Tax Rates

Using NBER's TaxSim, a program that calculates expected income tax rates from a random sample of actual IRS returns, Corrections produces a graph of after-tax income against before-tax income for several states.  This includes only State and Federal Income Tax, along with FICA taxes.  It assumes a married earner with 2 children, a rent of $1500, and no other deductions or income.  Tax rates are for 2010.

This is a worst case scenario in terms of total income:  all is labor income, which is punished most severely.  Capital income, quite rightly, is generally taxed at lower rates.

Corrections also plots marginal tax rates over labor income: how much is taken of each extra dollar you earn.

Share of Labor

A subset of the population does not like that economists use mathematics. Theories of various current events are often given.  Such theories, if they are to replace the sort of "economics 101" that is now taught, need to explain phenomena like the one displayed graphically below: the remarkable stability of labor's share of national income (click to enlarge).

It's almost a miracle it has fluctuated so little in the past 64 years, as the proportion of women in the U.S. workforce (for example) rose from 15% to over 50%, while proportion of men employed shrank a small amount.  

Explaining stylized facts like these is the first step in being taken seriously.  

On the Pulpit, Rabbis Earn More Than Christian Clergy

Normally, Corrections avoids old articles.  However, Jewish Daily Forward article "On the Pulpit, Rabbis Earn More Than Christian Clergy" (September 15th, 2010) wonders aloud why rabbis are paid, on average, more than christian clergy. It comes to no firm conclusions. Indeed, Corrections spent some time thinking on the curious problem: Catholics and Protestants appear to be paid between $25,000 and $40,000, while Reform and Conservative Rabbis appear to be paid between $137,000 and $147,000. A rather large gap.

Corrections came to the weak conclusion that the story was about opportunity cost and relative wealth status. However, the same publication came out, two weeks later, with the article "Rabbi Searches Are Tough, but Are They Illegal?" (September 29th, 2010). This article mentions nothing about pay, and merely describes the theological implications of a cartel of Rabbis:

The RA requires synagogues to enroll exclusively in its search process, filters the selection of candidates the congregations may interview, and prohibits candidates and congregations from finding each other directly. Any Conservative rabbi who seeks a pulpit outside the RA’s centralized process, and any congregation that interviews candidates from other movements, will be penalized.

It bespeaks either a deep ignorance of economics or a willing deception of their readers that the Forward did not connect the two. To note that Rabbis have a firm cartel with punitive powers on the one hand, then wonder why Rabbis are paid so much on the other is ludicrous.

Cartels artificially limit supply to raise prices. It utterly clear to Corrections that the Rabbinical Assembly is a cartel of Rabbis that artificially constricts supply and raises wages. The Rabbinical Assembly's cartel also possibly increases quality above what the market would demand to further drive up price, though there is no evidence for this either way (merely a likely possibility). A depiction of what the Rabbinical Assembly is practicing may be found graphically below (click to enlarge).

Value of College Degree Is Growing, Study Says

New York Times article "Value of College Degree Is Growing, Study Says" (September 21st, 2010) gets the correlation/causation distinction correct. However, it doesn't give the clear causal reasons why better educated and wealthier people eat more healthily and exercise more: while people often face the same price of an activity, they often face different shadow prices, the relevant price for making decisions.

The report, first issued in 2004 and updated in 2007, also described social benefits: those with a bachelor’s degree, it said, are more likely to volunteer, vote, exercise and have health insurance and pensions. They are also less likely to smoke, be obese or have low-birth-weight babies. It did not assert that a college education, by itself, was responsible for all those differences.

'Correlation is not the same as causation,' Ms. Baum said. 'But that said, the people who have done careful statistical analyses, controlling for demographic characteristics like income and family background, have overwhelmingly concluded that there’s some causation here, that some things that happen to you in college, for example, would make you more likely to adopt healthier behavior.'

Better educated and wealthier people have more incentive to live longer because their time is worth more. Take Kevin Murphy's shadow price of a cheeseburger example (briefly mentioned at the end of this interview). Eating unhealthy cheeseburgers shortens your life, but you gain happiness from them. The time of a low-wage person should be valued by that low-wage person as their wage (or outside wage, if the two are only approximately equal). While state-dependent utility disclaimers apply, the thrust of our argument will be robust to secondary and tertiary corrections.

Let us imagine that the time a rich person is willing to give up for an extra hour of his life is $200, but a poor person is only willing to give up $100. Then if a cheeseburger takes an hour off of an individual's life (for instance), then the true cost to a rich person is $204, while the cost to a poor person is $104. The shadow prices the two individuals face are different. Unhealthy decisions cost rich people more because they value their lives more.

When people decide to become educated, they induce themselves to have different marginal utilities and therefore make different decisions due to facing different shadow prices--a cheeseburger is more expensive for a rich person.

The Littlest Redshirts Sit Out Kindergarten

New York Times article "The Littlest Redshirts Sit Out Kindergarten" (August 20th, 2010) discusses the "redshirting" of kindergarteners, the practice of holding them back a year so they have an age advantage. Corrections is dubious that the practice could become a problem, and that it will wane, despite "the signs."

