A new breakthrough in empirical methodology for studying causality in economics

  On October 11, 2021, the Royal Swedish Academy of Sciences announced that this year’s Nobel Prize in Economics will be awarded to D. Card, J. D. Angrist, and G. W. Imbens for “contributions to the empirical aspects of labor economics” and to G. W. Imbens for “methodological contributions to the analysis of causality. Angrist and Imbens for their “methodological contributions to the analysis of causality”. Prior to this, the work of T. Haavelmo, winner of the 1989 Nobel Prize in Economics, and J. Heckman, winner of the 2000 Nobel Prize in Economics, was closely related to causal research.
  Card received his Ph.D. from Princeton University in 1983 and later became a professor of economics at the University of California, Berkeley, and director of the Labor Research Program at the National Bureau of Economic Research. He is the co-author of Myths and Measurements: The New Economics of the Minimum Wage (1995), Handbook of Labor Economics (1999), and In Search of Economic Excellence: The Economic Effects of Economic Reform in the United Kingdom (2004).
  Angrist received his Ph.D. from Princeton University in 1989 and is now the Ford Professor of Economics at MIT, a Fellow of the American Academy of Arts and Sciences, and a Fellow of the Econometric Society. He is the co-author of Fundamentally Harmless Econometrics: A Guide for Empirical Researchers and Proficient Measurement: A Journey of Inquiry from Cause to Effect (both in Chinese translation).
  Inbens received his Ph.D. from Brown University in Providence, R.I., in 1991 and is now Professor of Applied Econometrics and Professor of Economics at Stanford University, where he focuses on causal inference methods in econometrics. He is a member of the Econometric Society and a Fellow of the American Academy of Arts and Sciences.
  Throughout the thousands of years of human social development, the problem of cause and effect has been of great interest to philosophers, who have put forward many influential and profound ideas; and in the course of modern scientific development, scientists have further explored causal inference in practice, trying to reveal the causal connections between things. Econometrics, as an instrumental approach to the study of economic problems, has played a key role in advancing the empirical approach to economic research for 100 years since its establishment in the 1920s. For example, in the 1960s and 1970s, the main task of empirical researchers in economics was to try to explain, for example, the drivers of income or GDP growth, resulting in a range of theories and models of economic growth. Currently, economics is increasingly trending toward empirical or research on empirical studies. As we enter the 1990s, the most important concerns of empirical researchers, including the three laureates, are about the estimation of causal effects and the analysis of assessment policies, rather than being limited to obtaining general econometric models of economic variables.
Card’s empirical research in labor economics

  As a rule, in empirical economic analysis and research, the economic data one obtains are essentially “observational data” rather than “experimental data”. It is a challenging task for economists to use observational data for causal inference studies. In many disciplines, randomized controlled trials (RCTs) are considered the gold standard for achieving this goal. However, in the social sciences, many important questions cannot be studied through randomized controlled trials due to financial, ethical, or practical constraints. On the one hand, given the use of observational data for research, researchers cannot intervene in experiments based on their own purposes, cannot do controlled experiments, and cannot do random assignment treatments (also known as interventions in medical research). On the other hand, using observational data to study causality or causal effects involves two challenging problems: one is confounding or endogeneity, that is, the omission of certain contextual factors that affect both treatments and outcomes, leading to bias and decision errors in studying causality; the other is selectivity bias or missing data, that is, observational data that are not representative of the overall picture that the researcher is concerned with.
  Over the past 30 years, there has been an explosion of work using natural experiments to study causal inference in microeconomics. A “natural experiment” is an event that occurs naturally, without the control of the researcher, or where macro policy has an effect on the study variable similar to that of a randomized trial. The idea of using natural experiments for causal inference dates back to 1944 with the econometrician Havelmo’s “Probabilistic Methods in Econometrics”. And the American sociologist D. T. Campbell’s paper “Reform as Experiment” (1969) was the first study to propose the use of a quasiexperimental approach (quasi-experimental approach). Campbell and D. L. Thistlewaite, professor of psychology at Vanderbilt University, collaborated on “Regression Discontinuity Analysis: An Alternative to Post hoc Experiments” (1960), which investigated and developed an important empirical method, the regression discontinuity design, as a way to estimate causal effects from natural experiments.
