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rent equivalent terms. However, these effects can add up to a sizable effect over a lifetime. <br />6 Welfare Effects of Rent Control <br />6.1 Welfare Decomposition: 1994-2012 <br />We begin our investigation of the welfare effects of rent control by decomposing the impacts <br />of the 1994 ballot initiative on its beneficiaries, relative to the control group. We discuss <br />here mature households. The expressions for young households are exactly analogous. <br />6.1.1 Derivations <br />In any given year t between the years of 1994 and 2012, the average utility difference between <br />the treatment group and the control group is given by: <br />DU° _ (ut (� of -1) + Et [sz t x, of -1]) pt (x of -1) (pt (ot-1) —pt (ot-1)) (12) <br />oz_, <br />EE (ut (x, of -1) + Et [t ,:Xtl x, of -1]) (pt (x, of -1) — pc (x, of -1)) <br />ox -1 v; <br />where recall ut (x, of -1) = u (x, wt, 0, of -1) and the utility function is defined in equation (3). <br />The expression pt (xl ot_1) again denotes the conditional probability of choosing x E {S} U,7, <br />given that the current state is ot._I, pt (ot_1),p° (ot-1) denote the probabilities of being in <br />state of -1 for the treatment group and control group respectively, and pt (x, ot_1) , p° (x, of -r) <br />denote the joint probabilities. The conditional expectation Et [Eit,l x, ot_1] denotes the ex- <br />pected logit error conditional on choosing x from state of -1. Of course, equation (12) simply <br />says that the average utility difference is the weighted average utility received by the treat- <br />ment group minus the weighted average utility received by the control group. <br />We can decompose this average utility difference by substituting in for the utility function <br />35 <br />