“Redshirting” of kindergartners — the term comes from the practice of postponing the participation of college athletes in competitive games — became increasingly widespread in the 1990s, and shows no signs of waning.

The Times doesn't articulate the tradeoffs that altruistic parents face when deciding when their children will enter school. Children gain some initial advantage entering Kindergarten later because they are older and more mature, and they may gain a measure of happiness by not entering into school immediately. What they lose is that year of their life that they might have spent working or retiring. There are two important empirical questions the Times should have addressed when discussing this issue. First, whether or not there is an advantage to entering kindergarten late, and if so, the time-profile of this benefit. Second, whether or not the net present value of the time profile for benefits due to entering early is greater than, or less than, the net present value of the time profile for benefits due to not entering early.

What are the benefits to entering class early, assuming there are any? On the one hand, if the "alpha dogs" of a class get a larger share of the resources, confidence, and attention, then we might expect benefits to late enrollment to explode over time. Alternatively, if students enter with a fixed advantage and all students learn equally over time, then the benefits to being a year older than one's peers decays over time. Two prototypical time paths are displayed graphically below (click to enlarge). The plot simply shows an advantage, measured initially at 1, and its decay or growth over time. The black line separates two answers to our second question. If a plot stays above the black line, then benefits grow or stay constant, and below, benefits decay or stay constant.



Evidence indicates that the blue line of decaying benefits is the empirical reality. Elder & Lubotsky find that benefits are relatively short lasting in "Kindergarten Entrance Age and Children's Achievement, Journal of Human Resources" (2009) (gated) (ungated). The authors use exogenous changes in state age cutoffs and consequential differences between predicted and actual entrance ages to produce identification (a counterfactual).

Elder & Lubotsky indicate that there are benefits, however fleeting. What are the costs? Earnings rise as one gets older (falling as one enters retirement age). Inspired by Empirical Age-Earnings Profiles (Kevin M. Murphy and Finis Welch, Journal of Labor Economics, April 1990), Corrections offers a similar treatment, using historical cohort averages of earnings from the Current Population Survey (available at the Census Bureau). We use the data (not plotted) to fit a cubic polynomial of earnings over time or age for cohorts born in 1940 or 1950, displayed graphically below. The first plot has earnings (all earnings in current dollars) by age (click to enlarge) the second plot has earnings by year (click to enlarge). Both plots use median data from males only (all races).





To overcome the cost of putting off one's earnings profile by one year, how much would an individual born in 1940 have to be paid? In this primitive analysis, ceteris paribus, if the net present value of putting off one's education is greater than $8,500, an individual should do it.

Corrections might further add that even if the trend has been increasing, it is likely to find some equilibrium. As the proportion of "alpha-dogs" increase, their allotment of resources above the baseline presumably decreases--the benefits of postponing decrease, while the costs, as discussed above, remain the same. This leads to an interior equilibrium, (the equilibrium proportion of late-entrants is .247, the point of intersection) as displayed below (click to enlarge). In this case, no benefit is gained to waiting, and individuals are indifferent to waiting or not.

A Sin and a Shame

New York Times editorial "A Sin and a Shame" (July 30th, 2010) offers another installation of Bob Herbert painfully writing about concepts he does not understand, and quoting figures that do not support his point.

The recession officially started in December 2007. From the fourth quarter of 2007 to the fourth quarter of 2009, real aggregate output in the U.S., as measured by the gross domestic product, fell by about 2.5 percent. But employers cut their payrolls by 6 percent.

Herbert then suggests that these figures mean that "cruel, irresponsible, shortsighted policy" has taken hold in American corporations. However, using a simple bread-and-butter real business cycle model involving investment-specific technological change, solved with Matlab program Dynare (this is a DSGE model, or Dynamic Stochastic General Equilibrium Model), we can show the relative movements can the result of far-sighted optimizing behavior, rather than the result of capital in the hands of individuals destined for the Fourth Circle of Dante's Inferno for their avarice, as Herbert perpetually suggests in various columns.

Below, we plot the impulse-response functions of one such model, in which firms maximize profits from a Cobb-Douglas production function, households have log-preferences, capital depreciates, produced goods are either invested or consumed, and both technology and quality of investment good are independent stochastic first-order autoregressive processes. (For the interested, this flavor of model is prototypically described in "The Role of Investment-Specific Technological Change in the Business Cycle", published in the European Economic Review (2001) by Greenwood, Hercowitz and Krusell). We examine what happens when we have a negative investment quality shock. The impulse-response functions to a are plotted below (click to enlarge):

How should we interpret these figures? First, for those unfamiliar, impulse-response functions plot the response of all other related variables to an exogenous shock over time. Here, we plot the reactions of all other variables in percentage points of their own standard deviations to a one-standard deviation negative shock to investment good quality. The "direction" of reaction can be seen by comparing the black line, which is the reaction of a variable to our shock, to the red line, which is a "baseline." We forgo concern about the size of the shocks and focus on the qualitative reactions of each variable.

