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From |
"James Hardin" <jhardin@stat.tamu.edu> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: Murphy-Topel |

Date |
Thu, 19 Sep 2002 08:36:48 -0500 |

NOTE: In order for you to follow the questions posed and the answers given, you must have access to the journal article in question. Giacomo <gc4@duke.edu> writes: > I have two questions regarding James Hardin's article on the > Murphy-Topel estimator in the latest issue of the Stata > Journal: > > 1) with respect to the Sandwich estimator, I am unclear on > how the matrix Cs2 is computed. In particular, I would > appreciate if you could clarify how the relevant columns are > identified based on the variables included in the equations > (see page 260); I interpret this question as computational rather than theoretical, so I assume that the formula itself is not the problem. If I am mistaken, just post a followup. Generally speaking, I prefer to use summation notation to show the calculation of each element of a covariance matrix. However, when using Stata you are much better off looking at matrix notation. The reason is the power of the -matrix accum- and -matrix vecaccum- commands. If we focused on summation notation, we would end up trying to code long loops calculating each element. This is terribly inefficient. The equation in question describes one of 4 pieces of a partitioned matrix. All that is needed to get that submatrix is the code fragment (6 lines) at the bottom of page 260. Below, I will identify in parentheses the code identifying each of the 6 lines. The equation is actually the sum of two terms. The first term looks like: W' Diag(...) X where in the particular example, we have X = [age income ownrent selfemp _cons] W = [age income expend zhat _cons] To calculate this term, we generate cons = 1 so that we can specify it twice in the -matrix accum- command. We are going to end up calculating much more than we need, but that is OK. We specify (line 1) matrix accum Cs1 = age income ownrent selfemp cons /* */ age income expend zhat cons /* */ [iweight=...] , nocons The first part of the varlist is X, the second part is W, the diagonal part enters as weights, and we specify nocons since we explicity included the constants. The results are X' Diag(...) X X' Diag(...) W W' Diag(...) X W' Diag(...) W We just keep the lower left part of the result (line 2). Now that we have the first term, we notice that the second term looks like Diag(...) X If we put the Diagonal(...) part into a new variable dd (line 3), we can then calculate the desired vector as (line 4): matrix vecaccum Cs2 = dd age income ownrent selfemp cons, nocons There is now one last detail to take care of. The second term (now stored as Cs2) is really only added when we are taking derivatives of X after having taken derivatives for the zhat component of W. So, the row vector Cs2 is really a row of an otherwise zero matrix that is additively conformable with Cs1. In other words, we create a 5x5 zero matrix and then set the fourth row to Cs2; zhat is the fourth element of W above. The remaining lines (lines 5 and 6) of code perform these manipulations. So, only 6 lines instead of a double or triple nested loop with lots of bookkeeping. Read about the matrix commands. Look at the likelihood ado-files for Stata estimation commands for other examples. Make -accum- and -vecaccum- your new best friends. > 2) how would the computation of the Sandwich estimator > change if I compute robust standard errors by clustering the > observations in the two main equations? Probably, I should have included this extra formula. Nevertheless, there is nothing unusual about this modification. Look at the definition of the partitioned B matrix on page 256. Introduce a sum for every parenthesized element where the sums are over indices of the independent clusters. Since there is no cluster-type Murphy-Topel estimator, there is nothing to which I can compare the cluster sandwich estimator. So, there is no discussion of this in the paper. -- James ---------------------------------------------------------------------- James W. Hardin, Ph.D., Lecturer jhardin@stat.tamu.edu Department of Statistics, Blocker 416G 979-845-3141 (phone) Texas A&M University Mail Stop-3143 979-845-3144 (fax) College Station, TX 77843-3143 http://stat.tamu.edu/~jhardin ---------------------------------------------------------------------- * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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