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02-fixest.html
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<meta name="author" content="Rafael Felipe Bressan" />
<meta name="date" content="2021-10-08" />
<title>Regressions with fixest R package</title>
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WZWHK5LZgl9279229we2OBUX50kuVjv5QDo7PBwnsvrhWJF%2BYDIuVagZDxeFHOF1MEKbsBMEQS%2BKJjOVdXJ1BKw61EH%2BfeqSTzTz3I7ZA3Zuv%2Bwhshy3sDFL2TjctJR6n2SDsfFJ3A0I5ewXfAgugw7s%2B0XQG0SAfFVWHOEsr6TyphSHW5NHFc9J6Wa%2B7B3Dfp42HguHAUINniPlZCpQ%2Fl0CogDIrW%2F8u85iv7sGv8ZzGzYAxjwV%2FMCxTwobJQCTWU8HRPQeruaaXpRqestVdUOXso7dupeF7px4Z8%2Bed3arKFc44AIg51W9ch4kIIiUEocmSk4sBpCcj15oUDRJXYYExl37RmirrkIv55rLASYJJF%2BS3t0nopeptU%2BE%2BmLrLK%2BlPgQyid3mCBU6UP1rVz8R2n770zc%2FXf7x8s%2FNn9fvaFi3rmFHPfmMLWRP4lycho%2FjNPY4W82Os88wiJ34K4tdAIQjAOQkx8YArcM2PaAOjSZBL8uolzAJFFvGDXd8ej67P2AvKpUkOYghcnK7zl300RBcsExwzJ%2Fhbrd7GuYBwhgAIYtbTx%2F3%2Bd4klJ3gtKCQnGIz9InYZEzqG8EkjSzNavCB%2FcXYlcQshhyMsZrI6PYLWc3lOG%2FvlA4rHr%2F3uTFD3r38%2Fr%2B3fMKOke9W4oJ9G566u7au84CpOz%2Fct5R99wF7W6dIYjjnawrHIAh3hlungFOWgXoyzVKbHOr1eD19Il6vISsrrU8kSzbY%2B0QMGpdjgYh60zDTHJKHoyP4404pw27zB4o1o62gq%2BBLL299am8j%2Bzv774zj995%2FdgTOZsOfWr3rnTWPj2h8qGbo1%2FM%2F%2FkYYvmxfms7TtPrM54E7ns4vwBw0rFy%2FaNJjRRVTet31OgCBPABhongUDOCAzuE0h6gnxChToCJ1ulB0iH0jeqvscFBZotflk%2BhMQ5oJDqhrC%2Fl%2F%2FFxmAUlGYeK5Z6Jl5MDec2yJQdc%2Bl5ViNduL1avoZ805eGll04jy6COKheT8S%2BU6kQwdw%2BlW6nPpXF4qtEoBziwAye3mMnRLkqlPRLqZdQlsKxTcLghkqhzjrLL5M%2BWgUwldSkjbL1HPLrCf51d8MHbv66zu%2FmcGl5Kz0YNZ0%2Bmcf759kbEB29qGGrZiYWop2b2R9fYqnKnlWOVzqXqgNfQIB5LtRr8fQLLT7CyT0ZLaL2K0WFzU5e0TcfmojkckcgvcyhJ4pNlr8Bd63VyEhIbiGhfIBFGTq8R9lqcWB2Dl1G79Rn%2F9i8n08OU3L%2F760UX2E369YuvqVUPrI9VryFR8CXc5V%2FrYefbW7svv%2FYNdxUHv%2FOnFVQ1V8yse2Dde0UcAIY%2FzU4L0sA1FEQg3jJT0jVAJFBlqbOOrALk1dCOmkuHNF%2BmpaKOYunHhldNAlZhEyFGpz4R20C%2Bc47Vmu%2B6gqXo9lewuq5TfXrLnZORk9Ink5JjAlNwvYvJBoF8E5N8qd9nN3jrmj7mOx8OPLDXqolpgwv0zZkpuzaeTynf%2BvWjNvnr22b%2BbsfDJR7%2Be%2BcL6dQ1bXlu3CDvOWfHIMytnrhJPHt7x4L7eg%2F48%2B8C5U0euLuu%2Ff8ozr1xteHTRssdGru8V3kwfeHTMsN937%2FzksLEzFdlO5NQpNsMLWdAtnJlizzQYAAQu26AljUvWZbEQlyuJi1Ymcr8Iaal2jjKNg5qJ9Ctqx02jMyDFKHJw8TpUIvjHKhXZQlZ0%2FIwe1eO%2B%2B6%2FRVHpg2mv%2FuPbBuguPMtfKLU%2BtuXfjkIFraEVzg2tlMuZg6O57%2FvXBP1C3kZ3H9od2PPV81RMVE%2FaNAy3HEcaokRS34Ta%2BLAA8XotzQMRiizkRDVfN87X0JXae6NzkVR6Znehb6J8XL%2BY3IKovXMjn0oEDMrkmmc2iXu9yGm0DIkab6hgTZklwj%2FT6FDccpXsmn6Rjlxv%2BknyrTFMR8%2BU%2FcF9%2BDiRwh%2FUCiChwdeXD58cDhSwsRjeikNNcTo83%2F0AtP2DDKLywji1nhxSezMTjgo9eVHOy3LBbJgIQ0OsEsToiIFRHrIjI4wHOlfxEz6a4ZOTXTLq9eTjdTofW1bEH6up%2Bg5GIBDhGEr2BkRNVlMZTa%2FP3HKVyrMMKrF3H%2FKPYUAWjlGsXaRnXrxTIhrJwqp%2FbMtnphFYWIdgGoLWtddqASGuPzdA7YhNaqFZLvVJSEa48LZwUd4YSN4mJ%2Baq%2FctSSXgtmD6gf2emV91%2F9KNj38bHd9l3PX0tq19dMnzFw3OSsgsWjj%2BzqPXn0w4On3e9nZ%2BNJLYFZ1yqkQ2ITFEM5zzwyA%2B1KLJ1kVwpAjsvSTgx3S%2BrQQeiisxv5Ky%2B9kGbnqUmllmSFEhOP6%2FG4ug6C2nJQUPdSt0td36R1IFMgbsUalrqlQAbw4KK1v1BwIH%2FudKqm8NCQbeMHP2LUtVk3rv7Fb4712N3Tt%2FDeaWvZt3%2B8wA7swe6Y%2F5cvjv3I1rHJn%2BAyhLM44ODVn14%2F7bBUDpq%2Fhpxb8c388XfdM%2BrU3veu%2BTws17Pv7O79aFvzMnvxc3aaHRq8sAZX4jgUsP7CfvYntoNhGYquJiAAAKJNPAIyWLjk0ojFqENR0SwqyILNaiG9I0bRYhFECoKD518xh6iplZYz%2B5W8H0OIlBsz%2FtURB6IHmnaT7itJORvb6A94cnbjGZYvHrnSg0zENwfPGTGddQIKJwCEo9xyW8ALGdA7nO0UUg1Wn89iEGQLjwd01iRrUlXEarWAxVcVsTjAWxUBevt4QnM9%2FgxBMbluwe4SAjxpj%2FmcgN0ef3cCt2IAhVVLsR%2F7%2BTIjjZjU9PTeY1ew4I9%2FOvhn8cCeI%2FNf9BnK2Pk3%2FkZ7TF00%2B6HoquhndauXPAGAMIdb09Oqr8gOu6jFpbdQb5IDekccglHi%2FHK2DL%2B4emRymUNIE3%2BRo3WokKfbtNP37Cs0%2F7rxjQ0X2Cvs2Rex%2FNNLuysbxBB7lX3FPmdvl64rwyU44QusOVSzuj8AUTgmDuEc04FdsYcWQQ8COJyiuSoiUsFSFREct4ppwc9rSBlA%2BZuAPZTBx2Az2Uo2CY%2FhIHysic%2F1z59PI%2FdU5CtWz%2BaJB9gi9gKmYebVKZgHgMq89Bc%2Br1GJWSSDAQXQoWAyS%2FreEUlCQsTeEUKRr3B03DZmUZBwxy%2F6S%2FMZmh%2BdTYZHt5OF4oH1LKc%2BeilhJj0UhpMlAKQ6pAbjTRPxSW45Q0CbAac3asPzwaNfrY9LTuyi2ilOhUvnI8SSohNapUJK7wiAaDLZe0dMgujtHRGdt4%2B8%2FHaphRyV9%2Brq5lT1xe9nfPc0a2IrDuKQL%2F%2F9bve3DrL%2Fso%2FQj0kbVrGXCYuWZWXjUhzzD7xn%2F%2BD6GvYau8Q%2BZe8H8LUY7WK6yuVQ2KdHBJ0giCCaTTraO6LTiQaJoshJV81RgnG%2FQbydi5f%2FDYnpjc2ssZGSRrI3Ws1z7dXkYQC8NoLNxfFqVpwaNht1OotVT4GzFDJj9GrpGI15%2BJJiPpxLMg0v6dVv9AONx9jclFWuR6fyFGvI0TNxvRC%2BUjHmnkjBViRGg4Ix0Yn6RGzLWkgJZRVRDKHw1TvRrzc2NpL1J6JN5M0l0dc5snnk4%2BjCBF0QIT1soQCCJCMFzgtw3EBXxTekkO0%2B0aio0pV%2FbIp9V%2BKIgpPrUZJOFCUev%2FJSmsuNBjuVjDK1gKQgp2DnLbuZlRjwuJUAn2MY4nce4COtZjadZSsCntbhh6zRomMm0bbpo%2Bbh4oGrVQLPOume7Uev%2FBCXo1IDsUG7sFsvcaytVpDB7jBS2aqjKCdypaUI4xPzabNJKZdj%2BWvNn%2BtsW4%2FRVB2xkGeEk582NR%2FnE3ZMwaxy2guAqFp99FZ5bu%2BIXqDW3hHqvLVNiOltBiTmueJRtpW9oZgjHIE9sBOOujo9%2Bv1%2Ffvn5h%2F9Eeb77LHuYa%2B94HIt1bArbxs6yU1iIuRjEAnYqZp%2BE8erqdUBRONnA%2Bc75DE6XQaiKGAySLDuqIjKVEtavhpXmSgW%2FmlplYChutYXx7Ay7tLsRZ5PWUePGL949euKoYPr7t1HOh2jK6mdXrVC5wHaoXLBCCp%2BZp8MeAIEa%2BOqmZtns6x0xC7KTL2yZM%2BMtlRs3J6I2pViG8q258sX7OOxndrH0tpz5ki3rzuqxivyf%2FDnN%2BWMCN1SGs8yIxKS3y0aDQdYTwePVm8EMVRGzmVDK5UepkSi6cntnp2Ku8ktw20SOf5bGNm4BcRXyGdhfcfkJ9jQ7%2FVXTzl2vfEZGRLeJB94%2Fzf4%2BLjqZjFi9cuWqJwDVHIFw29ha4V6a0wSQ5BSFrGxTGvV4uH30CFSfoEoJiY4mt0CGlozy8D%2Bo5jgx%2B6jmBbwy4BEI%2B9d3rHnZ0I%2FGN%2B7usnL1ey%2BxM389WLx%2F1%2BINHRbWXfoDLjz%2B6Z07su%2BYN73vyIFFvd959sV3qtf2nfFA35F3FQw8AoDgABCGcv7JvJ7iABSRUp1epgK3CYLmFeJ5qGYSi7k3IEsbWYFQyQrE9PWqJzjM14yPj2OHrLDdhgYZZafDrqOCmQ8UpzGUuFzsLkUnVHMYs4uij%2F2F%2FcJfFxrfee3ld8QDzf2vsC8wo5nuaa44%2BMabh%2BghQAAA4XW1%2FpMcNqJgMuooCJQqiPLlrxWvQhjgF8%2F%2FSgXTwej3O6M%2FNmF1x8zWHdVaFh%2F5uU3bnwXkmg1yXz6aT6km%2BQwpyW6LRdQn2Q0U9TGTotqUGOKqNclWAjJldKcyenwSZ0h8cyc75y5CT3v2xU42u%2BnL9p6UYpSa0Nne7yy%2B1EQ%2F7PaW6%2Fdbm0N88llHNx18ic5qnrv59RXv0YUK93QAQr1q9QNhhyCJ3ORLiskXFJMvtDT5KhocAz63Yu7rj%2FPIY0oTXmKdjuAkfHg%2F60QWROeQZnI4%2Bgq5M9oX4lybrUY5GWGrIBJRpnoDiChTUeOcJmE%2BqKL%2BGCJdcNEhlrSb%2BQ6T8%2BR887zoCZJPFyv1ZQBBscZ6pWKmQyqDLKBgMIoCNwcUdUrMcuuKmVot8AvlzU6qi9roq82%2F0LSFwoaNC69OAIQGdoRMVnSRY2mRUFAYoxcJlTDIOdBSfeJRD5nMSvEEu4B%2BdkS6svyKX6HWC0A%2Bi1c2Kd5c2XRy3h0mgYbo%2F4spg%2FKNEDuCzdrMFFACSacHOUgFevPMXj5rMb9CfMoLfOrSA%2BKF5b9KyigFJCgExOMgQVJYD1TWiQQEwrO%2BG5rpVFUTC3DfaPxsA1vG9pEg3dQ8jnwV9QJea2Zv0k3XKtUKsJLHIlEqwBgjmU%2FLQUfRp9mbCwCxTjhHHZIf9OA8AILRID2BkJ%2Bs1ZoxwDW1OMStBHU83G1fm5MZ0%2B4QzhUdK3f33F8MRKk50lPCUEXzoVc4K1NnTEvz%2BRw6yqMpYkzrFSFGI7jd1ooIt4LJFRHRA24o%2F98LVH4tX7NllapJZ7zS6LZn8QVeLKsVKjrQrxv43GPPvUychyc%2FVveH0F3HR77xCrNs%2FmPDWy89tOWB3js3Y1%2Bb1GPe7Jq5dxTuORZ11TZuHC3LD00fOhwI7OVWtVZygRPSeVUt0%2BD1Wq2mVGqiGX4zmNwOu8HOhccRljzgqoiArYV5DSXF1SDB1sddEk825YBijeRQiVcrvHAqyJ5Pv%2F3%2Bk0l%2F7GwKzGzQ6Wa811i%2FqXFjfb0wlJ1jP%2FDXxwMGLpdcbNHcsTuWvv7ll29fOPPJXwAQpnMOLxWGxbIaK6VuPU3ySmaOmQ0cHDPPzVmNGM9qlJ1DHgNzu6hmOGTcZXYV9f8d8HTbUOn8QrbvuW11Tz3swiw0oRPvyPQu96Sywe9%2B2mlNGRBlVqGU88fB%2BdM97E%2BVvGCx2CV7ht%2FhtgIgmqhez9mjt1FnRYR6bscerSYTkLTqvTcUDPLPA6osi%2BJOiG7ST%2F%2Fn2W%2B%2F%2B%2BTCTLMsNCxmTzdu3Ny4evOmNS9gNlr5647tA%2Frh0V%2B%2Fmfny%2B4Gv3r54%2Bi%2BfxLF0cN44IRk6hdOTDF4jpdzqtkrxGit4uRskyaUyyqIw6paZQyiRZQ632%2B%2BJsUuivNbh53Kb%2Bx%2F2JYp%2Fe%2F%2B7qFl8eecf%2FzBk65bfb7WQLstc2AZl1GMH9v3fJxx%2Fp2pttp%2F%2Bc%2FeGrS8oUksFoBYpHVxK3cVlMjkJ4UaSuj0GvhQMgKIsVkScspUqq0GtY98IAxWmOZS1p2QNgeJSXkPW3DX3mE%2BzrxreeANH3lObN6LH8KHopW83l9G3%2B3TugmsDC9PnPNkLgEKQuYQCzplcKIVu8HC4a56vQ5YpvYtY4ESnSHIzW6Vn%2BQzd72xlLbYWV0R0nXpFDJm6XKvOqvPk5pJekVxrm%2FJekTY2T7teEU9KnHUa%2Bzj%2F8pXd%2BrzbxD1uragaVBdAqDC%2BjaAUkrJv%2FOXKcGMXmJOnbhQXF%2FF3QsHJVnf87VhB3sSqoa%2Fte5X9jf3r7FdPzMgtC%2FccNOnTtwb3ZPb6ZWdOPLzh7amPD50%2F4z8%2F1T4uVE5ICkzt9ewxXYdBbfPqVx54ddvqMauTndXFnYfmBnY%2B2PS66ypEhs2ZFOn5IO08%2FZFvfn4cEPYCCD24nnuUzM5i0nFz7dF7vEkWvcMhVEQcNgOA3q0Y7xjlCatesVT2mALbtRUfM1P06cfm%2F%2BGZhgadoWD%2FjBMnyJuLfn%2Fkk%2BjrfHXnDOow4N5XP4gWAxDYDoDjxAtAwcr9tZ3PJCDa7Ga5MmImVlQ04%2F3EwqZSIqAJJVQc3NDQ1CG3TceObXI7CJWYU1Zc0qFDaSkAubaKudSxTZAEd4Q9TqPRrNP5kj22yognrLcC1z6ISzW5xSTOhATTljhb3v2det7Zv%2FeNGZnLt9g16B6h%2BaqNHZHv0yaP8TSV89QGJTzetxgMRqNOEkSdYHeYAGw2nY7KRje1xiKGfD5zeUyFyuJsRTUiQi0bdclYkzcER73JeuD5E2zOnB07dKSgy2icydpGlxLpQTZOcjW%2FXTo9NjcO5nNT4GQCoiASQHfca2tMVBjHYVRo6SRfJQGoCAfcdruDiz%2BgdwRo66xWHrfb4RPMPm5p0302p1UPDkUPuCLEt534Igi1bHVIVIgEzfAqepHh1bRDypryyOa1DVNmblnVsDhFl79rIuIAXcHhmYdfJicWLNj3cnSLcv%2Fzx9HjQmV99dDDg8e8%2BheuMZq2cnxdUBBOApeiri69x23S22xcWW02g%2FV2ytpSV72Jmrp7m4JG6NDUt95RNPXwJ%2Bq8d0XUSWM2dhSfU9EknsU6wSyDnOwzeLgds1GbYvxvmcVylSHFilGFxE4PYRT74fKaf%2FwOTZcvobX5lZ3PPffii88%2F10Cy2I%2FswyeR%2FAFNmMfeZ1f%2F8rfzH545p1j5vdyW1apU%2B6E8nOEzCrKsS3foHJkBwQhWq7siYrXprboUaHXDzMdZ0GLBqpaeO2hPAhMUr62Y%2BgRHrThpU8Niry7c%2BPBf%2F%2Bf7yzvryabGFc8%2B6xowcMRg1kUqqh9azT5h%2F1GcNr14%2BGTWl29fevfUeYVXHNNSlVexqMKW6qHJyT6bL8OfnOK1pqalecxOp8wtv80MFRHz%2F%2BY2VT5yJ1l63Ul6r3vQ0njtQyL9GzaIW15cvXnjnI8uf%2FfJ57P0SQsajObpM%2Fd9mHXp3YunT59birloRDO2a6z%2F9T38eEzFCzE9okGOpw1ywy6zXm8wEF4DsZrB4FYtg03rc2nRkaE5IY15ZEfvjt4eRQtfaahz6rrsFoaZNlk%2FfTbaJFSenDQjlrnS6XyW1twOtIplrqLzeuZaEfHYJKq%2Frj%2F5t8pdueG5kbsG25Hfpq50%2Bj%2Fe%2F%2BtjA%2FbXzF82%2BdmN88r%2FevSPL3Z6ftEjj7Yds%2BJ13jSzsaHnpjbt7h4Uvrdr2aAH%2ByzaXLm4R1W3O7p2KO71FCCkX%2FuG7BQrwKPWJlwu3jPioEKS1%2BC0OXtFLGGbVeaCkj1xU3kqIVjV5ONWqo52xVGXhtxKNuHyEMcdA5NSJuSy17ZurRiBXdlrw2vN8lyzHQeQZdU9%2F83mRWePngiAsIOvrjKhElx8fh86ZZPJ4DS4PSaz2aZzWdVV7TFqEbMS%2F4daVmW0rJcrhBY127EvX9TPNNQl6UP7Z7zztlAZLeMO6GMSvnpozV2Dj54hp7RcjgiVau%2BHAQ0ms6hHK6jhiJZl%2BNX0NFTicIYQt7ER%2B76ptuiMte%2FtYyP4oI%2F8o0cx9iPtrx6K5UpSgI%2FWinsblz4lNc3rsZipYBZ0yQ7ubnTuxCyYK7c2A1U2Z2Rlk8LhUHSq1BmbsoRPKeSfcBbp2qSdPsY%2B3jNxsk5nLHCcaHqjg0snBF7dzc6QBZ3OvHR%2FdK5QyUaz6j5l%2B4tJbXTp7trW9eRvHClACAIIOpXGzLBdFiVAUWlxQZ3RLaD1pnQ4ngmjmhUfYgteQT9m%2FJktwFVH2Cn27hFSQLxsGO6IfhU9jUdYD0AgfL1LfHw3z%2FsVMqnHK5jB7OBLO0UHfIJCVam1GRJo46KKOdrSUrLvuwFOnfnuS%2FtYTsWfl%2FStKu2xq3cXzuCVn9wf%2Bpn87mrGy5vtC03HtkAsZ6YPCZW3yJl7RUQr6npF0P2%2F5cz0oeZ%2FksHR0%2BTL6D5y31Q6eN685sPxrixetlPl5%2FYlJxu9AFbZRbmnpqlpTq09K3F7TdV%2FbpXcPJZTfEtxCddDvj7d3EK4ZLfHjedrpx794PFH58%2F49MClCxdM44aRZaRxE%2BaPjywnw0Zg4ebdS6Xj7NzZoCl4FhAvMxuZrfluorSo0RSABN%2BtlHzx8nKeJv3cDAiV7Ijaw5Oq4OwWDQ4H8UFqqsXiE2laujso0QScEzYFFXSDxYr7U7DPVNCV5Dj2pcRw4eKhDx%2BZ%2F9jjp45OnvHwVFIePIvB49LSPRvZ%2ByPvJcsjvOq5cRenZNg4zJn2qEvdpyXVQg6tAS%2FXAzu1JvkcpuoIdVglCaojEuTngS3pjfw38rSkOlOZT8nQVNOmbD9lKoU5HFg8t2TMUz2mRrqPyi95omTcisrHK%2FsMJSfuLFn%2FUKvsVinhsvqH%2FRkZSeoOPFuKdcJwrcuYCALV8343AGpSu4xtNPOWXcZcCQNO1%2FXt0PNKk%2FGszp3Ly0IVZPfVC2Lfxb3C5ZVhQDjK7fd5dVemazjNozNTahCARxo62irVJxKnwUz4SzDKgg%2B07k9ljt9sw2apra1KOJCldLR6NAOuqD89OWHNwpPHcdniPisKChY%2BtHv7My8sX%2FFdifTO%2Bxlov4LNXXfvoH7vstCH5z462QkQypUYSDzBpV4Zzk5y6s3mZI%2BdGD1OMS3dlORL6h%2FR%2B3xOcNr6RpxJIPa5uRWkRdPQzZ6Nm29lf5Lfinl2ypuduEqQxqONXTatnD0HG9jQblU05erVU2%2B99f%2FEEzUL%2B%2F1uGTs397MxS%2B7YtDz%2FxwtzsfO%2BU4psZqMkeIVtnHNByAibW0GmBSxtctLd7iwZeNSYn1gJchaVBku9il8r9co82Ja9clCxDnKwNLs0IXQ6VLV4%2BOLx8%2BeOq7t%2FUVXVgmF14%2BYuGrN42MKqeVtnzHh627QZW8mHj01aNmxh794Lhz059ZEFD%2FCHvfj7JZN%2BN2XbM1Onbd8BiscDEJT9Fw8MDrdzWGSj0WYS9URPTS6LW%2FYmGSwW2So5HBScbqsz3UmsTqvThG7JlATlWg%2B33RHrzL7lpjuGUOGj1uaovjBEKnH2HjYCJfY6dmGv72BvYGd%2BARu7j1wgZ5vZ3Ma57Ec08RslQBKsgaxUVYkkUR726QUqUDlmFjgmiYqtbgjFLYRiI5p%2FYebmnxVpXPuF1kupUABdeGdcdiE4pdy0Dj5fmkmCgNS13E07lbRqK%2Fn1%2FmCviN%2Btt%2FWK6OGGznh%2Fs4t9I39VVFmLztSUlwuwZdCiRC2l%2FKk33lG0dHD%2FqprTbw5%2FZmTxqMV9Z8yYvelw%2FcCqjf%2F%2B6K9P9H9t4KLl7R%2BcvmJR99W%2Ff6Ggbs3LPQbRnMF1WW0mD5q1NDW4IJjSKdy5prTH%2BklDl%2BfctXrZxm5rs9r27dWuY8e8oqHTRvWb0MVZPfnuKWXOMUCwWLTQ8eKH6u5TWpiTanKAI8lnpW495N90QCAhzctKeI%2FFxVnZpaXZWcU4pzgrq7Q0K6tYnFrUrl1RYUFBYfwOQGEM7xzvEdt5hxKeSwWDXmrNT0936a1esbSDZAKH1ZRuIuCwOYjJYXKk5AWcoRQByhNPBdhblgFRMxHuG90bnN2obu8KDjc3eYHM1py5DiFU2NqhNXTQOXMWz10weE77sRWvffDZq0880vHB5vXv4PB3les1tv2D02z76xP2YNvdezD3pT3s7N497JOXhMCeTTu3t%2F2dq9X3n575qfMjIXZI%2FQ7b%2Fu6brOGD0zj0rT%2BwD%2F%2BwB3P2xr8GQKCCushU8W1OdzqUhlt5pRQDokeJazP8rQwGh88D1EYJNTvSOakf3feGku9qVGpqG4xTV8ojfbXWGSt18iYUtdZJXEnDlt0%2FedPztWvHjM%2BbtnB%2BHauecmLUlAeov2bk6HHjJkhCcGFoRIcJs1jnI2OaCgRBqd8NhFraSI%2BCBGbICTupxI21YNTrBbMkWKwmUYegHGS5WbPRiyhjVuw2EAfPVEriM1kjLsUhtexzTK9lO0kQ1%2Fdk29mzvXB9yo23qh9EHfeDXhAhJWwiKKAki0J1RCSQr20nattixUJOXfM71Bv9Hhc%2BCdeuaV3LRAIbAAjXdUoX16r7wqGgF3iOLui5Zpn1JodXKu1gsnFoi9Pi0DmtjnQHAR63E4fT4bythikCCP22ZKVVoUS%2Bhp0Bqm51Fnr%2BL2UjHz5YPXLwfRNx36B%2Bl3eeXrwWxYbNVy%2F8n%2BpGrtwd7tNtSfXsNFaLo9jTdPZ89ub%2FpXB47YrkEiRpzW3r%2BoJ09UfBJLnmAoG5dBi5LJ5U83Z%2F2GIGp7L7nGwzHPNQhS3J7yWaAKe27LkytvA6c%2FfPn39g4Oqa%2Bfun195VPX3qwLunC2vmH9i%2FoGZlTdOCgdOm3l0zdZoiv%2FGASic8yQYLAMhwBiA6Q93NqCLLub9OUmpcstOLaHGCwAsItnQvZqjyadHEUVx6cz%2B0JMt%2Bsjy645vIQH91edGont0XbPj9msiaPXiIVI2%2FNHhk35IePbMLh0yeP6V6%2FZPPA4KflKlzBqAsnGkVRaCONIPUOstxn%2FMhJ%2BnrRKMzxUmcTl2yP92s88eVhKvIfTe2KDHRmKtlyd%2F2PpPpA3vsPbRzw4w1sz%2F8snbmA6Or7%2Bw%2BpUPP8mXDl2wVvqx%2BwJu%2F%2FYmVHWb32L5q0oAeXXrkBYa2LZl5056LnkfvwhP6xD0X5YAIN3pyAOvaT85494494cnCD133dnN3O1oEqNZDegiV4IHicLJoMOhs4HS6dC6%2BLeC2ulLMRKks6LWkMWHX6XqfaELKyMnTOhsGs13PNCxJNkz%2BZ%2F0Qg6GhAeewK698pKaNLwyr2caOScrsU1mzMEJygRWCYYcgIoBopDa7TidSq4jaQa%2F8RJkG7MortqVTEvILI6Z9PL1rzacn%2F%2Fov0pY1S3t%2FraYhx5WrKDBA2ED6Yh0dqvitsEECMJuofkCEQsyAJOqq2jzatUOseZR82L1nz%2B7xMwlZzIVNAOBQIge7xQhgUfrILXa7jtog%2F71CzQq3qDNoZYbSkOzBpo31obZtOw24a8BDQx4ubWIXRk7UT9S1Kckrtu%2BbHgSEvqQKP1d3kPleHwFKDSZuX2mGBGlK3sc5EGO7FpnEzw8MXLlQ8pQsvpNv4K4ld9471NP2%2FhFAoDt1kaPi26q3zgo7lONnEnBvHfMfbr3iP964r4XTTjgzJSYsWHJ0V%2F3qF3eu3%2FB8lN07fsKwYRMeGCZM3nHw8LPP7T%2Bw%2FTH%2Bb%2FYjjwCBau4hdsY9BF%2BZRr1AgMrEoJdu5R%2F4fBhELEUxdqM72c5aTGef1%2BIQVnvjPTGxCb3wfhzek01IufGW24c%2BAOIZzq8gnCYLACAbHrsGKMNHNDV6EPR%2FosTBA8ziYuCw7Tjs%2BThseQz2CwV2Ou3PYeV9xMZBVchkAMkvnuAQM34FFf4CxEZ9KD5qXmxUIBBiM2mNMBxSoY3Sba1zpQWwlbVVwCXk5EIqmmhqKj93lzEgkm2zG3tH7IEWecP9w%2B9rGZ4ohslCYnXDUm9MGF2J0ihbnJBfkf59Rs7q4vv9Y9X1ozq9%2BdbRTwPhSMnYbk2zOnXtXqqkXKHH1tZM7NOvw5ip2e0XjzjcWDEhMjB%2FyIz70jFvcU%2FeGRvmVKrdoPJ0bltbq9R1v%2FYaDgTdn4hNzIa84ltA1MLCGETS7SCOQSAGkdoSIv86xGsg3HKMrOsQE6CUQxiaKGmtgtyAkWIwIMNxKIN5QK4xAIk3MIIVnNA%2FfAdPM%2BwIOhPaRNEtuvROycm7kHm7iMHM7wabASUqOtByowkglmHm5an5G8bOiYau9y%2FSAF7vYVQ2zqR5UUeUXdxLDtMT0SMkNXqR9Lhag0cfURpetbZG%2FAvZr2jRHOZSOkc5ztkqzrMIAf55rM9N5VmbON8PqhxBs8aRmyFqoTwG4b4dxLFrV2MQyS0hsq5DTACHylWC%2FhhXgUA%2BgFip9id54Z5wod3t1glmAKcgCUk%2BrogS11erXC6%2FJJ%2BWL8jcIsuyoNfbqiJ6Kri17tNEXW55EDWhHZV7uVhLarxnM5QhVqpNqbM3bcJ9eBf%2Bbn%2F07S9xNlt4lIyKtaWSunqyntWxHSQcba5nhhhNYrmqS%2B3jurSmJdWx7jiVLwUx3sKsmLb5bgdRi4YYhP92EMegKQaR3RIiX4PgeGy65RhZ1yEmwMdxnW4b5z7CQrQJJmEDGMEX1st6ino0mXXgy0%2B0x2rMHLeOu0ewbTh8BHua7RiLw9m2MThS2DCa%2F3fbaLyfPTsaR%2BCIsWwrAOXzv877434CJ6RAQFkZnnRvmsAPExtcAA6rqFMCF0%2Ba32f2945YHTpRoDazQHnjnES1lrm3%2BFq4%2BYgL%2Fygm0lglwc7fxSoM1BZEj3qKzovZ1zsLv1479tEH9ykddGe2jnx04rGmh6Mjpu%2F9zy%2FNwbFk68SdWpPhmOUDNr2FDyl9dMMXV699l61D26bmvgOVZjp2ZRN9qTc7xVdOrI9LlUxpXLoVMfk7Nb7fDFELp2MQKbeDOAZzYhAZLSGyrkNMgA3xlRNMtEfCbHWUTvF5CmKjOFSQeO%2FfrHjvH9%2BpMOtFUbKDBB6vWeALiC8fs96sl2LdkZoVarkRrHVH8v9lCDcaJGexM%2BzzQ42NZ9GHnuYrO3mL5LvvUdvFy4zXWq%2FB6ei%2FV%2B5Y9yQAqv0oW6R0aK94ppxcMTUAXpMJUu25YkGhw5Hbrl12RaQd5LrV3S5tj%2Bvm0xpaZCBL2vZIQjWCo6Q2%2F2lnOTKUqE%2F1UYJv5ZAOKb36Lxv32p%2BOTCrfUnn27ofnjujZq094yVz2TcPf%2Fv7%2B58IPi6dX3OnPyC0L3b917LZdPTcF8w%2F0mVQxcHZN%2BcTisqHF1YMuXO0r7Nv3562c52pXkOTnPL8TACXovgLUVWlXOH6L57V56vN2t3t%2B7FP1eajFc%2FGz689fe%2BUW3xc%2FvP58whegruiOKsCNGRZehzj%2BcwyiTQwCqAIhKbtXOVDENWdkOJQLre3tedlIaF%2BWlJTe3ghi5y4pbYNtKyK%2BAqGgV6RD66BdECyZQU%2BxzqKriLgsNtBaO9R97viBxZsNL1corarUot3Jy%2F%2BqHSkOv7bLFExMz5TiAMaaVIb%2Fwg7NmPnUc0VVb4%2Ba%2F3xO8a6Hj%2F0reqcOO967tWbwurHswpy73lz03Mt7Jg1ZtfPpwzvoK7OWGon8BOY%2F%2ByddrEUqp%2Fie%2B4eMYP%2F9%2ByRWGwjyVpav5k5sXH9%2F5MVNo2XdQ6Sw4ektO5V1zXc4lW4kzreeMU%2BJFaqnVDtxVIn1ikl8vyqRVppEbn5e21993vp2z4%2F9rD7PafGcS1R7PsEQk1d7TaLX%2FgqAo9URXolZHHYXKGOgqI3xIgApTICovZYRgzDHIa79iUMMSoA4xl6IQTg0iG84RDrHQ4OYwA4CqBbHZ9d89VRlx1zyq6euqsJ5fsnUqhXwYN5jsTttkj7YRp9eETFSj91nsfLIR0%2B9LqSttY3QmLJw6%2F3b430QyITiIlAqxdlBMcj%2FlHpUk%2B6gRVqnV4kwil39%2Be%2FsK5T%2F9sUYXdkp9n3vr4YN77ll3OW%2Bpzc8v7NpC3vppe0vPUtC7Ev2FzR%2FcQmlWcInr25%2BcGHXgtrefZ6cNHMlm8b%2BtaaRbXjh4Aku21jXgbraqmOrzaLyJC1RNqNUrt0Vk%2F1HquySb%2Fe8drD6PPN2z4%2Bp45Ngi%2Bd8fu35a9%2Ff4vtcJtrzCSkx3Wh3fS2Ph2YhR9gJVO1CD4WTPAaDTSACKjsZTifKZjMqJ%2FQQ8tX1yhOfG8nPjUN6iccXE96Pp8ejezqVFHXsFCrqot3J8iefZP%2Fq3KW8Y1m4nPwYfwOUY3tEGCUsjvv7PvxEa3orl8vQ6iZn76u47uxt1M%2Bb2Kjnf3P2ZWVxBdGcfXw7QXSpTl4Si1SnX6L2X2yaUjNt%2BDw0Xd40o6Z25NzmV4rxTJ9pvAljfYjl95r63Iuxboyetf0XbEBQGjL6zuy7cMOvu8aRRcWffLRjTHRO6DzXjNjutSq5e2KSf0PVDI8mmZuf107VNOfWz4851OeBFs%2B5ZLXnE%2FyxtZarrfrYDqw6wr2xGWIjpKsAWu%2BI2t%2BVyXex0jOkFJfNZpfsrQMOsKeYPHqqT%2BNdjB7q5euvRZPnb3oYUWsXUUomXo%2FW9JUVbx7J4HugOKR748Sz333%2Fyd8fMwk63mSElTs38OYRzF9LmyID2Efsvwpjn83sV86KdcDaFQ1NOXQi58u3ce%2FZMxo1nF6Nmgn7Y%2FTmxejV%2BpuEyuv9TaJArLfsb%2BIw6gkU6UvxFLggHe4Ot0uSrE5nKpjtqZKY4bc6eDxpBaOR51hGGj%2BVwg8UUAc4b5zk4det2ia1fWVJO2TlvZF9aafq7NnSl1EYN4y9zJ7BYRgeN5RaonxdR8%2BRfs09fmXXEH%2Becs89LqzDiTgeF3ljSZmwlZ1m55QTGn6hNi32qy1yujAU0iAXCmBQuG26zkI8nqx8t7tVlk4oDOW1Mbbh0RHvSCKixdiunWg32pIyxcyKCIieFj7YoVjVRAeseV9R9a0q5rdyvYktTFkxnyvWs%2FNzup6pu8B%2BROnrBae6djz2%2BInL0aAOq4Y%2Fe8%2BQDVf9G154buPm5xvWCb3mrjKRjN%2B7vp4xEwtQh3q8Y%2Ba0KbPYz19MYDO5tw1mkLIPz3985rOPP%2F10x9NP7wBEE68Q7pH8YFF6wGWwWXmN0KJs3CSfKkwsE%2FIgzx1QzhIE0DR3nLfB89CcmUMWLuFF2u%2BWPJGTu3C%2Bt3TBoiIAgpP5iG2lhdp%2BkEMyxSpMejflw753u9KSrHUfcfpp29njxj46a8zY3z3YPRTq3rmsqJu4b9TM2lGjps8c3qFLlw78AkQdn%2Bk78TN1N5wPn%2BSzg2gC%2FnKrZc73En4mKLYb3o4vKU6BwvQ0olRTQpJEXXkDB%2FTOLAxZRpmn39tucP%2FKjIL21tHmqcL5rLZZnbvMquO3Tl1n1aldEci5Ff%2FFEyCCePMvngykw%2BK%2FeMIh5f8VUtYgffQ49lB7%2BR0HUNTpQenhP6WBBkscHEs5y%2BQZ1WF29yx63DMUTVyicNM3RdTpRZly061Rq55Od5RisXIk%2FbGKDPGARzmLjqmfcouq%2Fe4LkcAKAEQZizSpY1khOWwS0KwXbHbQUZP2M1%2Bx3pUgbyrhA%2FvjeGG9tcNjs9M6maNnb2B4FnXTeR1Tw7TF6DZldL0ZRcHuMIs2WRn9LW10DWe%2Fei9JQJ4ELUkjOsxJ7m6%2BQYbnXvbTY2Ow6D6FHh%2F7lTTBZZSVLOtqB8g4iCCHzeZK%2BdC1Y38ymWJ3vb5SBnteXszG7cAfyXB6EYzgPBD%2FURrIP3Wr6u%2BOqQ9OmDF94qRp5JtZj%2F9u9sx5C%2Ficym8TiHvgB8gGOwAEwU4c%2FM4nELJA1RaoJelK5ZPTbBAIlYikk0WuCInpvPM3e2CJ%2B16ASv2UpGqjUBAIkMRRWhRNSeqtK6QAyGYBkJXxUyYgEkE7ZYLxAQJIVjbPWkkXx4%2BZIJRzr1gnnuT0TQ2Xp3rTPZ5kI5Hl5NZ2wZDslYJtjN4kb%2F%2BILklMTUvtHyFp1rT0tPw0qqdJaUlpzsxM6BvJlJ0W3iDhg5ZN3bwwdMsfKruRW2ZQbuRlt9evdcorVpPyolGwuJT%2FdUDsCHUKOz4AWfRHQvA065Z1snHLxtW7%2FoddaNewgZANO4LY%2Bn9OPN%2BrQSxmD80rC7ed1%2FRm9%2FpuaEacl3tH9TwUsfXIpYPVzprl6o4iBXdYT0AUtDAtYc3y%2BEuJtrjkUwGEVlI650ylKvE%2B5ABA%2FHNTwuf9lc%2BBgItUcf0%2FAgZwQedwuks0ypTyaYjSqY%2BiqLe60l3E5aIWOZ1mxPuV70toergeGwR4g0v8V2eKi0otVJZJ05xV7GHcsHQO%2B0ESk9LSjDup6913x%2FKzVKdeX9THFGzb1v5TDDfpQ45bECoJ9%2B43cBcf0nCXXr%2FF8%2F43notvxJ6rVEnqc1TWG05X9cp%2BAAQRKWiHl2Knck80KgqljCAC4Aq1QvJpPHP6XaxCImp1FiUv6pwAUXstt2Ud9NrbHGJCAsQx9ufEKktsFtJBzroOMYF9EK%2FV%2BGK1mv8PflNJUQAAAAABAAAAARmahXJJOF8PPPUACQgAAAAAAMk1MYsAAAAAyehMTPua%2FdUJoghiAAAACQACAAAAAAAAeAFjYGRg4Oj9u4KBgXPN71n%2FqjkXAUVQwU0Ap6sHhAB4AW2SA6wYQRRF786%2B2d3atm3b9ldQ27atsG6D2mFt2zaC2ra2d%2FYbSU7u6C3OG7mIowAgGQFlKIBldiXM1CVQQRZiurMEffRtDLVOYqbqhBBSS%2Fohgnt9rG%2BooxYiTOXDMvUBGbnWixwgPUgnUoLMJCOj5n1IP3Oe1ImajzZpD0YOtxzG6rSALoOzOiUm6ps4K8NJPs6vc%2F4cZ1UBv4u85FoRnHWr4azjkRqYKFej8hP3eqCfDER61uyT44DbBzlkBTwZD8h8%2FsMabOD3ZmFWkAiUs5f4f2SFNZfv6iTPscW%2BjOHynEzEcLULuaQbivCdW5SDNcrx50uFYLzFHYotZl1umvNM1tgNWX%2BV%2F3gdebi3ThTgVEMWKYci4kHZhxBie3TYx3rHbGr%2BPdo7x4dIHTKe5DFn%2BO%2Fj%2BW2VnE3ooW6isf0LIUENvZs1gf%2FLHojJwdpplCP5gn%2F5gi26FoYa19ZVFOJ6Sxuoz%2Fq2Ti20IKVJdnqvYJwnhfPH%2F2f6YHoQF30aZaK9J8T026RxH5fA%2FWPW%2F8IW4zkpnIfoFLifGB86v0ffm5nbyRs5iaHR3hNBD0HSfTzoPugRM%2BhdN0x052KoHLBS0tdgpidAiEesDsgWYO73RWQz2LWIwjqnMe%2FuYISQtlbyf2NlT9Q9PoBcBnrO6I5ELoMeyHkNnIXGdv809H%2FDXNOTeAEc0jWMJFcQxvFnto%2F5LjEvHrdbmh2Kji9aPL4839TcKPNAa6mlZUyOmZk6lzbPJ3bo56%2F%2FCz%2BVaqqrat5rY8x7xnzxl3nvo%2B27jFnz8c%2FmI9Nmh2XBdMsilrBitsnD9rI8aiN5DI%2FjSftC9mIf9pMfIB4kHiI%2BhWfQY5aPAYYYYYwpcyfpMMX0aZzBWZzDeVygchGXcBlX8ApexWt4HW%2FgLbzNbnfwLt7DJ%2Fp0TX4%2BUucji1hCnY%2FU%2BcijVB7D46jzkb3Yh%2F3kB4gHiYeIT%2BEZ9JjlY4AhRhhjytxJOkwxfRpncBbncB4XqFzEJVzGFbyCV%2FEaXscbeAtvs9sdvIv3cjmftWavuWs2mg6byt3ooIsFOyx77Kos2kiWsIK%2FUVPDOjawiQmO4CgdxnAcJzClz2PVbNKsy2ZzvoncjQ66qE2kNpHaRJawgr9RU8M6NrCJCY6gNpFjOI4TmNIn36TNfGSH5RrssKtyN%2B59b410iF0sUFO0l2UJtY%2F8jU9rWMcGNjHBEUypf0z8mm7vZLvZaC%2FLzdhmV2XBvpBF25IlLJOvEFfRI%2BNjgCFGGGNK5Rs6Z7Ij%2F45yNzro4m9Ywzo2sIkJjuBj2ZnvLDdjGxntLLWzLGGZfIW4ih4ZHwMMMcIYUyq1s8xkl97bH0y3JkZyM36j%2F%2B58rvTQxwBDjDDGNzyVyX35Ccjd6KCLv2EN69jAJiY4go%2Flfr05F%2BUa7CCzGx10sYA9tiWLxCWs2BfyN%2BIa1rGBTUxwBEfpMIbjOIEpfdjHvGaTd9LJb0duRp2S1O1I3Y4sYZl8hbiKHhkfAwwxwhhTKt%2FQOZPfmY3%2F%2FSs3Y5tNpTpL9ZQeGR8DDDHCGN%2FwbCbdfHO5GbW51OZSm8sSlslXiKvokfExwBAjjDGlUpvLTBY0K5KbiDcT672SbXZY6k7lbnTQxQI1h%2B1FeZTKY3gcT2KvTWUf9pMZIB4kHiI%2BxcQzxGfpfA7P4wW8yG4eT%2FkYYIgRxvgb9TWsYwObmOAITlI%2Fxf7TOIOzOIfzuEDlIi7hMq7gFbyK1%2FA63sBbeJtvdwfv4j28zyaP8QmVL%2FimL%2FENJ5PJHt3RqtyMbbYlPfQxwBAjjPEN9ZksqkMqN6PuV7bZy7LDtuRudNDFwzx1FI%2FhcTzJp73Yh%2F3kB4gHiYeIT%2BEZ9JjlY4AhRhjjb1TWsI4NbGKCIzjJlCmcxhmcxTmcxwVcxCVcxhW8glfxGl7HG3gLbzPxDt7Fe%2FgY%2F%2Begvq0YCAEoCNa1n%2BKVyTUl3Q0uIhoe%2B3DnRfV7nXGOc5zjHOc4xznOcY5znOMc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A7%2BtETl5RXdNNZGDm%2BvXYXWjgLDRzEhoLBAYv0%2F0NHAAAAAADBQ8CvAAFAAgFmgUzAAABHwWaBTMAAAPRAGYB%2FAgCAgsIBgMFBAICBOAAAu9AACBbAAAAKAAAAAAxQVNDACAAIP%2F9Bh%2F%2BFACECI0CWCAAAZ8AAAAABF4FtgAAACAAA3gBY2BgYGRgBmIGBh4GFoYDQFqHQYGBBcjzYPBkqGM4zXCe4T%2BjIWMw0zGmW0x3FEQUpBTkFJQU1BSsFFwUShTWKAn9%2Fw%2FUpQBU7cWwgOEMwwWg6iCoamEFCQUZsGpLhOr%2Fjxn6%2Fz%2F6f5CB9%2F%2Fe%2Fz3%2Fc%2F7%2B%2Bvv877MHGx6sfbDmwcoHyx5MedD9IOGByr39QHeRAABARzfieAFjE2EQZ2Bg3QYkS1m3sZ5lQAEscUDxagaG%2F29APAT5TwRIgnSJ%2Fpny%2F%2FW%2F%2Fv8P%2Fu0Bigj9C2MgC3BAqKcM3xgZGLUZLjNsYmQCsoGY4S3DfYZNDAyMIQAKyCHTAAAAeAGNVEd320YQ3oUaqwO66gUpi6wpN9K9V4QEYCquKnxvoTRA7VE5%2BZLemEvKyvkvA%2BtC%2BeRj6m9Iv0VH5%2BrMLEiml1XhzPdNn3n0rj6%2FEKn2%2FNzszO1bN29cv%2FbcdOtqGPjNxrPelcuXLl44f%2B7smdOnjh09crhe279vqrpXPuM%2BPbmzYj%2B2rVws5HMT42OjIxZnNQE8DmCkKiphIgOZtOo1EUx2%2FHotkGEMIhGAH6NTstUykExAxAKmEqSGMFl6aLn6J0svs%2FSGltwWF9lFSiEFfO1L0eMLMwrlT30ZCdgy8g2S0cMoZVRcFz1MVVStCCB8raOD2Md4abHQlM2VQr3G0kIRxSJKsF%2FeSfn%2By9wI1v7gfGqxXBmDUKdBsgy3Z1TgO64b1WvTsE36hmJNExLGmzBhQoo1Kp2ti7T2QN%2Ft2WwxPlRalsvJCwpGEvTVI4HWH0HlEByQPhx468dJ7HwFatIP4BBFvTY7zHPtt5Qcxqq2FPohw3bk1s9%2FRJI%2BMl61HzISwWoCn1UuPSfEWWsdShHqWCe9R91FKWyp01JJ3wlw3Oy2Ao74%2FXUHwrsR2HGHn4%2F6rYez12DHzPMKrGooOgki%2BHtFumcdtzK0uf1PNMOxwDhN2HVpDOs9jy2iAt0ZlemCLTr3mHfkUARWTMyDAbOrTUx3wAzdY%2BniaOaUhtHq9LIMcOLrCXQXQSSv0GKkDdt%2BcVypt1fEuSORsRUwgrZrAsamYJy8fu%2BAd0Mu2iYFhexjy9FIVLaLcxLDUJxABnH%2F97XOJAYQOOjWoewQ5hV4Pgpe0t9YkB49gh5JjAtb880y4Yi8AztlY7hdKitYm1PGpe8GO5vA4qW%2BFxwJfMosAk2X9n9X2cVVfnA36pzHNHJGbbITj75NTwpn4wQ7ySKfAu9u4kVOBVotr8LTsbMMIl4VynHBizBEJNVKBAfMNA9867j0InNX8%2BranLw2s6DOmqIHBIbDfQR%2FCiOVk4XBY4VcNSeU5YxEaGgjIEIUZOMi%2FoeJag4mEB3PUOweCaG4wwbWWAYcEMGKn9mR%2FsegY3R6zdYg2jipGKfZctzINQ%2FvxkJa9BOjR44W0OpTKAskcnjLTcKyuU%2FSVIWSKzKSHQHebYW9mfGYjfSHYfbT3%2Bv877XhsIwGzEUaleEwITyE2u%2F0q0Yfqq0%2F0dMDWuicvDanKbjsB2RY%2BTQwOnfvbMUhiNPFyDCRwhZhdjE69Ty6FjoOoeX0spZz6qKxxu%2Bed523KNd2do1fm2%2FUa6nFGqnkH8%2BkHv94bkFt2oyJj%2BfVPYtbzbgRpXuRU5uCMc%2BgFqEIGkWQQpFmUckZe2fTY6xr2FEDGH2px5nBcgOMs6WelWF2lmiKEiFjITOaMd7AehSxXIZ1DWZeymhkXmHMy3l5r2SVLSflBN1D5D5nLM%2FZRomXuZOi16yBe7yb5j0ns%2BiihRdlFbd%2FS91eUBslhm7mPyZq0MNzmezgspUUgVimQ3kn6ug48mntu3E1%2BMuBy8u4JnkZCxkvQUGuNKAoG4RfIfxKho8TPoEnyndzdO%2Fi7m8Dpwt4XrnSBvH45462t2hTEX4Bafun%2Bq8jIzK%2FAAEAAgAIAAr%2F%2FwAPeAF8egd8lFXW9zn3PmX6PNMnPZNJMRRDMkzmDYgZMRRDCEmMMUPJIgZEepHlRYyIiNhRUdYuS4ksy9reLDYsdOmLLC%2FLy7L2CgKrrCJkLt%2B9T2YyYPl%2BD8804J5zT%2Fn%2FzznPBQKbACSTvAEoqJAdtUhUJpQYjBJVAUrKSkIOJ1ZUOEKOUGkfV8ARiPB7E72m87WJZF58ibzhXPVE6QsAAnMufI4H9XXsUBh1UpOJSJLmQNWqNsasLkKhsrKnA%2FT1HCF9PQzSAPYtD5V5PW4lmFeIK86EcCRbObLp2lGjGxpH4%2Bf0wLkjjU3NDSNGxYSMxbSdDkzomhE1SypQalCISvniob1lDuTL7injC1O%2BMr%2FxmeJtxeRt%2FiJviJ8mmrjFOr0BJCZ3QAbkQFu0ypCZ45HcRqNJQkiT%2FLKsOO02s2Ryudze7CxVUnw%2Bv9%2BtmKTcgEEymzPRlgN2e5rHaeOXyeeiisnJFagMOSsqSkr45kL8Tr450SfM5%2Fy1V66pGvBwTV1BcYcDEX67QjQkbo8cigTplyVI2OHh%2F6zdXHO4%2BiR6SjoxMPzo8O21h2tPx7O2lmylNV%2FtY5Nwubj3fXUA%2F8BuFveBr74CoNB84V6pSnFCLhRCL7g7OijfR7Oy3FalR49AcXYRFBnsQUcgkAYO6H15j6wiAGu%2BI%2BAo6pleFDAWKJZMX%2BaImNunWOpiskIVH796ewAqEzvV9gqX9nQ4Qd8S%2F1V%2FScSM%2FrmsTP9FfNUNIvzuVlRPMFxY5PB6fY6iwsJw3%2FJIOOTx%2BlT%2BWzaR%2BxYWecrR7fWFFanqi%2F33nnn9%2Bv%2BMvXr7mk933%2Fv5Gy3PrN6yZjg7WFV1D5s2oGoh7nx%2Bk2vvTrkeDT0HKlieXvvakkfecj%2F5uKnhm6iNHRk27a6bevTL%2BclH3ulVkX3cBTJUXjip%2FCDvBiO4wQ95PB6qo%2Flen0%2BWTRpofo8nLa04mB3UgpeX5PbMLEzzKz4%2FtapOlXt5a1llpXhN7FF7r8zJ37o%2FiN15Q2XhvsE8RdajOqwFyrwFGETXr%2F0F9u9dNnZsWW9869X1azow9qe%2Fkpc7D52mPRf%2F%2FHcJFrR1npvf9sWX336EO7%2F9x7lqeUMn6frt8y%2B%2F%2FZD%2FJjzecOGEAnxvWdzjpTAzWtHbGjRhlhdMXqvLVZSWnl5kpSoChLJVtcwXSPea8vNLSrT0dEnTegyPaZIUqIlJLnSKhAV%2FpfBuhb9EbE53bYVIM%2F3S45hfiZ%2B7th8IFPHN5QuXcscms1vF8kiAZ2qBsEEEFQX7FnJDeNy%2B8nIF2JLZ7%2F77DPtk3rJhVV9vefPD%2B57CzCF98cr82%2Bs631s4%2FvbxrKPf1XjT0Iqrh%2F%2BuafTMxR%2B9e%2B%2BmxqZnxzzx5l8embstxo7PeX0Ju3DjoqYJA7C611hyd3hAtH%2FzpD5jAAVm4DM6Zjj5C5WIAIu9DuxCIB0kuvEBAKGBbSTz%2BL%2B3Qm7UZjaZqCSBqtrN%2BVQgmAMTua3joeaMhBTicTt9wULS8PSj5x58eNk9Z5c9RUrRiPte3MTKzvyHRd5Yh9vFygP4yq3JlfmyfHG%2Bso1LyP%2F5yqgRNVjuDPclRSGvk7Q%2B%2FejZJY89%2FOA5sTT7ifVb%2Bzru%2FOEM7tv0EisFhErSJGUpbrBBOOo3ms0ypVZUVc0umUyqilarYrDxpN1aJrKQuykJwvwz%2FyPMUOCTXSqlRa6CiEzJy8U4J8DWf%2FjpM%2FeeOMZeLMKpxYqbPTyx088Oz8MKtnMuFqefm4gzAKEZPpUqpG1g5qivGRSjkSKAxWo2giJRKOFCysqS4vjNhQXCAa4Bxz1HEI%2ByNlx0FBextqOk9SjezW49yhaIHbGzuBtOggKe1wgFWVapDCXbdSNt5ghfoNCgMxLA3X1v%2B%2BdV%2Beg%2FvIsdR9MJYWVcS5rISqDg%2BCuVQQLkSiTc7QoHPANIGq49dw6wi7GwgmvujZoUrrSRNsaMLqjsmfjnkYu4aU6SlJZ28xECNyqt0mMrM2pBricBidueiNS5iDcRA0ir4h%2By4yQgGJP%2FDwLVF05IQ%2BW9XLoPLou6LYoTFPCnGT0jYkaV2kfEaBok8y%2B1kkYCeeDQnIEyQI2nUrlDE3kkDT3PzsfZhXMoxZHGw2OmTRl7w%2BSpLeQoW8gexttwNi7C6ewO9hD7%2FusTaELr8eOAMA%2BA1nJtTNAj6jJKAAZEs8WgqihJRgX9wJHOkYoXkf8iwR2RiKKqRRiitWw3lYdnr30cDzNae%2F8Tw%2F1L3sS5gFALINXpKDQgmp1pQxW86M3O8aoqMTlNtTGnSjATM2tjXEgCYfS3hKyuCkFHkzBeScI6WKhFVxLuD%2BEQLt4TkOo6CU5f1drrhvrrVly%2FdspDayfe%2B8EtQx7fuJG0HcbZLyyc1r%2B5qXbojtE1xa0dt4x%2F5c31r9hA6MYtP5DrVgijoiV5Po6KKs3MBOCVStFlgez8bG57v8%2Fvq4tZ%2FGilfr8pX7VqJm1EzJQGeg3j5%2FxX8ruWMbrG4oduFyXxMEFyQlkpkMeJTvhKbCMY1j%2Fo2ykPlEmSr335KxvYPvbZydev29P65KNrX58%2Bc92zfxv6%2BKil76PnU1Sl6fe%2Bl694%2F%2FzIweMjUO1ZPnH2TU3fxqa09%2Bl%2F6OHXAQgEAaSZuhddMDiaZ1epkRAzpTKAxyVzrnGh7JLreGi7qF1VqO5WvoGQ0DwF584uo3cpz4sCBzc9T9SAQPKgoqI082X2QfxhshCzXmZ5Jmoo6MvOYAk7gCWH6cudN5%2B98oSroZZNBoRWbuEw1ygDmqI9OZ36aJrbbTPYqIFmZrldRpdFA27ONADF4%2FHXxjyKYhkRU9LgYsIJ6e%2BpgHAkGUjkgUhLSBg2N9w3IMwpylMaKScT%2Fn6efcC%2BPLN8xActmMGOhu%2B4bH6EpsV%2FyAgOoO0n9%2F%2BHnR2B5h7hr455LAPJ1%2Bwc%2B1i1AYGhXOs6eQf4IR%2BuigYUp8WSlweZTnAWFNpz6mJ2u4d60kbEPGnUwENEvUTbVJbqTCjIAQJlPo8IXEUNdQEJcCAhMvd%2Fgvy8Q3E6TmsbErv%2B%2BZ2tRuuN%2F7f1X%2BzsNyv%2FvYhoN066sbVlcRuZiq%2FiWvuP7rEb%2F7LuhyPfsFPLMffdxfMnz7%2B1fu5qEc0RPdM6QIHLo14FgCDKRFYNMiWU1MaoAsLfupYpQwobhpDby4OfkoJ4iZQWPyy9jNLm8wLSdEtUyzvBB3lwOVwbLXYqnl6U%2Bo3%2BQo%2FHnp1ttBtL%2BihOZyBQXGwBS0Z9zJIGwfoYXGwTYYlLnVeWdKFwoCSqAj0%2FLqoW8qk7kShFiku3kK9cfCPVHyDedt%2FqpeyLL06zk4uXtU1DyfXfE2fPmrng0Ccjbhg%2Bflxtq7zz3ZUzXhrU%2FO6sjqN73mrbXD2iY%2FKzm89vbBp7Y%2F3VcwaOI3vqq674XdnlYysH1Ym8GajvcgekQQFURnOzZJfFEgyCCwqLtNy6mKZRrzd9RMyrUkMdR%2BNfdbfu7DIBzCIaw0J5kS16edcXuNOdBXwbyU1J1ewxtvTOqxtHP%2F3%2BJIOl3xOz3v0nmr9Y%2Bf2d8VNjp4xrbbm7jQ5mdazJdtYzasufW2r%2B83%2FH0fEE%2B3DTXbdNum1%2BHfd4stOSZuvMURh1OXnyAPjtnsaYXeumMPAnaOwXTOb4NVYT72PqU%2BxG7xcf6mPNQAQX6%2FIUcHKmcllV1UUlBRXFZdIaYyZNUjgzJ6Rpm8u6mKrApzM0vUgYbrTrbF2SFHbS18Xa5GhSmF5P7JYqZODSiqKajIK%2FVYNEqQIEZRigFxShVFwJURhGD6JU0ZlDP443kvW7ccNSPH2abWFfCns140peoYDeNeZHHSqlRgkMcp00ViJSV30QKhkjagSue7JMQH4304%2FFkrTgKC9Tjh69VLueUScBrhFPNVAUJJTKEur6Ce0u1dCFuorNZH28UayJb2IaDjjNtKWsWmioXPicrpB365FYFc3LTU9PA%2BB2dlqdhUV2QCMFCAazGmNBl900ImaXkg7mVCR4KJVkyfpRJFR5F86oRckaXOFoe0m%2F7W6YevPVY5uWvzf1w3P7vm99YGyIHU4139VjH6ob1tLvqqpxR9u2r5m2onVI9RVXsHUX9eMTLkxQdnCc6AuVEIv2VCsq3G5XOGzt77rMZaWBtEDvNOgN0au8hkhEMg3QTPzqkVUq5feAklS7rOucMleiPU7ivc6kQtuiYCqrfNTdlVF8fxLxCKgtj3iUQC44%2BjrzOa06UfyDSESH3x2j106vnpWmTXnhlT1o%2BUfT%2Fqt9NdGau79%2FZhf73%2BexCP2T2Pz%2FZefZXez6I%2FgIyv%2FEkRs7Yf3IFpM1FG27n5x%2B%2BNQ9Q%2FotPPTGQSQBH%2FPd%2F9Yf%2Fvjjne1sx152gh0p6f3eKHwYW3%2FEZZ93sA627uCCpcfMzwj7AIC8WN4IKljh6miAWKkBQZHNZgqip6CSZLOSmpjVSs0yBZocIpTouZRiZWGortKL8gsDiITjI5Uik%2BLHJ7FXiYTziRJnywoMgWdwNFstbzxXRcbikdvy72CqiPvXAaQznI%2Ft4Idczsm9VLdbktKzzeY83vfZ7QGDlqalDY9ZNLRSTbODPb0mZneCvyYG9BLcSxY9KQVDSTe5ArmSp7voCQYwWfE4HPqnwOu4AyOYNn%2FC%2FfPZh2fjx7C84%2FaZ8xev2nXHraxT3vDKpkVrHaacdQ%2B%2B%2FxGdXTuy8Zr4NrZo3PgNgDCXI%2FUBnh9eKI36VZeLN%2BNWnxscUBNzSKpskmtiJleyNBOvSfVEKuQRD2%2B0Iw4l2BUdoTI%2BZiikBS%2B9h9OfOtrxL7aJvdiOkQOHDrc2tEs72U%2FHmW846xyGi3DSZ3j9azd1FvUDImwoz%2BE2NIBd1OtGAIdVkjTZUhOTqWTlLbMzaamUcEELnGVzAbVA0BHKleew8ew2Ng534wR8gL3Dxq5ZjO%2FxGuQP7A55A7ubrcHDnUMBdY8RLs0Mg6L5BgnAqphMiBbFWBOzKNxLAnII3zehaKqJofOXXkp5iCsitPAkbol0bqDV8RN4ijmIm4tl7zK2BLqkUsalGqFvNN1AqVkBQDQJoSl5QlZS0MVSLhaCX7P9dHD8OHKMEwKWxLu8KBdxL6ZDTbQo3e8nNquVEFemy2DIsGlmjQdbOr9BNkt%2Br%2BzlsmTu1FB3wd0z5VlnstgW8BBwKLpv9YJL5RlPdMKNOALkU1L14E93sr%2ByVfg43vTxgZtW%2FGXnd1vevKGVHafhuOnyAlyMU3AcPjDybB377rOT591Y2mUHeYJu%2FUg004jIzW%