1372:
25:
1105:
2038:
2258:
1367:{\displaystyle {\begin{aligned}y_{i}&=\alpha +\beta (x_{i}-\nu _{i})+\varepsilon _{i}\\y_{i}&=\alpha +\beta x_{i}+(\varepsilon _{i}-\beta \nu _{i})\\y_{i}&=\alpha +\beta x_{i}+u_{i}\quad ({\text{where }}u_{i}=\varepsilon _{i}-\beta \nu _{i})\end{aligned}}}
2288: − 1. Suppose that the level of pest infestation is independent of all other factors within a given period, but is influenced by the level of rainfall and fertilizer in the preceding period. In this instance it would be correct to say that infestation is
1833:
2429:
model, when predicting the quantity demanded in equilibrium, the price is endogenous because producers change their price in response to demand and consumers change their demand in response to price. In this case, the price variable is said to have
304:, a variable that is correlated with both the independent variable in the model and with the error term. (Equivalently, the omitted variable affects the independent variable and separately affects the dependent variable.)
1110:
1094:
1694:
1607:
386:
481:
2131:
540:
2033:{\displaystyle z_{i}={\frac {\beta _{2}+\gamma _{2}\beta _{1}}{1-\gamma _{1}\gamma _{2}}}x_{i}+{\frac {1}{1-\gamma _{1}\gamma _{2}}}v_{i}+{\frac {\gamma _{2}}{1-\gamma _{1}\gamma _{2}}}u_{i}}
1825:
997:
1749:
676:
716:
939:
1456:
1024:
2377:
2341:
899:
839:
759:
214:
194:
1476:
859:
779:
234:
2123:
2096:
2069:
1776:
1506:
1429:
1402:
567:
416:
879:
819:
799:
739:
696:
650:
630:
610:
590:
129:. The problem of endogeneity is often ignored by researchers conducting non-experimental research and doing so precludes making policy recommendations.
43:
418:
is omitted from the regression model (perhaps because there is no way to measure it directly). Then the model that is actually estimated is
1032:
2253:{\displaystyle \operatorname {E} (z_{i}u_{i})={\frac {\gamma _{2}}{1-\gamma _{1}\gamma _{2}}}\operatorname {E} (u_{i}u_{i})\neq 0}
1613:
1526:
313:
424:
2693:
2638:
2619:
2480:
2406:
489:
2396:
106:
75:
2666:
2590:
2514:
61:
2387:
Generally speaking, simultaneity occurs in the dynamic model just like in the example of static simultaneity above.
1781:
136:
Besides simultaneity, correlation between explanatory variables and the error term can arise when an unobserved or
2572:
2708:
944:
1699:
Estimating either equation by itself results in endogeneity. In the case of the first structural equation,
1517:
110:
79:
2280:
processes. It is common for some factors within a causal system to be dependent for their value in period
239:
When the explanatory variables are not stochastic, then they are strong exogenous for all the parameters.
2733:
1702:
2738:
2728:
2699:
2688:
2531:
909:
Suppose that a perfect measure of an independent variable is impossible. That is, instead of observing
145:
1516:
Suppose that two variables are codetermined, with each affecting the other according to the following
2582:
2576:
39:
655:
126:
701:
2658:
2652:
2506:
2500:
266:; however if the correlation is not contemporaneous, then the coefficient estimate may still be
912:
259:
114:
2264:
Therefore, attempts at estimating either structural equation will be hampered by endogeneity.
1434:
1002:
2362:
2326:
884:
824:
744:
295:
271:
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179:
137:
130:
1461:
844:
764:
219:
125:
in the estimation leads to biased estimates as it violates the exogeneity assumption of the
2101:
2074:
2047:
1754:
1484:
1407:
1380:
545:
394:
301:
267:
263:
243:
102:
94:
8:
2293:
255:
2723:
2530:
Antonakis, John; Bendahan, Samuel; Jacquart, Philippe; Lalive, Rafael (December 2010).
2289:
864:
804:
784:
724:
681:
635:
615:
595:
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275:
1508:, does not cause endogeneity, though it does increase the variance of the error term.
