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difference. <br />We finally convert our estimated utility differences into rent equivalent dollar amounts. <br />Consider an individual in the control group who pays the average San Rancisco rent in year <br />t, which we denote as Rt. We now proceed iteratively. The dollar rent equivalent OWRent <br />of the utility difference DUR`nt in year t due to rent differences can be calculated as the <br />solution to : <br />which gives: <br />YM exp �Wt + OWRont) _ M exp (Rt) = AUR,e at <br />( <br />AYVoURent Rent = In t +exp A) — Rt. <br />1'M <br />The dollar rent equivalent incremental impact of transfers can then be calculated as: <br />P°veii _ _ <br />OWn"y°ff AU <br />=1n +exp(Rt+AWRent) — (Rt+AWRent) <br />GYM <br />Now let AUt I'° denote the utility differences, with t E { 1, ..., 7} corresponding to the ordering <br />in equation (13). Iterating on our procedure gives the dollar rent equivalent incremental <br />impacts of each element of the decomposition: <br />AUPayot9 <br />OLVt = 1n + exp CWt + AWtl � — �Wt + E AWt, <br />GYM e�<c L'<L <br />6.1.2 Results <br />The results of this decomposition are reported in Table 5. We find that the beneficiaries of <br />the 1994 rent control law received large welfare benefits between the 1994-2012 period. Older <br />households received a total rent -equivalent dollar benefit of $119,625, reflecting an annual <br />benefit of $6,646. These benefits were front loaded, with households earning a cumulative <br />benefit of $74.514 and average annual benefit of $8,279 during the 1995-2003 period Cumu- <br />lative benefits equaled $45,111 during the 2004-2012 period, reflecting an annual average of <br />38 <br />