econ4f03ass22022AG (1)

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Jan 9, 2024

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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.
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