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## Help with Eviews Assignment on Regression Analysis

The severity of the injury is one factor that will affect the duration of benefit claims. Severe injury means a longer time of stay in the hospital, which connotes a longer duration to benefit claim. Another factor is the income level of the injured worker. If he is in the high-wage class, he can afford treatment without claiming benefits, so there will be a longer duration of benefits claim. The size of the firm is another reason. The larger the size of the firm, the more the bureaucracy and the more the number of claims. This means it may take longer for those claiming benefits to be able to claim them. The number of claims is also another reason. The higher the number of claims, the longer it will take to have the benefit. The correlation coefficient between the duration of benefits and the benefits policy change dummy is 0.0332. This implies a weak positive relationship between the duration of benefits and the benefits policy change dummy variable exists. The proposed regression model is

The regression result presented in table 1, column 1, shows that the reform has a significant effect on the duration of claiming benefits as the coefficient is significant. Specifically, the average duration after reform is higher than before reform by 1.68 weeks, and the p-value is0.0022<0.05. The coefficient of higher is significant (p=0.019<0.05), and the coefficient is -2.53, which means that high earner claims benefit later than low earners by 2.53 weeks. Similarly, the previous wage also has a significant coefficient (p<0.001), and the estimate means that a dollar increase in the previous wage increases the number of weeks claiming benefits. Hosp has the largest effect at 14.13 and is significant (p<0.001). This means the average week to claim benefits for workers that are hospitalized is 14.13 weeks higher than for those not hospitalized. The type of injury does not matter in the equation as all p-values for the categories of injury type are greater than 0.05. occurs also have a large effect as workers diagnosed with the occupational disease have an average week to claim benefit greater than those not diagnosed with the occupational disease by 10.04 weeks, and the difference is statistically significant (p=0.001). Finally, a year increase in age increases the number of weeks claiming benefit by 0.094, and the effect is statistically significant (p<0.001). All variables accounted for 9.99% of the variation in the dependent variable, which is a poor fit, but this is due to the fact that most of the explanatory variables are dummy variables. The overall model is statistically significant as F=61.99, p<0.001. The diagnostic test carried out in the Eviews assignment by our expert are the test of assumptions of normality, serial autocorrelation, heteroscedasticity, omitted variable tests, and stability tests. For the normality test, the histogram displayed in figure 1 shows that residuals are skewed to the right, and the Jarque-Bera statistics reject the null hypothesis of normality, which means residuals are not normally distributed. For autocorrelation, in table 2, the p-value of the Breusch-Pagan LM test is <0.0001, which means we do not go with the null hypothesis that residuals aren’t correlated. Similarly, the test for heteroscedasticity rejects the null hypothesis of homoscedasticity (p<0.001), which means that the model suffers from heteroscedasticity. The omitted variable test also strongly rejects the null hypothesis of no omitted variable (p<0.001), which means there is a specification error in the model. Finally, the CUSUM plot shows that the model is stable over time. As shown in figure 2, the curve did not exceed the significance bound. The model to estimate now becomes

From the result, the coefficient of the interaction is not significant as p=0.6355<0.05.this means that high earners are not differently affected by the change in benefits cap than the low earners. Given that the coefficient of a change is still significant with the addition of the interaction term and the sign did not change, it means its effect is not determined by the worker being a high earner or not. Therefore, the coefficient is likely to be causal. The Ramsey reset test was used to check for functional misspecification. The result shows that the test statistics are 1385.8, p<0.001, which means rejection of the null hypothesis that there is no misspecification. Therefore, we conclude that the functional form of the model is misspecified. The regression model becomes:

Using the Wald test to test the significance, the result (table 2) shows that F(1, 7131) is 1.250, p=0.2635>0.05. Therefore, we cannot reject the null hypothesis that it is not significantly different from 0. We conclude that the marginal effect of age is not significantly different from 0.       Similar detailed results are provided as a part of our EViews assignment help service. It shows that the coefficient of Kentucky is not significant in the model which infers that there is likely no state-specific effect that drives the result in b