2662:
2634:
2615:
2586:
2554:
2510:
2476:
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2352:
176:
is articulated in such a way that a variable or variables is exogenous for parameter
122:
2546:
157:
2550:
118:
2682:
2717:
2558:
2401:
144:
both independent and dependent variables, or when independent variables are
2447:
86:
2273:
247:
141:
98:
2703:
2648:
2496:
2439:
251:
2434:
once the demand and supply curves are known. In contrast, a change in
2684:
Endogeneity: An inconvenient truth. Podcast with Prof. John
Antonakis
2443:
1026:
is the measurement error or "noise". In this case, a model given by
2435:
2272:
The endogeneity problem is particularly relevant in the context of
2529:
2277:
2284:
on the values of other factors in the causal system in period
1089:{\displaystyle y_{i}=\alpha +\beta x_{i}^{*}+\varepsilon _{i}}
1689:{\displaystyle z_{i}=\beta _{2}x_{i}+\gamma _{2}y_{i}+v_{i}}
1602:{\displaystyle y_{i}=\beta _{1}x_{i}+\gamma _{1}z_{i}+u_{i}}
381:{\displaystyle y_{i}=\alpha +\beta x_{i}+\gamma z_{i}+u_{i}}
258:
model then the estimate of the regression coefficient in an
270:. There are many methods of correcting the bias, including
1099:
can be written in terms of observables and error terms as
476:{\displaystyle y_{i}=\alpha +\beta x_{i}+\varepsilon _{i}}
2475:(Fourth ed.). Australia: South-Western. p. 88.
300:
In this case, the endogeneity comes from an uncontrolled
2532:"On making causal claims: A review and recommendations"
133:
techniques are commonly used to mitigate this problem.
286:
The following are some common sources of endogeneity.
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182:
2581:(Second ed.). New York: McGraw-Hill. pp.
535:{\displaystyle \varepsilon _{i}=\gamma z_{i}+u_{i}}
34:
may be too technical for most readers to understand
2633:(Sixth ed.). Malden: Blackwell. p. 139.
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2657:(Second ed.). New York: MacMillan. pp.
2505:(Second ed.). New York: MacMillan. pp.
2359:is strongly/strictly exogenous for the parameter
121:from variables which are predetermined. Ignoring
2715:
1458:, they are correlated, so the OLS estimation of
307:Assume that the "true" model to be estimated is
196:. Even if a variable is exogenous for parameter
151:
2614:(Sixth ed.). Upper Saddle River: Pearson.
1820:{\displaystyle 1-\gamma _{1}\gamma _{2}\neq 0}
1481:Measurement error in the dependent variable,
569:term has been absorbed into the error term).
2473:Introductory Econometrics: A Modern Approach
2470:
93:broadly refers to situations in which an
62:Learn how and when to remove this message
46:, without removing the technical details.
2709:Seth Godin's simple views on endogeneity
2571:
992:{\displaystyle x_{i}=x_{i}^{*}+\nu _{i}}
74:For the concept in economic theory, see
2628:
216:, it might be endogenous for parameter
2716:
2647:
2609:
2495:
2323:is sequential exogenous for parameter
44:make it understandable to non-experts
904:
18:
2407:Dependent and independent variables
1744:{\displaystyle E(z_{i}u_{i})\neq 0}
289:
117:whose values are determined by the
13:
2603:
2397:Virtuous circle and vicious circle
2212:
2135:
698:is correlated with the error term
107:endogenous and exogenous variables
76:Exogenous and endogenous variables
14:
2750:
2676:
2382:
2267:
281:
23:
2471:Wooldridge, Jeffrey M. (2009).
1511:
1309:
941:, what is actually observed is
2565:
2523:
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2241:
2218:
2164:
2141:
1732:
1709:
1357:
1310:
1253:
1224:
1165:
1139:
1:
2457:
671:{\displaystyle \gamma \neq 0}
152:Exogeneity versus endogeneity
111:simultaneous equations models
2695:Lecture on Simultaneity Bias
2551:10.1016/j.leaqua.2010.10.010
2412:
711:{\displaystyle \varepsilon }
276:Heckman selection correction
80:Endogeneity (disambiguation)
7:
2610:Greene, William H. (2012).
