296:
955:
In addition, the AIDS system has been used as a brand demand system to determine optimal consumption rates for each brand using product category spending and brand prices alone. Assuming weak separability of consumer preferences, the optimal allocation of expenditure among the brands of a given
844:
53:
27:) is a consumer demand model used primarily by economists to study consumer behavior. The AIDS model gives an arbitrary second-order approximation to any demand system and has many desirable qualities of demand systems. For instance it satisfies the
529:
660:
944:, the AIDS system is derived from the "Price Invariant Generalized Logarithmic" (PIGLOG) model which allows researchers to treat aggregate consumer behavior as if it were the outcome of a single maximizing consumer.
402:
669:
968:) which was developed by James Banks, Richard Blundell, and Arthur Lewbel. It considers the existence of non-linear engel curve which is not expressed in the standard almost ideal demand system.
291:{\displaystyle \log(c(u,p))=\alpha _{0}+\sum _{k}\alpha _{k}\log(p_{k})+{\frac {1}{2}}\sum _{k}\sum _{j}\gamma _{kj}^{*}\log(p_{k})\log(p_{j})+u\beta _{0}\prod _{k}p_{k}^{\beta _{k}}}
876:
579:
919:
952:
Many studies have used the AIDS system to determine the optimal allocation of expenditure among broad commodity groups, i.e., at high levels of commodity aggregation.
410:
1062:
Banks, James, Richard
Blundell, and Arthur Lewbel. "Quadratic Engel curves and consumer demand." Review of Economics and statistics 79.4 (1997): 527-539.
584:
323:
839:{\displaystyle \log(P)\equiv \alpha _{0}+\sum _{k}\alpha _{k}\log(p_{k})+{\frac {1}{2}}\sum _{k}\sum _{j}\gamma _{kj}\log(p_{k})\log(p_{j})}
313:
level. This specification satisfies homogeneity of order 1 in prices, and is a second order approximation of any cost function.
1088:
956:
product category can be determined independently of the allocation of expenditure within other product categories.
988:
998:
987:, Angus Deaton, John Muellbauer, The American Economic Review, Vol. 70, No. 3. (Jun., 1980), pp. 312–326.
1083:
849:
28:
44:
537:
317:
888:
1030:
1022:
964:
An extension of the almost ideal demand system is the
Quadratic Almost Ideal Demand System (
925:
1078:
941:
524:{\displaystyle w_{i}=\alpha _{i}+\sum _{j}\gamma _{ij}\log(p_{j})+\beta _{i}\log\{x/P\}}
1072:
1034:
937:
32:
1026:
878:, These budget shares equations share the properties of a demand function:
655:{\displaystyle \gamma _{ij}={\frac {\gamma _{ij}^{*}+\gamma _{ji}^{*}}{2}}}
397:{\displaystyle w_{i}={\frac {\partial \log c(u,p)}{\partial \log p_{i}}}}
1013:
Baltas, George (2002). "An
Applied Analysis of Brand Demand Structure".
310:
35:, is consistent with budget constraints, and is simple to estimate.
31:, aggregates over consumers without invoking parallel linear
320:), but are however simpler to put in term of budget shares
882:
homogeneous of degree 0 in prices and total expenditure
43:
The AIDS model is based on a first specification of a
891:
852:
672:
587:
540:
413:
326:
56:
913:
870:
838:
654:
573:
523:
396:
290:
316:From this, demand equations are derived (using
846:Under relevant constraints on the parameters
8:
960:Extensions of the Almost Ideal Demand System
518:
504:
899:
890:
851:
827:
805:
783:
773:
763:
749:
737:
718:
708:
695:
671:
640:
632:
619:
611:
604:
592:
586:
539:
510:
492:
476:
454:
444:
431:
418:
412:
385:
340:
331:
325:
280:
275:
270:
260:
250:
231:
209:
190:
182:
172:
162:
148:
136:
117:
107:
94:
55:
885:sum of budget shares add up to 1 (i.e.,
977:
871:{\displaystyle \alpha ,\beta ,\gamma }
7:
372:
343:
14:
305:stand for price of L goods, and
833:
820:
811:
798:
743:
730:
685:
679:
568:
556:
482:
469:
367:
355:
237:
224:
215:
202:
142:
129:
84:
81:
69:
63:
1:
985:An Almost Ideal Demand System
666:is the price index defined by
574:{\displaystyle x=\log c(u,p)}
924:satisfy the symmetry of the
914:{\displaystyle \sum w_{i}=1}
1105:
581:is the total expenditure,
21:Almost Ideal Demand System
1027:10.1080/00036840110085996
1050:Applied Demand Analysis
1089:Mathematical economics
915:
872:
840:
656:
575:
525:
398:
292:
1048:Thomas, R.L. (1987).