### EViews Assignment Help on Model Fitting

The first step taken by our Eviews assignment helper is to visualize the time series plot of CPI. We see from the plot (figure 2.1)  that the series increases over time, which means the variable is trending over time. Using the Augmented Dickey-Fuller test, CPI isn’t stationary at levels as the test statistics is -3.12, p=0.1022. This means we could not reject the H0 that the variable is a unit root, and thus it’s not stationary at levels. However, at the first difference, the test statistics are -14.08, p<0.001. This means we H0 that the first difference is a unit root and thus stationary at the first difference. The plot of the differenced CPI is shown in figure 2.2. As seen from the plot, the trend has been removed through differencing. Next, we plot the correlogram for the differenced series, and the plot is shown in table 2.1. Looking at the ACF plot, we see that there is a significant spike at lag one, and the plot decay at further lag, which suggests MA of order 1. For the partial autocorrelation function, we see that there is a significant spike up to lag two before dying off, which suggests an AR of order 2. Moreover, we see a significant spike at lag 12 of the partial autocorrelation function. This suggests a seasonal AR of order The suggested model is now SARIMA (2,1,1) (1,0,0). We will check a few other models that are more parsimonious in order to ensure the assumption is met. Estimating the model and comparing the model with more parsimonious models, we see that the model performs better based on the Akaike criterion. As presented in table 2.2, the model “SARIMA (2,1,1) (1,0,0)” has the lowest AIC value of -0.639. We now turn to the diagnostic test for the model. First, we examine the covariance stationarity of the model by checking the inverse root of the ARMA polynomials. From the unit circle in figure 2.3, we see that none of the points lies outside the unit circle, which implies that covariance stationarity is met. Next is to check whether the residuals are white noise by visualizing the PACF and ACF of residuals as well as the Q-statistics to determine the presence or otherwise of autocorrelation. The result is displayed in table 2.3. We see that both the ACF and PACF die off quickly, and the Q-stat is not significant up till lag 11, which means that there is no significant autocorrelation among residuals. Finally, we checked the normality assumption by plotting the histogram of the residuals, as shown in figure 2.4. We see that the plot is skewed, and the Jarque-Bera test strongly rejects the H0 of normality. This means that assumption of normality of residuals is not met.

### Interpretation of the Results by our Eviews Assignment Helper

Given the above, our EViews assignment helper interprets that the residuals are not normally distributed, but the model is stationary, and the residuals are not serially correlated. Moreover, none of the coefficients is significantly different from 0. We use Eview's automatic ARIMA method, and it returns not so parsimonious SARIMA (2,1,4)(2,0,1) with an AIC value of -0.656, which is bigger than that of our own proposed model. Doing a diagnostic of the residuals shows that the residual is not also normally distributed. The covariance stationarity is also not met as some points lie almost outside the unit root circle. The no-autocorrelation of residuals is not also satisfied with this model, which means our proposed model performs better than it. Figure 2.5presents the time series plot of the four variables. All the variables behave similarly over time, and we see they increase for most part of the time, and there is a significant trend as the values of the variables increase over time. This means there is a trend in all the variables. The H0 of the unit root test is the series has a unit root, while the H1 is that the series is the opposite. The result is presented in table 2.4. For consumption, at levels, the p-value of the test is 0.6878>0.05, which implies that we accept the H0 of a unit root. Thus, consumption is not stationary at levels. For the first difference, p<0.001 suggests that we do not go with the null hypothesis of a unit root. Therefore, consumption is stationary at first difference. For investment, at levels, the p-value of the test is 0.3702>0.05, which means that we have to go with the H0 of a unit root. Thus, investment is not stationary at levels. For the first difference, p<0.001 suggests rejection of H0 of a unit root. Therefore, investment is I(1). For money supply, at levels, the p-value of the test is 0.4237>0.05, which means that we have to go with the null hypothesis. Thus, the money supply is not stationary at levels. For the first difference, p<0.001 suggest not going with the null hypothesis. Therefore, the money supply is stationary at first difference. For GDP, at levels, the p-value of the test is 0.2751>0.05, which implies that we have to go with the H0 of a unit root. Thus, GDP is not stationary at levels. For the first difference, p<0.001 suggests rejection of H0 of a unit root. Therefore, GDP is stationary at the first difference. For all variables, at levels, we cannot reject the H0 of a unit root. However, we can reject it at first. This means all the variables for this analysis are stationary at first difference. Therefore, all the variables have the same order of integration “I(1)” Step 1: examine the order of integration to make sure both variables are I(1) This was done in 2 above, and we were able to show that both consumption and income are I(1) Step 2: estimate the model with OLS The model to be estimated using OLS is Step 3: save the resulting residuals from the model in step 2 Step 4: test for stationarity of the residuals from step 3. If stationary at levels, there is cointegration between the two variables. Otherwise, there is no cointegration. Step 5: Make the decision The ADF test result is presented in table 2.4. the test’s p-value is 0.01 <0.05, which connotes we do not go with the null hypothesis if unit root. Therefore the residuals are stationary at levels, and we conclude that there is cointegration between consumption and income.

The chosen ECM model is Our Eviews expert includes only one lag of independent variables because all other higher lags are not significantly different from 0 and no lag of independent variable because none is significantly different from 0. The lag of ECM represents the error correction term. The coefficient of the error term is -0.088 and significant (p=0.0025) as expected. This means that there is an 8.8% adjustment toward long-run equilibrium every quarter. It is a significant (p<0.001) short-run effect of income on consumption. A dollar increase in GDP increases consumption by 0.77. Therefore short-run MPC is consistent with theory (positive and less than 1).

