Effects of Inflation Rates and the Real GDP Growth Rate on The United States Unemployment Rate - Assignment Example

Effects of Inflation Rates and the Real GDP Growth Rate on

The United States Unemployment Rate

Gross domestic product is the primary determinant of a country's standard of living (Asari et al., 2011) among its citizens. Therefore, the analysis of GDP growth of the United States is an attempt to examine the correlations between the employment rate and inflation rate among its citizens. The research variables in this analysis were chosen based on the relevant economic concepts that define such interactions among economic variables. The analysis is conducted through a multivariate time series appraisal available in STATA. Notably, the results of the analysis below have indicated that the rate of inflation has significant impacts on the unemployment; however, the rate of unemployment has no significant negative impact on the U.S. gross domestic product.

Question 1

Table 1: Summary regression output

Summary Regression output:

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.915797

R Square

0.838684

Adjusted R Square

0.810146

Standard Error

13546.7

Observations

56

ANOVA

df

SS

MS

F

Significance F

Regression

4

4.96E+10

1.24E+10

67.58709

9.26E-20

Residual

52

9.54E+09

1.84E+08

Total

56

5.92E+10

Question 2

Question 3

When a regression (estimation command) routine ignores a variable, it does so because of the reliance among the independent constraints in the proposed model (Heckman, 2005). Dependency is identified by performing a regression where omitted variable is specified as the dependent variable. In this scenario, the remaining variables are defined as independent variables. Therefore, dependency should be generated deliberately to complete the new regression model provided in Table 2.

The regression output shows that the coefficients have the correct magnitude and proper sign. The fact that the omitted-variable or specification bias is positive could have been anticipated before running the first regression (Heckman, 2005). The OVB caused by omitting the year of observing the effects of inflation rates in the real GDP growth rate on the US unemployment rate is expected to produce a positive sign because the expected sign of the coefficient of the Year of observation is positive. Similarly, the positive sign of the coefficient occurs because the anticipated correlation between the year of inflation and the annual GDP growth rate is positive (Heckman, 2005). The scatter diagram of the dependent variables (fitted values of dependent variables) versus the residuals of the model shows further compressive corrections (see Appendix 1).

The results of the Ramsey retest test are provided in the table below:

The results indicate that there are no omitted variables in the model. The p-value for the square term for both the Breusch-Pagan test and Ramsey Reset test are significant. The p-value is 0.01<p<0.05 is an indication that there is significance in the results from Ramsey Reset test. This significance is an indication that the model is specified incorrectly. It is easy to understand the importance in this case because the relationship between the rate of unemployment, which is dependent and inflation rate and GDP growth rate, which are independent. Therefore, it is fitting to insert higher degree terms. One option is to enter the squared parameter term into the regression. The output of the ovtest and linktest are no longer significant after rerunning the regression model.

Question 4

Although the linear correlation assumed in this regression is often adequate in understanding functional forms, there are cases where non-linear functional forms are more appropriate than their primary use (Asari et al., 2011). The scatter plot of dependent variables versus independent variables is a significance non-linear functional form in understanding non-linear correlation (see Figure 1 below).

Figure 1

Simply altering variables x and y, and approximating a regression model using the modified variables is one of the simplest ways of attaining a non-linear specification. Natural or logarithmic transformation process requires changing all the observed values to be greater than zero.

Question 5

A misspecification of a functional form primarily means that a linear regression model fails to account for certain crucial nonlinearities (Tong, 2012). Omitting an important variable certifies the requirements for model misspecification. Functional forms misspecification often leads to other parameter estimators.

Question 6

The nested models technique was applied in the estimation of the new design specification. Nested models are often tests the potential confounding or mediating factors. The models usually begin with a design that has a single key predictor, then adding succeeding variables believed to confound or mediate its association with the dependent variable.

In this paper, the presentation of the results of nested model specification analysis involved stating the table titles as a series of the nested models. The model is then organized using column spanners to group the statistical test result and effect estimate for each model. Each spanner is labeled with a short description/name summarizing the specs for each model, as shown in TABLE 3 below. Model 1 and Model 2 that are the identification techniques, are applied in naming the column spanners.

