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5 A Structural Spatial Equilibrium Model <br />The reduced form shows that rent control can either increase or decreases tenancy durations <br />depending on whether the tenant receives a buyout or eviction or instead remains at their <br />residence at below market rents. To quantify how tenants trade off these decisions and <br />to quantify the welfare impact of rent control to covered tenants, we estimate a dynamic <br />discrete choice model of neighborhood choice. <br />5.1 Model Setup <br />Each year t, a household decides whether to remain in its current home, a choice which we <br />denote as S, or to move, in which case the households chooses a neighborhood j E j to live <br />in. We denote the household's choice as x E {S} U J. The relevant state variables for the <br />household's decision problem are the current neighborhood jt -1 E J, the number of years <br />lived in the current neighborhood r,,,t_1 E NU {0} , the number of years lived in the current <br />house Th,t-1 E NU {0}, and whether the residence is rent -controlled dt-1 E {0, 11 . We also <br />have a state variable at -1 E {Y, M} denoting whether the household is in a young (Y) or <br />mature (M) state of life. We let Bt -I _ (jt -1, 7a,t-1, 7h,t-1, dt-r, at -r) denote the household's <br />current state variable. The transition dynamics of the state variable are straightforward. We . <br />have it = j (xt), where: <br />7 (xt) = 7t --r if xt = S <br />j (xt) = xt otherwise. <br />This equation simply says that the neighborhood remains the same if the household decides <br />to remain in its current home. Otherwise, the new neighborhood is given by the household's <br />choice. The implications for years in the current neighborhood and years in the current <br />19 <br />