Specifically, we see that when investment in durable goods this period gives less (lower quality investment goods), we see a decline in both production and labor (increasing back to steady state (or stable growth path) over time), while seeing an increase in productivity, precisely the sort of reaction Herbert pretends is irrational. This is a product not of shortsighted policy, but of perfect foresight (though not perfect information).

Indeed, one doesn't need to examine even simple real business cycle models to explain why we should see productivity rise, labor fall, and production fall by less than labor in the short run. In the United States, labor can be treated as a consumable good. Labor is more flexible than durable goods. In a simple analysis, we can hold capital as fixed and labor is flexible in the short run, while in the long run, both are flexible.

We might imagine our aggregate production function is Cobb-Douglas, using labor and capital, depicted graphically below (click to enlarge). We also denote a dark black line, indicating a schedule for production given fixed capital. Therefore, we might consider any point on this graph viable combinations for inputs and corresponding output in the long run, while considering only the dark black line viable in the short run (were we to have that specific level of capital, .5 in this case).

We could simply graph the dark black line in two dimensions (click to enlarge). This represents production along a fixed capital stock, as we would see in the short run:

On this graph, we can see our whole story: output, labor supply, and productivity. Marginal labor productivity, which may be defined as $$\Delta$$output/$$\Delta$$labor, is the slope of any point on this line. Average productivity is simply the ratio of output to labor. We can see that any time we shift downward along the supply schedule, labor will, on average, be more productive. Note that this is not true in the long run, because capital will shift as well (this Cobb-Douglas is constant returns to scale in the long run, decreasing returns to scale in the short run). We can display this on the same graph, also writing out productivity below two sample points (click to enlarge):

All this is to say that if we make less, our average productivity increases when we are in a regime with decreasing marginal returns to scale. It appears Bob Herbert's real complaint is about decreasing marginal returns, or his ignorance of economics, rather than "corporate greed" or "shortsightedness."

As a last point, Crypto-Marxists like Herbert appear to adopt the poor understanding of capital and labor that Marx shared with Malthus. The belief that capital (land, in Malthus's case) is fixed, and labor is elastic (people have more children and "soak up" any wage higher than subsistence living).

Productivity tells the story. Increases in the productivity of American workers are supposed to go hand in hand with improvements in their standard of living. That’s how capitalism is supposed to work. That’s how the economic pie expands, and we’re all supposed to have a fair share of that expansion.

Corporations have now said the hell with that.

This is incorrect. If corporations could always just say "to hell with that" and not pay workers as much, they would have done so at some point in the past 150 years. Over the last 150 years, the return on invested capital has remained unchanged, while real wages have continued to rise. The mistake that Marx, Malthus and Herbert make is to believe that capital is fixed (inelastically supplied) while labor is flexible (elastic), and so capital gains all benefits from a shift in productivity.

To be clear, the mistaken idea is as follows. Society has a productivity gain. There is a large excess pool of labor that will compete away any higher wages, while capital remains fixed. Therefore, because labor competes all gains away, capital gets all the benefits of a productivity gain.

The reason this idea is mistaken is that there is a large excess pool of possible capital--its primary "input" is simply foregone consumption, and that can be supplied rather easily, if the real interest rate is high enough. Real wages have gone up over time, while real return on capital has not.

The opposite is true--capital is elastic, while labor is relatively inelastic, explaining why real wages have been the claimant on all increases in productivity over the last 150 years.

What happened to all that anger over CEO pay?

Christian Science Monitor article "What happened to all that anger over CEO pay?" (July 12th, 2010) claims that CEO pay is too high:

In 2008, the CEOs of major US firms were paid more than 300 times the wage of the average American worker. Last year, they were paid just under 300 times average pay, according to new research by Mr. Pizzigati. Now that most of those firms have paid back the government, they're setting their own compensation levels again.

Those levels would astonish the bosses of top corporations in the late 1960s. Those CEOs got about 30 times the average wage of US workers.

Are today's bosses 10 times more capable? Is there a shortage of able managers? Nope and nope, says Pizzigati. "There is more management talent today than ever before."

This argument is riddled with flaws. First, no economic model could possibly imply that CEO pay is set by looking at the ratio of their wages to those of their employees. LeBron James is paid significantly more than his towel boy, so what? They perform completely different tasks, requiring completely different skills, in completely different environments. The question is not "are CEO's 300 times better that their employees at stocking shelves?" Rather, the question is "is the market for CEOs competitive?". The article itself suggests that there are plenty of qualified CEOs to choose from when starting a company.

Quarterly Journal of Economics article "Why has CEO pay increased so much?", by Xavier Gabaix and Augustin Landier model CEO pay. They match the best CEOs with the largest firms, and note that even when CEO talent is not very disparate across CEOs, small differences in talent can lead to very large difference in pay because of firm size. For example, the top CEO (in terms of talent) can increase the value of his company by only 0.016% relative to the 250th talented CEO, but this translates to paying the top CEO 500% more than the 250th CEO because of firm size. In particular, the authors find that

The six-fold increase in CEO pay between 1980 and 2003 can be attributed to the six-fold increase in market capitalization of large U.S. companies during that period. When stock market valuations increase by 500%, under constant returns to scale, CEO “productivity” increases by 500%, and equilibrium CEO pay increases by 500%.

