Friday, March 2, 2018

Thoughts on Latest Labor Market Concentration Paper

There is an interesting new paper by Azar, Marinescu, Steinbaum, and Taska on measuring concentration in the U.S. labor market using a dataset of nearly all online US vacancies from Burning Glass Technologies. This is obviously a very important issue and I am glad they are investigating it. However, I am concerned about how the authors define labor markets in this paper.

Specifically, they define labor markets based on USDA ERS commuting zone and 6-digit SOC occupation. So, if I understand this correctly, one labor market would be for Economics Professors (SOC: 25-1063) in the area surrounding Asheville, North Carolina (Commuting Zone 91). If that is correct, I can't help but think this definition of a labor market seems very narrow. To illustrate, I have two questions.

  • Aren't there occupations where using ERS commuting zones is less appropriate for defining the labor market? Economics Professors seems like an obvious example. Asheville doesn't have a local market for economics professors. Instead, if UNC Asheville posted a job an economist, they would get applicants from all over the country. The authors note that 81% of applications on are within the same commuting zone. However, it isn't obvious how well that result applies to the Burning Glass Technologies dataset.
  • Second, how common is it for the same person to apply to jobs in different occupation codes? Again, economists seem like a good example since they often apply to jobs in multiple occupation codes. For example, I have applied for jobs as an Economic Professors (SOC: 25-1063) and as a non-academic Economist (SOC: 19-3011). Are economists unique in this regard? Would a person that currently delivers food (SOC: 53-3031) never consider delivering office mail and packages (SOC: 43-5021)? If people are considering jobs across multiple 6-digit SOCs, maybe they are too narrow for defining labor markets?
To be fair, the authors defend defining labor markets using occupation by looking labor supply elasticities to make sure they are not too big (they argue an elasticity greater than 2 is an indication the market is defined too narrowly). They note that Marinescu and Wolthoff (2016)  found that, within a 6-digit SOC, the elasticity of applications with respect to posted wages is negative using data from So, if anything, they argue they are defining labor markets too broadly! However, a negative supply elasticity is a very counterintuitive finding. And it is based on a subsample of applications from a single website (only 20% of ads in the CareerBuilder dataset included wages and it isn't clear if selection bias is an issue). So would it really be enough to dismiss the more intuitive concerns raised in my second question above? I don't know.

Anyways. These are just my initial thoughts. It was a very interesting paper, so I will be eager to see what other people think as it gets passed around the web.

Sunday, February 18, 2018

Black Panther and the Tyranny of Markets

Black Panther opened this weekend and I was wondering why Hollywood doesn't cast more people of color in leading roles. Consumers are clearly willing to pay to see these movies. So, why haven't more studios tried to fill that demand? Is it because of racism in casting? Maybe. But I believe research by Joel Waldfogel, an economist at the University of Minnesota, may offer an alternative explanation.

In his 2007 book, The Tyranny of the Market, Waldfogel argues that the availability of product varieties can be limited when fixed costs are high. To see why this is the case, consider the following simplified example. Imagine there is a market for different color t-shirts. On the demand side there are 300 consumers that each want to buy 1 t-shirt per year and are willing to pay exactly $10 per shirt. However, 100 consumers want to buy 1 blue t-shirt per year and 200 consumers want to buy 1 green t-shirt per year. On the supply side, this market is served by 1 company that produces blue t-shirts and 1 company that produces green t-shirts. Will this market produce both blue shirts and green shirts? That depends on the costs of production.

Suppose we start in a world with no fixed costs, where each shirt can be produced at a constant marginal cost of $5 per shirt. In this world, every consumer will get the color they want. The blue t-shirt company will produce 100 t-shirts per year and earn $500 per year of profit. The green t-shirt company will produce 200 t-shirts per year and earn $1,000 per year of profit.

