Modeling the wage distribution

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Part I: (15pts) Consider modeling the wage distribution using a continuous distribution
with the following PDF:
f(x; θ) = (
0 x < 1
θ
xθ+1 x ≥ 1.
(1)
(i) Suppose that θ > 1. Prove that
E[X] = θ
θ − 1
. (2)
(ii) Based on (i), find an expression for the method of moments estimator ˜θ of θ. wage.dta
contains data on wage (in $10,000/year) across individuals. Report your method of moments
estimate of θ.
(iii) Derive the log-likelihood function. Find an expression for the maximum likelihood estimator ˆθ of θ.
(iv) Using wage.dta, report your maximum likelihood estimate of θ.
(v) Based on (1), derive the cumulative distribution function (CDF). Using the CDF and
your estimate from (iv), estimate the proportion of individuals whose wage is above 10 (in
$10,000/year). Repeat this exercise using your estimate from (ii). Summarize your findings.
Part II: (30pts) (Selected questions will be graded.)
Work on the following questions from Chapters 7 & 8 of the textbook.
Chapter 7: 10, 16, 24, 26
Chapter 8: 4, 8, 10
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Sample Solution

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ights of Persons with Disabilities (UNCRPD), and in particular, Article 24 requirement that the education system is directed to the development by persons with disabilities ‘of their personality, talents and creativity, as well as their mental and physical abilities, to their fullest potential.

The Commission’s analysis was that the aims of the Bill were in accordance with the requirements of the Equality Act 2010, the Human Rights Act 1998 and UNCRPD. These aims are;

  • To reform SEN provision.
  • To place children, young people and families at the centre of decision making, enable them to participate in a fully informed way, and with a focus on achieving the best possible outcomes.

The EHRC (2012) also emphasised the fact that the Bill provides an opportunity to strengthen compliance with the Equality Act 2010 in relation to duties on education providers to make reasonable adjustments for children with disabilities, and to set out how the new SEN arrangements and the Equality Act requirements can work together to make educational provision for disabled children fit for purpose, and in line with the requirements of the UNCPRD. Statements of SEN are to be replaced by new Education, Health and Care (EHC) Plans. However, some would argue that more clarity is needed with regards to the Bill and in the Code about how the support needs of disabled pupils without an EHC plan, who currently receive support under School Action or School Action Plus, are to be met.

The EHRC (2102) stated that they were aware that government is introducing these changes to address concerns from Ofsted (2010) that pupils are being given SA and SA+ support when actually what they need is better teaching. Ofsted stated in its report of (2010) that as many as half of

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