Table 3: Nested Model Table

Model I

Inflation rate

Model II

Inflation and unemployment rate

Model III

Inflation, unemployment, and square of inflation

Variable

4090.994

6504.203

6281.386

GDP growth rate

546.171

546.171

546.171

Question 7

In the test for the autocorrelation, it is assumed that if there is any autocorrelation, then, there is a positive autocorrelation at lag 1. In this scenario, the null hypothesis would be proved by the data is white noise. For a null hypothesis to be positive, the autocorrelation need read, p(1)≠0. The study also conducted at lag 1 using the standard t-based correlation test using the estimation of the correlation. In the evaluation process, non-overlapping pairs of samples are used to ensure that pairs of samples are independent under H0.

Question 8

Multicollinearity is assessed by examining the VIF (Variance Inflation Factor) and the tolerance. Tolerance and VIF are collinearity diagnostic factors that aid in identifying multicollinearity (Asari et al., 2011). Variable tolerance is measured by finding the value of 1-R2. A small value of tolerance shows that the variable been analyzed is nearly an excellent linear combination of the independent variables equation. Thus, the variable should not be added to the equation (Frost, 2013). Multicollinearity also occurs if a low value of tolerance is comparable to the non-significance and the values have large standard errors. The measured value for R2 in the first term of the multi-regression model was 0.93924. Therefore, the tolerance of the variables is 0.06076. This means, the variables including unemployment rate, GDP growth rate, and inflation rate have an almost perfect combination of the independent element (Years) of the regression equation variable.

Question 9

The model has no autocorrelation as indicated the d-statistic value of 1.238235. The rule of thumb for identifying autocorrelation is that if the value of d-statistic is close to 4 or 0, then the residuals are said to be highly correlated. In the case of the model above, 1.23835 is neither close to 4 nor 0.

Question 10

Multicollinearity is present in this model as indicated in the table above. Evidence of multicollinearity in a model is the occurrence of the largest VIF that is greater than 10. Additionally, the value of all VIFs’ means is also considerably greater than one; hence, the presence of multicollinearity in the model. The above table indicates that the mean of all VIFs is 7.5 and the largest VIF is 10.22.

Although the presence of multicollinearity is a problem in this model, no action will be taken to correct its occurrence. The F-tests from the regression indicate that the variables are jointly significant. Additioanlly, the VIFs, or bivariate correlations are evidence that the model’s structural multi-collinearity that also explains possible absence of individual significance. The creation of new predictor variables is the primary cause of structural multicollinearity in this study.

Question 11

The p values for each model tests the null hypothesis that the value of the coefficient is equal to zero (0) or it has no effect. P values of 0.05 show that the null hypothesis should be rejected. In other words, predictors with low p-values are likely to provide a meaningful addition to the model/term because changes in predictor values are connected to shifts in the response variable. Comparatively, insignificant (larger) p values suggest that transformations in the predictor are not connected with changes in the reply. The regression output provided in Question 1 of this paper shows that the predictor variables of the unemployment rate (p-value) is 1.11E-13, and the GDP growth rate (p-value) is 0.30112. These values are greater than the primary alpha level of 0.05. Predictor variables that exceed the conventional alpha level are considered statistically insignificant. The inflation rate and the square of the inflation rate are statistically significant because they have p values of less than 0.05, that is, 0.050445 and 0.030419 respectively.

Question 12

The study results indicate that the rate of inflation and GDP growth rate have significant positive impact on the rate of unemployment in the United States. This outcome is what was expected when looking at the economic principles on the connection between the unemployment rate and inflation rate as well as the growth rate of GDP.

Further, the study realized that some other variables are related to unemployment rates. For example, less real GDP growth rate would mean reduced creation of jobs; hence, high levels of unemployment. These factors were introduced to the multiple regression models and it was found that both real GDP growth rate and inflation rate on unemployment rate are statistically significant.

It will still be beneficial to explore the effects if inflation rate and real GDP growth rate on unemployment rate in the future. This correlation would be exciting to assess and potentially useful for the government to consider when making policies related to these issues. In this model, although the output of regression supports the hypothesis, the information provided for the current rates of inflation and real GDP growth rate is not very comprehensive. The missing information would potentially reverse the outcomes of this study. However, the presence of the correlation should not be overlooked and these results would help examine the relevancy between these aspects.