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over the possible choices which is specific to household i." Note that we are suppressing the <br />dependence of (j, 7, d) on x. If a tenant does not live in a rent -controlled property, she pays <br />market rents, given by Rt (j, 0) . Thus, there is no dependence on 7h. In contrast, the rent <br />paid by tenants in rent -controlled properties Rt (j, 1, 7h) is a function of the number of years <br />lived in the property. Crucially, note that the household has utility over exponential rents, <br />with coefficient gip,. We, of course, expect this coefficient to be negative. This assumption <br />ensures, due to the effects of Jensen's inequality, that rent control offers real insurance value <br />to tenants. We moreover allow for utility to depend on how long a household has lived in <br />the current neighborhood, as measured by parameter aa. Intuitively, households may build <br />up neighborhood capital over time which makes that location more attractive. For instance, <br />over time people form meaningful friendships with their neighbors and acquire valuable local <br />knowledge, such as that regarding local amenities. We allow both the rent utility parameter <br />and neighborhood capital parameter to depend on whether the household is in the young or <br />mature stage of life. <br />Households incur moving costs when they switch homes. We assume that there is a fixed <br />moving cost W0,. > 0, as well as a cost Va,o, > 0 that is variable with distance. We allow the <br />variable moving cost parameter to depend on current neighborhood capital 7,,t-1, with the <br />interaction effect measured by �T.a This allows for the possibility that the desirability of <br />nearby neighborhoods changes as one accrues neighborhood capital. In particular, <br />(Pa (x,it- r) = 0 if xt = S <br />(Pa (X, it -1) = �00,a + (Pd,ad (it, it-,) +WT,a (d (it,it--r) x 7,a,t-r) otherwise, <br />where d (jt, jt -r) denotes the distance between the old and new neighborhoods. We allow the <br />moving costs to vary with age. For example, it seems likely that households with children <br />will find moving more costly than households without children, since changing schools could <br />13We measure rents as monthly rents divided by 3000, measured in 2010 dollars. We divide by 3000 for <br />computational convenience. <br />21 <br />