Define and briefly summarize each concept both statistically, and, in informal terms.
• Maximum likelihood estimator
Let {𝑥ଵ, . . . , 𝑥} ∼iid 𝑁(𝜇, 𝜎
ଶ
) where 𝑓(𝑥|𝜇, 𝜎
ଶ
) = ଵ
√ଶగఙమ 𝑒
ି
భ
మమ
(௫ିఓ)
మ
.
a) Write the likelihood function 𝐿(𝜇, 𝜎
ଶ
|𝑋).
b) Write the log-likelihood function ℓ(𝜇, 𝜎
ଶ
|𝑋).
c) Compute 𝜇̂MLE.
d) Verify that your answer is a maximum by checking that the second derivative is negative.
2. Method of Moments Estimators
Define and briefly summarize each concept both statistically, and, in informal terms.
• First moment
• Second moment
• Method of moments
Let {𝑥ଵ, . . . , 𝑥} ∼iid Unif(0, 𝜃).
a) Compute 𝐸(𝑋).
currency peg, “to break the inflationary psychology… [m]ost populations are willing to sacrifice monetary sovereignty in the name of fighting inflation only when hyperinflation is fresh in their minds,” (Frankel p. 28). Inflation had been a persistent problem since before the transition phase. Since late in the 1970s Turkey has faced chronic high inflation; naturally, the high levels of spending led to fiscal imbalances and exchange rate adjustment, but further fueling the inflation was the delaying of stabilization, particularly in the 1990s, and the coalition government instead put in place populist measures like lowering the interest rates and keeping the lira overvalued (Nas p. 88). This is not unusual in political situations like Turkey’s. As Bird and Willet note, “coalition governments and those facing other configurations of political power that generate numerous veto players will often find their hands tied… If devaluation is perceived by the general public as carrying economic costs and is politically unpopular, it is hardly likely that opposition parties will want to be seen as entreating the government to devalue,” (Bird and Willet p. 66). Turkey’s persistent inflation, which was up to 60 percent before the 1994 crisis reached levels of 125 percent during it (Cömert and Yeldan, p. 8). The ‘94 crisis was not just the result of inflation, but was predominantly finance-led like the subsequent 2001 crisis would be (Cömert and Yeldan, p.21). But the program that was put in place to fix it would do little to help prevent the next crises, rather the reverse.
The 1999 Disinflation Program
In 1999, Turkey began a disinflation program based on an exchange rate stabilization plan. (Ekinci and Ertürk p. 29). This was backed by an International Monetary Fund standby agreement that amounted to $4 billion to fight inflation and support the fiscal adjustment (Nas p. 88). It hoped that by focusing on disinflation, it “would contribute towards the reduction of real interest rates to acceptable levels and the increase of the growth potential of the economy,” with tightening fiscal policy as the basis for the program (Öniş p. 9). What made the successive crises surprising is that they occurred in the during an IMF program. While domestic politics are certainly a primary cause, the IMF is not without blame. Domestically, the current account deficit grew partially because of the nature of Turkish politics. Following elections in April 1999, a coalition government was formed from a diverse range of party ideologies (Öniş p. 10) and major conflicts emerged over economic policy, namely the far-right nationalist party opposed the reduction of agricultural subsidies (which would have hurt them in future elections, as the rural poor was their base demographic). But under the pressure of the EU and others in the international community, reform was passed through, but “the half-hearted nature of the commitment… progressively undermined investor confidence and constituted one of the underlying sources of the speculative attack and the massive exodus of short-term capital in November 2000,” (Öniş, p. 11). While the IMF and the Washington Consensus did, likely prematurely, push developing countries to capital account and financial liberalization, it was Turkey’s own internal decision to do that in 1989 (Öniş & Rubin, p. 189). That does not mean the IMF is without blame in the 2000 crisis. One reason would be that it failed to collect the necessary information about Turkey’s disequilibrium in the bankin