Applied Econometrics Questions - Assignment Example

Sur Lecturer Applied Econometrics Questions Question β1 measures how median housing prices, which was measured in 000, in Bostonmetropolitan area changes in relation to the average room number in owner occupied housing. As such, when average room number in owner occupied housing increase by 1 unit, the demand for median housing prices increase by 0.294. Since β2 = - 0.055, when weighted distance to 5 main employment centers within the Boston region increases by 1 units, the demand for median housing prices decreases by 0.055. Similarly, β3 of -1.529 implies that when the concentrations of nitrogen oxide in parts per given hundred million increase by 1 unit, the demand for median housing prices decreases by 1.529. β4 of 0.234 indicates that demand for median housing prices increases by 0.234 when the dummy variable increases by 1 unit. Question 2 Given the model ln(MVi) = βo + 0.329 * RMi + 0.197* ln(DISi) + 0 * NOXi + 0 *DCHAS,i + εi, The guesstimate of the autonomous change (intercept) in model (1) = βo But, β0 = ln(MVi) - 0.329 * RMi - 0.197* ln(DISi) The intercept indicates the changes in median housing prices that is independent of the explanatory variables. That is, risk-free rates of change. Question 3 Estimating the model (1) by means of beta coefficients gives β1 and β2 as 0.566 and 0.261 respectively. This implies that the average room number in owner occupied housing and weighted distance to 5 main employment centers within the Boston region gives a below average return and risk as far as investing in median housing is concerned. This is because the beta values are below 1. Question 4 The alternative and null hypotheses indicating that ln(DIS) does not positively influence median housing prices is given as: Ho: β2 = 0 H1: β2 ≠ 0 Question 5 It is essential to keep in our mind that every coefficient is affected by the other independent variables in our model. Since independent variables are virtually always related and two or more independent variables can explain similar variation in median housing prices. Thus, each coefficient cannot explain the overall effect on median housing prices of its corresponding predictor variable, as would be the case if that coefficient was the only determinant in the model. Instead, each coefficient epitomizes the additional influence of adding NOX variable (concentrations of nitrogen oxide in parts per given hundred million) to the model, when the effects of every other independent variable is already accounted for in the model. Hence, β2 and β1 will change if other variable is added to the model (model 2) and their new value will be a better predictor of median housing prices. This explains why β2 has changed both its sign and value, from our model 1 to model 2, but β1 has only changed its value. Nonetheless, both the coefficients have changed in model 2. Question 6 According to this question, we introduced variable NOX*Dchas (product of two independent variables already in the model). As such, this extra variable is definitely correlated with the already existing predictor variables in the model and so we will experience multicollinearity effect. The combined effect of this additional variable is difficult to predict but it gives the true prediction. In our case, the extra variable in the model enabled a better prediction of β3. Moreover, the inclusion of variable NOX*Dchas (β5) suggested how the median housing prices changes due to the combined effect of NOX*Dchas Question 7 Yes, we can generally say that the regular standard errors are always smaller than heteroskedasticity-robust standard errors, so using heteroskedasticity-robust standard errors might be considered as an attempt to be conservative. For large samples, as was the case with our study, heteroskedasticity tests will virtually turn up positive and so the approach of using eteroskedasticity-robust standard errors is appropriate. Question 8 The models for this question are: ln(MVi) = βo + β1RMi + β2 ln(DISi) + β3NOXi + β4 DCHAS,i + εi……………( Charles river) ln(MVi) = β00 + β11 RMi + β22ln(DISi) + β33NOXi + β44DCHAS,i + εi………..( No Charles river) The corresponding alternative and null hypothesis will be: Ho: β2 = β22 = β3 = β33 (No significant difference in beta for the two regions) H1: β2 ≠ β22 ≠ β33 ≠ β33 (beta is statistically different for the two regions) We need to perform a F-test to test our null hypothesis as follows: We need to square the standard deviations, for the two models, to get the variances. Divide the biggest variance by the minimum variance so as to get the f-value in the right tailed test. Look for the critical F-value, according to the desired alpha value (0.05 or 0.10), in the F-table Compare our critical F-value with the calculated T-value. Reject Ho if the calculated F-value < the critical F-value. Question 9 Even if the BP test and White test gives the same conclusion concerning the existence of heteroskedasticity, this does not imply the Breusch-Pagan test is just as good as White test. This is due to the different functional form which each test assumes. BP test consider error variance as a linear function of at least one variable. The White test, on the contrary, consider the error variance as an exponential function of at least one variables. Moreover, with the BP test you need to pick only one determinant associated with the heteroscedasticity as opposed to White test where you can choose more variables. Question 10 If heteroskedasticity was present in model (3) and the error term exhibited a non-constant variance, there will be no concern that our estimates are biased only if the other assumptions regarding the use of a typical Ordinary Least Square estimator are satisfied. If the others assumptions are met, model 3 will remain unbiased. Question 11 RESET test for the correct specification is given by an F-test. Ho: The correct model specification is linear. H1: The correct model specification is actually non-linear. With that, the F test statistics is formulated by: F(M; n-k-i) = (SSRr – SSRur/M) / SSRur/ n-k Where the summation of squared residuals are given by SSRs for the individual regressions; M = number of restrictions; n = number of observations; k = number of parameters projected in the unrestricted model, implying that it is greater than the amount of variables that explained median housing prices because the intercept parameter is also included in the count. Essentially, the correct degrees of freedom should be used for the calculations. If the calculated F-test > critical F-value Ho is reject, implying the true specification of the model is not linear (non-linear). Limitations of RESET test The test does not specify hidden non-linear relations or any omitted variable bias. It is difficult to calculate the F-test. Lastly, regardless of the level of non-normality, the RESET test may be biased especially as the error grows. Question 12 There is proof of model misspecification since a p-value of 0.001, for RESET test, suggest that we reject that argument that any of the models had no omitted variables. This means any of the model might have omitted variable at 1% level. Question 13 Yes, model 3 nest model 1 since model 3 has all the variables of model 1, and more other variables. Question 14 Models are termed as non-nested when neither of them can be derived from the other through some limiting process, comprising imposition of inequality or equality constrains on any of the parameters of the model. In econometric assessment, non-nested models come up naturally when opposing economic models are used to describe the same phenomenon, like change in demand and prices, unemployment, or output growth. As such, one faces some difficulties in hypothesis testing for the models that are non-nested. The reality that this models belong to distinct families of distributions and none of them may be derived from the remaining makes their testing yield a number of probable outcomes. Interpreting the findings of such tests may thus seem complicated (Asteriou, 63). For most hands-on purposes, though, interpretation is not mostly hard. If one reject neither of the model, then the data set cannot allow him or her to conclude that either of them is false. Nonetheless, if one reject one model and not the other, then the model set that are worth extra investigation has been condensed in size. If all the models are rejected, the set has shall have been condensed in size more. Certainly, if there no other models exist, one should probably try to create some. As such, the signs of his or her test statistics can be useful because they will alert on whether he or she ought to create a model which combines elements of the rejected models, or one model which moves far away from either of the models. Work Cited Asteriou, Dimitrios, and S G. Hall. Applied Econometrics. Basingstoke [England: Palgrave Macmillan, 2011. Print. Read More