2BQJFm2GGhNrMaABoNsUijK3QmbMnfKFN2XPIHtjr%2FNdmE5uRrDZG78Xj5t2EIGAOCFiawBT%2BozgRw%2BbSAGXiPLwM0MRsr79e4NCw4Rxa5IJL6kRnJurq0bOKEZy79hDV4k7gVL5JHn1l4AdgYS%2BtfxVS0wMJpjIcRkNiOAzUBl2cq%2FUrNZoXwP3VtwpgBXF1eWAOXEQAdVfSMRDKBcx1awhYvEZm7FB7CZETKxJf4D39CN6%2FHf8XkJ6VIlly6LPUkqBVCQArccJKJUl6GXoPq6r3PD1MsbzldfSPxvRcyR3dAvmukGo9nI1bbxUPHKisdJjEQxq9QGilBcN36X0mUp6hA6Y9DpEYujXuXykscVRBpkK4wudhzbcaSC07GdfUgtRrZEms9Wzok3cw1WSi3nqklH6R3oPr8kYcedOm6WR9NMYETFagVwUFlRVM1MVW5RVLtHv11adI%2FEnAKwL1KEcM%2FJO9nv43fpSiwh81U7%2BqQGdrQtXseFv4FZvycdQPQ8%2BVKfDHgE0jgAfBZF8RpdNTGjRO01Mer6daQROSBexQQy16Hxpkj%2Bkj3BXubXE3gz1vNr%2FPlDb76Bs9nSNzaSY%2BxxdivejVP5tZCj0mP%2FOYvf4smfoAvtpHU62rkEFkhGowdsNrvdbQXBV3ZNM9TENGr%2FTSzoRn%2FZLXHoEyAo4ckJSx%2Bau%2BBBspEdYacX8yA6iCb0UGXmlKkTd504Fz8rb%2FgchAXYat0CdkjjEZynUFmSCDVIJg9AhmYypVOVEwBXRFK5UWSV22N7Ev4uHU92T9OQe%2BLX7PPaKziWzWZnfL9pJMZW1bO5OPS3LSUP1S3lg9poocvnk0ySppm8njQw8cTzu4wWMA6PAZgtFm40C%2FWaRcikzJbSWfPzuXKqQ0sxKLdfgl3BF0A82brsgaXLW7gB12EPzH7oTqxuZWvZKtp73M0Tm%2BPz4vvlDUeOLdxZwVwPk1KRVS2cQX0ce4s4n%2BRlpKcHICC7LeCGy4rdAbAELNlGX3ZNzCdRYyq%2BuhvwVHHWrRpn%2BIvGGoVFl%2FMhDadWMcJP9LZen9cr%2Bdin7JuOx%2FZeN2FqnzFL7767DtWvZu2f2TrnyermlsJrn977BC7f%2Flkz5g4srx3e8%2Borqypveeqmzf8qL%2F13n8KGgcUDKqrHbRP6FwNIYiqrimdLCgBFNBhVKlHOuxSdv3y2lARgcoLtYrOlOn53IGEMEF7k%2BdXC13JCQdThQHSbDQaX08hRhsdSYuuXVBAOtyLx4BHI6%2B6CYLnlEXbyLfYFex%2FD9zz7BAf0ztqVZ%2B7EwHn6YufCPz33%2FDraBqjXfyHBI2K%2BRonRKAOiVZYkC3BDJ%2Bq9VNpUJOaj%2BsXtVx6h57CC2dmLTMMKdPlKFXO0a4DY%2BdTwvZeN%2FqJLhrqRy8gSsx%2BT0e52yQh%2Bv2ynlszMrKwci9mcnemSzdRvt6NJiOSi%2BEtCbgo1UyM3WkiKOMKJUtMlGvCIi78nPihD2fPbzWFJ6WPdxqngfix9q9Sr9HQdwoJDth5mUy%2Fnm1hKoRixV%2FmpUJxwVT85trLi1EAa6twb%2BaS%2B9uuhNBsStmnSbVMVzTXLnPpUo6oYTYpJ0C2VLGYDkWXJqFCUkhDL9evG%2BooUZ3VpjZj8Izex59h6fnXg56wfNmF%2FDGMtC5Pi%2BGHyHdka%2F47Y4j27dJCYyF2B7wZVlZEQEERvNFFF4QqiSgVDdslOjEH5Z65AarLLowIDZAGWchEZbA%2FLwDo6mozsXBTfQUqoXleVJiZ0RugfzTJISFUVEExmlYuSRP1I0IAGUcZdOgxNpl1qFqqPbALSzPPvkbfjTVJ6vIrs30m%2FRXi%2F0ykkLWUbyWw9T7KjVgXRIIFRJlTBfN2EuvH0BNZX4iUpmc0y8bOPPmIblXMHz60Xa1gA6MDkVFt%2FZIKYnGpfnBa6sUmAHY9%2FmJhqI4S4fJ%2BQL55xoKIY%2BVYNoOZTiaaCvQtCfCFHMMy1CH34IX7GMmfKjQd%2FUoR8AzFIA%2BR3QIHeUTdBWVYkSTznFd6SVJko0DW%2BxLKLeyTRZYcwiGjADQ%2FjqVO8uP6KGOiGzmqyKN4maq1OtpHWXhja9SRIRonoRhEaJZ5K0NrOFyl%2F%2FvMAAGKNdIQ%2BqATAwK1gBjVKRVTIdwCUpB%2FrioP0XWLww7EvHPD6PGRL5ZkqbKpcLx3ptW2gZ%2Fz7GYIdmjju9pfm6E8Zq6OFTovBQvLy%2FP78LIMhaEkbFrNYZLfbPjjm5jWdnDM4JnvBk0Az%2Fy%2BZVYSeXlcUJWdMvMcN9%2B1u8h0omny9N6YT%2BhuGr1r0xzd%2BOr%2F5xbv%2FOn7T8Y9PswO%2FX3znY5MWPHHDsNfXvfono1K6rn7f%2BK3vx32E27h55MJbxwOBFVznDsUNTsjh7BvIojRg1Mw2n89szrWA2WPUFFDSh8QUL7iGxEC7mCz83SHi7H5mUeZ0aISzRVANCgTlw1AfH9d2D8WobftHX%2B7YNsMT%2BhpLLZbJM2ZOJJNvaZk%2BQ5rNdrPv2XH2t6XzFTdbPuiJ9jP3rwh0PPOXNWvWAMLoCyfoMWk2eDi6esRYymclxCubh8RkDexcM%2B%2BlZZJuOTk32SdwmnJoYkjgUBQyIf4DZqJx81Mjh9525cmTzcuHVf%2FBTQZgFvauOZFVwBH49ZIydr4kH4iQK81M2CcaDRi9Gi%2BobTZhqFy7xwIOIyi6fTTdPt5ft4%2BoT4Q%2BecShOXlPGioU%2FBLkji3iOnVPiAnZ9vHnOw9ON%2Fmw7Jv%2B1omT5kyVp7dNmDnLjWVoRx7zq9vG4YSfTjyy5vt7ViWNk9BynD61y%2BDMEKROSUpzOLKcJlOm3%2BOkzuoYFVUUVMesmuoZHFNTel5aloiry3bI3RbgrbNeR4XKwOMJ6AVAxMMtOP2GaQZcT2aVs%2B%2FY3zDt7LdoiJfID985vmNc3Qb61PyZM%2Bd3NmAPdGAahth3Jx%2B789Eel5%2B4rCjB7nSOkgMeuCKa7SZElSn1%2BqwAPhndyHVz283akJgZqJ4bgp8v7QVDiRwWFgxH9KfOeieocBWpiZ1l%2B9eu3bj%2Fufm1o2uv6ocGOq9zCZ23rKHh3ZdLPsoafsVgoKAwtzSV26sYyiEKd0SrzFlZAwZIfRwOUqzmSkGUpIHpPXr4fJFg8Kp0K1jRqlj7qv2GxYy5Eke5wr7FpDpWXFxYWDksVqi5e1fH3BkXz%2Bn4pxIOWz79gRHv0LneqJs2FQ76ewKfPao%2BpSsqEvmsj%2BykQFfCF6ZeRcGFyUQK8v26El%2F4WGzqS33OfxjpXbL2ndc3sTfYvm9%2BvP3WksHVg5tvOnmsZKGTFc2buvrNabOfa5w5%2Fdrrmura10otT%2FceNqZjJ5Xzew187smt%2F1i1bPw9We5Roeh1xYVrZ732vkM6L1UOHVlb2WcEHT5q0qRRuwBhBYC0lmeDB8LRdATw2Y0Wg8Fo9Nolp1MaEnNqJkCjR6D%2FJfU5336yUOPaKqJJEuCQeFQirWX7O%2B6YxfZjqapqE%2F61bQ958LsXt8S%2F40CwpeDekav%2Fvh0ILAPAD7lsA1jEZFcyGsFksprtJg9Rr4kR6DJ%2FZWoO7uobKtNnnyJUlrW3X3ttO14phMgLHn98yIjzPqkFgFxoY259XSt4oSTqd%2FL0JgaDT%2FNcE9PAaBctOk%2FsjOTEKYEwCRGJxwB6tajQpMDBcxoHXzN8CJbum6GLZe60066mRmnd%2BeJXN6mThXRIWPMH%2FUn%2BNdGgxLmTUKrIsmYzWa0Gg8lkN4P41WCzUcXkofbu2oTf3cjSZdpuokXRuGOyi1dx22KswGZWhYd5AffOIrF9jYxdh40sI74Et93MVivueDXr0gYPcG0ouF4DRIkAevQioLvExgPivyvuhO7qQJ5BQRgeLXS7XPrsKDMzI6PAajSaTPkuq9WRKzu46XwOzWzPRJNH7%2BG7krl7%2BOC8ePqbjJDCRIiEfKFykdziVfBd8q%2Bke9n%2B%2BuvnTGL7vy529F437Xwso%2FdL097ZwvbVXz9jOnlw3rz12%2BLfSS1Lh1%2B%2FurZpy%2BF4kfhtxYuQjGCut1tMFxHAq6vrscoOoatQFU0Xx29SyV%2FXLRG8TS0ierkyof%2BZtWWXEPbn7boC9dce3JHE5yf0pzhpostXLJYMcLnSvcYhMa9mp0Nidu8vu%2FxUrvPeVQMOCCQs6MzrxGVT5986ecr8W6dQmX3ELvzxh7swGyl%2FI6Xt6%2F70Qnv7mhfYKbbnQTS8jE7s8wA7B4LrOep1cC1ckMMn1Hl%2BRVFNlKpZmqrlcuQEq9U9hBOEwa5mQEaKzBKmSBWoSQVlTvPepDFCnPndRKFJtuemosq2GZrG9p%2FtaZv8wfaPbt58TGf7vePdSx%2Fwsv5K9SPtbB87%2FT%2Fs7H10mU722JDgM67pTN1euaIq8dIsyh%2BTpOUZ%2Bfg6PcNnz%2FZanE5V4I0FhsQsv8m6iSfIBUmS5S2dL8HBXl8ook%2BLIkFBaLdMkafPPzxZ2v7R5zsmPXeFIQMJ22e1lq48uri9oOMZ9uLa9lNYiho3Z9%2B6xqU%2FbcBDAybXN3ZFFJ3LddVEh0mcejw5BCxZZVnUS7wGFxqlMrTMRy%2BJIqpdWewrCD%2B6iu3%2Fsre97yvSbCP7xLR8SXyH1LKxZTYkqp%2F1XIZ4dpmjpLktAEU5bnchWNw5lhxTli9rcMynUdPgGPX%2BvJ2%2F2BgiqPTHK2HB5clePsGgXCkPt082oetPnbx1%2FbDrDtW395oycuG8yJd%2F3%2FXu6MZHa5Zcv2zRrf2wZn1HILfzsvKx%2Bb0rCstHz73%2B8VXN%2F8y%2F%2FJriK%2FqHR%2F%2B30LeE6xuRa8AjToRYDHa7y2UyEIfB4fWZnHbn4JjVYrfL3HVyQt3QpktOVnRhgnBcxKOXvoLpIyFPwCO6cjK3bsas9tdeeHRt8xasYDuu%2BTD4aeiNN0jGwgknTn4e%2F%2FyqK4UOT%2FGc4zM%2BcENZ1E8cDrfby3t%2Fj9NoJ7JNtumyPcmJ1sVDgItr7tQYgH%2BgrxdrpR2zt72PpSLjsXRp7XUHt5Mj8dki4Ynt%2FEpI9JkPcrlm6BV1m0GWiYgIK0G0GNEuC5llKWndDU1X%2Fx0SbTfiOtaElf%2FINyryZYexkjVJLfFF86aMXUzaumS4AZRtXEaWOMsoSyaOIVng81ETVTMyMjNzVEXJ9plMVLbbMxQ7yDqidR3RdPz2LIDSIO1WQ8wBsin%2FpGskRZpuUfew19lm7LMwJ1eRcrT7sG6R5NCsqBgvN92NPdk7uARPdt4vtTDH4m9q1lxH%2FPGvvE03jMkcer4XnuKKI5gApOW6bWqi%2BYoMaKSUSAQlGWWzQVWtfIZmMSoUAA1mj4T2S2cBqaROkYZeq3KlhdkClOu%2FmD2BI48cxZHsMWxja46fYO2kPwmyZ7A1fiy%2BDRewhcJLzK17ycs1KTC73ZrXK0koahm%2FJgob%2FpNT8no0p9XJMTHDAFyVskQJkKKvhBlTUzxHyokifvTqgNsSaw9mmBRz7n4cwoqu%2BvcfR9RErqqfl%2Bfkfr2%2FYcZNo8ic866XXnR8Z72xNZI450HXce2MIn%2BoKqkIYDYgmvQhAm8c7YR%2FMwyOoefSIULSSMJGySlCWEwR6LrOB4nC0uhAZiCmDrLp6%2B3xekDI4T38Id7D54ipCHUbcnIcfn%2BuNTMzIFGXy8qjKd9qSbTzYosp2hbbF7bnuBrm%2BREWRw08Coc18VTQ4xFQ6%2BEJhDmL2m6%2Fc%2FOZG4cpn31T3XpmM9quH32qucGAVz7Z9jEdXMUObcyzBF8xskNVg%2BknbU8BIO5gJWSlYgMK7tcIpZJMAaCyhONDYlbqCOKOo0cV29lA1ylOauB7yBN7yOHlOmgGQ75bkoI52TabW3Z7qCzl%2F3%2F2IIuHzuFynuSi2BZnlftyiBSnzxyCyzwcrImh4e0Xbhz2%2B9mfKtWtL7xTP39x26LeM2aFPyFVQ7CnuWmyw5K3EXsOrqIfh2dPY5tNjY2nGm7QTxGQIqmCtoEHIlG%2FAg4zmKnd7qNeu82mSJSaHQ5QoCRU1lYi9ElBdqqp5pwa1sv%2FRAMmELwQB0baym968pqFwxaOC99ePv7pgf89chFZcXX5l1NzcyPRii%2Bnphf8lzhBwpbiQanl0rP6Dg26zurbad4v56mukCugE0Wi7Vh7JsTasSV5lIO0dJbKBcljHAhLOdJqfN6cwad7QYchPV3OyCA%2Bn4mYMrPSXCNiBtuIGMiGNH4pGWmKygXqpwH4S8%2BePzvOII575nOCTh4R15lS69q26gmSEBt94OCr7YtF6z7vlm8b7mpdcN%2BrL%2FfHcyhjZk77c8arjmflv%2FBn9kZObzbAuFFEB4A0ST%2Bd2BztZXeaidFqTfd6iV%2FzO51ado7Fn%2BavjxnT0sDFqcleG3P6QR7xs%2BNNXUfUIJTSVqjbjT%2BpBpRfbpXXFSKawsFwiBuQbNyyZcyzs2sbcS679w9k3%2Fmvbhr%2B6qufy7sbvojGrt10dOm6WtZ5ttes1keObtl5BAjMBCYFpHXcnkW8R87TLC6j7EsnBrDZ8jIhM%2FOyYp9LSycWo2xQPZ4ctYBHz%2FYyHc11H2qb9S%2BiA4oURXyC3SM%2B0WGqPrVIoJJaFCmMXFRdbixfuGzBqEk3j1qwfGE43Pbogt%2BNn93Y9siC8v1T6%2BqnzxxRO50cnPC7BcsWhCMLly6MTZs8uu2RtlBo%2FiNtYyYOnz6ttm7aDBHpCoDEp%2BPghZnR%2F7I53U6Plce2UaYyMYkJqxeRED%2FHBp%2FidDkbYkCRuuwmm93WEFPtdgt6FMsl5xX9mtiW3kNfypcpEhAfkgPKkCfoEXdAGF7cGCBD0YAVbOGWH374gX38448%2FvsOW4BViZBv3vHrfq8eO8RdyHMhFiKNCMGoniiKGmUaJSlTVsUcEbCpFdAhyJGBIAFHnAbag8wAAgUm89lnw%2F0o5D7g2jvTvPzOzu9KCJNSFaAKEBMYHAokSuQpiY04OODjYsWxCcjbkNaluuPdyiXuaS0jHpPfeE0N68fVO%2FObSe%2B8uy39mVlqEzr76oeyi%2BbG7U3bK83yfkUZBGZwCMyKlaRaXRRTLC6E4JyfkAld4DKmpsbkrK0ttpSafxzc15nHqTVNjepQycUvmivi5NiuyMYtA0qyNo3NOVr9OFfZJmt75WUW7VMhOWtE4fsubj9zRP33SzuaW6LxFB3rWTJj4xSuvXdHyYsOAb%2Fbpj257c%2BOS5s4tvmrim7appHXPputbn8kPlVdURssit194%2FxklXdGr7p3261Hh7uKKUGH0uu2nzi8Pxya1V5qmAUYu4UfygiRwVi0%2FYrQaWIvIdGcQ4pBB7dzU9snCdpLZJF%2FSOXJNjdRPPa0uMhVd2TKurqk5Mq5FXFPXEB0%2F7ucNExvqGieOb6wDIIw7lSbR99oBPqhmvm9ikm0mm7%2Fc7yzPc%2BbV1IrpYEmnX1mlhbZglpActKMVbEo36zBrHWyifBGnSASrw44ZvIhr6bwgFCxiuH4R45HIul%2Bc91p4c3j55tf%2FfvilPddGFx5b8zJqf5X9DCi9v%2Fm10vvcrj6U09uHsg%2F0Ke%2F29invHSBfX7VJ%2BTAv99nwkcNvfNd82xjlI%2F4%2FSu%2BrLyi3%2FObXaPaLTJb0b6xlBfCX%2BDHKMLqgAOoieZk65HLlmXXU56PLK%2FRmGI2e9HQbys4GEGweShSEA0F1mAtak3BQbR1SPGxVVo3K6irbp3YM1ToJV3pGr452r7n58XnrWi6tr79h3tY9yqTy%2FKbYvMvxsYvGRLrPu%2FBCWegef0l%2BcNcmpeGP%2FqIz6oqkNPas06Fd6BEEkMAIbZHRaUaDTKd2RMKCgERqGDdkGNkrBpBGCE4XBIMoIpOMsR4lWko4kLBqJI%2BK5j8Faab66Q897w8yR4ALIR3yqYfpaPGg8hFyDSo70RG06A12%2FoayC49HL1E%2Fs9K3DL2QNXzKGb8fhTCZCCJkRZgzSkcQkogAAdYJoQTf6LXQWZQQHjx2hLz1I7pgEIaGErEHWAIzAAhaezTEW%2BS5kUqBYFHUgcViJEbamxB9uT%2FROLFE8QLBIegdsp5%2BnaSN8spKbara53ErgY4FlFnoIwadmhP5X7VaYcvuz5QHAu8h%2FcO3K%2Bs89eFTJuceP%2Bdft9utd0xUFqDpyj3kqh3K1%2BH6uhrlzX%2FZctHQEckuSNLhJG8MjPTGCNLRbwWDZH%2BFr%2F6Jm7D5hAmyIDMiQ0ZGTrbVkMkqRQ3FUq17vL06HSowmDyctbXd2N5201ln3XjW5a88G6uvnz2nLjJHWMg%2B7W0766bZL10emd02YWJ7G%2BNFAYSwiCGdcx%2BZGTqdRB35BoSomd9sMRrSZYQkAYOKeoYC8S5MM5WnxriwyfZwnAs9I2%2Fh3kG0RVlFY12UNylYiiCAo%2FgZTriVRKwOA5LAgiyuTNnkwQ4Hyucer4lJXb96j39EPHUF%2BJnjK%2F5%2BbriipGXeqiuf3np9%2B4YudA6O3jbYEQv6S2bt37Cle8be7rMBwVgcxo%2BIr4APJkRy7enY7QbIl%2FLTzVK65C8mdrvDIed4PSa5IIE5pbQ8dlABTRX6S6xu1DgHrezj3QjuuaN9%2Fn1P7N541ards5oXtJ3REgwFWsOdE%2Fb9v3W9wlu7a432i6at2N7wzOzzq6tvrAr76ePuDExYn%2BqLI0JEDyCnCdwXdyjui3uFjR%2FVNMjMIUk6ao6YiGZWHZ0i%2FDX75U5H1aEgAOK2LmrkhkxmMUmXJFnOsjrBQR%2FdrXNlOGl7yiCq4Y2Z%2BzTTkbYwT8qwtv73xo0CxS6XhZtDZ7WvpVaAD0ZnlC6fNWF%2Bvigy%2Byj67YoVdz%2FPrAF7Z8wo%2F9mM65SDUhQQLFSOCbslO2RAIOJINwsiAoTMFr0emUykKWYSWc8XiHtk4gMlbe5qgAb7UsMIa0IFwu6bbumd0PqX1%2F72IW5Tjkmn%2F3QfCVmPHEWCwiKd8Cj0e7KGEUURmUU6Ebk1RiCQCHSypSLhfEr%2F%2B2Eqe2hQsaNeALBCVcRlNjI7Fh1Y7Gaz0W60ySYW9pXNXt9QQI0EXB1%2F3PjAIiZPQYprQ3RWgnr3Xd88KXuOu%2FGW5v7s6Kwj6xc5btOZJpzh7hmf2cktXDiKGxPRSYI8MjopD%2BWfMDoJeePRSb4QbvyciNkVzReismdxFD2z4Oyi0vHr6MwOwnTUfEt8ic9KPBFjIvYqgzhkDw%2FxTGK3kxc9YlKPgt969IarH3%2FwwP4nFG9dY%2BPEiY2NdULbnf0v3Hr7wAu3dHR2dnTMm5cy6s2OlKZTy49OL2AW1Ib01FNiGh70BD7YIdHEB79%2FOej1B9UBL%2B6NL0aoFonqQehRdg4ip%2FLxIFqsSMPn2KuMXYbaUNsyJZw1fMrGrnIA6Qpa2n5Y%2BTuAYvg1fgUA6eAP5Nrjj4L8IMFW%2BuJUVye0D51Au5h8T7W6B7CZSZlyNlXeJ75ClUs8XEnM8as%2BEb9qmXpVwDBeWUH%2BLLTzNU5DpKiQug4YJk0jh0pMoyDbnI1lQp0JPk9rzJdhoRy8xZvKwaN4g9Cm5HHsnddbrUub3bCVWHLF4ldiF1wYPjM27aFzzp37w3lvHP3F7rOrUcnw6jY6d1dT86yJ4eiY0sOnTO6%2F%2FYLru%2Bj0cyyamXhHhoZU2lu3GPuhiOexHiQ0HfQPYqfoh9HVJ1B0w2%2F%2FheIgzFQV2SMV52iKgYTCOlIxU1N0cUXaQwR7uWRYkxbXSNDfPYvXhpfEa4MpdD7OPtrg4sg4yUbMNmIRLCjNZEJsvgbgEETRbiYUvqb4syENGQkj%2FJFkkzkxTAQrMmlscsKiQLvUAAeUNb8G7yQ062PCs0QKkEYsI9rR6nzH9imOvcoLeLew9%2FghbKIUT%2BhoLlq5jiPvcYqZDnXNrC6WKXZGjNP8%2BVlGYAXOBfY556p5%2BZaodTT0KC89ZE%2BUXqqiG9pSFPdShT1JcXDoO1XhHnmNmZqia%2BgnXgMYFag1wGbucZ7cAJnQGCmivUCW3ep0GlBamtthAIqVWwGovcRJi9eKLYy8TgmP0%2BBgddahWmkscQqUlpiPo4MhBwPPA1tV5FzFz7cKwm9%2Bd%2BCzzzahATIdd1Du%2FG5GoOPWnR9%2BofQoyl1qHsRXeDuriLez36eUA%2BdUeTlUxtt7N1fgvJMpulHDv1AchOdUhXek4hxNMZBQZI1UzNQUXVzB2vvoeGkj2IAMglnogXTIjaRLBGTZYORGZXcgqMUn8260FqnLBlSM7lL%2BuB%2BVocqr6Rhetkf5tfL7vfj3qKxH%2BSMavZf%2B%2BVuaSiUAhD7DLeIHkgA2yIZCCEdyXJ4cuz0tB9LAW%2BTMK3Ab3QxXJQWpdOWImbyK8arGGFaJqpEG2V2IO%2FyqihEFV1Wm94Xts3tnv8iA1RevaL1x1sDRP56CjrR2UWL1%2FZBiOG0%2BWqzyvXWXXHDpANrEwNWGNfM3DSi%2FfHYJ%2Frbsp%2B8e6j5uKR4aUmlIXgO18Vocrdaz1uOkKrqR6V8oDkKPqsgfqZipKbq4gr0RJcl9kqDwq4yNv3kb1KtYuCSJSmbrqZpIDiOjjbIoSpJTMDbFZEdTTJAFWdIRyZowKGrdjOZBjePIDroW0tZGwh2UUz1yNcPaH1CQ4fikjst3rbt0NcHv%2FagMUij5c2Vc18rz5%2FNZJM3JfMkD1dAaGU3tegXFxQDlWSZTbXkgUGPKKtBBcbEui2SWhkqnxEIQcFgyozFLwnGq7ZUx0g03TH%2FaTYLqcnOkuuX8iaFL8zhXsVAn4a3SSDRSWl1%2FRVfoo3fmXTau%2BubIbfnTo2vnNjQ0TVjXsWQjbb4%2BhL9FfuGvkV%2BcNqai1JldVTJn7srmu%2B7JLfy6KLhqVGhcaeOylsh5lbWnl49r6TrnKPVMv%2FLO%2FazH5ASbVEBr5VQ%2BUtQfAPb2jbbEazY1vfvCE6Xna%2BkHfxhi6RUj001a%2BkAasPTikemClt4lAX%2B3T%2BGCYcUDmqJ%2FlKrwqwogTCEpQjeUQBBOgS2RydU1JDM%2FP2g3GoNBuabG7%2FGMKZPlsC%2FfW50fjVVXsyDp7OxQNJZtNo6aSoF3p%2BS0NFDHPHgbYiBJgQZGv%2FERLZmZ0t5q6wkJKnqMhzBz8MufZG0ZXsZRzHYYrWJk1TDShwoZfiVWbn2rce4L19%2F03NdfPRtr2nHzvKc%2Femdx%2Fd3LDyM4XkaJq%2Bcfm%2FbY8bqFq1fv6FyOvX%2B1oHvwefbOru7Y0zcz5q91cn3Tq52bInXKZx9RCGvWp8UlOEsQzpxD6T%2F05acLVrNap952xtZhP0xWx0%2B0iY%2BfnCrjtT1FbQ2389oqStRWanr34n%2BeflDP00eNTBe09C6rWpeVidoeugYAvcGv8LTaXynTgF0DGRLXuBwA%2Fy5J0T00eaRi6JdU8UmS4qDyuqqwJBTvUMXlkqApuriC9Vdu9UkSBIfk5fPVpZGx4MYuV46oJ%2BkEY0tOTnr6qEKLpcQNmZh%2BSJ2ImdjppB56CnnSKS02%2BRpiJifBU2MEnYC8izsQ2clwI9I%2B1YYLf3Gtkw8SVgdtm4XAwyNdtX46hDAvXCL2GCmnN3ZetuitjjuuvUr5%2F0PfKX9DwuFDDfpT17zfga0rz19x8fIFq84TXdXF99Wdtr1n%2Fm5lz4fKh8pLyPrJR8gyV%2Bhdtuva4%2FMv2Lj1ih27%2Blg74MwMf2tPV9%2FaEPAZUHI97ucl3KK2k5t4PReeOJ319ZfAyRW8pRiS%2BgUt3aSlD6jpeSPTBS29y6C2pIDWK8yCw0JYeIl7wbKhNGJ1pqWZBQEIyYUcNwVKAXHz0vPBYdBQiw8WTxJRTWOGj2%2BK1tf%2FPFpXNzVaf2ojO%2BKOwcEvTpva%2FPOG6c1EmNrUMqWhpRkIfcaHKAN0OZ81eEfOGnzxWQOjb0jBFAZx%2FC%2BzhmCNsJ9hQWsvOLVn0n5GBm1eUrt%2FzK5jR21o%2FOiJKy9AhwzKa%2F6alefjSoYJlXV2dVyL7IwUqpp%2BQes1ytH2RjTouvnWlnFKMOP2oSGVpeD1c2ZST4ByefGmpvMavgVOruA1XMnTC0emC1p6V0B9A0u1np977PkV5qi9zXh%2BBQ8XJOgmziYWsLhqD%2B1vHQZzli2Dxi8VWsCcbXDIRM6dEpOdxEnL%2BCQocxLLTDtnDWdWTT4Wyh0nAU7ot8Herhf%2F%2FuZLf5xv0ulUfvGjOONEDrXMYEgzK%2BCtE9qVsXpQVixvbB7mnLQ8CVqeut5Qc%2F0zNdcJKk9oH6byMk5M5VGJGk2mO108BE7wQmekxuJwGFF%2Bvs6WAeDL0umKLHa6drMgI7HQX0YznaWSNBddcwhCLotpRQ5tBcd%2BThplmiAy%2BBMMx2M6XcOLuERnVGvx%2B3WnH9vn31Wm9Cv3oTPQhPGbvaRDW9Q9dstdd%2FXVrfR7t8jpaBvqQuejTSZZXeCR145%2B8%2B1PDivZbnPyN%2BhT3SphMXhgNARhQWRMoMKEHQ6%2FX19RkWu3V%2BXr9aEchzvgiMYCATCbfxaNmc3YJNDOmfLEZnDT4VwQvFNiQupwHj45Cp00iOdT56kG4bniI7dDo6KTeT2fSk%2BLtyhf7dl5pPfHLSgb4QUvT7nsi2%2BR%2BbhTt2fL%2BU90tDx99FwN5Pu4fbWMBnC3%2FZprdiD9%2FciByqY1XcvYaf26naXlbOCeHGf7BhavuJhFHD0h%2FFXwSAVgZP0Zi5ozAMh6jE0ZWF4vsh39sg5pyx2NKqQzEZ2XGU%2BdFNAgrdc1Ne977elTUafn6kbhr2ed0XJ29tMLqh5sYBENqFX4M4lKD8Q9ehmS1eqmkUWyR8ay7CDxvRTYHVKNZ7qk8YhEdy1YcOklCy%2B67Pqa0tKaiorSGvGlCzavv%2BiCDZu7ykKhsrKqKkDwa%2BHPgkEygQuqIm4KNEUEQjLdBhvobPTrYvM6MzavFyCQ9fpZmoNENQebXw6qkISXvbF5mNVHiE23yjF6xRM27knfvXTUtKZoET%2B%2FfAk7F%2Buray7vKyjOr%2BKHAr4bGHqI3IN7%2BG5S%2BAS7SU0nbeih999Xlbp%2FqtQllG7Sj%2Fp4jIw7kiaIOqTTySBou5KZB5gLq7jGWhvCumKTs7N6sN5L%2Bp1zkG2h8t3HkHQFCVwRmQhIknSCRC8wvD8WUrffQHtNwbWDkz3iI84XlPdRySFI3luLeVIwEfnuWhIEtNuffHstwOzeZBl%2F%2BgzwRczUIGsiggSSZNFlkHRtI0Z%2BoT8E%2BbOoWSnwxY%2FoUzVPdILhSZyRP8ezp2Vz%2BE4SGJn%2FndpNDXwrMFMaMYjsRi%2BqN9Luoz60qB5QH885cqO31JNM8Ua1DBJFgVlJkOt5SRihMGIaeQcIpN7Ap91gROGgt0eWkkvbi2wunXrfKIyCdLA9wszuRplAgHssUq3uc6%2FavnXvvku37cGf9hzou3r%2FLbcAELbTizQXhfm75mXsYF6m6kEvys4gbKuXAofMQuS5LUhtbJnmP9AJy8gdX3yp56m7v%2BAps89kZzPacGPqPmctKUf%2BVkA7vpHbtCsijrgDV9RLQAg9pa0JI9VZmsxW0W%2FVN5vqlE12xKZeO24nRzp2bfoHPRPEf7z2SBs4vvHEBm8ApCxj83oe25YVSSeAEcaCFtqW8B8j5EX48mN%2F%2FIKMjge2AeK7BW0S%2B6EYdkQaJaL3%2BXI8RW5ntmywWIrSafaLika5cnP12dklBpdLzpRy83Knx0heRt66PJxOMvMy82yFPiiEabFCndlkMzXHbNp2YiNNoxZenyxzKUghO%2FCtQOhvro%2FH5DgKdA420DrVfS4oWELdb%2F7qWvq7BuL7XXhXXu9CVyrtGKN5yj0hZNq9ecn93ynPj9q6VMBLtvjQpG%2Be6ps7ebnwys5f3ucNFDzwTXgIxqK0Tx5wFVff9zVyT%2F%2FQ4%2BXsWgfzjp%2B0n6MTYDbdHRriMbs%2FSh7wQyNfQ04lboD45x8nfd7MPgcMBhzF34tPQRpYGbthFXUmWnBEBixim90k62TJikTRaiW6PJLPDTwBLSYu4RpNwn%2B8DhpfWI1CfA%2BzWrZnHP5%2BzefKBrTh0zXKHkmuzliH39q3rwfXHT%2FUN3Nu1gWuZ9Wn05u0pyuGRuJWn14KAMTT4QTpzcPp0q6k3PF0dS8BvtMDAcsjIIiIQGKXQLYPAt8FgTU2uvZ8EQDruB3sL%2FEV7krVDmZIWNNupYoPkxTdQ3NGKoYYgS4mKQ4q76sKS0JxHADfqZupKbq4gq9wuaT6%2FwCVeR0IAAAAAQAAAAEZmiehT9dfDzz1AAkIAAAAAADJQhegAAAAAMnoSqH7DP2oCo0IjQABAAkAAgAAAAAAAHgBY2BkYODo%2FbuCgYGr9zfPv0quXqAIKrgJAJZXBsIAeAFtkQOsGEEQhv%2Fbnd272rZtG0Ft27ZtW1G9dYMiamrbZlgrqN17M89K8uVfTna%2FoRs4AwCUGVBCU0zQl7DAlEIZWoPOfhXUs0BbVQAL1CG0ZepQd9STPdUW9dQ61FGN%2BU5LpOW1pswUpmU0hZj%2BTGOmWnQ2lPNyV2rEoO%2FA%2BmUw0CwATG8cNjkwyXzEYZrG9Of5NUyy%2BXBY7Q4Hm9a8tgCH%2FWU4bOcwPfmsjc7GvDcYPWk7StjU2G8qAf5xwHQE6D%2BzHRXUbqzi96bmrEQNEeim4V965jWnB%2Bho0sNRHnTn7E5H0V3nQAlaAGsawqkxWKfGhDPoO2Ts%2FGdwsk5fIecd011vh9O%2FOaegHO9toBWAfYLM5JBSxvoNquliyEeDvUucbeXvMd55vIqRtTGMJTnzAkP5bdnsXvTX6VGOPkbfYe%2ByRgh%2F6xHoLms6QDmmlvyFPThTB2PEtbczfMbr3XUu1JD7fmqUjaYre68jzpPD3wJIH6QH0RyQ5L6Ui%2FGeGFqDOZLiPj7iXnpkDsKJ5%2BTwO3LmEe8JYecb2fcazoXMC%2FEd4z0J7EFS3MdH3EuPJJX07gom%2Bff4%2FDMcpS1ee85bBLQNGO84cgiqPerpVcghUBEeK%2FS1jzBBfUZbwUv5X%2F7bkOlslqCEwJ5TBw4lBFsBJdRuHA4vYk%2Fown8RLYvLrQAAeAEc0jWMJFcQxvFnto%2F5LjEvHrdbmh2Kji9aPL4839TcKPNAa6mlZUyOmZk6lzbPJ3bo56%2F%2FCz%2BVaqqrat5rY8x7xnzxl3nvo%2B27jFnz8c%2FmI9Nmh2XBdMsilrBitsnD9rI8aiN5DI%2FjSftC9mIf9pMfIB4kHiI%2BhWfQY5aPAYYYYYwpcyfpMMX0aZzBWZzDeVygchGXcBlX8ApexWt4HW%2FgLbzNbnfwLt7DJ%2Fp0TX4%2BUucji1hCnY%2FU%2BcijVB7D46jzkb3Yh%2F3kB4gHiYeIT%2BEZ9JjlY4AhRhhjytxJOkwxfRpncBbncB4XqFzEJVzGFbyCV%2FEaXscbeAtvs9sdvIv3cjmftWavuWs2mg6byt3ooIsFOyx77Kos2kiWsIK%2FUVPDOjawiQmO4CgdxnAcJzClz2PVbNKsy2ZzvoncjQ66qE2kNpHaRJawgr9RU8M6NrCJCY6gNpFjOI4TmNIn36TNfGSH5RrssKtyN%2B59b410iF0sUFO0l2UJtY%2F8jU9rWMcGNjHBEUypf0z8mm7vZLvZaC%2FLzdhmV2XBvpBF25IlLJOvEFfRI%2BNjgCFGGGNK5Rs6Z7Ij%2F45yNzro4m9Ywzo2sIkJjuBj2ZnvLDdjGxntLLWzLGGZfIW4ih4ZHwMMMcIYUyq1s8xkl97bH0y3JkZyM36j%2F%2B58rvTQxwBDjDDGNzyVyX35Ccjd6KCLv2EN69jAJiY4go%2Flfr05F%2BUa7CCzGx10sYA9tiWLxCWs2BfyN%2BIa1rGBTUxwBEfpMIbjOIEpfdjHvGaTd9LJb0duRp2S1O1I3Y4sYZl8hbiKHhkfAwwxwhhTKt%2FQOZPfmY3%2F%2FSs3Y5tNpTpL9ZQeGR8DDDHCGN%2FwbCbdfHO5GbW51OZSm8sSlslXiKvokfExwBAjjDGlUpvLTBY0K5KbiDcT672SbXZY6k7lbnTQxQI1h%2B1FeZTKY3gcT2KvTWUf9pMZIB4kHiI%2BxcQzxGfpfA7P4wW8yG4eT%2FkYYIgRxvgb9TWsYwObmOAITlI%2Fxf7TOIOzOIfzuEDlIi7hMq7gFbyK1%2FA63sBbeJtvdwfv4j28zyaP8QmVL%2FimL%2FENJ5PJHt3RqtyMbbYlPfQxwBAjjPEN9ZksqkMqN6PuV7bZy7LDtuRudNDFwzx1FI%2FhcTzJp73Yh%2F3kB4gHiYeIT%2BEZ9JjlY4AhRhjjb1TWsI4NbGKCIzjJlCmcxhmcxTmcxwVcxCVcx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</head>
<body>
<section class="page-header">
<h1 class="title toc-ignore project-name">Regressions with <code>fixest</code> R package</h1>
<h4 class="author project-author">Rafael Felipe Bressan</h4>
<h4 class="date project-date">2021-10-08</h4>
</section>
<div id="TOC" class="toc">
<div class="toc-box">
<ul>
<li><a href="#installation-and-dataset-ingestion">Installation and dataset ingestion</a></li>
<li><a href="#cleaning">Cleaning</a></li>
<li><a href="#linear-regressions">Linear Regressions</a>
<ul>
<li><a href="#simple-regression">Simple regression</a></li>
<li><a href="#multiple-regression">Multiple regression</a></li>
<li><a href="#multiple-estimations">Multiple estimations</a></li>
<li><a href="#step-wise-estimations">Step-wise estimations</a></li>
</ul></li>
<li><a href="#instrumental-variables">Instrumental Variables</a></li>
<li><a href="#fixed-effects">Fixed-effects</a>
<ul>
<li><a href="#difference-in-differences">Difference-in-Differences</a></li>
<li><a href="#event-studies">Event Studies</a></li>
</ul></li>
<li><a href="#tidying-up-multiple-regressions">Tidying up multiple regressions</a></li>
<li><a href="#useful-links">Useful Links</a></li>
<li><a href="#references">References</a></li>
</ul>
</div>
</div>
<section class="main-content">
<p>The package <code>fixest</code> provides a family of functions to perform estimations with multiple fixed-effects, instrumental variables and provides clustered standard errors without the need to use a third-party package. The two main functions are feols for linear models and feglm for generalized linear models.</p>
<div id="installation-and-dataset-ingestion" class="section level1">
