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Q. Consider a researcher interested in the causal effect of class size in primary school on educational attainments. The research strategies he is contemplating are (i) regression-control; (ii) randomization; (iii) difference-indifferences and (iv) regression-discontinuity. Explain the workings of each method along with the identification assumptions that enable causal inference. Discuss advantages and problems with each method.

Answer 1

1. Regression Control

Controlling for a variable is the attempt to reduce the effect of confounding variables in an observational study or experiment. It means that when looking at the effect of one variable, the effects of all other variable predictors are taken into account, either by making the other variables take on a fixed value (in an experiment) or by including them in a regression to separate their effects from those of the explanatory variable of interest (in an observational study).

In an observational study, researchers have no control over the values of the independent variables, such as who receives the treatment. Instead, they must control for variables using statistics.

Observational studies are used when controlled experiments may be unethical or impractical. For instance, if a researcher wished to study the effect of unemployment (the independent variable) on health (the dependent variable), it would be considered unethical by most institutional review boards to randomly assign some participants to have jobs and some not to. Instead, the researcher will have to create a sample where some people are employed and some are unemployed. However, there could be factors that affect both whether someone is employed and how healthy he or she is. Any observed association between the independent variable and the dependent variable could be due instead to these outside, spurious factors rather than indicating a true link between them. This can be problematic even in a true random sample. By controlling for the extraneous variables, the researcher can come closer to understanding the true effect of the independent variable on the dependent variable.

2. Randomisation

A method based on chance alone by which study participants are assigned to a treatment group. Randomization minimizes the differences among groups by equally distributing people with particular characteristics among all the trial arms. The researchers do not know which treatment is better. From what is known at the time, any one of the treatments chosen could be of benefit to the participant.

Well, there are different options used by researchers to perform randomization. It can be achieved by use of random number tables given in most statistical textbooks or computers can also be used to generate random numbers for us.

If neither of these available, you can devise your own plan to perform randomization. For example, you can select the last digit of phone numbers given in a telephone directory. For example you have different varieties of rice grown in10 total small plots in a greenhouse and you want to evaluate certain fertilizer on 9 varieties of rice plants keeping one plot as a control.

3. Difference in differences

Difference in differences is a statistical technique used in econometrics and quantitative research in the social sciences that attempts to mimic an experimental research design using observational study data, by studying the differential effect of a treatment on a 'treatment group' versus a 'control group' in a natural experiment. It calculates the effect of a treatment (i.e., an explanatory variable or an independent variable) on an outcome (i.e., a response variable or dependent variable) by comparing the average change over time in the outcome variable for the treatment group, compared to the average change over time for the control group. Although it is intended to mitigate the effects of extraneous factors and selection bias, depending on how the treatment group is chosen, this method may still be subject to certain biases (e.g., mean regression, reverse causality and omitted variable bias).

In contrast to a time-series estimate of the treatment effect on subjects (which analyzes differences over time) or a cross-section estimate of the treatment effect (which measures the difference between treatment and control groups), difference in differences uses panel data to measure the differences, between the treatment and control group, of the changes in the outcome variable that occur over time.

4. Regression-discontinuity design

The regression-discontinuity design. What a terrible name! In everyday language both parts of the term have connotations that are primarily negative. To most people "regression" implies a reversion backwards or a return to some earlier, more primitive state while "discontinuity" suggests an unnatural jump or shift in what might otherwise be a smoother, more continuous process. To a research methodologist, however, the term regression-discontinuity (hereafter labeled "RD") carries no such negative meaning. Instead, the RD design is seen as a useful method for determining whether a program or treatment is effective.