As a new economist at the health ministry, you are interested in evaluating the determinants of life satisfaction (happiness) among the adult population. In particular, you are interested in whether obtaining more education helps improve life satisfaction. As part of the research team, you collect data on a random sample ofthe adult population in the year 2010. You collect data on the following variables: happy - variable equal to 1 if a person is happy. and 0 otherwise educ - number of years of completed education income - income in $10,000 bins age - age in years married - variable equal to 1 if a person is married, and 0 otherwise goodhealth - variable equal to '1 if a person selfreports to be in good health, and 0 otherwise Using the data, you estimate a simple regression model forthe impact of collected variables on life satisfaction, as follows: (D1) happy; 2 ,80 + leduci + zincomei + 33agei + 4marriedi + sgoodhealthi + u,- The STATA output below reports OLS results of Model (D1). reg happy income educ age married goodhealth Source SS df MS Number of obs = 1,112 F(5, 1106) = 16.52 Model 10.9922574 5 2.19845148 Prob > F = 0.0000 Residual 147.201088 1,106 .133093208 Rsquared = 0.0695 Adj Rsquared = 0.0653 Total 158.193345 1,111 .14238825 Root MSE = .36482 happy Coef. Std. Err. t P>|tl [95% Conf. Interval] income .0045113 .0046803 0.96 0.335 -.0046718 .0136945 educ .0147934 .0037622 3.93 0.000 .0074115 .0221753 age -.0002674 .0006739 -0.40 0.692 -.0015896 .0010549 ' married .0869298 .0230887 3.77 0.000 .0416272 .1322324 goodhealth .1206719 .0252924 4.77 0.000 .0710455 .1702983 _Cons .4616051 .0680543 6.78 0.000 .328075 .5951353 1.[1 points] Interpret the estimates of 1, the coefficient on educ 2. [2 points] Suppose you do the Breusch-Pagan test and obtain an F-value of 10.50 and a p-value of 0.000 for the test. What do you conclude based on this result? What is a solution to the concern raised by this test? 3.[3 points] Propose a strategy to test if the population regression in Model (D1) differs across males and females. Write down the null hypothesis for the test. 4. [4 points] The below STATA output reports OLS results of the following regression model: (D2) happyi = 00 + 01 educi + 02 income; + 03 age; + 04malemarried; + 05 femalemarried; + 06 malenotmarried; + 0 goodhealth; + u where malemarried = 1 if respondent is a male who is married, femalemarried = 1 if respondent is a female who is married, and malenotmarried = 1 if respondent is a male who is not married. . reg happy income educ age malemarried femalemarried malenotmarried goodhealth Source SS df MS Number of obs 1, 140 F (7, 1132) 12 . 68 Model 11 . 6062918 7 1. 65804168 Prob > F 0 . 0000 Residual 148 . 056866 1, 132 . 130792285 R-squared 0. 0727 Adj R-squared 0 . 0670 Total 159 . 663158 1, 139 . 140178365 Root MSE . 36165 happy Coef. Std. Err. t P>Itl [95% Conf. Interval] income . 0049881 . 0046143 1 . 08 0. 280 - . 0040655 . 0140417 educ . 015014 . 0036814 4. 08 0. 000 . 0077909 . 0222371 age - . 0003447 . 0006621 -0.52 0. 603 - . 0016438 . 0009544 malemarried . 0513895 . 027587 1 . 86 0 . 063 - . 0027378 . 1055169 femalemarried . 0713725 0348369 2. 05 0 . 041 . 0030202 . 1397247 malenotmarried -. 0563924 . 0304529 -1 . 85 0 . 064 -. 1161428 . 003358 goodhealth 1219508 0248959 4. 90 0 . 000 . 0731034 . 1707981 _cons . 485331 . 0677461 7. 16 0. 000 . 352409 . 618253(i) With respect to gender and marital status of individuals, which is the base category? (ii) What is the difference in life satisfaction between males who are married vs males who are not married. (iii) What is the difference in life satisfaction between females who are married vs females who are not married. ( iv) Using information from both models, what do you conclude about the effect of marriage on life satisfaction? 5.[3 points] One economist in your team says that there is measurement error in the way variable goodhealth is measured. Your colleague says that individuals' socioeconomic status (such as income and education) likely correlated with their self-reported health. What is the effect of this measurement error on your estimates? 6.[7 points] Since you had taken an Econometrics course in your undergraduate degree, you are not persuaded with the results in Model (D1). You convince your team to re-interview the same individuals 2 years later and estimate the following model: (D3) happyit = di + Yo + Vieducit + 12incomeit + 13ageit + 14marriedit + Isgoodhealthit + uit where (i) represents individuals and (t) represents time period. (i) What is the term a; called? Given an example of a variable that is accounted for by the term aj in Model (D3). [2 points] The STATA output below reports the OLS results of Model (D3) using first difference estimation, where D1. or D. implies first differences of variables, e.g. DI .happy = happyit - happyit-1 . DI.income = incomeit - incomei,t-1 , etc. reg D1 . happy D1. income D1. educ Dl. age D1. male D1. married D1 . goodhealth Source SS df MS Number of obs 811 F (6, 804) 2. 05 Model 1. 7534327 6 . 292238783 Prob > F 0 . 0573 II II Residual 114. 801438 4 . 142787858 R-squared 0 . 0150 Adj R-squared 0. 0077 Total 116. 554871 810 . 143894902 Root MSE 37787 D. happy Coef. Std. Err. t P> It/ [95% Conf. Interval] income D1 . -. 0146599 . 006593 -2. 22 0. 026 - . 0276015 -. 0017183 educ D1 . . 0101117 . 0097663 1. 04 0. 301 - . 0090587 . 0292822 age D1 . 0080325 . 0172932 0. 46 0. 642 - . 0259126 . 0419776 male D1 . - . 0187777 . 0278041 -0. 68 0. 500 -. 0733549 . 0357995 married 01. 0517323 . 0449671 1. 15 0. 250 -. 0365346 . 1399991 goodhealth D1 . 0683106 . 031544 2. 17 0. 031 . 0063924 . 1302289 _cons . 0116769 . 0364386 0. 32 0. 749 -. 059849 . 0832029 (ii) Does your conclusion on the effect of education on life satisfaction change? Does your conclusion on the effect of marriage on life satisfaction change? Explain why your results in Model (D1) and Model (D3) are very different. [3 points] (iii) Your colleague says that the new conclusion is not true because explanatory variables vary only a little over time. Is this assertion true? Explain [2 points]