best way to achieve it wouldn't be perfectly straightforward. Economists should keep at it. And while Frank may mock the "trademark blog styling of the well-known economist Brad DeLong," he is well-known for a reason. People read what he writes. They read it and they think about it. He should keep writing. Frank is dubious about the effectiveness of teaching Berkeley students about inequality-- but informed and ambitious young people seem like a pretty good demographic to reach. We should keep teaching them.

I agree with Frank that inequality, or call it the social question, is a big deal, The Big Deal. And I agree that it shouldn't be left solely in the hands of economists. But his disdain for the way economists treat inequality as a complex technical issue-- "Oh, it is extremely complex. It requires so many charts"-- is misplaced. It is both a technical issue and more than a technical issue. Let economists take on the technical issues in accordance with their expertise. Encourage others to take on the "more than technical" issues in accordance with their own. Paul Krugman won't save us, but he shouldn't stop trying.

Tuesday, March 11, 2014

Female Econ Majors: It's Not About Grade Grubbing

Claudia Goldin's analysis of male and female undergraduate economics majors is getting a lot of press. Goldin writes:
"Women who thought they would major in economics often become discouraged when they don’t get sufficiently high grades in introductory courses. Men are far less likely to be discouraged by similar grades. In other words, the gradient of major choice with respect to grades in the “gateway” courses is steeper for women than for men."
Amanda Hess at Slate summarizes the article, "Women May Be Underrepresented in STEM Because They're Too Concerned With Grades." Similarly, Catherine Rampell writes that "Women should embrace the B’s in college to make more later." These articles, I think, miss a bit of nuance. 

I don't think the real issue is that young women are just more "grade-grubby" than young men-- which is actually a pretty harmful stereotype. Grades serve as a signal, both to others and to the student. As Goldin notes, male students disproportionately choose to study economics before entering college. Economics professors are also disproportionately males. Economics grad students, who will be the undergrads' teaching assistants, are disproportionately males. A female undergrad may wonder if she really "belongs" among economists. So if she gets a B in Econ 101, she may put more weight on that than a male student would. If she already had doubts about whether she belonged in the major, she's going to put more weight on the signal from her grade. 

I don't think Goldin meant to imply that college women are just "in it for the grades" more than college men. Their decisions on major are more sensitive to grades, but for reasons other than perfectionism. This is why Goldin emphasizes Janet Yellen's nomination to head the Federal Reserve as an important milestone that could draw more women into the field, by showing them that they belong. She writes, "Yellen’s ascension at the Fed will show more women that economics isn’t an exclusively male field."

Wednesday, February 19, 2014

Accounting for Changes in Inequality

The Berkeley macroeconomics reading group has three themes for this semester: (1) factor shares, wealth, and inequality, (2) misallocation, and (3) financial stability. Each week, a different student presents a paper from one of the topic areas. Today, as part of the first topic, I am presenting the paper "Accounting for Changes in Between-Group Inequality" by Ariel Burstein, Eduardo Morales, and Jonathan Vogel (2013).

Here are my slides. And here is the abstract:
We provide a framework with multiple worker types (e.g. gender, age, education), to decompose changes in aggregated and disaggregated between-group inequality into changes in (i) the supply of each worker type, (ii) the importance of different tasks, (iii) the extent of computerization, and (iv) other labor-specific productivities (a residual to match observed relative wages). The model features three forms of comparative advantage: between worker types and computers, between worker types and tasks, and between computers and tasks. We parameterize the model to match observed changes in worker type allocation and wages in the United States between 1984 and 2003. The combination of changes in the importance of tasks and computerization explain the majority of the rise in the skill premium as well as rising inequality across more disaggregated education types, whereas labor-specific productivity changes drive between-worker wage polarization.
The paper is motivated by the rise in the skill premium, fall in the gender premium, and rise in wage polarization (i.e. relative decline of wages in the middle.) The authors want to know about the role of computerization in these trends. An important idea of the paper is that certain types of workers (e.g. females) may either have a direct comparative advantage at using computers, or might have an indirect comparative advantage in the sense that they have a comparative advantage in occupations in which computers have a comparative advantage. In the first case, we would observe female workers using computers more than males within the same occupation. In the second case, we would observe females being over-represented in the occupations in which all workers use computers a lot.

Using data on computer use and occupations for several years between 1984 and 2003, the authors find that, while women use computers more than men, this is due to indirect comparative advantage. Women are more often in occupations in which all workers use computers more. In contrast, highly educated workers have direct comparative advantage with computers-- they use computers more than less educated workers within the same occupations.

As the price of computers falls, the relative wages of workers with direct comparative advantage in computers rises. So computerization can explain some of the rise in the skill premium (that is, the rise in wages of more educated compared to less educated workers.) A major part of the rise in the skill premium is also attributed to "task shifters," that is, factors like structural changes and international trade that alter the relative demands for workers across occupations.

Computerization does not raise the relative wages of workers with indirect comparative advantage in computers, so computerization does not explain the fall in the gender premium (that is, the fall in male compared to female wages). Both the fall in the gender premium and the relative decline of wages in the middle are attributed to changes in "labor productivity," which in this model is a residual term, meaning it is not actually explained by the model.