What happens if we add a fixed cost like, say, $600 per year to rent a factory? Product diversity declines because it is impossible for the blue t-shirt company to stay in business (they will lose $100 per year). Only the green t-shirt company survives because it had a large enough consumer base to cover those fixed costs. In other words, the bigger group gets the varieties it wants and the smaller group does not.***

Waldfogel found that his story describes local radio markets pretty well--bigger groups get more stations they want. I believe this story may also apply to the movie industry. Like our example above, studio movies are characterized by large fixed costs. Studios pay millions just to produce the first copy of the movie and the cost of printing subsequent copies of the movie are small in comparison. As a result, if a studio wants to make a profit, they need to attract big audiences so they can earn enough revenue to cover their fixed costs. This could lead Hollywood to cast fewer people of color, because there is a pernicious belief that these actors “do not travel” to wider, international audiences.

Unfortunately, there have not been any rigorous studies on whether high fixed costs are limiting product diversity in the movie industry. However, there is some suggestive evidence from related industries. For example, several studies have found that there is more diversity in casting on television than there is in the movies. I suspect this is because even though tv shows are more expensive to produce than ever before they are still much cheaper to make than most studio movies. Lower costs would allow networks to take more chances with shows that might only appeal to a small audience.

Of course, if this argument is right, it means that Hollywood is not casting people of color because they are afraid they wont be accepted by wider audiences. There is mounting evidence that this just isn't true. However, Hollywood may still be reluctant because it is so hard to determine why one movie succeeds and another does not. Maybe the success of Black Panther will serve as the final piece proof that Hollywood needs that good actors of any race can appeal to all audiences? That would certainly make for happy ending.  

***Note that this decrease in available product varieties only occurs if fixed costs increase. If marginal costs increased from $5 to $9, both groups still get the t-shirt they want and the manufacturers just earn less profit. If marginal costs increase over $10, then neither company earns any profit and no one get the t-shirt they want. In other words, either everyone gets what they want or no one gets what they want.

Saturday, December 30, 2017

Everyone Keeps Getting Becker's Crime Model Wrong

In a recent JPE article, Steven Levitt claims that Gary Becker's 1968 paper on crime makes predictions that are at odds with reality. Specifically, he claims that Becker's model predicts that the most efficient way to deter criminals is by combining a low probability of punishment (p) with an extremely severe penalty or fine (f) when a criminal is caught. Obviously, no developed country has a criminal justice system that functions this way. So, either the whole world is wrong or Becker was mistaken. Right?

I really respect Levitt, but this just isn't so. 

Becker's predictions depend on the risk preferences of criminals. If criminals are risk averse, then Levitt is right that the optimal policy is to have a very low p and a very high f. To see why, suppose you start off with the opposite policy--a high p and low f. What happens if you decide to cut p in half and double f? The expected value of the penalty stays the same (pf = (p/2)*(2f)), but crime becomes more risky because you have increased the variance of the outcomes. On the one hand, this is bad news for risk averse criminals because they receive less utility from riskier crimes (see Figure 1). On the other hand, this is good news for taxpayers because imposing penalties is typically cheaper than trying to catch criminals. In other words, you are deterring criminals more and at a lower cost. If you keep increasing f and decreasing p, you will find that the cheapest way to deter risk averse criminals is to have a very low p and very high f. Just like Levitt said!

Unfortunately for Levitt, Becker did not think that criminals are risk averse. Instead, he spends a good chunk of his 1968 article arguing that criminals are risk lovers. In that case, making crime riskier actually INCREASES their incentive to commit crimes (see Figure 2). So, having a very low p and very high f is no longer the optimal policy. Becker goes on to argue that actual US policy seems consistent with the implications of his optimality analysis. In other words, Becker argues the exact opposite of what Levitt says.

Levitt is not the first person to mischaracterize Becker's paper in this way. In 2015, Alex Tabarrok wrote a blog post making a similar argument. Tabarrok's post was later boosted by Tim Worstall and Noah Smith. It is a shame that this keeps happening, especially in places like the JPE! It leaves the impression that Becker's paper is inherently flawed, possibly not worth reading. In reality, it is actually a good example of how to apply theory to understanding real-world problems. These authors have done much better in the past, and they could do much better now if they chose.