  Into the 1990s, Card and his collaborators used a number of natural experiments to analyze a range of important causal issues in labor economics. The successful use of natural experiments in labor economics has led to instrumental variables, double difference methods (also known as DID), and other methods that provide a general research paradigm for studying causal relationships or causal effects.
  There are several well-known century-old dilemmas in labor economics: (i) What effect will immigration have on the employment and income of local residents? (ii) Will setting a minimum wage cause more people to lose their jobs? (iii) What is the impact of investment in education on income? In a series of papers published in the early 1990s, Card conducted an in-depth, rigorous, yet transparent analytical study of these three conundrums, drawing on novel, a priori, and more plausible ways of addressing these questions to obtain new and more reliable answers. These initial research efforts by Carder have clearly played a key role and made the most important contribution to further stimulating and advancing the reanalysis and theorizing of how labor markets work.
  The Impact of the Minimum Wage on Employment
  The minimum wage may be an important policy tool for reducing poverty among low-income people. Economists have long studied the effects of minimum wages on employment. However, a binding minimum wage can increase wage costs, which may reduce employment. Thus, it is not really clear whether low-wage workers will ultimately benefit from the minimum wage. Textbook models of competition suggest that employment will decline substantially if a higher minimum wage is implemented to the point of being raised above the equilibrium level.
  Prior to the 1990s, the evidence on the impact of the minimum wage tended to be consistent with the textbook model. However, identifying the causal effects of the minimum wage is challenging, especially in a time series context. Minimum wages are usually implemented or changed for a reason, and the underlying cause may be related to changes in employment prospects. For example, when the business cycle is in a recession, it manifests itself in lower employment and lower wage growth, especially for lower income earners. At the bottom of the income distribution, relatively low wage growth may, in turn, require higher minimum wages to facilitate the protection of poor workers. If policymakers acted on these demands, it would be the case that declining employment would lead to higher minimum wages, rather than the other way around.
  In 1992, the Industrial and Labor Relations Review devoted an issue of its symposium “The New Minimum Wage Study” to the results. These papers reported the results of analyses using time-varying data within U.S. states to facilitate the estimation of the minimum wage’s impact on employment. In contrast to studies using time-series data, these studies have the flexibility to control for common time trends. The findings in these papers are to some extent inconsistent with previous studies on similar issues. Two of these papers are by Card, along with papers by other researchers such as L. Katz and A.B. Krueger.

  In the paper “Does the Minimum Wage Reduce Employment? A Case Study of California 1987-1989,” Card compares the evolution of wages and employment in California, which raised the minimum wage by 27 percent in 1988, with the corresponding evolution in a set of comparison states where the minimum wage policy did not change. From 1987 to 1989, wages for teenagers in California increased by 10% more relative to the comparison states, and despite the increase, there is no evidence of a decline in teenage employment. In fact, the employment-to-population ratio in California increased by 4% compared to the comparison states. This double difference-in-difference estimate appears to be driven by an increase in the labor force participation rate.
  Another paper by Card, “Using Regional Wage Differences to Measure the Impact of the Federal Minimum Wage,” takes advantage of the fact that changes in the national minimum wage have different effects on states, depending on the initial wage distribution in each state. For example, an increase in the U.S. federal minimum wage in 1990 may have affected more than 50 percent of teenagers in some Southern states, while in some New England states, the percentage was only 5 percent. The Card study found that wage increases were greater in states with a higher proportion of affected teens, but the ratio of teen employment to population did not change.
