H0: βlgdp2 = βmse2 = βlexp2 = βlintr2 = βiy2 = βgcony2 = βlblakp2 = βpol2 = βttrad2= 0 Essay Examples

Assignment 3: Third Regression

(a) Describe the economic issue.
The Gross Domestic Product (GDP) of a country is a measure of production. It is the result of the sum of the values of all the units engaged in production. The larger it is, the more productive the country is. The rate at which GDP grows is different on each country, and varies from year to year. Several factors could influence GDP growth, including the current value, residents’ education level, residents’ life expectancy, human capital, political instability, etc. Specifically, life expectancy and residents’ level of education might be strong predictors for positive GDP growth, because people that live longer tend to have a better health, and thus live in a country with better health system, and educated people have better jobs and are more productive to their countries. Therefore, it could be assumed that a country with a better healthcare system, better education system, and more productive people tends to be industrialized, and thus has a higher GDP growth.
(b) Describe the data
The Barro data consists of 161 observations on national growth from 1965-75 and 1985-87. It has 15 variables: country, annual change per capita GDP, initial per capita GDP, male secondary education, female secondary education, female higher education, male higher education, life expectancy, human capital, education/GDP, investment/GDP, public consumption/GDP, black market premium, political instability, growth rate terms trade.
c) Describe the model
The aim of the model is to predict annual GDP change. Since all variables seemed to intuitively be related and possibly influence the outcome variable, a full model was built, containing all variables. However, after performing model diagnostic procedures, and based on deviance and the Akaike Information Criterion (AIC), it was seen that most of the education-related variables did not help to explain annual GDP change, so these variables were excluded from the final model. The final model was coded in R as m2 <- lm(y.net ~ lgdp2 + mse2 + lexp2 + lintr2 + Iy2 + gcony2 + lblakp2 + pol2 + ttrad2, data = data).
(d) State your hypotheses in terms of the model

For the Wald test (to test if any of the coefficients are equal to zero or not):

H1:

βlgdp2 or βmse2 or βlexp2 or βlintr2 or βIy2 or βgcony2 or βlblakp2 or βpol2 or βttrad2 ≠ 0

Where β is the coefficient for each variable. If a coefficient is equal to zero, it does not show a linear relationship with the outcome variable.

The F-test follows a similar set of hypothesis, but in reference to the explained and unexplained variance:

H0: explained and unexplained variances in the model are equal
H1: explained and unexplained variances in the model are not equal
(e) Present the regression results:
***p < 0.0001. **p < 0.001.

Based on these data, the adjusted model explains 56.41% of the total variance of annual GDP change. All predictors are statistically significant at a 5% level. When all predictors are zero, the annual GDP change is - 0.0201220. The interpretation of the coefficients is as follows: for each unit increase in male secondary education, life expectancy, investment/GDP and growth rate terms trade, the annual change in GDP increases by 0.0135911, 0.0659546, 0.0730448 and 0.1847272 units, respectively. Similarly, for each unit increase in initial per capita GDP, human capital, public consumption/GDP, black market premium and political instability, the annual change in GDP decreases by 0.0296259, 0.0022812, 0.1165247, 0.0309600 and 0.0205462 units, respectively.
(g) State whether your hypotheses were supported by the data
All predictors are statistically significant at a 5%. Therefore, there is enough evidence to reject the null hypothesis for the Wald test. Additionally, the F-statistic is significant (p value : <2.2e-16) which means that there is a linear relationship between the predictors and the outcome variable.
(h) Draw conclusions
In this model, male secondary education, life expectancy, investment/GDP and growth rate terms trade help to increase the annual change in GDP, whereas initial per capita GDP, human capital, public consumption/GDP, black market premium and political instability decrease it. The model might be improved by including interactions between the variables (e.g. between male secondary education and life expectancy).
(i) Graphs
Figure 1. QQ Plot for model 2
Figure 2. Studentized residuals plot for model 2
Figure 3. Leverage plots for model 2
Figure 4. CERES plots for model 2