Download Exercise 6 (+additional question) in Mankiw:

THE ECONOMETRIC EXERCISE
How to prepare for exam: do exercises of textbook.
INSTRUCTION for econometric exercise.
Form groups about 3 people in size, or work individually.
Use any econometrics program; eg EXCEL, SPSS and Minitab.
You can also include other variables from:
Source: http://www.worldbank.org/research/growth
Start with cross-section regressions and answer the following questions:
1a. Test whether poorer economies grow faster than richer ones?
Is there convergence in GDP per capita between OECD-countries for the period 1950-2004?
(I) In other words, do initially poor countries tend to have a higher growth rate in GDP per
capita than initially rich countries during this period?
(II) Also plot the natural logarithm of GDP per capita for the countries against time in a
diagram.
(III) Also calculate the standard deviation of GDP per capita across the OECD-countries in
1950, 1960, 1970, 1980, 1990, 2000, and 2004. The standard deviation of GDP per capita
should be expressed in percent, which is given by STD(GDP per capita)/MEAN(GDP per
capita).
The standard deviation expressed in percent is called the coefficient of variation.
Is the dispersion of GDP per capita diminishing over time between the OECD-countries when
the coefficient of variation is used? In other words, does the coefficient of variation diminish
over time?
1b. Split the period 1950-2000 in 10-year periods and run a separate regression for each 10year-period. In other words, run a regression for the 50s, one for the 60s, one for the 70s, etc.
Find out whether the result of convergence/divergence is robust over time. In other words, do
we get the same results regarding convergence/divergence in income per capita in every 10year period?
Use Real GDP per capita.
Is the result driven by outliers?
Plot the growth rate of GDP per capita against initial GDP per capita to find out.
(Do not do:1c. Sometimes the neoclassical growth model is tested in terms of GDP per
worker, where worker is defined as a person between 16-64 years. Test the hypothesis of
convergence in GDP per worker across the OECD-countries for the period 1950-2004.
In other words, test whether the average annual growth rate of GDP per worker between
1950-2004 depends on the level of GDP per worker in 1950.
You should also calculate the coefficient of variation for GDP per worker for the OECDcountries in 1950, 1960, 1970, 1980, 1990, 2000, and 2004.)
2. Multivariate (= more than one independent variable) growth regressions:
Include also other explanatory variables that according to the neoclassical growth model
impact the economic growth rate; the investment rate (Investment/GDP) and the growth rate
of the population.
Are the empirical results consistent with the model?
Test for the period 1950-2000.
The investment rate should be measured as an average for the period in question.
For the period 1950-2000 include also the variables public consumption and a measure of
openess as explanatory variables (together with initial GDP per capita, investment rate and the
growth rate in population) in the regression equation. What are their estimated impacts on the
economics growth rate? Note that the degree of openness is not explicitly included in the
neoclassical growth model; it can however be seen as one of several measures of the level of
technology, A, in this model ).
Also public consumption and openess should be measured as averages for the period 19502000.
Additional question: Is the estimated growth effect of the investment rate dependent on what
other variables are included as explanatory variables in the growth regression? Study this for
the period 1950-2000.
This question deals with the topic of multicollinearity.
Make a correlation matrix to see how the different variables correlate. Is there any reason
from this table to suspect multicollinearity.
INTERPRET AND COMMENT THE RESULTS! Are the empirical results consistent
With the neoclassical growth model?
Both the Solow model and the overlapping generations model taught by the book by
Auerbach and Kotlikoff are neoclassical growth models as the marginal product of capital
decreases when K increases, holding everything else constant.
PANELREGRESSIONER
Create a panel data set for the period 1950-2004 that is split up into 5-year periods: Thus there
are 11 observations for each country.
Answer the following questions:
1. Is there convergence in income per capita when you run a panel regression?
In other words, is it good for growth to start out poor?
1a. Create time dummy variables and include them as explanatory variables.
Does the explanatory power of the regression increase.
Interpret the estimated coefficients in front of the time-dummy variables.
What are the motives behind including time dummy variables in growth regressions?
2. Include also the investment rate and the growth rate of the population. What are the
estimated effects of these variables and of initial income per capita?
Include time dummy variables.
Next, include public consumption and the degree of openess as explanatory variables. What
are the estimated effects?
Is the estimated effect of the investment share on the economic growth dependent on what
other variables are included in the regression equation?
Also make a correlation matrix in order to see how the different explanatory variables
correlate with each other. From this matrix do you suspect the problem of multicollinearity?
Basic question: Do we get the same basic results from the cross-sectional regressions as we
get from the panel regressions? If there are any differences what can explain such differences?
