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is the average difference in accumulated neighborhood capital between treatment and con- <br />trol, Eet_1 Em 1 [x � S] �pr (x, Bt -1) - pC (x, Bt -1)) is the average difference in number of <br />moves between treatment and control, and <br />EBt 1 Ex dj,j,-,1 [x � S] �pt (x, Bt_1) - pC (x, Bt -1)) is the average difference in distance moved <br />between treatment and control. Each of these can be readily calculated using the reduced <br />form methodology described in Section 4. The average utility difference due to transfers and <br />the average utility difference due to amenities can be similarly calculated by combining our <br />structural estimates with reduced form differences -in -differences analysis. <br />Deriving an expression for the utility difference clue to idiosyncratic valuations AUtm,Logit <br />is a bit more complicated. We have that: <br />AUiWagit = �: �: Et [Eitx, Bt -11 (Pt (x, Bt -1) - Pt (x, Bt -1)) (14) <br />et -1 .m <br />We therefore need an expression for the conditional expectation Et [Eimtjx, Bt__1] . Using Bayes' <br />rule, we get: <br />(' j�j A (�dmt+mt �.'°�Bt-11—"t�m�,Bb-1 �� d —e Eamt <br />dEi <br />,1 Eixt 1 1 '.Ax� E—2—et " E at <br />Et [Eimt�xe Bt -1] = A (xI8t-1) <br />7�j—e—('iPt hlOt-11-1n pt (-'I —Eg¢t —e—Ei <br />f Eixt l lm,�x e i®t � e e xt <br />dEimt <br />A (Ot-r) <br />where in the second equality we used the Holz and Miller (1993) inversion vt (x, Bt -1) - <br />vt (x', Bt -1) = lnpt (xlat— 1) -lnpt (x'1Bt-1) . Substituting into equation (14), we derive: <br />Dut aIL,Logit = E E J E;mt (ri E e (�dat+ln en (=lee-1%-'lu nt('�'Ien—li�� c—ei: tee_=intd.E'xmtX <br />� <br />0t-1 x X#x <br />(pt (Ht -1) -p, (Ht -1)) <br />(15) <br />Since we have empirical estimates of each of the probabilities, we can estimate this utility <br />37 <br />