In this light, high CEO pay makes sense. When a company's value increases greatly, the decisions of a CEO require him to handle more and more money. While the value of the company increases, his productivity increases. Meanwhile, individual workers on the factory floor do not handle more and more responsibility or produce more output as the firm grows, and should not be paid as though they do.

LeBron James: True to his generation

LA Times OpEd "LeBron James: True to his generation" (July 13th, 2010) suggests that young workers are more mobile than older workers. Apparently, this all has to do with generational-characteristics, not economics.

If younger workers have displayed anything as employees, it's that they prize mobility more than they do fidelity to their employers.

"Stability and company loyalty are high values for . . . those whose worldviews were shaped by experiencing the Great Depression in their formative years," Chip Espinoza, Mick Ukleja and Craig Rusch write in their new book, "Managing the Millennials." "But the work world has changed."

At all ages, workers seek to find a job at which they can earn the highest wage, and employers seek the best workers. Since it is not possible to know one's productivity perfectly before actually working at a particular job, workers will not necessarily find their best job immediately, and will continue to look for jobs until they find the one that they believe suits them best. Hopefully, by the time they are 50 all workers will have found their best job.

In addition, unlike their older counterparts, young workers sometimes are building their human capital while working. For example, they may be enrolled in a part time business school. When they are done, the will be able to find a better job. This move has nothing to do with "disloyalty," since firms rarely have higher-level positions ready and waiting for such workers.

The notion that young workers should stay put is completely out of equilibrium, and would likely only occur when productivity differences and wage differences between jobs were trivially small. In the current job market, this is not the case.

Farm Work should be an honored, palatable job for Americans

Los Angeles Times article "Farm Work should be an honored, palatable job for Americans" (July 10th, 2010) bemoans the decline in wages for farm workers but completely ignores the economics behind these fluctuations.

By 1981, the contract provided about double minimum wage, at which point we were probably the best-compensated grape pickers in the world. We had paid holidays, and for high-seniority workers, two weeks' paid vacation; disability and unemployment insurance; family medical insurance (with 60 hours of work or more in a month); even a modest pension plan. The Coachella Valley had a UFW medical clinic for the workers and their families, and a legal aid center to help with taxes, Social Security and other issues.

The legacy of David Freedman Co. under the UFW contract is one all Americans can be proud of. It is proof that American agriculture does not have to be based on the labor of an underclass denied the rights and benefits of other workers.

Sadly, only one UFW contract remains in the Coachella Valley, and wages and benefits are not as generous as they were 25 years ago.

In fact, wages in these competitive markets are not set by the sentiments of Americans, but rather by market forces. For example, if demand for produce increased, then firms would want to increase their production. However, most farmers were likely constrained in their ability to purchase more capital (farm equipment) and so were only able to increase their demand for farm labor. This caused an increase in farm worker wages.

Again, the reason that wages increased by as much as they did may simply have been that in the short run, capital is inelastic. In the long run, it is perfectly elastic. Thus, the long-run rise in wages would be heavily mediated by substitution into high capital-share production.

America's 'casualty gap'

Los Angeles Times opinion editorial "America's 'casualty gap'" (May 28th, 2010) reports the difference between the percentage of total wartime casualties suffered by members of poor communities relative to members of rich communities.

Nationally, in the Korean, Vietnam and Iraq wars, communities in the lowest three income deciles suffered 35%, 36% and 38% of the casualties, respectively. Yet communities in the top three income deciles sustained significantly fewer casualties — 25%, 26% and 23% of the casualties, respectively.

The United States has a volunteer army. Soldiers are compensated by regular pay, hazard pay, enlistment bonuses, government benefits, and well-earned gratitude from present and future generations. When the United States has a volunteer army, which it has since December 1972, the last month in which an individual was conscripted into the U.S. Armed Forces, it is an exercise in futility to argue any sort of discrimination. Individuals freely choose the Armed Services over their other options. They further choose their branch of service, as well as their military occupational specialty, generally speaking. If poorer people choose the military, it would appear, in a rough analysis, that they are benefitting more from its presence.

This may be especially true during wartime. Corrections cobbled together military pay for E-2 (an enlisted pay-grade corresponding to a Private in the Army, PFC in the Marine Corps, Airman in the Air Force, and Seaman Apprentice in the Navy and Coast Guard. It is a pay grade relatively rapidly achieved for enlisted men. Military pay sheets for every year were not easily available. Corrections imputed pay for those years in which it is not, denoted by a circle. Years featuring a war in which more than one-hundred Americans died (as well as the first three years of Operation Enduring Freedom, in which fewer than 100 Americans died) are denoted in red, while years without such a conflict are denoted in blue. It appears to Corrections, generally speaking, that post-draft wartime has caused more rapid increases in inflation-adjusted military pay. Therefore, it is difficult to discern without more careful calculus whether or not individuals are being compensated for the risks they are taking--with heterogeneous valuations, we might expect wartime military service to be better for poorer Americans who choose to serve, rather than worse. Our data is displayed graphically below (click to enlarge).

