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house are clearly similar, with: <br />and <br />Tn (xt) = Tn,t-1 + 1 if xt E {S, jt -1} <br />T„ (xt) = 0 otherwise. <br />Th (xt) = 7-h,t-1 + 1 if xt = S <br />Tn, (xt) = 0 otherwise. <br />Finally, we assume that each period young households transition to mature households with <br />exogenous probability �. This is clearly a simplification, made due to limitations of the <br />data, but captures the idea that households experience certain life events such as marriage <br />and having children at different ages.12 Mature households do not transition back into <br />young households. We denote the (probabilistic) transition function as Bt = O (xt, Bt -1) . <br />We identify the set of neighborhood locations ,7 as the San Francisco zipcodes, the counties <br />(other than San Francisco County) in the Bay Area, and an outside option denoting any <br />location outside of the Bay Area. <br />We assume that a household i has the following per -period utility from their housing <br />decision: <br />u (x, Wt, Fite Bt -1) = -ya eXp Rt (i, d, 7h) + n'aTn +W a, (x, jt-1,Tn,t-1) (3) <br />+ A (x, dt-1) +wjt + Est, <br />where Rt (j, d, Th) denotes the rent paid at the chosen location, tpa (x, jt -1, Tn,t-1) are mov- <br />ing costs, At (x, dt_1) are possible monetary transfers from landlords to tenants, w t is an <br />unobservable neighborhood taste shock, and etxt is an idiosyncratic logit error taste shock <br />12I11 principle, we could tract the exact age as a stage variable, but this makes the state space very large. <br />