  Katz and Krueger’s paper, “The Impact of the Minimum Wage on the Fast Food Industry,” exploits the fact that firms will be affected differently by changes in the minimum wage, depending on the proportion of the workforce that used to be below the new minimum wage. Surveying fast food restaurants in Texas before and after the 1990 and 1991 federal minimum wage increases in the U.S., they report results consistent with Card’s: starting wages increased at the more affected firms, and employment increased at these firms. Indeed, one lingering concern with studies using panel data is that it is not clear why some states raised the minimum wage and others did not. Perhaps states that have implemented stricter minimum wage policies have been exposed to negative labor market shocks, or vice versa. Ideally, one would like to keep the employment outlook unchanged and only change the magnitude of the minimum wage change. To achieve this, Card and Krueger delve further and examine the employment effects of minimum wage increases in New Jersey using a double-difference approach in Minimum Wage and Employment: A Case Study of the Fast Food Industry in New Jersey and Pennsylvania (1994). In February 1992, New Jersey raised its minimum wage from $4.25 to $5.05 per hour, while neighboring Pennsylvania did not raise its minimum wage. They inferred causality by investigating employment at 410 fast-food restaurants in the two aforementioned states before and after the minimum wage adjustment under the assumption of no interaction in time and space, removing confounding.
  Soon after, Card and Krueger’s co-authored Myths and Measurements: the New Economics of the Minimum Wage (1995) also contained new analyses such as the impact of the minimum wage on firm value, the robustness of previous time series and panel data evidence, and international evidence on the minimum wage as well as updates and extensions of the authors’ 1992 and 1994 papers. The book was republished in 2016 to mark its 20th anniversary of publication, thus demonstrating its broad and far-reaching impact.
  The impact of immigration on labor markets
  Immigration is a hotly debated political issue in many countries. The concern is that labor supply shocks resulting from large inflows of immigrants may hinder labor market opportunities for local workers through declining wages and employment prospects. However, this concern is influenced by a number of factors. First, the output of local workers depends on the ability of their labor to replace or supplement that of new immigrants. Second, changes on the supply side of labor are expected to cause changes on the demand side of labor, so firms are expected to move into areas with higher immigrant inflows and invest in technologies that are better suited to the characteristics of immigrant workers. Third, changes in demand for goods and services due to immigrant inflows may affect the labor market outlook for local workers.
  The question of how immigration affects local workers living in an area, especially low-skilled residents, is not clear. Answering this question empirically is challenging because it is difficult to say what would happen in an area without the influx of immigrants. The problem is that immigrants may shift to growing labor markets, and even without immigrants, growing markets, the economic outcomes for locals are different from other markets. Most early attempts at answering this question used changes in the number of immigrants in U.S. metropolitan areas aggregated to the local level to estimate the parameters of the production function. The overall result was that the effect on natives was small and the effect on immigrants themselves was large.
  Two of Card’s findings reinvigorate research on the labor market effects of immigration. Both studies deal with the disruptive effects of migration to burgeoning local labor markets.
  One of them, Card’s “The Impact of the Mariel Smuggling Incident on the Miami Labor Market” (1990), capitalized on a unique event in U.S. history known as the Mariel Smuggling Incident. between May and September 1980, approximately 125,000 people left Cuba, 50 percent of whom settled permanently in Miami. This was the largest non-military sea crossing in history to date, and is known in history as the Mariel Smuggling Incident. In just a few months, Miami’s labor force grew by a staggering 7 percent. Carder compares wages and employment in the Miami labor market before and after the Mariel Smuggling Incident with employment in four comparison cities. With an appropriate selection of comparison cities, the Mariel smuggling episode provides a classic natural experiment. Despite the large influx of new and unskilled immigrants to Miami, Card’s 1990 paper shows no evidence that the wage rate and unemployment rate of lower-skilled non-Cuban workers were affected. Card offers two explanations for why wages and unemployment did not respond to the migration event: first, there is evidence that locals and former immigrants to Miami decreased as a result of the Mariel smuggling incident; and second, the industrial structure of the Miami labor market was able to absorb a large influx of unskilled immigrants because of the history of past migration. There was also discussion about whether the results of the Mariel smuggling incident were applicable to other incidents. As Kade points out, Miami has a history of receiving Cuban immigrants, a fact that may have influenced the results. In general, the locational choice of immigrants has considerable historical dependence. Thus, there is a good reason why most Cuban immigrants go to Miami rather than elsewhere.
