Assignment:
1. The Big Mac Index
Since 1986, The Economist has been publishing the Big Mac Index as a crude measure of whether international currencies are at their "correct" exchange rate, as judged by the theory of purchasing power parity (PPP). According to PPP, a unit of currency should be able to buy the same bundle of goods in all countries. The Economist uses a McDonalds Big Mac as its representative bundle of goods.
The Excel file attachment contains the following data for 14 countries/currency zones on 13 October 2010:
bmlocal Price of a Big Mac in local currency.
exch Actual exchange rate (number of units of local currency per US$1).
The price of a Big Mac in US dollars on 13 October 2010 was $3.71. If the theory of PPP is correct (as outlined above), for each country exch should equal ppp, where ppp is the ratio of the price of a Big Mac in local currency to the price of a Big Mac in US dollars (i.e. ppp=bmlocal/3.71).
Consider the following regression model:
yi = β1 + β2xi + ui
where yi = loge(exch) and xi = loge(ppp) for country i, for i=1...14. loge( ) is the natural logarithm function.
(a) Using Excel, create columns showing xi, yi, xiyi and xi2.
(b) Calculate Σxi, Σyi , Σxiyi and Σxi2
(c) Use the formulae and to obtain values for the OLS estimators and .
(d) Create columns showing ei and ei2, where ei = yi - - xi
(e) Use the formula to obtain a value for the standard error of the regression .
(f) Use STATA to run the regression, and confirm the results you obtained in parts (c) and (e) above.
(g) If the theory of PPP is correct, what values of β1 and β2 would you expect?
(h) Do the regression results support your expectations? Justify your answer by reporting the results of appropriate hypothesis tests.
(i) On the basis of your results, comment on the usefulness of the Big Mac Index and the PPP theory of exchange rate determination.
2. Determinants of growth in per capita GDP
The Excel file attachment contains cross-sectional data for 36 countries for the following variables:
ypc80 = Per capita GDP in 1980 (US dollars)
ypc00 = Per capita GDP in 2000 (US dollars)
seced = Proportion of secondary school age population enrolled at secondary school in 1980
credit = Ratio of private credit issued by banks and other financial institutions to GDP in 1980 (interpreted as a measure of the level of development of the financial sector)
In this exercise, we will use this data to estimate a regression model for the determinants of growth in per capita GDP for the period 1980 to 2000. The model specification is as follows:
yi = β1 + β2 x2i + β3 x3i + β4 x4i + ui
where yi = loge(ypc00) - loge(ypc80) x3i = loge(seced)
x2i = loge(ypc80) x4i = loge(credit)
A reason for expressing the variables in logs is that with this specification, β2, β3 and β4 can be interpreted as elasticities.
(a) Read the data into Stata, and generate new variables to represent the natural logarithms of the original series. To do this, enter the following commands:
gen y1=log(ypc00)-log(ypc80)
gen x2=log(ypc80)
gen x3=log(seced)
gen x4=log(credit)
(b) Run the regression (i.e. regress y1 x2 x3 x4). Comment briefly on the implications of the signs of the estimated coefficients , and for the determinants of growth in per capita GDP.
(c) Evaluate each of the following assertions. In each case, formulate an appropriate null and alternative hypothesis, and assess whether or not the statistical evidence lends support to the assertion.
(i) "Countries that were poorer in 1980 tended to grow faster over the next 20 years than countries that were richer in 1980."
(ii) "Growth in per capita income over any period depends only on the level of per capita income at the start of the period."
(iii) "Collectively, the explanatory variables used in this regression are useful in explaining the cross-sectional variation in the growth of per capita income."
(iv) "The elasticity of growth in per capita income with respect to the proportion of children in secondary school education is 0.4."
Attachment:- Data of bigmac.rar