2390:
10:
2755:
293:
105:. The distinction between
73:
2425:For example, in a simple
1478:will be biased downward.
934:{\displaystyle x_{i}^{*}}
2654:Elements of Econometrics
2539:The Leadership Quarterly
2502:Elements of Econometrics
1451:{\displaystyle \nu _{i}}
1019:{\displaystyle \nu _{i}}
170:strong/strict exogeneity
2631:A Guide to Econometrics
2629:Kennedy, Peter (2008).
2372:{\displaystyle \alpha }
2336:{\displaystyle \alpha }
2292:within the period, but
894:{\displaystyle \gamma }
834:{\displaystyle \alpha }
754:{\displaystyle \alpha }
209:{\displaystyle \alpha }
189:{\displaystyle \alpha }
16:Concept in econometrics
2373:
2337:
2254:
2119:
2098:are uncorrelated with
2092:
2065:
2034:
1821:
1772:
1745:
1690:
1603:
1518:"structural" equations
1502:
1472:
1471:{\displaystyle \beta }
1452:
1425:
1398:
1368:
1090:
1020:
993:
935:
895:
875:
855:
854:{\displaystyle \beta }
835:
815:
801:, the distribution of
795:
775:
774:{\displaystyle \beta }
755:
735:
712:
692:
672:
646:
626:
606:
586:
572:If the correlation of
563:
536:
477:
412:
382:
260:ordinary least squares
230:
229:{\displaystyle \beta }
210:
190:
113:, where one separates
78:. For other uses, see
2374:
2338:
2255:
2120:
2118:{\displaystyle u_{i}}
2093:
2091:{\displaystyle v_{i}}
2066:
2064:{\displaystyle x_{i}}
2035:
1822:
1773:
1771:{\displaystyle z_{i}}
1746:
1691:
1604:
1503:
1501:{\displaystyle y_{i}}
1473:
1453:
1426:
1424:{\displaystyle u_{i}}
1399:
1397:{\displaystyle x_{i}}
1369:
1091:
1021:
994:
936:
896:
876:
856:
836:
816:
796:
776:
756:
741:is not exogenous for
736:
713:
693:
673:
647:
627:
607:
587:
564:
562:{\displaystyle z_{i}}
537:
478:
413:
411:{\displaystyle z_{i}}
383:
296:Omitted-variable bias
294:Further information:
272:instrumental variable
231:
211:
191:
166:sequential exogeneity
131:Instrumental variable
2612:Econometric Analysis
2363:
2355:, then the variable
2327:
2132:
2102:
2075:
2048:
1834:
1782:
1778:while assuming that
1755:
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1435:
1408:
1381:
1106:
1033:
1003:
945:
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885:
865:
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825:
821:depends not only on
805:
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745:
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682:
656:
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616:
596:
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490:
425:
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314:
302:confounding variable
262:(OLS) regression is
244:independent variable
220:
200:
180:
160:, the notion of the
127:Gauss–Markov theorem
95:explanatory variable
2578:Econometric Methods
1072:
975:
930:
632:separately affects
146:measured with error
2734:Econometric models
2369:
2333:
2319:. If the variable
2250:
2115:
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2030:
1817:
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2739:Corporate finance
2729:Estimation theory
2640:978-1-4051-8257-7
2621:978-0-13-513740-6
2482:978-0-324-66054-8
2432:total endogeneity
2427:supply and demand
2353:the Granger sense
2299:Let the model be
2210:
2018:
1963:
1915:
1316:
905:Measurement error
874:{\displaystyle z}
814:{\displaystyle y}
794:{\displaystyle x}
734:{\displaystyle x}
691:{\displaystyle x}
645:{\displaystyle y}
625:{\displaystyle z}
605:{\displaystyle z}
585:{\displaystyle x}
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2545:(6): 1086–1120.
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290:Omitted variable
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172:can be defined.