Figure 1. Making Crime Riskier Deters Risk Averse Criminals

Following Becker (1968), these figure assumes the following. If a criminal is not caught, they get to keep all of the income they "earned" (Y). If they are caught, they have to pay some penalty or fine (f), leaving them with (Y-f). The probability the criminal is caught is p. In this figure, I illustrate the impact of increasing f from f to 2f and decreasing p from p to p/2 on a risk averse criminal.

Figure 2. Making Crime Riskier Encourages Risk Loving Criminals
Following Becker (1968), these figure assumes the following. If a criminal is not caught, they get to keep all of the income they "earned" (Y). If they are caught, they have to pay some penalty or fine (f), leaving them with (Y-f). The probability the criminal is caught is p. In this figure, I illustrate the impact of increasing f from f to 2f and decreasing p from p to p/2 on a risk loving criminal.

Monday, October 23, 2017

Resolving a Cocaine Paradox with Derived Demand

Earlier this year, Tom Wainwright appeared on Russ Robert's EconTalk to discuss his new book, Narco-nomics. This book is about the economics of the drug trade. During their conversation, Wainwright described how governments in countries like Colombia eradicate millions of acres of coca leaf crop every year as part of the "war on drugs." The idea behind this policy is that by making coca more expensive, we will also make cocaine more expensive since it is the drug's key ingredient. However, to the chagrin of policy makers, the price of cocaine has not risen much (if at all).

Wainwright's explanation for this seeming paradox is that 1) the price of coca represents a small portion of the price of cocaine (less than 1%), and 2) drug cartels have market power that allows them to negotiate lower prices with coca leaf growers. These both sound like good reasons to me, but I think Wainwright maybe forgetting one other reason that output prices might not be rising along with input prices. Specifically, Roberts and Wainwright carry on their conversation as if the price of all other inputs into cocaine production stayed the same in the face of coca eradication. But why should we expect that?

Coca seems to have no substitutes in the production of cocaine. So all other inputs should be complements in the production process. That means an increase in the price of coca will lead cocaine producers to use less coca and less of all other inputs. As cocaine producers purchase less of these other inputs, the price of these other inputs will fall to clear their respective markets. As a result, the price of coca goes up, the price of other inputs goes down, and the price cocaine will increase by less than the price of coca (possibly much less if the supply of other inputs is very price inelastic).

Since the "other inputs" used in cocaine products beside coca leaf include the violent aspects of the drug trade, I wonder if this analysis implies that those services would be in less demand? If so, maybe coca eradication at least makes trafficking less violent? I kind of doubt it, but it is something to think about.

Anyways, if you want to think about this some more, you can do so more formally using the derived demand model that I explored in my last post. Here's a quick visual representation of the analysis above using the derived demand model. For simplicity, I drew this assuming you need 1 unit of coca and 1 unit of "other services" to make 1 unit of cocaine. As you can see, the price of coca goes up, the price of other inputs goes down, and the price of cocaine goes up by less than the price of coca.

Sunday, February 26, 2017

Primer on Deriving Demand for Inputs in a Fixed Proportion Production Process

The demand for inputs in the production of final goods is ultimately derived from the demand for the final products themselves, which is why input demands are sometimes called "derived demands." This relationship can sometimes be lost in all the math surrounding modern textbook treatments. I think this is why it is best to introduce students to the concept of derived demand using an example where an industry uses a fixed-proportion production process. Here the math is so simple that it doesn't get in the way of the economics of how output markets influence input markets (and visa versa).

However, few modern textbooks discuss this special case (exceptions include Friedman's Price Theory and Becker's Economic Theory). I think that is a shame. So, I thought I'd write a short primer on deriving an industry's demand for inputs into a fixed proportion production process. First, I provide an intuitive explanation for how to derive the inverse demand for an input using Alfred Marshal's famous knife manufacturing example. Second, I provide a formal discussion of how to derive the elasticity of input demand. Third, I show how this simple example illustrates Marshall's four laws of derived demand. Lastly, I provide some links to additional reading.

