<p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span lang="EN-US" style="FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><font size="3">You are given the following data on 2,800 respondents in the Australian National Longitudinal Survey of Youths with Jobs in 1994:<p></p></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span lang="EN-US" style="FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><p><font size="3"> </font></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 72pt; TEXT-INDENT: -54pt;"><span lang="EN-US" style="FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><span style="POSITION: relative; TOP: 6pt; mso-text-raise: -6.0pt;"><shapetype id="_x0000_t75" stroked="f" filled="f" path="m@4@5l@4@11@9@11@9@5xe" opreferrelative="t" ospt="75" coordsize="21600,21600"><stroke joinstyle="miter"></stroke><formulas><f eqn="if lineDrawn pixelLineWidth 0"></f><f eqn="sum @0 1 0"></f><f eqn="sum 0 0 @1"></f><f eqn="prod @2 1 2"></f><f eqn="prod @3 21600 pixelWidth"></f><f eqn="prod @3 21600 pixelHeight"></f><f eqn="sum @0 0 1"></f><f eqn="prod @6 1 2"></f><f eqn="prod @7 21600 pixelWidth"></f><f eqn="sum @8 21600 0"></f><f eqn="prod @7 21600 pixelHeight"></f><f eqn="sum @10 21600 0"></f></formulas><path oconnecttype="rect" gradientshapeok="t" oextrusionok="f"></path><lock aspectratio="t" vext="edit"></lock></shapetype><shape id="_x0000_i1033" oole="" type="#_x0000_t75" style="WIDTH: 11.25pt; HEIGHT: 18pt;"><imagedata otitle="" src="file:///C:\DOCUME~1\IBM\LOCALS~1\Temp\msohtml1\01\clip_image001.wmz"><font size="3"></font></imagedata></shape></span><font size="3"><span style="mso-spacerun: yes;"> </span>=<span style="mso-tab-count: 1;">          </span>Hourly earnings in the respondent’s main job at the time of 1994 interview<p></p></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 18pt;"><span lang="EN-US" style="FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><span style="POSITION: relative; TOP: 6pt; mso-text-raise: -6.0pt;"><shape id="_x0000_i1034" oole="" type="#_x0000_t75" style="WIDTH: 15.75pt; HEIGHT: 18pt;"><imagedata otitle="" src="file:///C:\DOCUME~1\IBM\LOCALS~1\Temp\msohtml1\01\clip_image003.wmz"><font size="3"></font></imagedata></shape></span><font size="3">=<span style="mso-tab-count: 1;">
                                </span>Educational attainment (highest grade completed)<p></p></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 18pt;"><span lang="EN-US" style="FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><span style="POSITION: relative; TOP: 6pt; mso-text-raise: -6.0pt;"><shape id="_x0000_i1035" oole="" type="#_x0000_t75" style="WIDTH: 17.25pt; HEIGHT: 18pt;"><imagedata otitle="" src="file:///C:\DOCUME~1\IBM\LOCALS~1\Temp\msohtml1\01\clip_image005.wmz"><font size="3"></font></imagedata></shape></span><font size="3"><span style="mso-spacerun: yes;"> </span>=<span style="mso-tab-count: 1;">     </span>Mother’s and father’s educational attainment<p></p></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 18pt;"><span lang="EN-US" style="FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><span style="POSITION: relative; TOP: 6pt; mso-text-raise: -6.0pt;"><shape id="_x0000_i1036" oole="" type="#_x0000_t75" style="WIDTH: 17.25pt; HEIGHT: 18pt;"><imagedata otitle="" src="file:///C:\DOCUME~1\IBM\LOCALS~1\Temp\msohtml1\01\clip_image007.wmz"><font size="3"></font></imagedata></shape></span><font size="3">=<span style="mso-tab-count: 1;">       </span>Composite score on cognitive tests in the Vocational Aptitude Test<p></p></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 18pt;"><span lang="EN-US" style="FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><span style="POSITION: relative; TOP: 6pt; mso-text-raise: -6.0pt;"><shape id="_x0000_i1037" oole="" type="#_x0000_t75" style="WIDTH: 17.25pt; HEIGHT: 18pt;"><imagedata otitle="" src="file:///C:\DOCUME~1\IBM\LOCALS~1\Temp\msohtml1\01\clip_image009.wmz"><font size="3"></font></imagedata></shape></span><font size="3">=<span style="mso-tab-count: 1;">       </span>Gender<p></p></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 18pt;"><span lang="EN-US" style="FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><span style="POSITION: relative; TOP: 6pt; mso-text-raise: -6.0pt;"><shape id="_x0000_i1031" oole="" type="#_x0000_t75" style="WIDTH: 17.25pt; HEIGHT: 18pt;"><imagedata otitle="" src="file:///C:\DOCUME~1\IBM\LOCALS~1\Temp\msohtml1\01\clip_image011.wmz"><font size="3"></font></imagedata></shape></span><font size="3">=<span style="mso-tab-count: 1;">       </span>Ethnicity (aboriginal, Caucasian, “others”, that