162:usual exogeneity
158:stochastic model
138:omitted variable
67:
60:
56:
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47:
27:
26:
19:
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2604:Further reading
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2347:does not cause
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920:
914:
911:
910:
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886:
883:
882:
866:
863:
862:
861:, but also on
846:
843:
842:
826:
823:
822:
806:
803:
802:
786:
783:
782:
781:, since, given
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467:
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274:regression and
221:
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83:
68:
57:
51:
48:
40:help improve it
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28:
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17:
12:
11:
5:
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2677:External links
2675:
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2598:
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2573:Johnston, John
2564:
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2446:change on the
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2399:
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2315:) +
2269:
2268:Dynamic models
2266:
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2157:
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2112:
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2085:
2081:
2058:
2054:
2044:Assuming that
2042:
2041:
2027:
2023:
2014:
2010:
2004:
2000:
1996:
1993:
1987:
1983:
1977:
1972:
1968:
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1840:
1816:
1813:
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1804:
1798:
1794:
1790:
1787:
1765:
1761:
1751:. Solving for
1740:
1737:
1734:
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1719:
1715:
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1708:
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1696:
1683:
1679:
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1255:
1250:
1246:
1242:
1239:
1234:
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1218:
1214:
1210:
1207:
1204:
1201:
1198:
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1188:
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1167:
1162:
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1149:
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1132:
1129:
1126:
1124:
1120:
1116:
1112:
1111:
1097:
1096:
1083:
1079:
1075:
1070:
1065:
1061:
1057:
1054:
1051:
1048:
1043:
1039:
1013:
1009:
986:
982:
978:
973:
968:
964:
960:
955:
951:
928:
923:
919:
906:
903:
890:
870:
850:
830:
810:
790:
770:
750:
730:
707:
687:
667:
664:
661:
641:
621:
601:
581:
556:
552:
529:
525:
521:
516:
512:
508:
505:
500:
496:
484:
483:
470:
466:
462:
457:
453:
449:
446:
443:
440:
435:
431:
405:
401:
389:
388:
375:
371:
367:
362:
358:
354:
351:
346:
342:
338:
335:
332:
329:
324:
320:
291:
288:
283:
280:
225:
205:
185:
153:
150:
109:originated in
70:
69:
31:
29:
22:
15:
9:
6:
4:
3:
2:
2751:
2740:
2737:
2735:
2732:
2730:
2727:
2725:
2722:
2721:
2719:
2710:
2707:
2705:
2701:
2697:
2692:
2690:
2686:
2681:
2680:
2670:
2668:0-02-365070-2
2664:
2660:
2656:
2655:
2650:
2646:
2642:
2636:
2632:
2627:
2623:
2617:
2613:
2608:
2607:
2594:
2592:0-07-032679-7
2588:
2584:
2580:
2579:
2574:
2568:
2560:
2556:
2552:
2548:
2544:
2540:
2533:
2526:
2518:
2516:0-02-365070-2
2512:
2508:
2504:
2503:
2498:
2492:
2484:
2478:
2474:
2467:
2463:
2449:
2445:
2441:
2437:
2433:
2428:
2422:
2418:
2408:
2405:
2403:
2402:Heterogeneity
2400:
2398:
2395:
2394:
2388:
2380:
2366:
2358:
2354:
2350:
2346:
2330:
2322:
2318:
2314:
2310:
2306:
2303: =
2302:
2297:
2295:
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2287:
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2279:
2275:
2265:
2247:
2244:
2236:
2232:
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2222:
2215:
2204:
2200:
2194:
2190:
2186:
2183:
2177:
2173:
2167:
2159:
2155:
2149:
2145:
2138:
2128:
2127:
2126:
2110:
2106:
2083:
2079:
2056:
2052:
2025:
2021:
2012:
2008:
2002:
1998:
1994:
1991:
1985:
1981:
1975:
1970:
1966:
1957:
1953:
1947:
1943:
1939:
1936:
1932:
1927:
1922:
1918:
1909:
1905:
1899:
1895:
1891:
1888:
1881:
1877:
1871:
1867:
1863:
1858:
1854:
1847:
1842:
1838:
1830:
1829:
1828:
1814:
1811:
1806:
1802:
1796:
1792:
1788:
1785:
1763:
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1738:
1735:
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1723:
1717:
1713:
1706:
1681:
1677:
1673:
1668:
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1641:
1635:
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1627:
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1618:
1610:
1594:
1590:
1586:
1581:
1577:
1571:
1567:
1563:
1558:
1554:
1548:
1544:
1540:
1535:
1531:
1523:
1522:
1521:
1519:
1509:
1493:
1489:
1479:
1465:
1443:
1439:
1416:
1412:
1389:
1385:
1352:
1348:
1344:
1341:
1336:
1332:
1328:
1323:
1319:
1304:
1300:
1296:
1291:
1287:
1283:
1280:
1277:
1274:
1272:
1265:
1261:
1248:
1244:
1240:
1237:
1232:
1228:
1221:
1216:
1212:
1208:
1205:
1202:
1199:
1197:
1190:
1186:
1176:
1172:
1168:
1160:
1156:
1152:
1147:
1143:
1136:
1133:
1130:
1127:
1125:
1118:
1114:
1102:
1101:
1100:
1081:
1077:
1073:
1068:
1063:
1059:
1055:
1052:
1049:
1046:
1041:
1037:
1029:
1028:
1027:
1011:
1007:
984:
980:
976:
971:
966:
962:
958:
953:
949:
926:
921:
917:
902:
888:
868:
848:
828:
808:
788:
768:
748:
728:
719:
705:
685:
665:
662:
659:
639:
619:
612:is not 0 and
599:
579:
570:
554:
550:
527:
523:
519:
514:
510:
506:
503:
498:
494:
468:
464:
460:
455:
451:
447:
444:
441:
438:
433:
429:
421:
420:
419:
403:
399:
373:
369:
365:
360:
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352:
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344:
340:
336:
333:
330:
327:
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318:
310:
309:
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305:
303:
297:
287:
282:Static models
279:
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92:
88:
81:
77:
66:
63:
55:
45:
41:
35:
32:This article
30:
21:
20:
2653:
2630:
2611:
2577:
2567:
2542:
2538:
2525:
2501:
2491:
2472:
2466:
2448:demand curve
2442:would be an
2431:
2421:
2386:
2383:Simultaneity
2356:
2348:
2344:
2320:
2316:
2312:
2308:
2304:
2300:
2298:
2285:
2281:
2276:analysis of
2271:
2263:
2043:
1698:
1515:
1512:Simultaneity
1480:
1376:
1098:
908:
720:
571:
485:
390:
306:
299:
285:
241:
238:
173:
169:
165:
161:
155:
135:
123:simultaneity
90:
87:econometrics
84:
58:
52:January 2023
49:
33:
2649:Kmenta, Jan
2497:Kmenta, Jan
2440:preferences
2296:over time.
2274:time series
1827:results in
1377:Since both
1315:where
542:(thus, the
142:confounding
91:endogeneity
2718:Categories
2704:Mark Thoma
2458:References
2438:tastes or
2294:endogenous
1431:depend on
268:consistent
256:regression
252:error term
248:correlated
174:Exogeneity
103:error term
99:correlated
2724:Causality
2559:1048-9843
2444:exogenous
2413:Footnotes
2367:α
2331:α
2290:exogenous
2245:≠
2216:
2201:γ
2191:γ
2187:−
2174:γ
2139:
2009:γ
1999:γ
1995:−
1982:γ
1954:γ
1944:γ
1940:−
1906:γ
1896:γ
1892:−
1878:β
1868:γ
1855:β
1812:≠
1803:γ
1793:γ
1789:−
1736:≠
1655:γ
1632:β
1568:γ
1545:β
1466:β
1440:ν
1349:ν
1345:β
1342:−
1333:ε
1284:β
1278:α
1245:ν
1241:β
1238:−
1229:ε
1209:β
1203:α
1173:ε
1157:ν
1153:−
1137:β
1131:α
1078:ε
1069:∗
1056:β
1050:α
1008:ν
981:ν
972:∗
927:∗
889:γ
849:β
829:α
769:β
749:α
706:ε
663:≠
660:γ
652:(meaning
507:γ
495:ε
465:ε
448:β
442:α
353:γ
337:β
331:α
250:with the
224:β
204:α
184:α
115:variables
101:with the
2651:(1986).
