The Many Uses of Elasticity: An Example from Law Enforcement Policy

In this chapter, we have studied several types of elasticities, starting with the price elasticity of demand. Elasticity is a general concept that economists use to measure the effect of a change in one variable on another variable. An example of a more general use of elasticity, beyond the uses we discussed in this chapter, appears in a new academic paper written by Anne Sofie Tegner Anker of the University of Copenhagen, Jennifer L. Doleac of Texas A&M University, and Rasmus LandersØ of Aarshus University. 

The authors are interested in studying the effects of crime deterrence. They note that rational offenders will be deterred by government policies that increase the probability that an offender will be arrested. Even offenders who don’t respond rationally to an increase in the probability of being arrested will still commit fewer crimes because they are more likely to be arrested. Governments have different policies available to reduce crime. Given that government resources are scarce, efficient allocation of resources requires policymakers to choose policies that provide the most deterrence per dollar of cost.

The authors note “we currently know very little about precisely how much deterrence we achieve for any given increase in the likelihood that an offender is apprehended.” They attempt to increase knowledge on this point by analyzing the effects of a policy change in Denmark in 2005 that made it much more likely that an offender would have his or her DNA entered into a DNA database: “The goal of DNA registration is to deter offenders and increase the likelihood of detection of future crimes by enabling matches of known offenders with DNA from crime scene evidence.”

The authors find that the expansion of Denmark’s DNA database had a substantial effect on recidivism—an offender committing additional crimes—and on the probability that an offender who did commit additional crimes would be caught. They estimate that “a 1 percent higher detection probability reduces crime by more than 2 percent.” In other words, the elasticity of crime with respect to the detection probability is −2.

Just as the price elasticity of demand gives a business manager a useful way to summarize the responsiveness of the quantity demanded of the firm’s product to a change in its price, the elasticity the authors estimated gives a policymaker a useful way to summarize the responsiveness of crime to a policy that increases the probability of catching offenders.  

Source: Anne Sofie Tegner Anker, Jennifer L. Doleac, and Rasmus LandersØ, “The Effects of DNA Databases on the Deterrence and Detection of Offenders,” American Economic Journal: Applied Economics, Vol. 13, No. 4, October 2021, pp. 194-225. 

Card, Angrist, and Imbens Win Nobel Prize in Economics

David Card
Joshua Angrist
Guido Imbens

   David Card of the University of California, Berkeley; Joshua Angrist of the Massachusetts Institute of Technology; and Guido Imbens of Stanford University shared the 2021 Nobel Prize in Economics (formally, the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel). Card received half of the prize of 10 million Swedish kronor (about 1.14 million U.S. dollars) “for his empirical contributions to labor economics,” and Angrist and Imbens shared the other half “for their methodological contributions to the analysis of causal relationships.” (In the work for which they received the prize, all three had collaborated with the late Alan Krueger of Princeton University. Card was quoted in the Wall Street Journal as stating that: “I’m sure that if Alan was still with us that he would be sharing this prize with me.”)

The work of the three economists is related in that all have used natural experiments to address questions of economic causality. With a natural experiment, economists identify some variable of interest—say, an increase in the minimum wage—that has changed for one group of people—say, fast-food workers in one state—while remaining unchanged for another similar group of people—say, fast-food workers in a neighboring state. Researchers can draw an inference about the effects of the change by looking at the difference between the outcomes for the two groups. In this example, the difference between changes in employment at fast-food restaurants in the two states can be used to measure the effect of an increase in the minimum wage.

Using natural experiments is an alternative to the traditional approach that had dominated empirical economics from the 1940s when the increased availability of modern digital computers made it possible to apply econometric techniques to real-world data. With the traditional approach to empirical work, economists would estimate structural models to answer questions about causality. So, for instance, a labor economist might estimate a model of the demand and supply of labor to predict the effect of an increase in the minimum wage on employment.

Over the years, many economists became dissatisfied with using structural models to address questions of economic causality. They concluded that the information requirements to reliably estimate structural models were too great. For instance, structural models require assumptions about the functional form of relationships, such as the demand for labor, that are not inferable directly from economic theory. Theory also did not always identify all variables that should be included in the model. Gathering data on the relevant variables was sometimes difficult. As a result, answers to empirical questions, such as the employment effects of the minimum wage, differed substantially across studies. In such cases, policymakers began to see empirical economics as an unreliable guide to economic policy.

In a famous study of the effect of the minimum wage on employment published in 1994 in the American Economic Review, Card and Krueger pioneered the use of natural experiments.  In that study, Card and Krueger analyzed the effect of the minimum wage on employment in fast-food restaurants by comparing what happened to employment in New Jersey when it raised the state minimum wage from $4.25 to $5.05 per hour with employment in eastern Pennsylvania where the minimum wage remained unchanged.  They found that, contrary to the usual analysis that increases in the minimum wage lead to decreases in the employment of unskilled workers, employment of fast-food workers in New Jersey actually increased relative to employment of fast-food workers in Pennsylvania. 