is not aboriginal <p></p></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 54pt; TEXT-INDENT: 18pt;"><span lang="EN-US" style="FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><font size="3">or Caucasian)<p></p></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 18pt;"><span lang="EN-US" style="FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><span style="POSITION: relative; TOP: 6pt; mso-text-raise: -6.0pt;"><shape id="_x0000_i1032" oole="" type="#_x0000_t75" style="WIDTH: 17.25pt; HEIGHT: 18pt;"><imagedata otitle="" src="file:///C:\DOCUME~1\IBM\LOCALS~1\Temp\msohtml1\01\clip_image013.wmz"><font size="3"></font></imagedata></shape></span><font size="3">=<span style="mso-tab-count: 1;">       </span>Whether the main job in 1994 was in the government sector or <p></p></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 36pt; TEXT-INDENT: 36pt;"><span lang="EN-US" style="FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><font size="3">the private sector<p></p></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span lang="EN-US" style="FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><p><font size="3"> </font></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 54pt; TEXT-INDENT: -18pt; mso-list: l0 level1 lfo2; tab-stops: list 54.0pt;"><span lang="EN-US" style="FONT-FAMILY: Arial; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;"><font size="3">(a)</font><span style="FONT: 7pt "Times New Roman";">   </span></span></span><span lang="EN-US" style="FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><font size="3">As a policy analyst, you are asked to investigate whether there is evidence of earning discrimination, positive or negative, by sex or ethnicity in (1) government sector, and (2) the private sector.<span style="mso-spacerun: yes;">  </span>Explain how you would do this, giving a mathematical representation of the regression specification(s). Also illustrate your answer graphically.<p></p></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 36pt;"><span lang="EN-US" style="FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><p><font size="3"> </font></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 54pt; TEXT-INDENT: -18pt; mso-list: l0 level1 lfo2; tab-stops: list 54.0pt;"><span lang="EN-US" style="FONT-FAMILY: Arial; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;"><font size="3">(b)</font><span style="FONT: 7pt "Times New Roman";">   </span></span></span><span lang="EN-US" style="FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><font size="3">You are asked to investigate whether the incidence of earnings discrimination, if any, is significantly different in the two sectors.<span style="mso-spacerun: yes;">  </span>Explain how you would do this, giving a mathematical representation of your regression specification(s).<p></p></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 18pt;"><span lang="EN-US" style="FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><p><font size="3"> </font></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 18pt;"><span lang="EN-US" style="FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><p><font size="3"> </font></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 150%;"><b style="mso-bidi-font-weight: normal;"><u><span lang="EN-US" style="FONT-FAMILY: Arial;"><font size="3">Question 2. <p></p></font></span></u></b></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 18pt; LINE-HEIGHT: 150%;"><span lang="EN-US" style="FONT-FAMILY: Arial;"><p><font size="3"> </font></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 36pt; TEXT-INDENT: -18pt; LINE-HEIGHT: 150%;"><span lang="EN-US" style="FONT-FAMILY: Arial;"><font size="3">a)<span style="mso-spacerun: yes;">   </span>Consider the Cobb-Douglas production function that relates output (Y) to capital (K) and labour (L) which can be written as:<p></p></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 18pt; LINE-HEIGHT: 150%;"><span lang="EN-US" style="FONT-FAMILY: Arial;"><p><font size="3"> </font></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 126pt; TEXT-INDENT: 18pt; LINE-HEIGHT: 150%;"><span lang="EN-US" style="FONT-FAMILY: Arial;"><span style="POSITION: relative; TOP: 3pt; mso-text-raise: -3.0pt;"><shape id="_x0000_i1030" oole="" type="#_x0000_t75" style="WIDTH: 69.75pt; HEIGHT: 15.75pt;"><imagedata otitle="" src="file:///C:\DOCUME~1\IBM\LOCALS~1\Temp\msohtml1\01\clip_image015.wmz"><font size="3"></font></imagedata></shape></span><font size="3">.