APPENDIX Table 1: Regression table

 Variable 1st model 2nd model 3rd model Kentucky Michigan AFCHNGE 1.686*** (0.545) 1.473* (0.711) 1.683*** (0.551) 1.026 (0.723) 0.940 (1.574) HOSP 14.128*** (0.641) 14.123*** (0.647) 14.126*** (0.647) 14.148*** (0.645) -2.381 (1.663) TOTMED 0.000*** (0.000) 0.000*** (0.000) 0.000*** (0.000) 0.000*** (0.000) 0.004*** (0.000) HEAD -2.308 (2.091) -2.284 (2.092) -2.293 (2.092) 0.831 (2.080) -5.272 (5.106) NECK 3.204 (2.598) 3.207 (2.598) 3.187 (2.597) 5.851** (2.573) -1.631 (6.349) UPEXTR -0.743 (1.605) -0.735 (1.606) -0.740 (1.606) 1.299 (1.639) -3.379 (3.502) TRUNK -2.108 (1.720) -2.103 (1.720) -2.110 (1.720) -0.728 (1.753) -0.117 (3.774) LOWBACK 2.290 (1.609) 2.298 (1.609) 2.267 (1.611) 4.435*** (1.637) -2.354 (3.551) LOWEXTR -1.345 (1.623) -1.337 (1.623) -1.345 (1.623) 1.034 (1.654) -4.460 (3.572) PREWAGE 0.018*** (0.003) 0.018*** (0.003) 0.018*** (0.003) 0.009** (0.004) -0.015 (0.01) OCCDIS 10.045*** (3.055) 10.036*** (3.055) 10.019*** (3.056) 8.781*** (3.289) 11.042* (5.916) AGE 0.094*** (0.022) 0.094*** (0.022) 0.146 (0.132) 0.055** (0.022) 0.171*** (0.053) HIGHEARN -2.539** (1.082) -2.786** (1.202) -2.567 (1.085) 0.828 (1.466) 7.460 (5.320) interaction 0.534 (1.125) 0.599 (1.108) 1.910 (2.864) age^2 -0.001 (0.002) C -2.770 (1.832) -2.673 (1.843) -3.636 (2.842) -2.359 (1.931) 6.596 (4.838) N 7146 7146 7146 5622 1524 R-squard 0.1015 0.1016 0.1016 0.1162 0.3898 Adj R-squard 0.0999 0.0998 0.0998 0.1140 0.3841

Table 2: Diagnostic test result

 serial correlatio test test statistics 8.785276 p 0.0002 heteroscedasticty test test statistics 41.65042 p 0 omitted variable test test statistics 1381.607 p 0 omitted variable test(model 2) test statistics 1385.8 p 0 marginal effect of age test statistics 1.251 p 0.2635

Skewness and Kurtosis

Histogram using EViews Figure 1: Histogram of Residuals

Figure 2:CUSUM plot

Time Series Plot Figure 2.1: Time series plot of CPI

Figure 2.2: Time series plot of the first difference Partial Correlation Table 2.1: ACF and PACF of DCPI

Table 2.2: AIC of selected models

 Models AIC 2,1,1:1,0,1 -0.66656 2,1,1:1,0,0 -0.63528 2,1,1 -0.63917 1,1,1 -0.63944 1,1,1:1,0,0 -0.63576 1,1,0 -0.6133 0,1,1 -0.63481

AR/MA Polynomials

Time Series Plot of Macroeconomic Variables.

Figure 2.5: Time series plot of Macroeconomic Variables. Table 2.4:  Unit Root test

 Levels first dif Decision tStat Prob.* tStat Prob.* I(1) CPI -3.12268 0.1022 -14.0812 0.000 I(1) CO -1.82652 0.6876 -14.5337 0.000 I(1) I -2.41551 0.3702 -13.9855 0.000 I(1) M -2.31405 0.4237 -5.493 0.000 I(1) Y -2.61316 0.2751 -13.9622 0.000 I(1) Engle Granger -4.01243 0.01
Table 2.5 ECM result
 Variable Coefficient DCO(-1) -0.102* 0.059 DY 0.777*** 0.074 ECM(-1) -0.088*** 0.029 C 0.002*** 0.001 N 170 R-squared 0.4108 afj R squared 0.4002
Table 2.6: Diagnostic test of ECM’s residuals
 serial correlatio test test statistics 0.1632 p 0.8496 heteroscedasticty test test statistics 5.009182 p 0.0024
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