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1 # PS8.8, for Application in Section 8.4 2 open data8-3 3 genr y=exphlth/pop 4 genr x=income/pop 5 # estimate model by OLS and save absolute residuals, squared residuals, 6 # and their logs 7 ols y const x seniors 8 genr absuhat=abs($uhat) 9 genr usq=$uhat*$uhat 10 genr lnusq=ln(usq) 11 # generate square and cross product variables; the flag -o generates cross 12 # product 13 square x seniors -o 14 # Testing and estimation for the Glesjer approach 15 ols absuhat const x seniors sq_x sq_seniors 16 # estimate residual s.d. from the auxiliary regression 17 genr sigmahat=absuhat-$uhat 18 # compute LM test statistic and its p-value 19 genr LM1=$nrsq 20 pvalue X 4 LM1 21 # print sigmahat and note that only one estimate is negative 22 print sigmahat 23 # replace negative value with original sigmahat and get weights 24 genr d1=(sigmahat>0.0) 25 genr sigma2=(d1*sigmahat)+((1-d1)*absuhat) 26 genr wt1=1/(sigma2^2) 27 # Estimate model by FGLS which is the same as WLS 28 wls wt1 y const x seniors 29 # Testing and estimation for the Breusch-Pagan approach 30 ols usq const x seniors sq_x sq_seniors 31 # estimate residual s.d. from the auxiliary regression 32 genr usqhat1=usq-$uhat 33 # compute LM test statistic and its p-value 34 genr LM2=$nrsq 35 pvalue X 4 LM2 36 # print usqhat and note that several estimates are negative 37 print usqhat1 38 # replace negative values with original usqhat and get weights 39 genr d2=(usqhat1>0.0) 40 genr usqhat2=(d2*usqhat1)+((1-d2)*usq) 41 genr wt2=1/usqhat2 42 # Estimate model by FGLS which is the same as WLS 43 wls wt2 y const x seniors 44 # Testing and estimation for White's procedure 45 ols usq const x seniors sq_x sq_seniors x_seniors 46 genr usqhat3=usq-$uhat 47 # compute LM test statistic and its p-value 48 genr LM3=$nrsq 49 pvalue X 5 LM3 50 # print usqhat and note that several estimates are negative 51 print usqhat3 52 # replace negative values with original usqhat and get weights 53 genr d3=(usqhat3>0.0) 54 genr usqhat4=(d3*usqhat3)+((1-d3)*usq) 55 genr wt3=1/usqhat4 56 # Estimate model by FGLS which is the same as WLS 57 wls wt3 y const x seniors 58 # Test using the Harvey-Godfrey approach 59 ols lnusq const x seniors sq_x sq_seniors 60 # compute LM test statistic and its p-value 61 genr LM4=$nrsq 62 # since the p-value is high, we do not reject homoscedasticity 63 pvalue X 4 LM4 64 # Because the coefficients for x and x-squared are significant, another LM 65 # test is done with just these 66 ols lnusq const x sq_x 67 genr lnusqhat=lnusq-$uhat 68 # compute LM test statistic and its p-value 69 genr LM5=$nrsq 70 pvalue X 2 LM5 71 # since the p-value is acceptable, we reject homoscedasticity and 72 # procede with WLS estimation 73 genr usqhat5=exp(lnusqhat) 74 genr wt4=1/usqhat5 75 wls wt4 y const x seniors