We note the sharp spike in pay occurred when Richard Nixon was engaged with the idea of an all-volunteer army.

Corrections should further add that including Operation Enduring Freedom, Operation Iraqi Freedom and Operation New Dawn in their analysis, without including the enrollment, average length of service, and rate of ascent figures for each income decile is egregiously misleading. In fact, both the lower class and the upper class are underrepresented in enrollment--this article's analysis would suggest that the middle class suffers disproportionately the costs of war.

In addition, a low-income recruit may not be identical to a high-income recruit, making it difficult to compare their wartime outcomes directly. For example, it is well known that income is correlated with education. If the army recruits more "high-quality" soldiers from higher income brackets, then we would expect these "high-quality" recruits to more quickly achieve higher and higher military rank, making them potentially less likely to be in the line of fire than their low quality counterparts. In this sense the article may be taking issue with the fact that more intelligent soldiers are less likely to die in battle. Similarly, if the poor serve longer than the rich, these statistics could be driven by the relative density of poor servicemen. Ultimately, the number of confounds in this analysis make it completely incredible.

What ever became of welfare moms?

Chicago Tribune article "What ever became of welfare moms?" (May 17th, 2010) offers the suggestion that no-one believes that potential jobs exist for individuals who are looking for them. Corrections isn't so sure.

No one sane assumes that today's unemployed are loafing, that jobs are 'out there' for them or that getting married would solve their problems.

The suggestion is that somehow, all individuals who are not unemployed due to minimum wage simply cannot get a job because there are no jobs out there for them. This idea is displayed graphically below (click to enlarge). The figure isn't copacetic with the empirical reality as Corrections sees it. Here, an increase in labor supply will only decrease wages while creating no extra jobs.

However, they still appear to be "voluntarily" unemployed, insofar as there are jobs they are unwilling to take. Let us examine job openings, layoffs, and the unemployment rate from the Job Openings and Labor Turnover Survey (for job openings and layoffs) and the Current Population Survey (unemployment rate). displayed graphically below (click to enlarge). All figures are seasonally unadjusted and relate to private job openings and layoffs.

As we can see from the figure, there is no giant increase in the availability of Summer jobs, and little discernible seasonal variation, save a spike in January layoffs. From this we might conclude the entire job market was being determined by demand-side economics--when firms want to hire, unrelated to the desire of individuals to work.

However, if we examine the teenage job market, we might expect a large supply shift during the Summer, because the cost of working has declined (they are no longer in school). If this is the case, and our first figure holds for teens, teen wages should go down but no more teens should work. However, this is not the case. We can see this through replication (note: our axes are different) of Figure 4 in Casey Mulligan's 2010 NBER Working Paper Simple Analytics and Empirics of the Government Spending Multiplier and other "Keynesian" Paradoxes (click to enlarge). The figure displays the total deviation in teen employment on yearly trend (in thousands). It clearly indicates that this Summer appears to be similar to past Summers in terms of employment--in spite of a supposedly inelastic labor demand. This suggests that labor demand is not in fact inelastic--it is elastic enough to support a large (million strong) (Summer) increase in labor supply.

As we see, teen employment in the two "crisis" Summers was almost exactly the same as it was from 2003-2007. That labor markets were this flexible for teens even while seasonally unadjusted job openings were not spiking dramatically. For Corrections point that labor demand is not inelastic to hold, the above is all that is required--earnings are not necessary (though preliminary examination of quarterly data indicates support for our claim). It should be quite clear that the increase in jobs is largely due to supply-side factors of workers rather than demand-side factors of firms.

However, in the interest of further making our point, we display "monthly" deviations from December-to-December trends of weekly earnings for our three relevant periods--2003 to 2007, 2008, and 2009 (click to enlarge). We note this is a bit artificial, as we use quarterly data with monthly trends. The general shape shouldn't change much, and it illustrates our point well.



There does not appear to be a consistent summerly (3Q) effect. No significant downward shift for the average of 2003-2007 and 2009, negative for 2008. If anything, this further indicates to Corrections that labor demand is relatively elastic, rather than inelastic. Were it inelastic, we would expect a Summer wage effect consistent across 2008 and 2009, due to the large increase in labor supply.

Corrections concludes that there do appear to be jobs out there for those who are willing to supply them--the labor demand of firms appears to be elastic enough to cause a positive employed individuals.

For Photographers, the Image of a Shrinking Path

New York Times article "For Photographers, the Image of a Shrinking Path" (March 30th, 2010) offers two quotes without rebuttal that deserve economic and statistical comment, and perhaps correction. The article describes how professional photographers have been hurt by declining demand due to the decline of printed material and an increase in supply from amateur photographers. It suggests first that amateur photographers have prices that are "too low," and second offers a comment that is true of any specific amateur but not of the aggregate.

