Question

Section 1 A) Suppose you are interested in studying the relationship between the number of books that college students read per month and their first monthly wage after graduation. Employing random sampling process, you collect a large set of data {(nbooks,, wage ), i = 1, ... , n} for these variables and observe the following pattern: a correct nbooks wage nbooks = nbooks 1 1000 2 1050 3 1102.5 4 1157.625 5 1215.506 6 1276.282 7 1340.096 1407.1 9 1477.455 10 1551.328 According to this table, students who report reading 1 book per month during college, average a monthly wage of 1000 CAD after graduating. Students who report reading 2 books per month, earn on earn on average a monthly wage of 1050 CAD after graduating, etc. 1) Which of the "level-level, log-level, level-log, log-log" varieties of linear regression models best represent this data? 2) Without running any regressions, what would be the "slope" parameter of the linear model that best represents this data? 3) Suppose we run an OLS regression with an incorrect model specification. (For example, "level-level" regression but the data actually follows a "log-log" interaction, "log-log" regression but the data in reality follows a "level-level" interaction). Would our OLS estimators be unbiased? You don't need to show any mathematical proofs, instead, think we run a or we run a about the assumptions that need to be true for unbiasedness to hold.

Answer 1

1) The Y variable that is wage conditioned upon X variable i.e., nbooks is a big number and therefore not consistent with the log values that give suppressed values. Nbooks is also a discrete variable and thus can’t be log values. Thus the regression model that best represents this data is level –level.

2) The change in wages conditioned upon nbooks on an average is around 60-61CAD with an increase in number of books (nbooks). Thus the slope coefficient is expected to be positive 60.

3) under incorrect functional form specification error, the OLS estimators may be unbiased within the sample however in case of forecast, it may be biased. Besides, the variances will be large deeming the t, F and other tests unreliable.