There is nothing original here. I am basically just summarizing some old notes that I wanted in one place. Hopefully someone besides me finds them useful.

1. Knives, Blades, and Handles
Suppose that knives are produced using a fixed proportions technology. Specifically, one handle and two blades are combined to create one knife. Figure 1 illustrates the demand curve for completed knives and the supply curves of each input (note that the Pb represents the price of two blades). 

Figure 1. Demand Curve for Final Product and Supply Curves of Inputs

So, how do we derive the demand for one input like handles? Well, let's think about what each curve is telling us. The demand curve for knives shows the most that consumers are willing to pay for a given quantity of knives. Similarly, the supply curve for each input shows the least that suppliers would have to be paid to provide a given quantity of that input. Thus, the most that knife producers would be willing to pay for a given quantity of handles is the difference between the demand for knives and the supply of blades (see Note XIV in Marshall's Mathematical Appendix). Put another way, the "demand price" for handles equals the "demand price for knives" minus the "supply price for two blades":

Figure 2 illustrates the derived demand for handles. Note that no handles are purchased when the price for knives equals the supply price for blades. This is because blades are so expensive at that level of output there is no money left over for handles.

Figure 2. Derived Demand for Handles

2. Deriving the Elasticity of Demand for Handles

We can use the inverse demand function for handles above to derive the elasticity of demand. I provide the details here, but the ultimate result is:

This formula can be useful in applied settings. For example, the EPA used this formula to calculate the elasticity of demand for small, stationary combustion engines (a key input in the product of irrigation equipment among other things) when considering adding regulations on that industry (see page 4-2).

3. Marshall's Laws of Derived Demand

This expression for the elasticity of demand illustrates several of Marshall's 4 laws of derived demand.

  1. "The demand for anything is likely to be more elastic, the more elastic is the demand for any further thing which it contributes to produce." (Note that as the elasticity of demand for knives increases, the elasticity of demand for handles increases).
  2. "The demand for anything is likely to be more elastic, the more readily substitutes for the thing can be obtained." (Not illustrated here because there is no substitutes for handles)
  3. "The demand for anything is likely to be less elastic, the less important is the part played by the cost of that thing in the total cost of some other thing, in the production of which it is employed." (Note that as Ph/Pk decreases, the elasticity of demand also decreases)
  4. "The demand for anything is likely to be more elastic, the more elastic is the supply of co-operant agents of production." (Note that as the elasticity of supply for blades increases, the elasticity of demand for handles also increases)

Side Note: Hicks later showed that Marshall's third law only holds if the elasticity of final demand is greater than the elasticity of substitution. An intuitive explanation by Saul Hoffman for why this is the case can be found here. However, we don't need to worry about that special case with fixed proportion technologies because the elasticity of substitution across inputs is zero. So the condition will always be satisfied.

4. Additional Reading

For more info on this topic, I'd recommend checking out these resources:
  • Becker, Gary. Economic theory. Transaction Publishers, 2007.
  • Diewert, W.E. "A Note on the Elasticity of Derived Demand in the N-Factor Case," Economica (May 1971): 192-198.
  • Friedman, Milton. Price theory. 1972.
  • Muth, R., "The Derived Demand Curve for a Productive Factor and the Industry Supply Curve," Oxford Economic Papers 16 (1964): 221-234
  • Hoffman, Saul D. "Revisiting Marshall's Third Law: Why Does Labor's Share Interact with the Elasticity of Substitution to Decrease the Elasticity of Labor Demand?." Journal of Economic Education 40, no. 4 (2009): 437-445.
  • Thurman, Walter N. "Applied general equilibrium welfare analysis." American Journal of Agricultural Economics 73, no. 5 (1991): 1508-1516.