“People that don’t have to make a living from photography and do it as a hobby don’t feel the need to charge a reasonable rate,” Mr. Eich said.

Corrections would suggest that most people are willing to pay to take pictures--pay in both their time and the money they spend on inputs (from the camera to developing film or other camera accessories. It is not beyond reason that some people would be willing to pay to have their pictures used. Were this the case, Corrections doesn't see why this is not a reasonable rate. For example, when the price of aluminium is very low, then one has to pay people (garbage men) to take one's aluminium cans away. When the price of aluminium is very high, individuals (recyclers) are willing to pay to take one's cans away. Corrections conjectures that there is no "reasonable price" for disposal of one's cans, just as there is no "reasonable price" for a picture.

Second, the Times offers a quote that concerns an individual photographer compared to a professional that is a fallacious argument.

“Can an amateur take a picture as good as a professional? Sure,” Ms. Eismann said. “Can they do it on demand? Can they do it again? Can they do it over and over? Can they do it when a scene isn’t that interesting?”

This may be true. However, if we have, at any given event, 1000 amateur photographers for one professional, then we might see the professional photographer beating the vast majority of those individuals. It is difficult for an amateur to beat the photographer once out of every hundred. However, because we sample from 1000 amateurs each time, even though any one is beaten by a professional, we expect ten total to have their pictures purchased over the professional's. It is wrong to compare one amateur to one professional--it would be more proper to compare the full alternatives--buy the best professional or the best amateur, and recognize we sample from the "amateur" bin more often.

Getting even on crack vs. powder

Boston Globe editorial "Getting even on crack vs. powder" (March 27th, 2010) discusses a possible gap between legal penalties for possession of crack cocaine and possession of powdered cocaine. It discusses the penalties between the two, and how there was a "100-to-1" penalty for holding crack. Corrections sees the matter as slightly more nuanced than the Globe allows.

The political wheels have begun to turn on correcting the imbalance in sentencing those who possess crack and powder cocaine, but more attention is necessary. Under current law, a person caught with five grams of crack gets the same five-year mandatory prison sentence as someone possessing 500 grams of powder. The 100-to-1 crack-to-powder ratio was enacted at a time that crack was thought to be far more addictive than powder and would spark unprecedented crime waves. Studies long ago disproved both notions, but the law remains on the books, and its burden falls disproportionately on black defendants. More than 80 percent of those incarcerated for possession of crack are black.

We noted in a previous post that addictive substances such as crack cocaine were a technological advancement on cocaine. It allowed for small cheap, unobtrusive, mass distribution in a way cocaine did not, a point lifted from Roland Fryer, Paul Heaton, Steven Levitt, and Kevin Murphy’s 2005 NBER working paper “Measuring the Impact of Crack Cocaine.” It is not immediately clear whether or not this phenomenally destructive drug would have been as prevalent as it was were cocaine itself not illegal. On the one hand, cocaine is an input into crack cocaine production. On the other hand, cocaine is a substitute to crack cocaine itself, one whose competitive availability is likely increased much more than crack cocaine’s, in light of crack’s popularity being in part due to cocaine’s inefficient illegal distribution system.

Crack cocaine is a technological advancement on cocaine--distribution is made easier. Therefore, it may make sense to "tax" it at a higher rate, if one catches individuals who deal in it much less often. That is, if one is caught half as often with crack cocaine, then a doubling of the sentence may "equalize" the penalties between the two crimes, an objective the Globe seems to pursue.

Corrections might further add that the law-race discrepancy may have less to do with politician racism than it might have to do with endogenous selection into drug markets. Let us imagine that individuals have three choices: to work for wages in the "above ground" economy (legal), to work selling powdered cocaine (powder), and to work selling crack cocaine (crack). Every job choice has two wages that are taken as a bundle--the average wage per hour and the expected years in prison one receives. A fortiori, assume wages are the same between the two groups.

Finally, imagine that while the wages of both whites and blacks are the same, blacks lose less from prison (as we shall see, a more reasonable assumption is that their outside wages are different). Let us say that a "conversion factor" between years in prison and wage is $2/year for whites and $1/year for blacks.

Then we display our hypothetical wages graphically below (click to enlarge):



In this case, we should see blacks specializing in crack, even though the sentence is higher, while whites split between legal work and powdered cocaine. The law itself caused blacks to enter into crack, rather than attempting to punish them unfairly. It's not clear whether or not sentencing caused racial segregation of this particular crime or discrimination by politicians caused the disparity in sentencing.

