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

Assignment 3: Third Regression

(a) Describe the economic issue.
The Gross Domestic Product (GDP) of a country is a measure of production, and results from the sum of the added values of all the units engaged in production. The larger it is, the more productive the country is. Several factors could influence the GDP, including the current value, residents’ education level, residents’ life expectancy, human capital, political instability, etc.
(b) Describe the data
The Barro data consists of a pooled sample of 161 observations on national growth. It includes two periods: 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. Initially, all variables seemed to intuitively be related and possibly influence the outcome variable. Therefore, 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, which 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:

Call:

lm(formula = y.net ~ lgdp2 + mse2 + lexp2 + lintr2 + Iy2 + gcony2 +
lblakp2 + pol2 + ttrad2, data = data)

Residuals:

Min 1Q Median 3Q Max
-0.039682 -0.009516 0.000706 0.010705 0.041037

Coefficients:

Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.0052312 0.0501211 0.104 0.917016
lgdp2 -0.0269992 0.0034041 -7.931 5.03e-13 ***
mse2 0.0142210 0.0031231 4.554 1.10e-05 ***
lexp2 0.0543598 0.0164661 3.301 0.001208 **
lintr2 -0.0025525 0.0008298 -3.076 0.002500 **
Iy2 0.0732430 0.0223252 3.281 0.001293 **
gcony2 -0.1109334 0.0281128 -3.946 0.000123 ***
lblakp2 -0.0315174 0.0048897 -6.446 1.55e-09 ***
pol2 -0.0193650 0.0061081 -3.170 0.001853 **
ttrad2 0.1773094 0.0391907 4.524 1.24e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.01645 on 147 degrees of freedom

Multiple R-squared: 0.5845, Adjusted R-squared: 0.5591
F-statistic: 22.98 on 9 and 147 DF, p-value: < 2.2e-16
(f) Interpret the regression’s results
The adjusted model explains 55.91% of the total variance of annual GDP change based on this data. All predictors are statistically significant at a 5% level. When all predictors are zero, the annual GDP change is 0.0052312. For each unit increase in male secondary education, life expectancy, investment/GDP and growth rate terms trade, the annual change in GDP increases by 0.0142210, 0.0543598, 0.0732430 and 0.1773094 units, respectively. 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 0.0269992, 0.0025525, 0.1109334, 0.0315174 and 0.0193650 units, respectively.
(g) State whether your hypotheses were supported by the data
The initial model, which contained all variables, showed that almost all the education-related variables (except male secondary education) were statistically non-significant at a 5% level (see R script for the results on this initial model). However, after model selection, all predictors are statistically significant. Furthermore, 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.