3. Allow for individual-specific fixed effects (=country-specific fixed effects). Practically you
allow for country-specific fixed effects by including a dummy-variable (d1,d2,…,d23) in the
excelsheet paneldata2007. If country-specific fixed effects (=intercepts) are significant if there
are some factors we have not controlled for that impacts the growth rate of gdp per capita
which are constant over time. Could e.g. reflect the effect of geography on economic growth
rate.
In other words, run the following regression:
G(GDPper capita) = F(td1,…td10;d1,..,d23;initial gdp per capita; investment rate; population
growth rate; openness; Gov/GDP)
STRATEGY TO COMPLETE GROWTH EXCERCISE.
Start by calculating (in excel) variables that are later used in the exercise:
The average annual growth rate of GDP per capita between 1950-1990, 1950-60, 1960-70,
70-80, 80-90, 90-2000.
Also calculate the average growth rate of GDP per worker between the years 1950-2004.
For exercise 2 you also need to calculate the average investment rate between 1950-2000, the
population growth rate between 1950-2000, average government consumption (as a share of
GDP) between 1950-2000, the average value of openness between 1950-2000.
How do I perform the regression analysis in EXCEL, Swedish version.
1. Välj 1. Verktyg. 2. Dataanalys. 3. Regression.
Dependent variable: c1:c10
Independent variables: a1:b10
If the dependent variable is in column c: row1 to row10.
If two independent variables are in columns 1-2: row 1 to 10
How do I perform the regression analysis in EXCEL, English version.
2. Choose 1. Tools. 2. Dataanalysis. 3. Regression.
Dependent variable: c1:c10
Independent variables: a1:b10
If the dependent variable is in column c: row1 to row10.
If two independent variables are in columns 1-2: row 1 to 10
When you have calculated all relevant variables it is a good idea to load the data into SPSS.
How do I do that?
Open SPSS for windows.
To load data in SPSS:
File; Open; Data; select crossnewstudent.xls
To perform regression analysis in SPSS:
Analyze; regression; linear; then you choose dependent and independent(s) variables;
Then you press OK, which gives you the regression output, which you may want to print out.
In exercise 1 you are asked to provide plots. In SPSS:
Graph;Scatter;simple; choose dependent and independent variable(s); OK
ANOTHER COMMENT:
Note however that points (“.”) should be replaced by (“,”) as SPSS is a Swedish version.
By including time dummy variables one allows the intercept to vary with time.
Data set for the OECD-countries for the period 1950-2004.
Source: http://www.pwt.econ.upenn.edu
You should use Penn World Table, PWT, (Summer-Heston data set) Version 6.2
I have structured data so that the assignment can be completed.
I have created 2 files: ”cross2007.xls” and ”paneldata2007.xls”.
Data in cross2007.xls are structured for the cross-section regressions.
Data in paneldata2009b.xls are structured for panel regressions.
The variables compiled are:
POP = population in 1000s.
RGDPL = Real GDP per capita (Laspeyres index) (2000 international prices)
By intl prices we mean PPP-adjusted.
ki = Real investment share of GDP (i %) (2000 international prices)
kg = Real government share of GDP (i %)
Note that G is government consumption as a share of GDP.
RGDPW = Real GDP per worker (1985 international prices)
open = (real Exports+real Imports)/real GDP.
In panelnew.xls data are structured for the panel regressions.
The variables are:
POP = population in 1000s.
popgrow = average annual growth rate of population for each 5-year period.
The first observation is the average annual growth rate between 1950 and 1955.
The second observation is the average annual growth rate between 1955 and 1960. etc
I have used the approximative formula for the average annual growth rate.
pcinc = real GDP per capita (Laspeyres index) (2000 international prices)
growth = average annual growth rate of real pcinc for each 5-year period.
First observation is average annual growth rate between 1950 och 1955.
Second observation is the average annual growth rate between 1955 och 1960…
Openk = (Exports+Imports)/GDP.
tidsdum1 = is a time-dummy variable that has the value 1 for the first time period and the
value 0 for other periods.
tidsdum2 = = is a time-dummy variable that has the value 1 for the second time period and
the value 0 for other periods.
By including time dummy variables as explanatory variables in the panel regressions one
allows the intercept to vary with time. For information on time dummy variables borrow
an econometrics book and look up the topic.
Tidsdum1 is a dummy variable for first country. The country dummies is to be included to
allow for country-specific fixed effectsIn contrast to the cross2007.xls, paneldata.xls contains no values on I, G, P, Open for the year
2004. In regressions where these variables are included as explanatory variables use the initial
values on I , G and Open as explanatory variables.
In crossnew.xls there are values for 1990 and then one can calculate average values for I, G
and Open which should be used as explanatory variables.
Example: I = (I(1990)+I(1980))/2, G = (G(1990)+G(1980))/2, och
OPEN= (OPEN(1990)+OPEN(1980))/2 vara de förklarande variblerna.