Question

3. Causality Define the following terms: Reverse Causality, Omitted Variable Bias, Measurement Error (Note: Give a general definition, not slides'example) Why are these things an issue when we want to make statements like "X causes Y" Two ways in which we try to overcome these issues is using Instrumental Variables and Regressions Discontinuity. Describe these and give an example of it from the lecture. a. b. c.

Answer 1

a. Reverse causality: Reverse causality means that X and Y are associated but not in the conventional way where a change in X causes change in Y but the reverse of it. For eg, when we run a regression of quantity on price, we assume that the change in price would cause a change in the quantity, but it is to be noted that the quantity available in the market also affects the price the commodity will sell for. So this reverse relationship of price on quantity is reverse causality.

Omitted Variable Bias: Under this, the regression model is not in the appropriate form as it should be. Suppose when we have wages as the dependent variable, in that model we cannot incorporate the innate ability of the worker to determine the wages. So under this condition, the important variables got omitted to cause a biasedness in deciding the value of the dependent variable.

Measurement Error: The measurement error is the difference between the actual value of the dependent variable and the predicted one from the model. This difference can be systematic or random. Suppose you are weighing the athletes. With the problem in the weighing scale let us say of a pound would wrongly predict the weight of all by one pound. In case of random error, even the correct scale would wrongly predict may be because some of the athletes are dehydrated or some are just wetter than others.

b.When we run "X causes Y", the model should take into account all the factors which must be controlled in order to correctly find the impact of the change in X on Y. With the above issues, the model is not appropriate, instead, it will not give the correct results but the biased results. Sometimes it would overestimate the value of the predicted variable such as in measuremnet error example and sometimes it would under predict such as in ommitted variable bias.

c. Instrumental variable is used to overcome this issue of biasedness. Under this, a third variable is used in the equation which actually captures the unobserved correlation among the variables so that we can find the true correlation between the explanatory and the dependent variable.

On the other hand, regression discontinuity uses the sample designed variables. It uses the pretest and posttest comparative strategy. It is used to compare the effectiveness of an experiment on the performance before and after. Suppose that we wish we measure how effective remedial classes are in improving the scores of individuals, so for that, the pre-class and the post class performance will be compared based on the pre-classes cutoffs. The best part is that one must not differentiate or decide which group of what people should be considered for the given experiment.

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