Question

Explain in detail the conditions under which is possible to use the Diff-in-Diff method to perform causal inference. Be as formal as possible in your explanation of how the method produces causal results

Answer 1

Answer:-Causal inference is the process of drawing a conclusion about a causal connection of the occurrence of an effect. The main difference between causal inference and inference of association is that the former analyzes the response of the effect variable when the cause is changed. The science of why things occur is called etiology. Causal inference is an example of causal reasoning. Inferring the cause of something has been described as:

1)Reasoning to the conclusion that something is, or is likely to be, the cause of something else.

2)Identification of the cause or causes of a phenomenon, by establishing covariation of cause and effect, a time-order relationship with the cause preceding the effect, and the elimination of plausible alternative causes.

Difference in differences method to perform casual inference: Difference in differences (DID or DD) 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 on an outcome 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.

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.

Card and Krueger (1994) example: Consider one of the most famous DID studies, the Card and Krueger article on minimum wage in New Jersey, published in 1994. Card and Krueger compared employment in the fast-food sector in New Jersey and in Pennsylvania, in February 1992 and in November 1992, after New Jersey's minimum wage rose from $4.25 to $5.05 in April 1992. Observing a change in employment in New Jersey only, before and after the treatment, would fail to control for omitted variables such as weather and macroeconomic conditions of the region. By including Pennsylvania as a control in a difference-in-differences model, any bias caused by variables common to New Jersey and Pennsylvania is implicitly controlled for, even when these variables are unobserved. Assuming that New Jersey and Pennsylvania have parallel trends over time, Pennsylvania's change in employment can be interpreted as the change New Jersey would have experienced, had they not increased the minimum wage, and vice versa. The evidence suggested that the increased minimum wage did not induce a decrease in employment in New Jersey, contrary to what simplistic economic theory would suggest. The table below shows Card & Krueger's estimates of the treatment effect on employment, measured as FTEs (or full-time equivalents). Card and Krueger estimate that the $0.80 minimum wage increase in New Jersey led to a 2.75 FTE increase in employment.

	New Jersey	Pennsylvania	Difference
February	20.44	23.33	-2.89
November	21.03	21.17	-0.14
Change	0.59	-2.16	2.75