Question

You have collected data for 104 countries to address the difficult questions of the determinants for differences in the standard of living among the countries of the world. You recall from your macroeconomics lectures that the neoclassical growth model suggests that output per worker (per capita income) levels are determined by, among others, the saving rate and population growth rate. To test the predictions of this growth model, you run the following regression:

= 0.339 – 12.894 × n + 1.397 × SK, R2=0.621, SER = 0.177(0.068) (3.177) (0.229)

where RelPersInc is GDP per worker relative to the United States, n is the average population growth rate, 1980-1990, and SK is the average investment share of GDP from 1960 to 1990 (remember investment equals saving). Numbers in parentheses are for heteroskedasticity-robust standard errors.

Calculate the t-statistics and test whether or not each of the population parameters are significantly different from zero.

Answer 1

To determine if each population parameter is significantly different from zero, we can calculate the t-statistics and compare them to critical values. In this case, both t-statistics are greater than the critical value, indicating that both population parameters are statistically significant.

Step-by-step explanation:

The t-statistics can be calculated by dividing the coefficient estimates by their corresponding standard errors. In this case, the t-statistics for the population parameters are as follows:

• t-statistic for n = -12.894 / 3.177 = -4.064
• t-statistic for SK = 1.397 / 0.229 = 6.094

To test whether or not each of the population parameters are significantly different from zero, you can compare the t-statistics to critical values from the t-distribution. If the absolute value of the t-statistic is greater than the critical value, then the population parameter is considered to be statistically significant.

For example, with a significance level of 0.05 (corresponding to a 95% confidence level), the critical value for a two-tailed test with 102 degrees of freedom is approximately 1.984. Since the absolute value of the t-statistic for n (-4.064) is greater than 1.984, we can conclude that the population parameter n is significantly different from zero. Similarly, since the absolute value of the t-statistic for SK (6.094) is greater than 1.984, we can conclude that the population parameter SK is also significantly different from zero.