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1 Problem Set IMIT 14.32 J. Angrist ( angrist@mit.edu )Spring 2009 Paul S !rimp" ( paul_s@mit.edu)

#u$iao %uang ( yhuang7@mit.edu )

&ue' T! eb 19

A. From Wooldridge: C.2, C.3, C. , C.!, C.7, C."

#. Additional pro$lems

1. %his pro$lem as&s you to use 'tata or 'A' to (ondu(t a series o sampling e*periments.

a. +ra !-- random samples o si e / rom a random num$er generator or a standard normal

distri$ution. %hen in(rease the sample si e to 32. Finally, in(rease the sample si e to 12/. 0lothistograms o the sampling distri$utions o i) the sample mean and ii) the sample arian(e, or ea(hthese three sample si es. o repeat your e*periments or three samples dra n rom another parametri(distri$ution o your (hoi(e e.g., a uni orm distri$ution). +is(uss the results o your e*periments in lighto the (entral limit theorem.

$. 4our e*periments produ(e 5samples o sample means.6 Compute the mean and arian(e o the samplemeans generated $y ea(h e*periment and (ompare them to the mean and arian(e predi(ted $y statisti(altheory. +oes the arian(e o the sample means i.e., the sampling arian(e) de(rease ith sample si e atthe rate predi(ted $y the theory +oes ormality matter or this

2. 4ou are as&ed to (ondu(t a so(ial e*periment to measure the e e(ts o a 8o$ 'ear(h Assistan(e program designed to help unemployed or&ers ind 9o$s. 4ou ill do this $y randomly (hoosing n 1e*perimental su$9e(ts and n 2 (ontrol su$9e(ts rom a pool o n 1 n2;n unemployed or&ers ho eresele(ted at random rom the population o ne assa(hussetts.

a. Find the (hoi(e o proportion treated, p;n 1?n, that minimi es the sampling arian(e o the di eren(e inemployment rates $et een treatment and (ontrols. %reat n as a &no n (onstant).

$. o assume that it (osts A dollars to (olle(t data on anyone in your e*periment and that the 9o$ sear(hassistan(e pro ided to the e*perimental group (osts dollars. 4ou (an (hoose any sample si e n) $utyou must spend no more than dollars on the e*periment. Again, maintaining the assumption that thereis no treatment e e(t, sol e or the alue o p hi(h minimi es the arian(e o the treatment?(ontrol

(ontrast gi en the e*perimenterBs $udget (onstraint. =nterpret your result and (ompare to part a).(. Why is it use ul to do e*er(ises li&e a) and $) hile assuming there is a(tually no treatment e e(t

o er)

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3. %a$le 3 in the Wood$ury and . . 'piegelman, paper on the reading list reports the results o t oso(ial e*periments e*amining the relationship $et een