<h1>Installation and dataset ingestion</h1>
<p>Install and load the package in order to use it.</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="co"># install.packages("fixest")</span></span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(data.table)</span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(fixest)</span></code></pre></div>
<p>We will use for this class a dataset containing a sample of 12,834 individuals in the labor force extracted from the 2019 annual supplement of the 2019 US Current Population Survey.</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>dt <span class="ot"><-</span> <span class="fu">fread</span>(<span class="st">"Data/cps_union_data.csv"</span>)</span></code></pre></div>
</div>
<div id="cleaning" class="section level1">
<h1>Cleaning</h1>
<p>Before doing any analysis or regressions we must first check what kind of data we have been provided and make the appropriate pre-processing in order to have a “ready to regress” dataset. Usually, one would drop any columns that: i) have no variation among observations, ii) have too many missing values. Observations that <strong>eventually</strong> have a missing value for some variable should be treated case-by-case. Can you impute those values? Is that variable relevant for this regression? Should be allowed only complete cases in the dataset?</p>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(dt)</span></code></pre></div>
<pre><code>## V1 CPSID CPSIDP public_housing
## Min. : 12 Min. :2.017e+13 Min. :20171200000302 Min. :0.000
## 1st Qu.: 40891 1st Qu.:2.017e+13 1st Qu.:20171204151101 1st Qu.:0.000
## Median : 84176 Median :2.018e+13 Median :20181200737602 Median :0.000
## Mean : 86055 Mean :2.018e+13 Mean :20177009551114 Mean :0.041
## 3rd Qu.:131144 3rd Qu.:2.018e+13 3rd Qu.:20181204062606 3rd Qu.:0.000
## Max. :179189 Max. :2.019e+13 Max. :20190307097802 Max. :1.000
## NA's :8701
## age female race marital_status
## Min. :15.00 Min. :0.0000 Min. :1.000 Min. :1.000
## 1st Qu.:30.00 1st Qu.:0.0000 1st Qu.:1.000 1st Qu.:1.000
## Median :42.00 Median :0.0000 Median :1.000 Median :1.000
## Mean :42.49 Mean :0.4963 Mean :1.557 Mean :2.971
## 3rd Qu.:54.00 3rd Qu.:1.0000 3rd Qu.:1.000 3rd Qu.:6.000
## Max. :85.00 Max. :1.0000 Max. :8.000 Max. :6.000
##
## veteran employed education worked_last_year
## Min. :0.00000 Min. :1 Min. : 2.0 Min. :0.0000
## 1st Qu.:0.00000 1st Qu.:1 1st Qu.: 73.0 1st Qu.:1.0000
## Median :0.00000 Median :1 Median : 81.0 Median :1.0000
## Mean :0.05756 Mean :1 Mean : 91.1 Mean :0.9758
## 3rd Qu.:0.00000 3rd Qu.:1 3rd Qu.:111.0 3rd Qu.:1.0000
## Max. :1.00000 Max. :1 Max. :125.0 Max. :1.0000
## NA's :83
## total_income_last_year wage_income_last_year own_farm_income_last_year
## Min. : 0 Min. : 0 Min. : -987.0
## 1st Qu.: 25009 1st Qu.: 23000 1st Qu.: 0.0
## Median : 44474 Median : 40000 Median : 0.0
## Mean : 61237 Mean : 55788 Mean : 113.9
## 3rd Qu.: 73005 3rd Qu.: 68000 3rd Qu.: 0.0
## Max. :1755499 Max. :1314999 Max. :1099999.0
##
## private_health_insurance medicaid class_of_worker
## Min. :0.0000 Min. :0.00000 Min. :21.00
## 1st Qu.:1.0000 1st Qu.:0.00000 1st Qu.:21.00
## Median :1.0000 Median :0.00000 Median :21.00
## Mean :0.8121 Mean :0.08446 Mean :21.98
## 3rd Qu.:1.0000 3rd Qu.:0.00000 3rd Qu.:21.00
## Max. :1.0000 Max. :1.00000 Max. :28.00
##
## class_of_worker_last_year union earnings
## Min. : 0.00 Min. :0.0000 Min. : 1.0
## 1st Qu.:22.00 1st Qu.:0.0000 1st Qu.: 480.0
## Median :22.00 Median :0.0000 Median : 794.0
## Mean :22.18 Mean :0.1152 Mean : 995.6
## 3rd Qu.:22.00 3rd Qu.:0.0000 3rd Qu.:1308.0
## Max. :29.00 Max. :1.0000 Max. :2885.0
## NA's :19</code></pre>
<p>Taking a look at the summary table above you can readly see that <code>public_housing</code> has 8701 NA’s and we should drop it. Moreover, <code>employed</code> is useless for regression since it has no variation at all, drop it. Some other NA values are found in <code>veteran</code> and <code>earnings</code> but they are not numerous. In this case you must have in mind what kind of regression you are running. Suppose your goal is to estimate the causal effect of union membership/coverage (variable <code>union</code>) on weekly earnings (variable <code>earnings</code>). Obviously, you should drop any observations where <code>earnings</code> is missing. Also, there are two columns that according to the provided dictionary (<code>dictionary.xlsx</code>) are categorical: <code>class_of_worker</code>, <code>class_of_worker_last_year</code> (the name class should’ve hinted you) and both <code>marital_status</code> and <code>race</code> which you may want to recode to be binary. Let’s do all of that.</p>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>dt <span class="ot"><-</span> dt[<span class="sc">!</span><span class="fu">is.na</span>(earnings)] <span class="co"># Keep only not NA in earnings</span></span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a>dt[, <span class="fu">c</span>(<span class="st">"V1"</span>, <span class="st">"CPSID"</span>, <span class="st">"CPSIDP"</span>, <span class="st">"public_housing"</span>, <span class="st">"employed"</span>) <span class="sc">:</span><span class="er">=</span> <span class="cn">NULL</span>] <span class="co"># drop whole columns</span></span>
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a>dt[, <span class="st">`</span><span class="at">:=</span><span class="st">`</span>(</span>
<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a> <span class="at">marital_status =</span> <span class="fu">ifelse</span>(marital_status <span class="sc">%in%</span> <span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">2</span>), <span class="dv">1</span>, <span class="dv">0</span>),</span>
<span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a> <span class="at">race =</span> <span class="fu">ifelse</span>(race <span class="sc">==</span> <span class="dv">1</span>, <span class="dv">1</span>, <span class="dv">0</span>),</span>
<span id="cb5-6"><a href="#cb5-6" aria-hidden="true" tabindex="-1"></a> <span class="at">age_2 =</span> age<span class="sc">^</span><span class="dv">2</span></span>
<span id="cb5-7"><a href="#cb5-7" aria-hidden="true" tabindex="-1"></a>)]</span>
<span id="cb5-8"><a href="#cb5-8" aria-hidden="true" tabindex="-1"></a>cat_cols <span class="ot"><-</span> <span class="fu">c</span>(<span class="st">"class_of_worker"</span>, <span class="st">"class_of_worker_last_year"</span>)</span>
<span id="cb5-9"><a href="#cb5-9" aria-hidden="true" tabindex="-1"></a>dt[, (cat_cols) <span class="sc">:</span><span class="er">=</span> <span class="fu">lapply</span>(.SD, factor), .SDcols <span class="ot">=</span> cat_cols]</span></code></pre></div>
</div>
<div id="linear-regressions" class="section level1">
<h1>Linear Regressions</h1>
<div id="simple-regression" class="section level2">
<h2>Simple regression</h2>
<p>Now we are ready to perform a simple regression of <code>earnings</code> on <code>union</code> (a binary variable) and interpret it. Is this a causal regression? Why?</p>
<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a>simple_reg <span class="ot"><-</span> <span class="fu">feols</span>(earnings<span class="sc">~</span>union, <span class="at">data =</span> dt)</span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a><span class="fu">etable</span>(simple_reg, <span class="at">cluster =</span> <span class="sc">~</span>class_of_worker_last_year)</span></code></pre></div>
<pre><code>## simple_reg
## Dependent Var.: earnings
##
## (Intercept) 976.5*** (19.40)
## union 165.7*** (15.80)
## _______________ ________________
## S.E.: Clustered by: class_of_w..
## Observations 12,815
## R2 0.00544
## Adj. R2 0.00537</code></pre>
</div>
<div id="multiple-regression" class="section level2">
<h2>Multiple regression</h2>
<p>Now let’s add some control variables to our regression. The Mincerian equation stipulate that <code>age</code>, age squared, <code>education</code> and <code>female</code> should play a role in determining <code>earnings</code>, let’s also add <code>race</code>, <code>marital_status</code> and <code>class_of_worker</code>.</p>
<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a>mult_reg <span class="ot"><-</span> <span class="fu">feols</span>(</span>
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a> earnings<span class="sc">~</span>union<span class="sc">+</span>age<span class="sc">+</span>age_2<span class="sc">+</span>education<span class="sc">+</span>female<span class="sc">+</span>race<span class="sc">+</span>marital_status<span class="sc">+</span>class_of_worker,</span>
<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> dt</span>
<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb8-5"><a href="#cb8-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb8-6"><a href="#cb8-6" aria-hidden="true" tabindex="-1"></a><span class="fu">etable</span>(mult_reg, <span class="at">cluster =</span> <span class="sc">~</span>class_of_worker_last_year, <span class="at">drop =</span> <span class="st">"class_of_worker"</span>)</span></code></pre></div>
<pre><code>## mult_reg
## Dependent Var.: earnings
##
## (Intercept) -1,444.1*** (19.81)
## union 94.22*** (15.78)
## age 60.98*** (1.755)
## age_2 -0.6218*** (0.0211)
## education 13.11*** (0.3877)
## female -334.7*** (11.27)
## race 27.01* (9.142)
## marital_status 104.8** (23.24)
## _______________ ___________________
## S.E.: Clustered by: class_of_work..
## Observations 12,815
## R2 0.33918
## Adj. R2 0.33866</code></pre>
</div>