Finally and briefly, we might view this slightly differently and come up with an even more interesting result. Imagine that blacks and whites are two agents producing one of three goods--legal work, powdered cocaine, or crack cocaine. Each individual has an endowment of two inputs--money, and sentencing time. In this assumption, blacks have a larger endowment of the input "sentencing time," so they specialize in the good that is relatively more intensive in sentencing time. If we eliminate the disparity, then the rents they were accruing because they held more of a relatively rarer input go away--blacks could be made worse off if we eliminate the disparity by Stolper-Samuelson Theorem (note that eliminating the disparity essentially floods the market with an infinite amount of "sentencing time" and returns to possessing it become zero). Stolper-Samuelson gives the idea behind why an unskilled worker in a country such as the U.S. may have their standard of living harmed by international trade because they are much less rare an input.

How Not to Write a Jobs Bill

New York Times editorial "How Not to Write a Jobs Bill" (February 11th, 2010) makes a reflexive claim about jobs and tax cuts that may not be valid. Specifically, the Times argues that tax cuts are unconnected to jobs. Further, it appears to support creation and maintenance of governmental jobs.

An $85 billion proposal put forward Thursday morning by Max Baucus, the chairman of the Finance Committee, and by Charles Grassley, the committee’s top Republican, scarcely began to grapple with the $266 billion in provisions for jobs and stimulus that President Obama proposed in his budget. It was not even in the same league as the modest House-passed $154 billion jobs bill.

Worse, about half of the proposal had nothing to do with new jobs. The single largest chunk, about $31 billion, went to renew expiring tax breaks that are generally useful but unrelated to jobs. Another $10 billion would renew an expiring Medicare payment formula so doctors wouldn’t face a pay cut

Harald Uhlig's 2010 Working Paper "Some Fiscal Calculus" suggests that in the long run, a discounted $2.60 is lost for every dollar the government spends, while tax cuts on labor offer up to $1.7 in gain. The relevant idea is that removal of distortionary taxes improve outcomes, while short-run multiplier benefits are temporary and small.

While time Times mentions tax cuts on labor, it focuses on fiscal aid to states and increasing the supply of government jobs. The Times demands more government jobs:

What senators don’t understand or choose to ignore is that state budget cuts mean layoffs. State and local governments are among the nation’s largest employers, responsible for 15 percent of the labor force, about the same share as the health care sector and far larger than manufacturing or the financial sector. Since August 2008, states and localities have eliminated 151,000 jobs.

From the perspective of Corrections, this may be good news for the economy. In "The Current Financial Crisis: What Should We Learn from the Great Depressions of the Twentieth Century?" (March 2009) Federal Reserve Bank of Minneapolis Working Paper, Gonzalo Fernández de Córdoba and Timothy Kehoe, reporting that sharp productivity drops are a main contributer to depressions, write:

With banks and other financial institutions in crisis, the government needs to focus on providing liquidity so that banks can provide credit at market interest rates, and using the market mechanism, to productive firms. Unproductive firms need to die. This is as true for the automobile industry as it is for the banking system. Bailouts and other financial efforts to keep unproductive firms in operation depress productivity. These firms absorb labor and capital that are better used by productive firms. The market makes better decisions than does the government on which firms should survive and which should die.

Corrections suggests the same goes for one of the few employers whose labor productivity appears fundamentally disconnected from wages, and whose labor allocation is distorted by a labor force that is 36.8% unionized, a figure that is approximately the highest private sector union density ever reached, in the mid 1950's. Government job shrinkage appears to serve a double purpose: increase productivity in the long run as well as serve as a (Ricardian) tax cut in the short.

A Wall Street pay puzzle

Washington Post column "A Wall Street pay puzzle" (January 18th, 2010) displays a complete lack of economic understanding in reporting financial pay. The column brings up an article by Larry Katz, but

A study of Harvard graduates found that those who went into finance "earned three times the income of other graduates with the same grade point average, demographics and college major," reports Harvard economist Lawrence Katz, the study's co-author.

Is it possible that what Wall Street does is three times more valuable to society than other well-paid occupations? That's hard to believe

The study cited, by Claudia Goldin and Lawrence Katz in the American Economic Review: Papers and Proceedings, was simply a survey with no exogeneous variation. The regressions they ran, therefore, cannot have causal implications, but merely descriptive ones. In other words, there may be an underlying reason why individuals who have the same grade point average, demographics and college major still have different wages: they are a different brand people, with different underlying motivations, ambitions, intelligence, or other unmeasured qualities.

The column then errs further, arguing that individuals in this situation would be paid three times as much as equal peers who go into other occupations because what they do is more valuable. If individuals are going into other occupations, and foregoing wages that are three times higher, it begs the question of whether or not there are compensating differentials involved. That is to say, when one sees two people they think are the exactly the same taking jobs with three times different pay, either the individual are different, or the job that pays three times as much has some undesirable attribute that makes the "real" pay equalize--otherwise both would take jobs in the same industry.

'If you've got a trade, you've got it made'

Los Angeles Times article "'If you've got a trade, you've got it made'" (January 13th, 2010) appears to make the assumption that the elasticity of demand for blue-collar work is inelastic--that blue-collar wages are relatively untouched by new entrants into the market.

Our nation needs blue- collar workers -- skilled mechanics, machinists, welders, carpenters and electricians, as well as computer, solar and cable technicians, etc. -- just as much as it needs college grads.