916:
873:
841:
657:
576:
526:
399:
293:
16:Consumer demand model
889:
850:
670:
585:
538:
411:
324:
54:
936:First developed by
645:
624:
287:
195:
911:
868:
836:
778:
768:
713:
652:
628:
607:
571:
521:
449:
394:
288:
266:
265:
178:
177:
167:
112:
1052:. Essex: Longman.
1015:Applied Economics
769:
759:
757:
704:
650:
440:
392:
256:
168:
158:
156:
103:
47:function c(u,p):
1096:
1063:
1060:
1054:
1053:
1045:
1039:
1038:
1021:(9): 1171–1175.
1010:
1004:
1000:The Piglog Model
996:
990:
982:
920:
918:
917:
912:
904:
903:
877:
875:
874:
869:
845:
843:
842:
837:
832:
831:
810:
809:
791:
790:
777:
767:
758:
750:
742:
741:
723:
722:
712:
700:
699:
661:
659:
658:
653:
651:
646:
644:
639:
623:
618:
605:
600:
599:
580:
578:
577:
572:
530:
528:
527:
522:
514:
497:
496:
481:
480:
462:
461:
448:
436:
435:
423:
422:
403:
401:
400:
395:
393:
391:
390:
389:
370:
341:
336:
335:
318:Shephard's lemma
297:
295:
294:
289:
286:
285:
284:
274:
264:
255:
254:
236:
235:
214:
213:
194:
189:
176:
166:
157:
149:
141:
140:
122:
121:
111:
99:
98:
45:cost/expenditure
1104:
1103:
1099:
1098:
1097:
1095:
1094:
1093:
1069:
1068:
1067:
1066:
1061:
1057:
1047:
1046:
1042:
1012:
1011:
1007:
997:
993:
983:
979:
974:
962:
950:
942:John Muellbauer
934:
895:
887:
886:
848:
847:
823:
801:
779:
733:
714:
691:
668:
667:
606:
588:
583:
582:
536:
535:
488:
472:
450:
427:
414:
409:
408:
381:
371:
342:
327:
322:
321:
276:
246:
227:
205:
132:
113:
90:
52:
51:
41:
29:axioms of order
17:
12:
11:
5:
1102:
1100:
1092:
1091:
1086:
1084:Microeconomics
1081:
1071:
1070:
1065:
1064:
1055:
1040:
1005:
991:
976:
975:
973:
970:
961:
958:
949:
946:
933:
930:
929:
928:
926:Slutsky matrix
922:
910:
907:
902:
898:
894:
883:
867:
864:
861:
858:
855:
835:
830:
826:
822:
819:
816:
813:
808:
804:
800:
797:
794:
789:
786:
782:
776:
772:
766:
762:
756:
753:
748:
745:
740:
736:
732:
729:
726:
721:
717:
711:
707:
703:
698:
694:
690:
687:
684:
681:
678:
675:
649:
643:
638:
635:
631:
627:
622:
617:
614:
610:
603:
598:
595:
591:
570:
567:
564:
561:
558:
555:
552:
549:
546:
543:
532:
531:
520:
517:
513:
509:
506:
503:
500:
495:
491:
487:
484:
479:
475:
471:
468:
465:
460:
457:
453:
447:
443:
439:
434:
430:
426:
421:
417:
388:
384:
380:
377:
374:
369:
366:
363:
360:
357:
354:
351:
348:
345:
339:
334:
330:
299:
298:
283:
279:
273:
269:
263:
259:
253:
249:
245:
242:
239:
234:
230:
226:
223:
220:
217:
212:
208:
204:
201:
198:
193:
188:
185:
181:
175:
171:
165:
161:
155:
152:
147:
144:
139:
135:
131:
128:
125:
120:
116:
110:
106:
102:
97:
93:
89:
86:
83:
80:
77:
74:
71:
68:
65:
62:
59:
40:
37:
15:
13:
10:
9:
6:
4:
3:
2:
1101:
1090:
1087:
1085:
1082:
1080:
1077:
1076:
1074:
1059:
1056:
1051:
1044:
1041:
1036:
1032:
1028:
1024:
1020:
1016:
1009:
1006:
1003:USDA Web site
1002:
1001:
995:
992:
989:
986:
981:
978:
971:
969:
967:
959:
957:
953:
947:
945:
943:
939:
931:
927:
923:
908:
905:
900:
896:
892:
884:
881:
880:
879:
865:
862:
859:
856:
853:
828:
824:
817:
814:
806:
802:
795:
792:
787:
784:
780:
774:
770:
764:
760:
754:
751:
746:
738:
734:
727:
724:
719:
715:
709:
705:
701:
696:
692:
688:
682:
676:
673:
665:
647:
641:
636:
633:
629:
625:
620:
615:
612:
608:
601:
596:
593:
589:
565:
562:
559:
553:
550:
547:
544:
541:
515:
511:
507:
501:
498:
493:
489:
485:
477:
473:
466:
463:
458:
455:
451:
445:
441:
437:
432:
428:
424:
419:
415:
407:
406:
405:
386:
382:
378:
375:
364:
361:
358:
352:
349:
346:
337:
332:
328:
319:
314:
312:
308:
304:
281:
277:
271:
267:
261:
257:
251:
247:
243:
240:
232:
228:
221:
218:
210:
206:
199:
196:
191:
186:
183:
179:
173:
169:
163:
159:
153:
150:
145:
137:
133:
126:
123:
118:
114:
108:
104:
100:
95:
91:
87:
78:
75:
72:
66:
60:
57:
50:
49:
48:
46:
38:
36:
34:
30:
26:
22:
1058:
1049:
1043:
1018:
1014:
1008:
999:
994:
984:
980:
965:
963:
954:
951:
948:Applications
938:Angus Deaton
935:
663:
533:
315:
306:
302:
300:
42:
33:Engel curves
24:
20:
18:
1073:Categories
972:References
1035:154033919
893:∑
866:γ
860:β
854:α
818:
796:
781:γ
771:∑
761:∑
728:
716:α
706:∑
693:α
689:≡
677:
642:∗
630:γ
621:∗
609:γ
590:γ
551:
502:
490:β
467:
452:γ
442:∑
429:α
379:
373:∂
350:
344:∂
278:β
258:∏
248:β
222:
200:
192:∗
180:γ
170:∑
160:∑
127:
115:α
105:∑
92:α
61:
311:utility
1079:Demand
1033:
966:QUAIDS
932:Origin
662:, and
301:where
1031:S2CID
534:with
39:Model
940:and
309:the
25:AIDS
19:The
1023:doi
815:log
793:log
725:log
674:log
548:log
499:log
464:log
376:log
347:log
219:log
197:log
124:log
58:log
1075::
1029:.
1019:34
1017:.
404::
1037:.
1025::
921:)
909:1
906:=
901:i
897:w
863:,
857:,
834:)
829:j
825:p
821:(
812:)
807:k
803:p
799:(
788:j
785:k
775:j
765:k
755:2
752:1
747:+
744:)
739:k
735:p
731:(
720:k
710:k
702:+
697:0
686:)
683:P
680:(
664:P
648:2
637:i
634:j
626:+
616:j
613:i
602:=
597:j
594:i
569:)
566:p
563:,
560:u
557:(
554:c
545:=
542:x
519:}
516:P
512:/
508:x
505:{
494:i
486:+
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478:j
474:p
470:(
459:j
456:i
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425:=
420:i
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365:p
362:,
359:u
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79:p
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23:(
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