  The other is J. G. Altonji and Card’s paper, “The Impact of Immigration on the Output of Low-Skilled Native Labor Markets” (1991), which leaves two major legacies to the literature on the economics of immigration: first, it sets up the most commonly used conceptual framework (essentially a demand-side model in which immigration is modeled as a labor supply shock) for analyzing the impact of increased immigration; and second, the authors The methodology employed to estimate the impact of immigration has been repeatedly applied in the literature. This “transfer share” approach is further refined by Card, who uses the prior settlement patterns of each ethnic group to predict overall migration inflows for urban and occupational groups. Typically, this instrument-generating transfer-share approach is common in applied microeconomics research, and the method has been applied repeatedly in migration economics.
  It is the research initiated by Card and subsequently explored that has led to a better understanding of the potential for policy to influence labor market outcomes, the impact of immigration on wage and employment differentials, and the role that firms play in shaping income inequality.

  Indeed, Card’s contributions go far beyond this; for example, he also studies important work related to labor market programs and unemployment insurance, as well as how unions and wage bargaining affect wage inequality. Not only is his work empirical, but in many cases he has been able to combine empirical research with an explanatory framework or explicit theory.
  In addition to this, Card has produced very meaningful and influential research in the area of the impact of investment in education, such as the two papers Card and Krueger co-authored in the early 1990s, “Does School Quality Matter? Returns to Education and the Characteristics of U.S. Public Schools” and “School Quality and Relative Earnings of Blacks and Whites: A Direct Assessment,” which examined the importance of school quality on labor market outcomes. Both papers use exogenous variation in school quality that comes from a period of heavy investment in school resources (1930s to 1950s), particularly in the southern United States. In contrast to much of the previous literature, Card and Krueger analyze how school quality affects labor market outcomes, rather than basing their study on test scores. This is a major innovation because school quality may have more impact than test scores, which narrowly measure an individual’s ability to succeed in the labor market. They also break the mold of the existing literature by clearly articulating their theoretical research design.
Contributions of Angrist and Inbens to Economic Empirical Methodology

  The initial boom in empirical research using natural experiments raised brand new and very important questions conceptually. For example, instrumental variable estimates of the returns to education are typically larger than the corresponding ordinary least squares estimates. In order to ground these findings in theory, researchers have naturally turned to the framework of heterogeneity in the aggregate when it comes to returns to education (heterogeneity is essentially the difference or variation in the study population, both at the individual level, called individual heterogeneity, and at the aggregate level, called aggregate heterogeneity. (In social science research, heterogeneity is ubiquitous); in the context of this setting, the sources of variation used in estimation play a very important role.
  Angrist’s paper, “Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records” (1990), examines the effect of participation in the Vietnam War experience on subsequent earnings. Clearly, this is endogenous. According to his examination, DoD enlistment is determined by drawing a draft lottery number (draft lottery) for men of military age, in which some upper limit is to be set, and when the number is less than the upper limit, the person is within the draft. Here, he defines whether the draft number is less than this upper limit as draft eligibility, and when draft eligibility is 1, the person is more likely to be a soldier in the Vietnam War, and the number is drawn randomly, so draft eligibility is a suitable good instrumental variable, which is undoubtedly an example of using natural experiments.
