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rents are lower than anticipated. We, therefore, instrument for the time t + 1 rent difference
<br />Rt+1 (j,1) - Rt_1_1 (j, 0) with Zt, equal to the one -period lagged value Rt (j,1) - Rt -1 (j, 0).
<br />Since Zt is in the time t information set, we have:
<br />Rt [Zt (fit W, O't_l) - 5(x, Bt -r))] = 0.
<br />Thus, our exclusion restrictions are satisfied and the parameters are identified.
<br />To identify the impact of tenure on utility am, consider two mature households living in
<br />non -rent controlled housing in neighborhood j, with different levels of initial tenure, T,,, and
<br />T'n.Suppose both households move to j* after one year. We thus have Bt_1 = (j, T,, 0, M)
<br />and 0't_1 = (j,Tn, 0, M) for some j E j and x = x' = S. Then equation (11) becomes:
<br />Y`�. = am ('rm, - 7-,n) +' t W , Bt -1) - � (x, Bt -1) + Xt3,.
<br />t
<br />In CA(SIj, 0, 7.)In 1 �A(j*Ij,0,7.)+ ,(31n � �pt+1(.i*Ij,0,T,)�
<br />Y = J -
<br />pt(Sh,O,Tn) Pt(j*j,O,Tn) 7h+1(j*Ij,0,T')
<br />Since both households live in non -rent controlled housing in the same neighborhood, they
<br />pay the same rents and receive the same unobserved amenity value. Indeed, the only payoff -
<br />relevant difference between the two populations is the number of years they have lived in
<br />the neighborhood. Thus, appropriately examining the relative probabilities of staying in the
<br />neighborhood is informative of the importance of tenure on utility or, in other words, of the
<br />magnitude of nM. Intuitively, as one builds up more neighborhood capital, the benefits of
<br />staying in the neighborhood an additional year. Thus, the relative probability of staying one
<br />more year versus moving away should grow if neighborhood capital is accruing.
<br />To estimate moving costs, we consider two mature households of equal tenure T. living
<br />in non -rent controlled housing in neighborhood j. Suppose that one household immediately
<br />moves to another house in the same zipcode and one household stays in the same home.
<br />Formally, Bt -1 = 0'
<br />t-= (j, T., 0, M), x = S, and x' = j. As was discussed in Section 5.2.1,
<br />this constitutes an immediate renewal since rents do not change and neighborhood tenure
<br />30
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