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are of equal tenure Tn. One was assigned to rent control status in 1994 and the other was <br />not. We examine the relative probabilities of these individuals staying in neighborhood j in <br />year t, using neighborhood j* as the renewal choice in the manner described in the previous <br />section. Under these assumptions, equation (1.1) gives the regression: <br />Yt . = yM [exp Rt (j, 1) - exp Rt (j, 0)] + <br />+A, [(R In Rt+r (j, 0) - In Rt (j, 0)) - (0 In Rt+r (j,1) - In Rt (j, l))] <br />+a2 [a (t+T� + 1) — (t+Tm,)] <br />V <br />+fit (Xl' Olt -0 - d (x, et -r) + Xjt,j" <br />t <br />In Pt (5l9, 1,'rn) In Pt (.7*�j, 1,Tn)� +0111 Pt+r (j* 1j, 1, 7n) <br />Y = - <br />Pt (5l9, 0,T�) Pt (j*h, 0,T.) Pt+r (j*lj, 0,7.) <br />Intuitively, this regression compares the probability of staying in the neighborhood for one <br />more year and then moving to j* versus moving to j* this year. This difference in probabilities <br />is then differenced between treatment and control, which differences out all the utility impacts <br />of living in j vs j* other than those which are impacted by rent control. <br />Note that we have included an additional error term X',,., reflecting measurement er- <br />ror in our constructed conditional choice probabilities. The key for identification is that the <br />unobserved amenity value wit differences out. We furthermore know that: <br />Et [(Rt (j, 1) - Rt (j, 0)) (� � , Bt-i� - � (x, Bt -1))] = 0 <br />due to rational expectations. That is, the expectational error is uncorrelated with any time <br />t information. In general, however, we do not have: <br />Et [(Rt -i -t (j, 1) - Rt+r (j, 0))t (x dt-r� - � (x, Bt -1)) 0. <br />The time t+1 rent difference may be correlated with the expectational error. This is intuitive. <br />For instance, neighborhood j may be better at date t + 1 than was expected since market <br />29 <br />