  Angrist’s research also points to the importance of focusing on heterogeneity. He used the Vietnam War period to estimate the effect of military service on later earnings by drawing lots. In the early 1970s, enlistment eligibility was determined by a random lottery of birth dates. Thus, draft eligibility as an instrument for service in Vietnam was likely to be heterogeneous in response in most cases. When processing effects vary from person to person, people making choices are likely to experience incomplete adherence to (natural) experiments. The fact that individuals volunteered for the military during the Vietnam War is an example of incomplete compliance, as these individuals signed up for service whether or not they were eligible for the draft. Conversely, some individuals who were eligible to enlist were exempted for health reasons or because they were still in school. In general, imperfect compliance with quasi-experimental and experimental variants is ubiquitous.
  Dealing with the combination of heterogeneity and incomplete compliance further raises questions to causal analysis. Prior to the work of Angrist and Inbens, researchers explored conditions that allowed for the identification of average treatment effects in the aggregate or treated aggregate. The general finding of the study was that these conditions tended to be stringent. An alternative approach is to place constraints on these effects. Unfortunately, such constraints are often too broad to be of practical reference value.
  As mentioned above, the use of observational data to study causality can involve endogeneity issues. To address the endogeneity problem in empirical economic analysis, economist P. G. Wright’s 1928 book, Tariffs on Vegetable Oils, first proposed instrumental variables to deal with the adverse effects of endogeneity on causal inference. Instrumental variables need to satisfy three conditions: (i) instrumental variables have no direct effect on the outcome of interest and can only influence the outcome through the treatment of the study; (ii) instrumental variables are independent of unobserved confounders; and (iii) instrumental variables and the treatment of the study have some correlation.
  Angrist and Inbens’ paper “Identification and estimation of local average treatment effects” (1994) proposes a different approach to the puzzle involving heterogeneity, non-dependence. Specifically, they step back and ask: What can be learned from randomized or natural experiments and what cannot be learned without imposing additional restrictions on the behavior of research subjects who cannot be directly observed? In their paper, they propose a new empirical methodological framework that builds on the potential outcome framework proposed by the American statistician J. Neyman in the context of randomized experiments (1923) and the potential data framework proposed by the American statistician D. B. Rubin in the context of observational data in his paper “Estimating Treatments of Causal Effects in Randomized and Nonrandomized Studies” (1974) over an outcome framework. Central to this framework is the allocation mechanism, the process of deciding which units receive which treatments, and thus which potential outcomes are realized and can be observed, and which potential outcomes are omitted.
  In contrast to Neyman’s assumption of random allocation and Rubin’s linking of allocation to propensity scores, Angrist and Inbens link allocation to the presence of instruments. In this way, the new approach merges the instrumental variables framework invented in economics with the framework of potential causal inference outcomes developed in statistics. Here instrumental variables can be the result of physical randomization, such as a randomized controlled trial, and this approach applies to the general framework of quasi-experimental and experimental work. They refer to this causal effect as the local average treatment effect (LATE) and demonstrate that, even in the presence of heterogeneity and imperfect adherence, instrumental variables can identify causal treatment effects under minimal assumptions as well as empirically plausible hypotheses. The effect identified is the average causal effect among the dependents, i.e., the causal effect of the overall subset of behaviors changed due to the value of the instrument. In fact, the basic framework proposed by Angrist and Inbens is widely used to identify the conditions under which treatment effects can be identified when applying existing causal inference methods such as regression discontinuity designs, double difference methods, and integrated control methods. Currently, the LATE framework is widely used not only in economics and other social sciences, but also increasingly in disciplines such as epidemiology and medicine.
  The work of the three awardees provides a solid foundation for design-based approaches, which primarily employ quasi-experimental methods, but also experimental and variational methods to estimate causal effects of interest. In summary, the winners’ results and methods have achieved a tremendous increase in capacity for addressing causal questions of great importance for economic and social policy, while surely laying a solid empirical methodology for furthering better understanding and answering social science questions, significantly changing the way empirical research has been conducted over the past 30 years, and greatly benefiting society.