(10 points) Download the “drugs” Excel file from the class D2L page. This data s
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(10 points) Download the “drugs” Excel file from the class D2L page. This data set is from an article by Frederick Schutt and Peter VanBergeijk in which they attempted to see if the pharmaceutical industry practiced international price discrimination by estimating a model of the prices of pharmaceuticals in a cross section of 32 countries. The authors felt that if price discrimination existed, then the coefficient of per capita income in a properly specified price equation would be strongly positive.[1] In addition, the authors expected that prices would be higher if pharmaceutical patents were allowed and that prices would be lower if price controls existed, if competition was encouraged, or if the pharmaceutical market in the country was particularly large.
The variables in the data set are:
P = pharmaceutical price level in the country divided by that of the United States
GDPN = per capita gross domestic product in the country divided by that of the US
CVN = per capita volume of consumption of pharmaceuticals in the country divided by that of the US
PP = a dummy variable equal to 1 if patents for pharmaceuticals are recognized in the country
DPG = a dummy variable equal to 1 if the country applied strict price controls
IPG = a dummy variable equal to 1 if the country encouraged price competition
Estimate the regression model representing price as a function of the five independent variables in the data set.
What is the R2 for the regression? Interpret this number.
Develop and test the appropriate hypothesis to determine whether the regression coefficients jointly have any explanatory power using the 5-percent level of significance. (Explain what evidence you used from your regression output in reaching your conclusion).
Develop and test the appropriate hypotheses concerning each of the regression coefficients individually using the t-test at the 5 percent level of significance. (Explain what evidence you used from your regression output in reaching your conclusion).
Do you think that Schutt and VanBergeijk concluded that international price discrimination exists? Why or why not?
[1] Price discrimination in economics refers to selling the same product to different consumers at different prices. For example, providing student or senior citizen discounts. The reason the authors felt that the coefficient of per capita income would measure price discrimination went as follows: the higher the ability to pay, the lower (in absolute value) the price elasticity of demand for pharmaceuticals (that is demand is more inelastic) and the higher the price a price discriminator could charge.
OBS P CVN DPC GDPN IPC PP Malawi 1 60.83 0.6 0 4.9 0 1 Kenya 2 50.63 1.1 0 6.56 0 1 India 3 31.71 6.6 1 6.56 0 0 Pakistan 4 38.76 10.4 1 8.23 1 0 Sri lanka 5 15.22 6.7 1 9.3 1 1 Zambia 6 96.58 2.2 0 10.3 0 1 Thailand 7 48.01 11.3 0 13 0 0 Philippines 8 51.14 3.9 0 13.2 0 1 South Korea 9 35.1 13.3 0 20.7 0 0 malaysia 10 70.74 8.9 0 21.5 0 1 Colombia 11 48.07 14.1 0 22.4 1 0 Jamaica 12 46.13 22 0 24 0 1 Brazil 13 63.83 21.6 0 25.2 1 0 Mexioco 14 69.68 27.6 0 34.7 0 0 Yugoslavia 15 48.24 40.6 1 36.1 1 0 Iran 16 70.42 21.3 0 37.7 0 0 Uruguay 17 65.95 33.8 0 39.6 0 0 Ireland 18 73.58 38 0 42.5 0 1 Hungary 19 57.25 47.8 1 49.6 1 0 Poland 20 53.98 50.7 1 50.1 1 0 Italy 21 69.01 45.9 1 53.8 0 0 Spain 22 69.68 54.2 0 55.9 0 0 United Kingdom 23 71.19 38 1 63.9 1 1 Japan 24 81.88 54.7 1 68.4 0 0 Austria 25 139.53 35.2 0 69.6 0 0 Netherlands 26 137.29 24.1 0 75.2 0 1 Belgium 27 101.73 76 1 77.7 0 1 France 28 91.56 101.8 1 81.9 0 1 Luxembourg 29 100.27 60.5 1 82 0 1 Denmark 30 157.56 29.5 0 82.4 0 1 Germany 31 152.52 83.9 0 83 0 1 United States 32 100 100 0 100 1 1Explanation / Answer
Given that,
The variables in the data set are:
P = pharmaceutical price level in the country divided by that of the United States
GDPN = per capita gross domestic product in the country divided by that of the US
CVN = per capita volume of consumption of pharmaceuticals in the country divided by that of the US
PP = a dummy variable equal to 1 if patents for pharmaceuticals are recognized in the country
DPG = a dummy variable equal to 1 if the country applied strict price controls
IPG = a dummy variable equal to 1 if the country encouraged price competition
Now we have to fit regression of price on these five independent variables.
We can do regression in MINITAB.
steps :
ENTER data into MINITAB sheet --> STAT --> Regression --> Regression --> Response : Price --> Predictors : select all the efive variables --> Results : select second option --> ok --> ok
Estimate the regression model representing price as a function of the five independent variables in the data set.
The regression equation is
P = 38.2 - 0.595 CVN - 15.6 DPC + 1.43 GDPN - 11.4 IPC + 7.31 PP
What is the R2 for the regression? Interpret this number.
R-Sq = 81.1%
It can expresses the proportion of variation in price which is explained by variation in independent variables.
Develop and test the appropriate hypothesis to determine whether the regression coefficients jointly have any explanatory power using the 5-percent level of significance.
Here we have to test the hypothesis that,
H0 : Bj = 0 Vs H1 : Bj not= 0
where Bj is population slope for jth independent variable.
Assume alpha = level of significance = 0.05
Here test statistic follows F-distribution
Test statistic = 22.35
P-value = 0.000
P-value<alpha
Reject H0 at 5% level of significance.
Conclusion : Atleast one of the slope is differ than 0.
We get significant result about F test
This procedure is also known as overall significance.
Develop and test the appropriate hypotheses concerning each of the regression coefficients individually using the t-test at the 5 percent level of significance.
Now we have to test the hypothesis that,
H0 : B = 0 Vs H1 : B not= 0
whereB is population slope for independent variable.
Assume alpha = level of significance = 0.05
Here test statistic follows t-distribution
Decision rule :
If P-value < alpha then reject H0 at 5% level of significance otherwise accept H0.
We see that CVN, DPC, and GDPN have p-value < alpha.
So reject H0 at 5% level of significance.
Conclusion : The population slope for CVN, DPC and GDPN are differ than 0.
For these three variables we get significant result.
P-value for IPC and PP is greator than alpha
Accept H0 at 5% level of significance.
Conclusion : The population slope for CVN, DPC and GDPN may be 0.
For these two variables we get insignificant result.
This test is known as test for individual significance.
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