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
(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
on-democratic regimes are forms of government which are controlled by only a small group of individuals, who “exercise power over the state without being constitutionally responsible to the public.” According R. Tannenbaum and W. Schmidt, such regimes result in “autocratic leaders [ruling] by issuing threats and punishments and evoking fear”, while Freedom House suggest there is widespread state control over “key political institutions, [and over] information on certain political subjects and key sectors of the media”, as well as a lack of viable opposition or competition for office. Today, we still see the existence of such authoritarian systems in practice, though mainly concentrated to certain regions of the world as shown in Figure 1. Thus the question arises: why do some non-democratic regimes survive longer than others? In this essay I am to discuss the possible reasons why some regimes outlive others, and the factors which could affect their success. To begin, I examine the economic factors which undoubtedly have a huge influence on the survival of non-democratic regimes. In many non-democratic countries today, an abundance of wealth held by the ruling elites compared with poverty among the masses helps dictatorships resist democratisation. Often, the ruling elites spend large portions of the funds available to them on suppressing resistance, for example, “China reportedly employs two million censors to police the internet (Bennett and Naim 2015)”, while in Peru under Fujimori, “the regime paid more than $36 million a year to the main television channels to skew their coverage, and reportedly offered one channel a $19 million bribe (McMillan and Zoido 2004, pp.82-5)”. This has an opportunity cost; spending on investment and development of industries is foregone, often leaving the citizens of a non-democratic regime stuck in the early stages of Walter Rostow’s 5 Stages of Growth Theory, as shown in Figure 2, which can leave countries primary- or secondary-sector dependent and under-developed. As John Harriss describes, such “economic development [is] conducive to democratisation, partly because [it] strengthens the ‘moderate’ middle class”: a social group of people who are better educated and financially-placed to resist being ‘bought-off’ by a dictator. Emerging middle classes therefore diminish the extent to which non-democratic leaders can bribe their winning coalition with private goods, as the pro>GET ANSWER