Heteroskedasticity Test - Assignment Example

Heteroskedasticity Test Student’s Name: Institution: Course Code: Date: Question 1 This is a range of values usually computed from sample data within which we expect the population value to lie. It is also called confidence interval and it calculated by the below formula Confidence interval = point estimate +or – margin error. Question2 This is the increase in the ultimate income that results from any newly introduced injection of spending. The impact of Multiplier takes place at any time when there is an introduction of an original demand into the circular stream. This is due to the fact that any introduction of additional income there is possibility of an increase in spending which can produce more income. The magnitude of the impact of multiplier is based on marginal propensity to save or consume. It is appropriate to note that when there is expenditure of any income, it becomes another person’s income. Marginal propensities illustrates the ratio of additional income assigned to a given economic activity like investment used by UK company, household savings and imports. Illustration If there is 80% expenditure on the new income in the production of some UK products, then the marginal propensity to consume will therefore be 80/100 which is equivalent to 0 .8. Question3 The main variation of OLS and GLS is that OLS is a method that is applied in the estimation of unknown parameters in regression model while GLS measure known parameter in linear regression model. It also tries to measure vector which depends on the observation of generated by when it is passed across mixing matrix and adding € at the end but GLS does not measure vector which is done by OLS.It is also the role of OLS to provide maximum possible estimate for vector in instances when there is the same variance in the parameter and has no positive relationship and noise € in transparent. This feature is not found in GLS which tend to provide a more generalized approach in the provision of maximum possible estimate in cases when there is coloured noise and only takes place when therenoise has correlation matrix. Question4 Instrumental variable is used for identifying models that is not able to be estimated by multiple regressions. It is also used to determine casual relationship in cases where controlled experiments are not feasible. The main feature which is considered when using instrumental variable is its ability to provide a positive correlation with endogenous explanatory variable and the inability to correlate with the error term in the explanatory equation Question5 Reduced form of equation is the question that is produced when any endogenous variable is solved through regression and its derivation is done by first starting with identifying certain relationship between different variables.Hausman test is a test of null hypothesis Ho where random effect is expected to be consistent and efficient when it is compared to H1 where random effect is inconsistent. This test is very efficient to check instrumental validity when there is a model and data where fixed effect estimation is appropriate. Question6 This is a model which is estimated by the use of GLS in a situation where the variance structure is understood and it is also produced by FGLS but in this case the variance is unknown. In comparison to fixed effect model, it is relatively difficult to approximate. Question7 2SLS estimation is a very important instrumental variable method which is used to estimate independent variable where there are more instruments than independent variable in the model. It is illustrated by the following equation. y = Xb + e In the above equation Y is (T x 1) vector of all variables which are not independent, X is (T x k) matrix of independent variables and b is (akx1) Vector which represent a parameter to be estimated in the model. In the same mode e is a k x1 vector error. In this case the independent variable matrix X has a positive correlation with e vector. Question8 This is an output model of any business processes where all the available variables are handled as non random values. In this case fixed model is used to produce optimal values that are used to provide inputs the business process in a case where random factors are projected to be missing or have little effect on the business process. Question9 The intuition of LM test to detect heteroskedasticiy is that after the completion of the test statistics it is important to compare the values with the critical values for the predetermined level of significant.When it is determined that the computed values of the test statistics are more than the critical valuesthen null hypothesis of constant error variable is ignored. In this case it is concluded that there is heteroscedasticity but incase there is no rejection of null hypothesis there is no evidence of heteroscedasticity. Question10 This is a technique which is used to estimate population parameter where it is began by determining the equation that produces its relationship with population moments. The best example is the determination of the expected values of power of random variables to the parameter which has been determined. Question 11 AR 1 is a model that is used to determine or predict time series and is affected by the availability of outliers while ARD1 is not affected by outliers. AR1 uses excitation noise of student t distribution while ARD1 uses AR coefficient to determine the model order. Question 12 Log DD= a0 +a1log P + e LogDD- a1log P =a0 +e Log (DD-) = a0 +e DD- = (a0+e) DD - (a0+e) = =DD - (a0+e) P= Part B Question1 (a) Income is included as a log because it is has a non linear relationship and it has an indirect relationship with medical expenditure. Age is included as a non linear relationship because it has random dependent variables. (b)It is possible for private health insurance to influence medical expenditures because health insurance always pays medical expenses at a given rate. It is influenced by the level of medical insurance cover. (C) The implication of fixed effect estimatorensures that the observed quantities are treated like non random quantities and also allow explanatory variables to be used as if they are originated from random causes. Question2 (a) Why is choice is correlated with U1? There is correlation of choice with U1 because Choice of school depends on the family income. It is also due to choice and U1 is directly depending on each other. (b)Is grant correlated with U1? Grant is has a positive correlation with U1 because it influence the occurrence of U1 (C) The reduced form of choice and what is needed for grant to be partially correlated with choice is = Score-1(β0+β2faminic+U1) and foe grant to be partially correlated the endogenous variable must be solved through regression and its derivation is done by first starting with identifying certain relationship between different variables. d) The reduced equation for score and explain why this is useful. The reduction of this is useful for economic analysis. It also standardizes the question to manageable level. Score = choice + faminic + U1 Question 3 (a) Interpretation of the equation The presence of terrorism in a country depends on the nature of the political regime and geographical area to which the country is situated. The equation aims to capture the relationship between political regime and terrorism. The type of the system identified is a fixed effect model system. (b) The estimation methodology is moment estimations which require the determination of equation used to produce the relationship of the terrorism with the population parameter for it top proceed. Question 4 (i) There evidence of heteroskedasticity from the above model because residual and predicted variables of the above equation are normally distributed and there is a strong relationship between the predicted values and the residual values. (ii)Yt=β1 (1/σt)+β2X2t/σt +β3X3t/σt +…+βkXkt/σt +ut/σt or Y*t= β*1+ β*2X*2t+ β*3X*3t+…+ β*kX*kt+u*t Where we have now that: Var(€*t)=Var(€t/σt)=Var(€t)/σt2=1 (iii)In the presence of heteroskedasticity and an order 1 autoregressive error, we have: where. Hence =/1-) Question 5 (i)The estimated difference in SAT score is 19.14 and the estimated difference is 0.8 significant. The fact that 0.8 appear in the acceptance region, it is important to accept null hypothesis. It is therefore important to conclude that the difference between the score before and after is insignificant. It is because of the problem of sampling distribution. (ii) The estimates test score of non black male is 354. I need to test the significance of null and alternative hypothesis to determine the significance of test statistics. (iii) The estimated difference in the SAT score of black female and non black female students is 79163.7936. It is important to formulate hypothesis where there must be a null and alternative hypotheses so that the test statistics can be done. The test statistics should be accepted whenthe estimated difference is higher than the confidence interval but rejected when it is less. This will help the statistician in decision making process. Read More