Question

Consider a researcher who is trying to analyze the relationship between a persons number of years of schooling, Si, and their hourly wages ($) in the labor market, W. Using adminis trative data (so, containing observations which represent a lot of different (wage,schooling) observation) the researcher wants to estimate the following model: W; = 312Sui 1. In this specific case, what could the disturbance term ui capture (give 2 examples with short explanations of why these are included in the disturbance term)? 2. We have stated a set of assumptions for the simple linear regression with nonstochastic regressors. Take any two of these assumptions (with the exception of normality of disturbance term) and explain why they may fail in this specific case. Be concise and precise in your explanations

Answer 1

1. In this specific case, the response variable is "hourly wages" which is to be estimated by the variable "number of years of schooling".

So, here the model is given by, , u_i is the error, here it is referred to as disturbance term. In this case, the disturbance term may be "attitude" of that person and "extra-circular activities".

W B2S;

2. For the simple linear regression model, if the assumption of the equal variance of the residuals does not hold true then it is known as heteroscedasticity, where the error variance is proportional to the regressor.

Another assumption is that u_i and u_j are uncorrelated for all i,j.

If this assumption is violated then it is known as auto-correlation or serial correlation.

In these specific cases, the two aforementioned assumptions may not hold true because in some of the cases the attitude and extra-circular activities may not vary person to person. Thus the assumptions are violated.