2575:(1972).
2499:(1986).
2436:consumer
2391:See also
678:), then
2700:YouTube
2689:YouTube
2659:651–733
2583:267–291
2311:,
242:If the
38:Please
2665:
2637:
2618:
2589:
2557:
2513:
2507:652–53
2479:
2343:, and
2278:causal
999:where
721:Here,
486:where
264:biased
2535:(PDF)
254:in a
156:In a
119:model
2663:ISBN
2635:ISBN
2616:ISBN
2587:ISBN
2555:ISSN
2511:ISBN
2477:ISBN
2071:and
1404:and
881:and
841:and
761:and
592:and
391:but
2702:by
2698:on
2687:on
2547:doi
2351:in
246:is
140:is
97:is
85:In
42:to
2720::
2661:.
2585:.
2553:.
2543:21
2541:.
2537:.
2509:.
2379:.
2125:,
1520::
901:.
718:.
278:.
236:.
168:,
164:,
148:.
89:,
2671:.
2643:.
2624:.
2595:.
2561:.
2549::
2519:.
2485:.
2450:.
2357:x
2349:x
2345:y
2321:x
2317:u
2313:z
2309:x
2307:(
2305:f
2301:y
2286:t
2282:t
2260:.
2248:0
2242:)
2237:i
2233:u
2227:i
2223:u
2219:(
2213:E
2205:2
2195:1
2184:1
2178:2
2168:=
2165:)
2160:i
2156:u
2150:i
2146:z
2142:(
2136:E
2111:i
2107:u
2084:i
2080:v
2057:i
2053:x
2040:.
2026:i
2022:u
2013:2
2003:1
1992:1
1986:2
1976:+
1971:i
1967:v
1958:2
1948:1
1937:1
1933:1
1928:+
1923:i
1919:x
1910:2
1900:1
1889:1
1882:1
1872:2
1864:+
1859:2
1848:=
1843:i
1839:z
1815:0
1807:2
1797:1
1786:1
1764:i
1760:z
1739:0
1733:)
1728:i
1724:u
1718:i
1714:z
1710:(
1707:E
1682:i
1678:v
1674:+
1669:i
1665:y
1659:2
1651:+
1646:i
1642:x
1636:2
1628:=
1623:i
1619:z
1595:i
1591:u
1587:+
1582:i
1578:z
1572:1
1564:+
1559:i
1555:x
1549:1
1541:=
1536:i
1532:y
1494:i
1490:y
1444:i
1417:i
1413:u
1390:i
1386:x
1358:)
1353:i
1337:i
1329:=
1324:i
1320:u
1311:(
1305:i
1301:u
1297:+
1292:i
1288:x
1281:+
1275:=
1266:i
1262:y
1254:)
1249:i
1233:i
1225:(
1222:+
1217:i
1213:x
1206:+
1200:=
1191:i
1187:y
1177:i
1169:+
1166:)
1161:i
1148:i
1144:x
1140:(
1134:+
1128:=
1119:i
1115:y
1082:i
1074:+
1064:i
1060:x
1053:+
1047:=
1042:i
1038:y
1012:i
985:i
977:+
967:i
963:x
959:=
954:i
950:x
922:i
918:x
869:z
809:y
789:x
729:x
686:x
666:0
640:y
620:z
600:z
580:x
555:i
551:z
528:i
524:u
520:+
515:i
511:z
504:=
499:i
469:i
461:+
456:i
452:x
445:+
439:=
434:i
430:y
404:i
400:z
374:i
370:u
366:+
361:i
357:z
350:+
345:i
341:x
334:+
328:=
323:i
319:y
82:.
65:)
59:(
54:)
50:(
36:.
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