Statistical solutions to microeconomic problems

The Nobel Prize in Economic Sciences for 2000 was awarded "to Heckman for development of theory and methods for analysing selective samples and to McFadden for his development of theory and methods for analysing discrete choice." Their work involved the application of statistical tools to microeconomic data.

Heckman did his BA in mathematics from Colorado College in 1965 and got his PhD in economics from Princeton University in 1971. He began taking classes at the University of Chicago but transferred to Princeton mainly because of his interest in development economics and the presence of Arthur Lewis there. His doctoral dissertation was titled 'Three essays on the supply of labour and the demand for goods' and was completed under the supervision of Stanley W Black. After getting his PhD, Heckman joined as faculty at Columbia University. In 1973, he moved to the University of Chicago, where he continues to be a distinguished professor in the Economics Department. He is also a professor at Law School and holds positions in the School of Public Policy and the Centre of Human Development. Heckman has also held faculty positions at University College, London, Yale University and the University of Southern California.

McFadden received a BS in Physics from the University of Minnesota in 1957 and a PhD in Behavioral Science (economics) in 1962, also from the University of Minnesota. His doctorate advisor was Leonid Hurwicz, who was awarded the Economics Nobel Prize in 2007. In 1964, McFadden joined the University of California at Berkeley as faculty and in 1977, he moved to MIT. He returned to Berkeley in 1991, where he is still the Director of the Econometrics Laboratory founded by him. In 2011, he joined the University of South California as a professor of Health Economics.

In this article, we will review the main works of Heckman and McFadden and how they are being applied in various policy areas.

Main works of James Heckman

Heckman is a versatile economist, with works ranging from econometric tools to development economics. In general, Heckman has been driven by providing an objective and scientific basis for policy making. He is perhaps best known for his work on selection bias. Simply put, Heckman realised that non-random samples frequently don't accurately represent the real world. To correct this 'bias' he proposed a method for correcting for sampling errors. The method, also known as 'Heckman correction', is a two-step approach correction, a two-step statistical approach. Without getting into technicalities, the first step is to specify the model based on economic theory in probabilistic terms and the second step corrects the bias by introducing a variable which is a transformation of the probabilities outlined in the first stage.

Heckman is also known for inter-disciplinary work in development issues. As the Chairman of the Centre for the Economics of Human Development, he leads a team of sociologists, psychologists, statisticians and neuroscientists. His notable work has been researching the effects of early childhood care on health, economic and social outcomes for individuals and society. In Heckman's words:

The highest rate of return in early childhood development comes from investing as early as possible, from birth through age five, in disadvantaged families. Starting at age three or four is too little too late, as it fails to recognize that skills beget skills in a complementary and dynamic way. Efforts should focus on the first years for the greatest efficiency and effectiveness. The best investment is in quality early childhood development from birth to five for disadvantaged children and their families.

Heckman has also pointed out that the absence of early childhood care leads to inequality in a number of areas such as inequality, inability, achievement, health and success in adult lives. He also suggests that cognitive abilities alone are not sufficient. Not only that, but investing in early childhood care also had the potential of overturning parental, environmental and genetic shortcomings. Extending his analysis to society at large, Heckman notes that this further leads to lower crime rates and better utilization of the adult human resource.

Heckman's work has led to something called the Heckman Equation, which basically says the following:

Invest (In early education of disadvantaged families)

+

Develop (Nurture early development of cognitive and social skills from 0-5 years)

+

Sustain (Early development with effective education through to adulthood)

=

Gain (Of a more capable, productive and valuable workforce)

Main works of Daniel McFadden

McFadden's main contribution was in providing econometric tools when the choices made by people were discrete, rather than continuous. For example, when one has to choose a mode of travel, the choice is between a few alternatives such as a bus, subway or taxi. In other words, the mode of travel is a discrete variable. This is different from the demand for goods, which is a continuous variable. Before McFadden's work, researchers assumed that all the variables they were studying were continuous. Economists needed a way to do empirical work on such discrete choices, but the tools to do so were missing. In 1965, when McFadden was teaching at Berkeley, one of the students Phoebe Cottingham was working on the California state highway department's choices on where to put freeways and asked for his help. Freeway placement is an example of a discrete, rather than a continuous, choice and while McFadden did provide a solution, his research in the area continued. In his own words:

In 1964, I was working with a graduate student, Phoebe Cottingham, who had data on freeway routing decisions of the California Department of Transportation, and was looking for a way to analyse these data to study institutional decision-making behaviour. I worked out for her an econometric model based on an axiomatic theory of choice behaviour developed by the psychologist Duncan Luce. Drawing upon the work of Thurstone and Marshak, I was able to show how this model linked to the economic theory of choice behavior. These developments, now called the multinomial logit model and the random utility model for choice behaviour, have turned out to be widely useful in economics and other social sciences. They are used, for example, to study travel modes, choice of occupation, brand of automobile purchase, and decisions on marriage and number of children.

Later, in 1974, he developed a method to deal with such discrete choices. This was called conditional logit analysis — a method for determining how individuals will choose between finite alternatives in order to maximize their utility. Through the analysis of discrete choice (i.e., the choices made between a finite set of decision alternatives), McFadden's work helped predict usage rates for public transportation systems, and his statistical methods were also applied to studies of labour-force participation, health care, housing (particularly for the elderly), and the environment. McFadden tested his model with data on people's transportation choices before the Bay Area Rapid Transit (BART) system was built in the San Francisco Bay Area. While the official forecast was 15 per cent, McFadden used his model to predict that only 6.3 per cent of Bay Area travellers would use BART. The actual number turned out to be 6.2 per cent.

In recent years, McFadden has been impressed with the work of experimental economists in cognitive psychology (Kahneman and Tversky) and their tools.

Conclusion

Even as a student at Princeton, Heckman was trying to find ways to deal with problems with microeconomic data. He got attracted to Labour Economics: a field in which Gary Becker and Jacob Mincer were working on big datasets on wages, and labour market equilibrium. Heckman realized that most of the sample sets of wages were not random. As noted earlier, Heckman provided a robust way to deal with selective samples. In particular, his work on selection bias has proved to be critical for later researchers. In addition, his work on early childhood development, which is still continuing, has provided a tool for reducing inequality in society and a boon to the disadvantaged.

Like Heckman, McFadden grappled with issues of measurement of economic variables and linking them to economic theory. As we know, many of the choices individuals make in real life are discrete choices: where to stay, how to travel, where to study etc. McFadden's work on how to deal with discrete choices provided a breakthrough and continues to be a big help in microeconomic research.

The writer is an IAS officer, working as Principal Resident Commissioner, Government of West Bengal. Views expressed are personal