<div id="multiple-estimations" class="section level2">
<h2>Multiple estimations</h2>
<p>The <code>fixest</code> package allows for multiple estimations (i.e. changing the dependent variable) at once. Suppose you want to regress not only <code>earnings</code> on <code>union</code> but also <code>wage_income_last_year</code> and <code>total_income_last_year</code>. You can do that in just one call to <code>feols</code> function.</p>
<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a><span class="fu">setnames</span>(dt, <span class="fu">c</span>(<span class="st">"wage_income_last_year"</span>, <span class="st">"total_income_last_year"</span>),</span>
<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">c</span>(<span class="st">"wage"</span>, <span class="st">"total"</span>))</span>
<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a>mult_est <span class="ot"><-</span> <span class="fu">feols</span>(<span class="fu">c</span>(earnings, wage, total)<span class="sc">~</span>union, <span class="at">data =</span> dt)</span>
<span id="cb10-4"><a href="#cb10-4" aria-hidden="true" tabindex="-1"></a><span class="fu">etable</span>(mult_est, <span class="at">se =</span> <span class="st">"hetero"</span>)</span></code></pre></div>
<pre><code>## model 1 model 2 model 3
## Dependent Var.: earnings wage total
##
## (Intercept) 976.5*** (6.816) 55,188.6*** (673.4) 60,643.3*** (735.1)
## union 165.7*** (17.82) 5,362.0** (1,650.7) 5,254.6** (1,766.1)
## _______________ ________________ ___________________ ___________________
## S.E. type Heterosked.-rob. Heteroskedast.-rob. Heteroskedast.-rob.
## Observations 12,815 12,815 12,815
## R2 0.00544 0.00059 0.00048
## Adj. R2 0.00537 0.00052 0.00040</code></pre>
</div>
<div id="step-wise-estimations" class="section level2">
<h2>Step-wise estimations</h2>
<p>You can also incrementally increase the complexity of your model by introducing new regressors. To estimate multiple RHS, you need to use a specific set of functions, the <strong>stepwise functions</strong>. There are four of them: sw, sw0, csw, csw0.</p>
<ul>
<li>sw: this function is <em>replaced</em> sequentially by each of its arguments,</li>
<li>sw0: starts with the empty element,</li>
<li>csw: it stands for <em>cumulative</em> stepwise. It <em>adds</em> to the formula each of its arguments sequentially,</li>
<li>csw0: cumulative, but starting with the empty element.</li>
</ul>
<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a>step_wise <span class="ot"><-</span> <span class="fu">feols</span>(earnings<span class="sc">~</span>union<span class="sc">+</span><span class="fu">csw0</span>(age, age_2),</span>
<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> dt)</span>
<span id="cb12-3"><a href="#cb12-3" aria-hidden="true" tabindex="-1"></a><span class="fu">etable</span>(step_wise)</span></code></pre></div>
<pre><code>## model 1 model 2 model 3
## Dependent Var.: earnings earnings earnings
##
## (Intercept) 976.5*** (6.722) 598.0*** (19.13) -852.2*** (48.65)
## union 165.7*** (19.79) 132.9*** (19.51) 100.2*** (18.80)
## age 8.998*** (0.4269) 83.45*** (2.348)
## age_2 -0.8467*** (0.0263)
## _______________ ________________ _________________ ___________________
## S.E. type Standard Standard Standard
## Observations 12,815 12,815 12,815
## R2 0.00544 0.03878 0.11076
## Adj. R2 0.00537 0.03863 0.11055</code></pre>
<p>More details are provided in <code>fixest</code>’s vignette on <a href="https://lrberge.github.io/fixest/articles/multiple_estimations.html">multiple estimations</a>.</p>
</div>
</div>
<div id="instrumental-variables" class="section level1">
<h1>Instrumental Variables</h1>
<p>As we all know, if we were interested in the causal effect of education attainment on earnings, we would not be able to run a multiple regression like above and interpret it as causal, <strong>education is endogenous</strong> with relation to earnings. Thus, we may resort to instrumental variable - IV - estimation to overcome this pitfall. Suppose, <em>just for the sake of this example</em>, that <code>veteran</code> status is a potential instrument to <code>education</code>. How can you estimate a two-stage least squares regression with <code>fixest</code>?</p>
<p>First notice that <code>veteran</code> still have NA values in it. Now you have to decide wether to impute values on it or just drop those observations. Let’s proceed dropping the NA values.</p>
<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a>dt2 <span class="ot"><-</span> dt[<span class="sc">!</span><span class="fu">is.na</span>(veteran)]</span>
<span id="cb14-2"><a href="#cb14-2" aria-hidden="true" tabindex="-1"></a>iv_reg <span class="ot"><-</span> <span class="fu">feols</span>(earnings<span class="sc">~</span>union<span class="sc">+</span>age<span class="sc">+</span>age_2<span class="sc">+</span>female<span class="sc">+</span>race<span class="sc">+</span>marital_status<span class="sc">+</span>class_of_worker<span class="sc">|</span>education<span class="sc">~</span>veteran,</span>
<span id="cb14-3"><a href="#cb14-3" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> dt2)</span>
<span id="cb14-4"><a href="#cb14-4" aria-hidden="true" tabindex="-1"></a><span class="fu">etable</span>(iv_reg, <span class="at">keep =</span> <span class="fu">c</span>(<span class="st">"education"</span>, <span class="st">"union"</span>), <span class="at">fitstat =</span> <span class="sc">~</span>.<span class="sc">+</span>ivf<span class="sc">+</span>ivf.p<span class="sc">+</span>wh<span class="sc">+</span>wh.p)</span></code></pre></div>
<pre><code>## iv_reg
## Dependent Var.: earnings
##
## education -10.61 (19.36)
## union 81.91** (25.13)
## ______________________________________ _______________
## S.E. type Standard
## Observations 12,732
## R2 -0.20462
## Adj. R2 -0.20556
## F-test (1st stage), education 3.3921
## F-test (1st stage), p-value, education 0.06553
## Wu-Hausman 2.7669
## Wu-Hausman, p-value 0.09626</code></pre>
<p>So, what have we done here? First notice how the <strong>endogenous variable does not appear on the RHS</strong> of the formula, it goes into a formula of its own after the vertical <code>|</code> bar delimiter. The formula for endogenous variables and its instruments takes the form: <em>endogenous ~ instrument</em>.</p>
<p>On the table presented above we opt to show only two coefficents by using the argument keep, <code>education</code>, our instrumented variable and <code>union</code>. Whenever using an IV approach to estimate something, it’s useful to perform tests of <strong>weak instrument</strong> and <strong>exclusion restriction</strong>. Here we are showing the first-stage F-test to assess instrument weakness and the Wu-Hausman endogeneity test where H0 is the absence of endogeneity of the instrumented variables. No wonder <code>veteran</code> status is a weak instrument, its correlation to education is very small at 0.0170532.</p>
</div>
<div id="fixed-effects" class="section level1">
<h1>Fixed-effects</h1>
<p>Let’s change the dataset, enough of earnings! Who wants to make money after all … In <strong>International Trade</strong> we have what is called gravity models in which we are interested in finding out the negative effect of geographic distance on trade flows. Gravity models typically include many fixed effects to account for product, period, exporter country and importer country. A very simple gravity equation would take the form:</p>
<p><span class="math display">\[
\log(trade_{nipt})=\beta \log(\text{distance}_{ni})+\gamma_n+\gamma_i+\gamma_p+\gamma_t+\varepsilon_{nipt}
\]</span> where we have the indexes <span class="math inline">\(\{n, i, p, t\}\)</span> respectively for the importer, exporter, product and period.</p>
<div class="sourceCode" id="cb16"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a><span class="fu">data</span>(<span class="st">"trade"</span>)</span>
<span id="cb16-2"><a href="#cb16-2" aria-hidden="true" tabindex="-1"></a>trade <span class="ot"><-</span> <span class="fu">as.data.table</span>(trade)</span>
<span id="cb16-3"><a href="#cb16-3" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span>(trade)</span></code></pre></div>
<pre><code>## Destination Origin Product Year dist_km Euros
## 1: LU BE 1 2007 139.5719 2966697
## 2: BE LU 1 2007 139.5719 6755030
## 3: LU BE 2 2007 139.5719 57078782
## 4: BE LU 2 2007 139.5719 7117406
## 5: LU BE 3 2007 139.5719 17379821
## 6: BE LU 3 2007 139.5719 2622254</code></pre>
<div class="sourceCode" id="cb18"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a>gravity <span class="ot"><-</span> <span class="fu">feols</span>(</span>
<span id="cb18-2"><a href="#cb18-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">log</span>(Euros) <span class="sc">~</span> <span class="fu">log</span>(dist_km) <span class="sc">|</span> Destination <span class="sc">+</span> Origin <span class="sc">+</span> Product <span class="sc">+</span> Year, </span>
<span id="cb18-3"><a href="#cb18-3" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> trade)</span>
<span id="cb18-4"><a href="#cb18-4" aria-hidden="true" tabindex="-1"></a><span class="fu">etable</span>(gravity, <span class="at">cluster =</span> <span class="sc">~</span>Origin <span class="sc">+</span> Product)</span></code></pre></div>
