Байқау деректерін пайдаланып себеп-салдарлық талдау: Екі айырмашылық әдісі

Statistical technique to use observational data for causal analysis
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 (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 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.

Difference in differences requires data measured from a treatment group and a control group at two or more different time periods, specifically at least one time period before "treatment" and at least one time period after "treatment." In the example pictured, the outcome in the treatment group is represented by the line P and the outcome in the control group is represented by the line S. The outcome (dependent) variable in both groups is measured at time 1, before either group has received the treatment (i. e., the independent or explanatory variable), represented by the points P1 and S1. The treatment group then receives or experiences the treatment and both groups are again measured at time 2. Not all of the difference between the treatment and control groups at time 2 (that is, the difference between P2 and S2) can be explained as being an effect of the treatment, because the treatment group and control group did not start out at the same point at time 1. DID, therefore, calculates the "normal" difference in the outcome variable between the two groups (the difference that would still exist if neither group experienced the treatment), represented by the dotted line Q. (Notice that the slope from P1 to Q is the same as the slope from S1 to S2.) The treatment effect is the difference between the observed outcome (P2) and the "normal" outcome (the difference between P2 and Q).

All the assumptions of the OLS model apply equally to DID. In addition, DID requires a parallel trend assumption. The parallel trend assumption says that are the same in both and Given that the formal definition above accurately represents reality, this assumption automatically holds. However, a model with may well be more realistic. In order to increase the likelihood of the parallel trend assumption holding, a difference in differences approach is often combined with matching. This involves 'Matching' known 'treatment' units with simulated counterfactual 'control' units: characteristically equivalent units which did not receive treatment. By defining the Outcome Variable as a temporal difference (change in observed outcome between pre and posttreatment periods), and Matching multiple units in a large sample on the basis of similar pre treatment histories, the resulting ATE (i. e. the ATT: Average Treatment Effect for the Treated) provides a robust difference in differences estimate of treatment effects. This serves two statistical purposes: firstly, conditional on pre treatment covariates, the parallel trends assumption is likely to hold; and secondly, this approach reduces dependence on associated ignorability assumptions necessary for valid inference. As illustrated to the right, the treatment effect is the difference between the observed value of y and what the value of y would have been with parallel trends, had there been no treatment. The Achilles' heel of DID is when something other than the treatment changes in one group but not the other at the same time as the treatment, implying a violation of the parallel trend assumption. To guarantee the accuracy of the DID estimate, the composition of individuals of the two groups is assumed to remain unchanged over time. When using a DID model, various issues that may compromise the results, such as autocorrelation and Ashenfelter dips, must be considered and dealt with.

The Card and Krueger article on minimum wage in New Jersey, published in 1994, authored by Juan Miguel Villa.