The following graphic from Nobel Prize website summarizes the study. (Note that not all economists have accepted the results of Card and Krueger’s study. We briefly summarize the debate over the effects of the minimum wage in Chapter 4, Section 4.3 of our textbook.)

Drawing inferences from natural experiments is not as straightforward as it might seem from our brief description. Angrist and Imbens helped develop the techniques that many economists rely on when analyzing data from natural experiments.

Taken together, the work of these three economists represent a revolution in empirical economics. They have provided economists with an approach and with analytical techniques that have been applied to a wide range of empirical questions. 

For the annoucement from the Nobel website click HERE.

For the article in the Wall Street Journal on the prize click HERE (note that a subscription may be required).

For the orignal Card and Krueger paper on the minimum wage click HERE.

For David Card’s website click HERE.

For Joshua Angrist’s website click HERE.

For Guido Imbens’s website click HERE.

COVID-19 Update – Apply the Concept: Can You Catch Covid-19 from Touching a Surface? Taking into Account How People React to Changing Circumstances

Supports:  Econ (Chapter 1, Section 1.3- in All Volumes)

Here’s the key point:   To forecast the effects of a government policy, it’s important for economists to take into account how people will change their behavior in response to the policy.

In forecasting the effects of a government policy, economists take into account how people will respond to the policy.  In general, when people’s circumstances change, including when the government enacts a new policy, people change how they act.  It’s easy to fall into an error if you fail to take into account how people’s actions might change—their behavioral response—as their circumstances change.  Let’s consider two examples.

First consider an example from the Covid-19 pandemic.  In May 2020, the federal Centers for Disease Control and Prevention (CDC) noted that few people were contracting the disease as a result of touching surfaces contaminated by the virus and that most people became ill by breathing in the virus while near an infected person. Some media outlets interpreted the CDC’s announcement as meaning, in the words of one headline: “CDC Now Says Coronavirus Isn’t Easily Spread by Touching Surfaces.” But is this conclusion correct? Consider two scenarios:

Scenario 1: Despite the spread of the coronavirus, people and businesses don’t adjust their behavior. People are unconcerned if they touch a surface, such as a doorknob, that may contain the virus.  After touching a surface, they don’t immediately wash their hands or use hand sanitizer.  No one wears gloves. Businesses don’t make a special effort to clean surfaces.

Scenario 2: Most people react to the spread of the coronavirus by avoiding touching surfaces whenever they can.  If they do touch a surface, they wash their hands or use hand sanitizer. Some people wear gloves. Businesses disinfect surfaces much more frequently than they did before the virus became widespread.

If Scenario 1 accurately described the situation in the United States in May 2020, we could reasonably draw the conclusion contained in the media headline we quoted: You are unlikely to catch Covid-19 by touching a contaminated surface. In fact, of course, Scenario 2 more accurately describes the situation in the United States at that time. As a result, the fact that few people caught the virus from touching a contaminated surface does not allow us to conclude that you are unlikely to catch Covid-19 that way because people adjusted their behavior to make that outcome less likely.

Now consider an economic example.  Suppose that a city decides to tax colas and other sweetened beverages.  If stores in the city are currently selling 100 million ounces of soda and the city imposes a tax of 2 cents per ounce, will it collect $2 million (= $0.02 per ounce × 100,000,000 ounces) in revenue from the tax per year?  We can expect that because of the tax, stores will increase the prices they charge for soda. Those price increases will cause consumers to change their behavior. Some people will buy less soda and, if the city’s suburbs don’t also enact a tax, some people will drive to stores outside the city to buy their soda. As a result, sales of sweetened beverages in the city will fall below 100 million ounces and the city will collect less than $2 million per year from the tax.

In both these cases, we would draw an incorrect conclusion if we failed to take into account the behavioral response of people to changes in their circumstances, whether the change is from the arrival of a new disease or an increase in a tax.  Economist sometimes call the error of failing to take into account the effect of behavioral responses to policy changes the Lucas critique, named after Nobel laureate Robert Lucas of the University of Chicago.

Question: An article in the Seattle Times published in late May 2020 noted that: “Half of new coronavirus infections in Washington [state] are now occurring in people under the age of 40….” Yet an opinion column in the New York Times published in March 2020 near the beginning of the pandemic noted that the coronavirus was disproportionately infecting older people.  Is one of these accounts of which age group is most likely to be infected necessarily incorrect? Briefly explain.

For instructors that would like the solutions to these questions, please email your name, course number, and affiliation to christopher.dejohn@pearson.com and we’ll send along a solutions manual.

Sources: Sandi Doughton, “Half of Newly Diagnosed Coronavirus Cases in Washington Are in People under 40,” Seattle Times, May 28, 2020; and Louise Aronson, “‘Covid-19 Kills Only Old People.’ Only?” New York Times, March 22, 2020.