<pre><code>## gravity
## Dependent Var.: log(Euros)
##
## log(dist_km) -2.170*** (0.1603)
## Fixed-Effects: ------------------
## Destination Yes
## Origin Yes
## Product Yes
## Year Yes
## _______________ __________________
## S.E.: Clustered by: Orig. & Prod.
## Observations 38,325
## R2 0.70558
## Within R2 0.21932</code></pre>
<p>Like the IV approach, we provide the fixed effects in a formula of its own, after the vertical bar. But notice one very important distinction, <strong>the formula for fixed-effects is one sided</strong>, that is, only the fixed-effects, put together by <code>+</code> signs, are included. Also, you are able to cluster your standard-errors by more than one variable.</p>
<div id="difference-in-differences" class="section level2">
<h2>Difference-in-Differences</h2>
<p>The <code>trade</code> dataset is a panel of several european countries stacked along the years, from 2007 to 1016. <strong>Just for demonstration purposes</strong> let’s assume the following scenario: countries DE, FR and GB implement a reduction in tariffs, starting in 2010. With the given assumptions, it is possible to estimate the effect of such a measure on trade flows by DID. We have three countries in the treatment group and the treatment happens from 2010 onwards. Let’s create two dummy variables for group and period and then estimate our DID model<a href="#fn1" class="footnote-ref" id="fnref1"><sup>1</sup></a>.</p>
<div class="sourceCode" id="cb20"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb20-1"><a href="#cb20-1" aria-hidden="true" tabindex="-1"></a>trade[, <span class="st">`</span><span class="at">:=</span><span class="st">`</span>(</span>
<span id="cb20-2"><a href="#cb20-2" aria-hidden="true" tabindex="-1"></a> <span class="at">d_g =</span> <span class="fu">ifelse</span>(Destination <span class="sc">%in%</span> <span class="fu">c</span>(<span class="st">"DE"</span>, <span class="st">"FR"</span>, <span class="st">"GB"</span>), <span class="dv">1</span>, <span class="dv">0</span>),</span>
<span id="cb20-3"><a href="#cb20-3" aria-hidden="true" tabindex="-1"></a> <span class="at">d_t =</span> <span class="fu">ifelse</span>(Year <span class="sc">>=</span> <span class="dv">2010</span>, <span class="dv">1</span>, <span class="dv">0</span>)</span>
<span id="cb20-4"><a href="#cb20-4" aria-hidden="true" tabindex="-1"></a>)]</span>
<span id="cb20-5"><a href="#cb20-5" aria-hidden="true" tabindex="-1"></a>trade[, d_treat <span class="sc">:</span><span class="er">=</span> d_g<span class="sc">*</span>d_t]</span>
<span id="cb20-6"><a href="#cb20-6" aria-hidden="true" tabindex="-1"></a>did <span class="ot"><-</span> <span class="fu">feols</span>(<span class="fu">log</span>(Euros) <span class="sc">~</span> d_treat<span class="sc">+</span><span class="fu">log</span>(dist_km)<span class="sc">|</span> Destination <span class="sc">+</span> Year,</span>
<span id="cb20-7"><a href="#cb20-7" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> trade)</span>
<span id="cb20-8"><a href="#cb20-8" aria-hidden="true" tabindex="-1"></a><span class="fu">etable</span>(did, <span class="at">cluster =</span> <span class="sc">~</span>Origin <span class="sc">+</span> Product)</span></code></pre></div>
<pre><code>## did
## Dependent Var.: log(Euros)
##
## d_treat 0.0078 (0.0397)
## log(dist_km) -2.387*** (0.5411)
## Fixed-Effects: ------------------
## Destination Yes
## Year Yes
## _______________ __________________
## S.E.: Clustered by: Orig. & Prod.
## Observations 38,325
## R2 0.27227
## Within R2 0.18419</code></pre>
<p>A DID specification can be interpreted and run as a canonical two-way fixed effects (TWFE). You can add control variables, like <code>log(dist_km)</code> either to make the unconfoundedness assumption more plausible or to improve the precision of your estimator.</p>
</div>
<div id="event-studies" class="section level2">
<h2>Event Studies</h2>
<p>What if we want to run the entire “event-study” where we estimate the treatment effect for the whole period at hand, even before the actual treatment takes place (placebo-like regression)? In a regression context, TWFE essentially amounts to an interaction between our treatment group dummy and Year variables. This is easily done using the <code>i(fact_var, num_var, reference)</code> syntax:</p>
<div class="sourceCode" id="cb22"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb22-1"><a href="#cb22-1" aria-hidden="true" tabindex="-1"></a>es <span class="ot"><-</span> <span class="fu">feols</span>(<span class="fu">log</span>(Euros)<span class="sc">~</span><span class="fu">log</span>(dist_km) <span class="sc">+</span> <span class="fu">i</span>(Year, d_g, <span class="st">"2009"</span>)<span class="sc">|</span>Destination <span class="sc">+</span> Year,</span>
<span id="cb22-2"><a href="#cb22-2" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> trade)</span>
<span id="cb22-3"><a href="#cb22-3" aria-hidden="true" tabindex="-1"></a><span class="fu">etable</span>(es, <span class="at">cluster =</span> <span class="sc">~</span>Origin <span class="sc">+</span> Product)</span></code></pre></div>
<pre><code>## es
## Dependent Var.: log(Euros)
##
## log(dist_km) -2.387*** (0.5411)
## d_g x Year = 2007 0.0742 (0.0778)
## d_g x Year = 2008 0.1161 (0.0663)
## d_g x Year = 2010 -0.0918 (0.0600)
## d_g x Year = 2011 0.0323 (0.0552)
## d_g x Year = 2012 0.0750* (0.0320)
## d_g x Year = 2013 0.1080* (0.0488)
## d_g x Year = 2014 0.0980** (0.0310)
## d_g x Year = 2015 0.1535* (0.0587)
## d_g x Year = 2016 0.1240** (0.0334)
## Fixed-Effects: ------------------
## Destination Yes
## Year Yes
## _________________ __________________
## S.E.: Clustered by: Orig. & Prod.
## Observations 38,325
## R2 0.27235
## Within R2 0.18428</code></pre>
<p>Here we set the last year before treatment takes place, 2009, as the reference, thus, its coefficient is set to zero and is not reported. Before that year we have placebo regressions, where one should not expect any effect. The coefficients post-reference are treatment effect estimations for each of those years, and the event-study may uncover dynamic effects<a href="#fn2" class="footnote-ref" id="fnref2"><sup>2</sup></a>.</p>
<p>The <code>Year</code> variable is taken as a factor (i.e. categorical) and interacted with the treatment group dummy, then the coefficient associated with that interaction is interpreted as the differential of the dependent variable between the treatment and control group on that specific year.</p>
<p>You can visualise the results with the command <code>iplot</code> to see only the interacted coefficients and their confidence intervals.</p>
<div class="sourceCode" id="cb24"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb24-1"><a href="#cb24-1" aria-hidden="true" tabindex="-1"></a><span class="fu">iplot</span>(es, <span class="at">cluster =</span> <span class="sc">~</span>Origin <span class="sc">+</span> Product)</span></code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
</div>
</div>
<div id="tidying-up-multiple-regressions" class="section level1">
<h1>Tidying up multiple regressions</h1>
<p>You can use data frames (and data.table in particular) to store models, lists, and other data frames in what is called a list-column. This will be a nested <code>data.table</code>, where some columns may be the usual vectors but the list-column will hold a <strong>list of more complex</strong> data structures. The table will store the products of your data analysis in an organized way, and you can manipulate the table with your familiar tools.</p>
<p>Imagine a <code>data.table</code> created to hold many parameterized models. One column to hold the dependent variable, another for regressors and one more for instrumental variables. Each row will have all the components related to a regression, therefore, the natural place to hold the results of such regression is in the same <code>data.table</code>, there enters the list-column.</p>
<div class="sourceCode" id="cb25"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb25-1"><a href="#cb25-1" aria-hidden="true" tabindex="-1"></a>r_ed <span class="ot"><-</span> <span class="st">"union+education+age+age_2+female+race+marital_status+class_of_worker"</span></span>
<span id="cb25-2"><a href="#cb25-2" aria-hidden="true" tabindex="-1"></a>r_iv <span class="ot"><-</span> <span class="fu">sub</span>(<span class="st">"education</span><span class="sc">\\</span><span class="st">+"</span>, <span class="st">""</span>, r_ed)</span>
<span id="cb25-3"><a href="#cb25-3" aria-hidden="true" tabindex="-1"></a>models_dt <span class="ot"><-</span> <span class="fu">CJ</span>(</span>
<span id="cb25-4"><a href="#cb25-4" aria-hidden="true" tabindex="-1"></a> <span class="at">y =</span> <span class="fu">c</span>(<span class="st">"earnings"</span>, <span class="st">"log(earnings)"</span>),</span>
<span id="cb25-5"><a href="#cb25-5" aria-hidden="true" tabindex="-1"></a> <span class="at">x =</span> <span class="fu">c</span>(<span class="st">"union"</span>, r_ed, r_iv))</span>
<span id="cb25-6"><a href="#cb25-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb25-7"><a href="#cb25-7" aria-hidden="true" tabindex="-1"></a>models_dt[, iv <span class="sc">:</span><span class="er">=</span> <span class="fu">ifelse</span>(x <span class="sc">==</span> r_iv, <span class="st">"|education~veteran"</span>, <span class="st">""</span>)]</span>
<span id="cb25-8"><a href="#cb25-8" aria-hidden="true" tabindex="-1"></a>models_dt[, form <span class="sc">:</span><span class="er">=</span> <span class="fu">paste0</span>(y, <span class="st">"~"</span>, x, iv)]</span>
<span id="cb25-9"><a href="#cb25-9" aria-hidden="true" tabindex="-1"></a>models_dt[, reg <span class="sc">:</span><span class="er">=</span> <span class="fu">lapply</span>(form, <span class="cf">function</span>(x){</span>
<span id="cb25-10"><a href="#cb25-10" aria-hidden="true" tabindex="-1"></a> <span class="fu">feols</span>(<span class="fu">as.formula</span>(x),</span>
<span id="cb25-11"><a href="#cb25-11" aria-hidden="true" tabindex="-1"></a> <span class="at">data =</span> dt2,</span>
<span id="cb25-12"><a href="#cb25-12" aria-hidden="true" tabindex="-1"></a> <span class="at">se =</span> <span class="st">"hetero"</span>,</span>
<span id="cb25-13"><a href="#cb25-13" aria-hidden="true" tabindex="-1"></a> <span class="at">lean =</span> <span class="cn">TRUE</span>)</span>
<span id="cb25-14"><a href="#cb25-14" aria-hidden="true" tabindex="-1"></a>})]</span>
<span id="cb25-15"><a href="#cb25-15" aria-hidden="true" tabindex="-1"></a>models_dt</span></code></pre></div>
<pre><code>## y
## 1: earnings
## 2: earnings
## 3: earnings
## 4: log(earnings)
## 5: log(earnings)
## 6: log(earnings)
## x
## 1: union
## 2: union+age+age_2+female+race+marital_status+class_of_worker
## 3: union+education+age+age_2+female+race+marital_status+class_of_worker
## 4: union
## 5: union+age+age_2+female+race+marital_status+class_of_worker
## 6: union+education+age+age_2+female+race+marital_status+class_of_worker
## iv
## 1:
## 2: |education~veteran
## 3:
## 4:
## 5: |education~veteran
## 6:
## form
## 1: earnings~union
## 2: earnings~union+age+age_2+female+race+marital_status+class_of_worker|education~veteran
## 3: earnings~union+education+age+age_2+female+race+marital_status+class_of_worker
## 4: log(earnings)~union
## 5: log(earnings)~union+age+age_2+female+race+marital_status+class_of_worker|education~veteran
## 6: log(earnings)~union+education+age+age_2+female+race+marital_status+class_of_worker
## reg
## 1: <fixest[27]>
## 2: <fixest[38]>
## 3: <fixest[27]>
## 4: <fixest[27]>
## 5: <fixest[38]>
## 6: <fixest[27]></code></pre>
<p>So, now we have a data.table called <code>models_dt</code> which holds parameters and fitted models, everything in one place. The column <code>reg</code> is a list-column, and each element of this list (corresponding to one row) is a <code>fixest</code> regression result. Now it is quite easy to select only a subset of models and present them in a table, for example.</p>
<div class="sourceCode" id="cb27"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb27-1"><a href="#cb27-1" aria-hidden="true" tabindex="-1"></a><span class="fu">etable</span>(models_dt[y <span class="sc">==</span> <span class="st">"log(earnings)"</span>, reg], <span class="at">keep =</span> <span class="fu">c</span>(<span class="st">"education"</span>, <span class="st">"union"</span>), </span>
<span id="cb27-2"><a href="#cb27-2" aria-hidden="true" tabindex="-1"></a> <span class="at">fitstat =</span> <span class="sc">~</span>.<span class="sc">+</span>ivf<span class="sc">+</span>ivf.p<span class="sc">+</span>wh<span class="sc">+</span>wh.p)</span></code></pre></div>
<pre><code>## model 1 model 2
## Dependent Var.: log(earnings) log(earnings)
##
## union 0.2782*** (0.0183) 0.1787*** (0.0220)
## education -0.0027 (0.0181)
## ______________________________________ __________________ __________________
## S.E. type Heteroskedas.-rob. Heteroskedas.-rob.
## Observations 12,732 12,732
## R2 0.01159 0.14682
## Adj. R2 0.01152 0.14615
## F-test (1st stage), education -- 3.3921
## F-test (1st stage), p-value, education -- 0.06553
## Wu-Hausman -- 0.90495
## Wu-Hausman, p-value -- 0.34148
## model 3
## Dependent Var.: log(earnings)
##
## union 0.1868*** (0.0179)
## education 0.0131*** (0.0003)
## ______________________________________ __________________
## S.E. type Heteroskedas.-rob.
## Observations 12,732
## R2 0.32650
## Adj. R2 0.32597
## F-test (1st stage), education --
## F-test (1st stage), p-value, education --
## Wu-Hausman --
## Wu-Hausman, p-value --</code></pre>
<p>This is a very simple, and short, example but sometimes the number of models we want to estimate grows exponentially and, in those cases this approach of holding models <em>inside</em> a data frame proves useful. Would he choose one name for each regression run, <span class="citation">Sala-I-Martin (1997)</span> would be in trouble to come up with <em>insightful</em> names…</p>
</div>
<div id="useful-links" class="section level1">
<h1>Useful Links</h1>
<p><a href="https://cran.r-project.org/web/packages/fixest/vignettes/fixest_walkthrough.html">fixest Walkthrough</a></p>
<p><a href="https://lrberge.github.io/fixest/">fixest Homepage</a></p>
<p><a href="https://www.rstudio.com/resources/rstudioconf-2020/list-columns-in-data-table-reducing-the-cognitive-computational-burden-of-complex-data/">List-columns in data.table</a></p>
<p><a href="https://www.youtube.com/watch?v=bQZGDKrbHoA">Prof. Nick Huntington-Klein video on fixest</a></p>
</div>
<div id="references" class="section level1 unnumbered">
<h1 class="unnumbered">References</h1>
<div id="refs" class="references csl-bib-body hanging-indent">
<div id="ref-callaway2020difference" class="csl-entry">
Callaway, Brantly, and Pedro HC Sant’Anna. 2020. <span>“Difference-in-Differences with Multiple Time Periods.”</span> <em>Journal of Econometrics</em>.
</div>
<div id="ref-de2020two" class="csl-entry">
De Chaisemartin, Clément, and Xavier d’Haultfoeuille. 2020. <span>“Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects.”</span> <em>American Economic Review</em> 110 (9): 2964–96.
</div>
<div id="ref-goodman2021difference" class="csl-entry">
Goodman-Bacon, Andrew. 2021. <span>“Difference-in-Differences with Variation in Treatment Timing.”</span> <em>Journal of Econometrics</em>.
</div>
<div id="ref-martin1997" class="csl-entry">
Sala-I-Martin, Xavier X. 1997. <span>“I Just Ran Two Million Regressions.”</span> <em>The American Economic Review</em> 87 (2): 178–83. <a href="http://www.jstor.org/stable/2950909">http://www.jstor.org/stable/2950909</a>.
</div>
<div id="ref-sun2020estimating" class="csl-entry">
Sun, Liyang, and Sarah Abraham. 2020. <span>“Estimating Dynamic Treatment Effects in Event Studies with Heterogeneous Treatment Effects.”</span> <em>Journal of Econometrics</em>.
</div>
</div>
</div>
<div class="footnotes">
<hr />
<ol>
<li id="fn1"><p>Remember, this is just for demonstration purposes. The following exercise is not historically accurate nor should make economic sense. Moreover, I have no clue whether we will find any statistical significance and if so, this is just a data artifact and should not be interpreted in any way.<a href="#fnref1" class="footnote-back">↩︎</a></p></li>
<li id="fn2"><p>There is a growing literature showing that the assumptions under this kind of regression is much stronger than the canonical DID (2x2), therefore, those event-study like estimations may be severely biased. See <span class="citation">Callaway and Sant’Anna (2020)</span>, <span class="citation">De Chaisemartin and d’Haultfoeuille (2020)</span>, <span class="citation">Goodman-Bacon (2021)</span>, <span class="citation">Sun and Abraham (2020)</span>.<a href="#fnref2" class="footnote-back">↩︎</a></p></li>
</ol>
</div>
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