<span style="mso-spacerun: yes;">          </span><span style="mso-tab-count: 2;">             </span>(7.1)<p></p></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 18pt; LINE-HEIGHT: 150%;"><span lang="EN-US" style="FONT-FAMILY: Arial;"><p><font size="3"> </font></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 54pt; TEXT-INDENT: -36pt; LINE-HEIGHT: 150%;"><span lang="EN-US" style="FONT-FAMILY: Arial;"><font size="3">i) <span style="mso-tab-count: 1;">        </span>Which type of nonlinear regression is the Cobb-Douglas production function described above? Give reasons to support your answer.<p></p></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 18pt; LINE-HEIGHT: 150%;"><span lang="EN-US" style="FONT-FAMILY: Arial;"><p><font size="3"> </font></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 54pt; TEXT-INDENT: -36pt; LINE-HEIGHT: 150%; mso-list: l1 level1 lfo1; tab-stops: list 54.0pt;"><span lang="EN-US" style="FONT-FAMILY: Arial; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;"><font size="3">ii)</font><span style="FONT: 7pt "Times New Roman";">                  </span></span></span><span lang="EN-US" style="FONT-FAMILY: Arial;"><font size="3">Explain how the above production function can be linearised to be estimated by OLS technique. What are the meanings of the </font><span style="POSITION: relative; TOP: 5pt; mso-text-raise: -5.0pt;"><shape id="_x0000_i1025" oole="" type="#_x0000_t75" style="WIDTH: 14.25pt; HEIGHT: 17.25pt;"><imagedata otitle="" src="file:///C:\DOCUME~1\IBM\LOCALS~1\Temp\msohtml1\01\clip_image017.wmz"><font size="3"></font></imagedata></shape></span><font size="3"><span style="mso-spacerun: yes;"> </span>and </font><span style="POSITION: relative; TOP: 5pt; mso-text-raise: -5.0pt;"><shape id="_x0000_i1026" oole="" type="#_x0000_t75" style="WIDTH: 15pt; HEIGHT: 17.25pt;"><imagedata otitle="" src="file:///C:\DOCUME~1\IBM\LOCALS~1\Temp\msohtml1\01\clip_image019.wmz"><font size="3"></font></imagedata></shape></span><font size="3"><span style="mso-spacerun: yes;"> </span>in the transformed model?<p></p></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 18pt; LINE-HEIGHT: 150%;"><span lang="EN-US" style="FONT-FAMILY: Arial;"><p><font size="3"> </font></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 18pt; LINE-HEIGHT: 150%;"><span lang="EN-US" style="FONT-FAMILY: Arial;"><font size="3">b)<span style="mso-tab-count: 1;">     </span>Consider the following two models, <p></p></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 18pt; LINE-HEIGHT: 150%;"><span lang="EN-US" style="FONT-FAMILY: Arial;"><p><font size="3"> </font></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 126pt; LINE-HEIGHT: 150%;"><span lang="EN-US" style="FONT-FAMILY: Arial;"><span style="POSITION: relative; TOP: 6pt; mso-text-raise: -6.0pt;"><shape id="_x0000_i1027" oole="" type="#_x0000_t75" style="WIDTH: 138.75pt; HEIGHT: 18pt;"><imagedata otitle="" src="file:///C:\DOCUME~1\IBM\LOCALS~1\Temp\msohtml1\01\clip_image021.wmz"><font size="3"></font></imagedata></shape></span><font size="3"><span style="mso-spacerun: yes;">        </span><span style="mso-tab-count: 2;">        </span>(7.2)<p></p></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 18pt; LINE-HEIGHT: 150%;"><span lang="EN-US" style="FONT-FAMILY: Arial;"><p><font size="3"> </font></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 18pt; TEXT-INDENT: 18pt; LINE-HEIGHT: 150%;"><span lang="EN-US" style="FONT-FAMILY: Arial;"><span style="POSITION: relative; TOP: 6pt; mso-text-raise: -6.0pt;"><shape id="_x0000_i1028" oole="" type="#_x0000_t75" style="WIDTH: 14.25pt; HEIGHT: 18pt;"><imagedata otitle="" src="file:///C:\DOCUME~1\IBM\LOCALS~1\Temp\msohtml1\01\clip_image023.wmz"><font size="3"></font></imagedata></shape></span><font size="3">= </font><span style="POSITION: relative; TOP: 6pt; mso-text-raise: -6.0pt;"><shape id="_x0000_i1029" oole="" type="#_x0000_t75" style="WIDTH: 254.25pt; HEIGHT: 18.75pt;"><imagedata otitle="" src="file:///C:\DOCUME~1\IBM\LOCALS~1\Temp\msohtml1\01\clip_image025.wmz"><font size="3"></font></imagedata></shape></span><font size="3">.<span style="mso-spacerun: yes;">             </span>(7.3)<p></p></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 18pt; LINE-HEIGHT: 150%;"><span lang="EN-US" style="FONT-FAMILY: Arial;"><p><font size="3"> </font></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt 18pt; LINE-HEIGHT: 150%;"><span lang="EN-US" style="FONT-FAMILY: Arial;"><font size="3">Explain how you would use the Fisher’s test (F-test) to determine whether the linear model is the best or the nonlinear for the data?<span style="mso-spacerun: yes;">  </span>Name any 3 approaches to nonlinear estimation.<p></p></font></span></p>