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equation becomes: <br />ut (x, Bt -1) - ut W, Bt -1) - In ( A (� t 1) _ [It (Ot-1) - It (Bt -0 (10) <br />r <br />r <br />\ t-1 <br />(ut+1 W , 0 / lxr' Ot-1/1\ -`Ut+1 U�, 8 (X, Bt -1))) <br />C ( <br />pt+1�pt+1 W,6VlHt-1/l1 V V <br />- <br />In », Q (xlet-1)) J + �t �x +Bt-1� - �t (� Bt -1)• <br />To fully remove the conditional value functions, we once again must remove the difference <br />in log sums It (Bt -1) - It (O'_1) . <br />We follow the same procedure as previously, subtracting equation (8) from equation (10): <br />In PtNot t 1)-1n(pt(7`Bt-1)�+0ln�Pt-pi (i',C(xet-1))� (11) <br />AVl8-) A(j*I9-) pt+1(j'©(xrl86-1)) <br />[Ut (x, Bt -1) - 4tt (x , Bt-1)� - [�'t (� , Bt -1) - 1tt (� ' Ot-1)] <br />+0 (ut+1 U*' Q (x, Bt -1)) - ut+1 U*, E) (x, Bt -1))) <br />+S2 (X Bt -1) - St (x, Bt -1) <br />Equations (9) and (11) provide a linear regression framework which we can use to fully <br />identify and estimate the parameters of the model. <br />5.3 Empirical Framework <br />We now discuss how to empirically operationalize the preceding considerations. <br />5.3.1 Constructing Conditional Choice Probabilities <br />We first need to construct empirical estimates of the conditional choice probabilities, pt (xI Bt -1). <br />In a given year t, we focus on those households who were part of the 1994 treatment and <br />control groups described in the previous section and who have not moved away from their <br />1994 residence. Given the latter restriction, we do not need to keep track of Th and we <br />therefore suppress the dependence of Bt -1 on this state variable in what follows. <br />27 <br />