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Now assume you additionally obtained data on average parental incomes (PI) and the ethnic composition (EC) of the pupils in school. You regress the score on

  • STR
  • PI
  • EC and
  • a constant.

State the main assumption for consistent estimation of the coefficient on STR. Assume a linear setting and sketch a proof for consistency of the OLS estimator for the coefficient on STR.

Normally, I use matrix form for this kind of question, then how can I prove for only one beta, I was thinking about Frisch-Waugh-Theorem but i cannot move on to proof it. Any idea ?

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