econ4f03ass22022AG (1)

ASSIGNMENT #2 Economics 4F03 2022 Section 3 Paul Contoyannis SUBMIT TO THE DROPBOX IN A2L. Due OCT 24 th @7.00pm 1. T h e f o l l o w i n g r e g r e s s i o n h a s b e e n e s ti m a t e d : Dependent Variable: disability1 Independent Variables: (1) Constant, (2) Person's age (ecage26), (3) male1 “male1” is equal to 1 for males and 0 for females; disability1 is equal to 1 for disabled and 0 for not disabled . regress disability1 ecage26 male1 Source | SS df MS Number of obs = 47705 -------------+------------------------------ F( 2, 47702) = 2979.42 Model | 1137.25995 2 568.629974 Prob > F = 0.0000 Residual | 9104.04738 47702 .19085253 R-squared = 0.1110 -------------+------------------------------ Adj R-squared = 0.1110 Total | 10241.3073 47704 .214684457 Root MSE = .43687 ------------------------------------------------------------------------------ disability1 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- ecage26 | .0084218 .0001093 77.04 0.000 .0082076 .0086361 male1 | -.0084567 .0040058 -2.11 0.035 -.0163082 -.0006052 _cons | -.0891858 .0060068 -14.85 0.000 -.1009592 -.0774125 ------------------------------------------------------------------------------ 1.1 Interpret the estimated values (including the constant) in the following two senses: a) What do the estimated coefficients mean mathematically? Use the estimated values in your answer. Cons – the predicted probability that a zero-year-old female would have a disability is -0.089; 2 marks male1 – at any age the predicted probability of being disabled is less for a male than a female; the difference is -0.008 2 marks ecage26 – each additional year of age is associated with an increase of 0.008 in the predicted probability of having a disability. 2 marks b) What are some economic reasons why the estimated coefficients might take on the values that they do? Cons- such a value is, of course, impossible since probabilities must be within the range from 0 to 1. 2 marks Disabilities (physical frailty) generally increase with age (our bodies wear out) and also reflect the accumulated impact of any unhealthy lifestyle choices, so a positve coefficient would be expected; 2 marks males, on average, have fewer disabilities that females, due to higher income or to other reasons, so the coefficient would be expected to be negatve 2 marks

1.2 You can use your estimated coefficients to form a linear function predicting the probability of a disability for either sex at any age. Solve this equation to find the age at which the predicted probability of a disability for a female is equal to 0. Remember that for a female, the variable male1 = 0. For what age range is the predicted probability of a disability < 0 for a female? Solve 0 = -0.0891858 + 0.0084218*ecage26 for ecage26; the answer is 10.6 ; 4 marks hence the predicted probability would be negatve for all ages younger than 10. 4 marks 1.3 Solve this same equation to find the age at which the predicted probability of a disability for a female=1. For what age range is the predicted probability of a disability >1 for a female? Solve 1 = -0.0891858 + 0.0084218*ecage26 for ecage26; the answer is 129.3 ; 4 marks hence the predicted probability would be greater than 1 for all ages older than 129 . 4 marks 1.4 Briefly explain what both of these findings tell you about the problem of estimating a linear regression when the dependent variable is a binary variable (i.e., either 1 or 0) Because the estmated relatonship is linear , predicted values are not restricted to the 0-1 interval, as they must logically be if interpreted as probabilities. Predicted probabilities outside the 0-1 range do not make sense . 4 marks N.B However, we note in this instance that a linear approximaton may provide a reasonable representation over the relevant (in this case) age range. That is not always the case, and should be checked. Alternatvely a probit or logit model can be used.

b) What are some economic reasons why the estimated coefficients might take on the values that they do? Constant-such a value is, of course, impossible since income must be non-negatve. 2 marks Income: generally increases with age reflectng some combinaton of experience and seniority. 2 marks Males: generally have higher incomes than females; among other factors, that is associated with a higher proporton of them working full tme or, indeed, employed, with their industrial and occupatonal mix; it reflects also the greater career interrupton experienced by women when they leave employment for childrearing and, to an extent, wage discrimination. This combinaton explains the positve coefficients on male1 and Maleage . 6 marks