As one retired plumber told me: 'No one is going to outsource your local repair guy. If you've got a trade, you've got it made.'

This ignores the fact that even if demand is completely inelastic for local repair guys, as the retired plumber suggests, supply can increase and reduce the wages of blue collar workers, rendering them more vulnerable than the times admits. The process by which wages fall is displayed graphically below (click to enlarge).  Indeed, one expects that this is the reason for what has happend to U.S. born blue collar workers (using partial identification, we conjecture that we can say that demand increased more than supply increased, as wage differentials have fallen and quantity of workers has increased).  Larry Katz and Claudia Goldin's diagram for the high school/college wage gap from their Brookings Papers on Economic Activity (2007) is also displayed graphically below (click to enlarge).

Judges Consider New Factor at Sentencing: Military Service

Wall Street Journal editorial "Judges Consider New Factor at Sentencing: Military Service" (December 31st, 2009) waves its hands at, but fails to actually observe any externalities in military service that require the parallel justice system it describes. Specifically, it notes that military veterans coming back from foreign deployment have received special judicial treatment in light of their service.

As more soldiers return home from combat overseas and end up in the criminal-justice system, a number of state and federal judges are deciding to show former soldiers leniency in light of their service. Some veterans are receiving probation coupled with psychological treatment, generally for nonviolent crimes that normally would land them in prison.

The article gives an example of one judge's reasoning:

'We dump all kinds of money to get soldiers over there and train them to kill, but we don't do anything to reintegrate them into our society,' says John L. Kane, a federal judge in Denver. Earlier this month, Mr. Kane sentenced an Iraq war veteran convicted of bribery to probation instead of prison.

Yet Judge Kane's argument does not appear to have sound foundations, in the understanding of Corrections. The United States has a volunteer army. Individuals who sign up are doing so because the total discounted lifetime path of wages (cognitive and monetary) are higher than their next best alternative. If they were not, individuals would choose their "next best" (contradictorily, their best) alternative.

If the cost of joining the army, including the probability an individual survives, breaks down psychologically and commits crimes upon their return is too high, individuals will opt out of military service. They will do so until wages are increased or the future costs that cause them to commit crimes are decreased. This is the proper market solution to unfortunate military conditions. If military service is unattractive and unfortunate, fix it through wages, rather than through fringe benefits, like reducing disincentives on producing negative externalities to others (crime), an unsound economic proposition.

Individuals who perform military service are paid in a variety of ways. The public honors them as protectors of freedom. They are paid a wage. They gain fringe benefits through discriminatory governmental hiring practices. The military should make sure it is paying in the most efficient manner, and it is by no means clear that removing disincentives from criminal activity is welfare-enhancing.

The only case in which offering these fringe benefits to soldiers makes sense to Corrections is if ex ante the military has difficulty predicting the single individual of many to pay higher wages in the form of a light sentence, and ex post it can identify them, that the value of this benefit is high, and the moral hazard it poses is low, an unconvincing conjecture.

One might add that there could simply be sample selection in sentencing. Individuals with military service might be less prone to recidivism, incarcerating them less effective, and lighter sentences may be efficient. The article does not address this, though Corrections sees it as a possibility.

Foreign interpreters hurt in battle find U.S. insurance benefits wanting

Los Angeles Times article "Foreign interpreters hurt in battle find U.S. insurance benefits wanting" (December 18th, 2009) provides an interesting observation without explanation. Specifically, Iraqi interpreters, injured in Iraq while running the same risks as American soldiers there, are not given the same benefits.

Payments intended to provide a decent standard of living in Iraq or Afghanistan leave the recipients below the poverty level in this country.

and

'When we were in Iraq, we were exactly like the soldiers,' Hadi said. 'Why are we treated differently now?'

After establishing that Iraqi interpreters are paid less, the article deepens the question. A normal, reflex response might be to say that Iraqi interpreters were paid less because they were worth less. After all, in competitive markets, people are paid at least what their second-best-offer is. The article gives evidence that interpreters were worth just as much, in terms of productivity, as U.S. soldiers on the ground.

Retired U.S. Army Col. Joel Armstrong, who served in Iraq and was a leading proponent of the 2007 troop buildup, or 'surge,' that helped reduce violence in the country, said Iraqi interpreters were crucial to the strategy's success.

'Without them, you really can't operate effectively as a force. It's just impossible,' Armstrong said.

Taking the Times at its word, the lapidary answer to Corrections is that when it comes to interpreters of Iraqi Arabic living in Iraq, the U.S. Army is all but a monopsony, a single consumer of a good for which there are many producers. In that vein, Iraqi interpreters will not be given their marginal product of labor, while U.S. soldiers, for which the U.S. Army is not the sole option, shall.

We note that even though contractors hire interpreters, we view them simply as intermediaries, and the article's concern about AIG disputing insurance payments will be reflected in higher ex ante wages rather than ex post coverage. This is true especially if private insurance can be purchased, while risk aversion makes the system less efficient.