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  1. ==(a) What is the marginal rate of return to obtaining the 12th year of schooling?== $$MRR_{12th}=\frac{49000-37000}{37000}=32.43%$$

    ==(b) What is the marginal rate of return to obtaining the 13th year of schooling? Ignore the tuition cost.== $$MRR_{13th}=\frac{51000-49000}{49000}=4.08%$$

    ==(c) Does the 13th year look like a good investment based on the MRR and the discount rate?==

    No, the 13th year does not look like a good investment solely based off the MRR and the discount rate. The PDV equation results in an outcome that is less than the original wage of 12 years of schooling: $$PDV_{13th}=\frac{51000}{(1+.05)}=48,571$$

    ==(d) Is it necessarily true that 12 years of schooling is the optimal choice? If not, write down the formula(s) that would allow you to determine whether, for example, 12 years of schooling is preferred to 16 years of schooling.==

    It is not necessarily true that 12 years of schooling is the optimal choice as the 13th year of schooling may be needed to reach the most optimal outcome. This can be demonstrated with the PDV equation $$PDV_{16th}= -1000 - \frac{1000}{(1+.05)} - \frac{1000}{(1+.05^2)} - \frac{1000}{(1+.05^3)} + \frac{67000}{(1+.05^4)}=$64049.82>$49000$$

    ==(e) What does the marginal rate of return to the 13th year of schooling calculated in part (b) miss in terms of the benefit of completing the 13th year?==

    The MRR of the 13th year alone does not take into account its necessity in completing higher education along with additional benefits such as consumption value, the marriage market, and more.

    ==(f) What is different about the MRR in this example relative to the example in the notes?==

    Here, the MRR of schooling does not follow a perfect log shape as each additional year of schooling does not always produce a lower MRR.

    ==Now assume that r varies in the population such that we observe individuals choosing all possible schooling levels. Assume that the wage-schooling locus is the same for everyone. Is the following regression appropriate for estimating the marginal rate of return to an additional year of school? (Hint: Pay attention to functional form....)==

    No, there should be an additional parameter than accounts for the changing r value.

     

  2. ==Describe in your own words how Ashenfelter and Krueger (1994) attempt to estimate the causal effect of schooling on wages. Now, instead of using identical twins to estimate the return to schooling, I decide to estimate the return to schooling looking at the differences in log wages for non-twin siblings. Do you think this will get me closer to the true marginal rate of return to schooling? Explain.==

    Ashenfelter and Krueger attempt to estimate the causal effect of schooling on wages by looking at pairs of twins who, presumably, are identical in traits, abilties, upbringing etc. By having such similar backgrounds, Ashenfelter and Krueger assume they can analyze the returns to schooling as it relates to years of education while holding other factos relatively constant. Of course, the fact that the twins ultmately choose different educations proves there is some inherent difference between them to some degree.

    Looking at the differences in log wages for non-twin siblings will likely produce a result that is closer to the MRR to schooling as the log wage regression directly estimates the MRR. Though characteristics between the siblings will likely have greater variation than the twins, using the log wage regression accounts for much of this.

  3. ==Think about your own decision to attend college. Does our simple model of schooling accurately describe your (or your parents) thought process? If not, briefly describe the key factors behind your decision to continue schooling.==

    No, our simple model of schooling does not accurately depict my thought process as my returns to schooling. My return does not follow a constant rate in recognition of the overall path my career requires to achieve my chosen goals. The 13th, 14th, and subsequent years of education are necessary steps for me to meet the educational requirements of my future job. Rather than my schooling being purely motivated by financial gain, I consider several additional factors such as interest, passion, environment, location, and more. Because I consider more than maximizing profit in my decsion to attend college, this simple model of schooling does not accurately apply.