It is good practice when testing a hypothesis to state both the null and alternative hypotheses: Maths and statiscal methods Course Work, TCD, Ireland

1. All solutions should be typed (you can copy and paste tables and regression results from excel into word). Do not forget to include the cover sheet.

Note: It is good practice when testing a hypothesis to state both the null and alternative hypotheses, as well as the decision rule.

We are going to examine the effects of exchange rate regimes on growth. To start with we allocate countries into one of two groups for each available year, those with fixed exchange rates (where the govern- ment adjusts the interest rate to keep the exchange stable) and those with floating exchange rates (where government sets the interest rate to achieve some other goal and the market determines the interest rate).

Countries may appear in different groups in different years as policy changes over time, but in any given year a given country will have either a fixed or floating exchange rate.

1. Average growth [30 marks] Divide the data into two groups, those with legally floating exchange rates and those without (ignore the dirty floating variable for now)

(a) Estimate the growth rate for each of the two groups and their variances. Ignore the time dimension, so that, for example, you have a single sample mean growth rate for the fixed exchange rate group calculated from the growth rates of all countries whenever they have a fixed exchange rate

(b) Use the sample to test whether floating exchange rate countries in general grow faster than countries with fixed exchange rates, assuming the population variances are the same

(c) Explain what “the power of the test” means and then calculate the power of the test we did in part b if countries with floating exchange rates generally grow 1% (so 0.01) faster?

(d) Test whether the population variances are different. If there is evidence that they are different then repeat part b making the appropriate assumption about the variances.

(e) Does this tell us whether countries should adopt floating exchange rates? Explain why or why not. (f) How might we better address the question?

Page # 2 2. Regression [40 marks].

Estimate the regression below GrowthRate; = By +8,X1i+ ByXoe+ 8yX3a t+ ByXai + 85X5i + BpXoe + BrXta tei X,,; = Investment as a % of GDP Xj; = Growth in the Terms of trade X3,, = Population in millions X4; = Average years of Schooling X53; = How open is the economy to the global economy (higher is more open) Xe; = Initial GDP per capita (in $1000) X7; = Takes the value 1 if the exchange rate is legally floating in this country in this year and 0 otherwi (a) How do you interpret the coefficient estimates and the R??

(b) Are the coefficient estimates statistically significant?

(c) What does the F-test tell us?

(d) Do these results agree with those in question one and if not why might this be? In practice things are as simple as this and some countries follow what is sometimes called a “dirty float”. This is where the exchange rate is not strictly fixed but there is some government intervention to try to keep the exchange rate more stable than if it were purely floating. To try to account for this estimate a new regression as follows Grow thRate; Bo + By X14 + BgX24 + 63X34 + B4X 4,6 + 85X51 + Be Xo,8 + 67X74 + Bg X86 + & Xg; = Takes the value | if the exchange rate is “dirty floating” in this country in this year and otherwise.

(e) Compare this regression to the previous one.

(f) What, if anything, does this tell us about the effects of the exchange rate regime on growth? What data and methods might help us to analyse the topic better?