Assignment brief:

**Question One (Sub-total Marks: 11)**

**Question Two (Sub-total Marks: 14)**

**Solved Assignment**

**Question One**

### 1.**Eviews regression outcome for the following log-linear model**

Based on the regression output in the table above its evident that all the coefficients are statistically significant at 5% level of significance except for LNX2. This is because the coefficient associated with LNX2 reports a p-value greater than 0.05 level of significance. Therefore, we can conclude that LNX3 , LNX4,LNX5 AND LNX6 are the significant predictors for the model.

**2.Overall significance of model (1)**

To test the overall significance of the model we will consider the F-statistic and its associated p-value. From model 1 above the p-value associated with F-statistic is 0.000<0.05. Therefore, we can conclude that the model is statistically significant, indicating that at least one of the independent variables has a significant effect on the dependent variable (LNY).

**3.Re-estimated model (1) with significant variables**

Based on Model 1 & 2 its evident that both have almost similar R-squared(approximately 94%) . This means that the two models have the same explanatory power. However, model (2) has one fewer variable, which makes it simpler and easier to interpret. Therefore, I would say that model (2) is better than model (1).

**4.** **Test the null hypothesis of no structural change between the first period** **(observations: 1-35) and the rest of the sample period by using the Chow breakpoint** test.

Based on the Chow Breakpoint test result above ,we are testing the null hypothesis that no breaks at specified breakpoints. Since the p-value associated with F-statistic is statistically significant we reject the null hypothesis. So the newly regressed model is shown below.

The model above ,indicates a regression model with dummy variable(0 -for period without break,1-from the break point period) and the interaction term for all the regressors .Overall, the model is statistically significant. However, the dummy variable is not statistically significant.

**5. If model (1) represents a Cobb-Douglas production function with five production** **factors, should the assumption of constant returns to scale in the production process be** **accepted? Explain briefly and precisely.**

To assess whether the assumption of constant returns to scale is supported by the data, we can calculate the sum of the estimated coefficients for the five production factors in Model (1) . If the sum is approximately equal to 1, it suggests that the production process exhibits constant returns to scale.

0.004423 + 0.136268 + 0.173899 + 0.236394 + 0.006047 = 0.557031

Therefore, since the sum deviates significantly from 1, it is evident that constant returns to scale assumption is violated.

**Question 2**

### 1.**The savings function model (i) and comment on the estimate of the slope coefficient.**

From the table above the slope coefficient associated with the model is 0.06.The slope coefficient of 0.60 indicates that a 1% increase in income leads to a 6% increase in savings.

### 2. **Saving model with no constant**

The key difference between models (i) and (ii) lies in the presence of the intercept term. Model (i) includes an intercept (α), while model (ii) does not and the results of the two models are identical. This is because the intercept term is not statistically significant, so it can be dropped from the model without affecting the results.

Model (i) with an intercept term represents a linear relationship between savings and income, allowing for a constant level of savings even when income is zero. The intercept (α) captures the autonomous or inherent level of savings that is not directly related to income. The slope coefficient (β) in model (i) represents the marginal propensity to save (MPS), indicating the change in savings for a unit change in income.On the other hand, model (ii) without an intercept assumes that there is no inherent level of savings when income is zero. It implies that savings start at zero when income is zero, and the slope coefficient (β) captures the entire relationship between savings and income. This model suggests that all savings are directly influenced by changes in income.

The theory behind models (i) and (ii) is the theory of consumption and savings. This theory states that people tend to consume a portion of their income and save the rest. The amount of income that is saved is called savings. The amount of income that is consumed is called consumption.

### 3. **Re-estimate model (i) using income in billions**

From Model (iii) above, the slope coefficient of model (iii) is much smaller than the slope coefficient of model (i). This is because the income variable in model (iii) is measured in billions of dollars, while the income variable in model (i) is measured in million dollars.

In conclusion, the results of models (i) and (iii) are different because the income variable is measured in different units. Model (iii) is more accurate because it uses income measured in billions of dollars.

**4.** **Extend model (i) to explore possible changes in savings behaviour in the 21st century(from March 2000 onwards)**

The table above presents model (iv) that captures the data from March 2000 onwards.

From the result, the slope coefficient of model (iv) extended to the 21st century is higher than the slope coefficient of model (i). This suggests that people in the 21st century are saving a large proportion of their income. Therefore the output suggests that there is a notable change in savings behavior after March 2000.