Understanding diamond pricing using unconditional

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pricing depending on cut shape. The price of diamonds increases markedly with the carat weight, ... explained by a whole-number effect. In other words ... weight can only be rounded up to the next hundredth from nine thousandths of a carat.
Understanding diamond pricing using unconditional quantile regressions Nicolas G. Vaillant, Fran¸cois-Charles Wolff

To cite this version: Nicolas G. Vaillant, Fran¸cois-Charles Wolff. Understanding diamond pricing using unconditional quantile regressions. 2013.

HAL Id: halshs-00853384 https://halshs.archives-ouvertes.fr/halshs-00853384 Submitted on 22 Aug 2013

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1 23F BCE1

K31

1

1 ?E3F1

0EF31

1

1 ?FBECC1

1 1 111116FE;1DBFEC1F1456F39A64811B"B371 1 1 1

33B31

9FB33F1

1

1

1

7M1 1 AB651)'1*A786A8AD31D14A9CD341E6AF571

40

Frequency (in %)

30

20

10

0 100000

1 1 1

6FE;13AFCC133BC1CB1331F1456F39A64811 1

1

741 1 AB651,'13514A9CD341E6AF5%5AB816598AD37AE1

14

Price (ln)

12

10

8

6 -1

0

1 Carats (ln)

2

3

1 1

6FE;13AFCC133BC1CB1331F1456F39A64811 1

1

7!1 1 AB651-'1D34A8AD391938A51578AC98571D18514A9CD341E6AF5%5AB816598AD37AE1

2.2

Carat weight coefficient

2 Brilliant diamonds

1.8

All diamonds 1.6

1.4 0

10

20

30

40 50 60 Quantile of diamond price

70

80

90

100

1 1 1 1 1 1 1 1

6FE;13AFCC133BC1CB1331F1456F39A64811

1

1

1 1 Number of diamonds 4,000

6,000

8,000

1

.4 .41 .42 .43 .44 .45 .46 .47 .48 .49 .5 .51 .52 .53 .54 .55 .56 .57 .58 .59 .6 .61 .62 .63 .64 .65 .66 .67 .68 .69 .7 .71 .72 .73 .74 .75 .76 .77 .78 .79 .8 .81 .82 .83 .84 .85 .86 .87 .88 .89 .9 .91 .92 .93 .94 .95 .96 .97 .98 .99 1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.2 1.21 1.22 1.23 1.24 1.25

2,000

AB651/'1C561D14A9CD3471$1F96981%5AB81

6FE;13AFCC133BC1CB1331F1456F39A6481 5E1;19AE1C3DE1BC1FECFBE11B3C1ACE1EBA1BC1DFBCE1EEE16'13175@13F3C1 1 1 1 1

0

1

7&1

561 1 AB6510'1*A7FD38A3A8$1A314A9CD341E6AF541$1F96981%5AB81 6@6"6M&13F31

6'6"6@&13F31 100

60

75

40

25

Price increase (in %)

Price increase (in %)

Price increase (in %)

40

50

6M6"64&13F31

60

20

20

0

0 0 -20 -25

-20 .4

.45 Row price

.5 Carat weight

.55

.6

.5

Price net of composition effect

.55 Row price

.6 Carat weight

.65

.7

.7 Carat weight

.75

.8

Price net of composition effect

1

1

6!6"6&&13F31

6&6"76&13F3C1 60

30

40

40 Price increase (in %)

60

Price increase (in %)

40

20

.65 Row price

1 646"6!&13F31

Price increase (in %)

.6

Price net of composition effect

20

20

10 0

0

0 -20 .7

.75 Row price

.8 Carat weight

.85

.9

-20 .8

Price net of composition effect

.85 Row price

.9 Carat weight

.95

1

30

30 Price increase (in %)

20 Price increase (in %)

40

20

10

0

Row price

1.15

1.2

20

10

0

-10 1.1 Carat weight

1.1

1

40

1.05

1.05

Price net of composition effect

756"78&13F3C1

30

1

1 Carat weight

1 776"75&13F3C1

10

.95 Row price

1 766"77&13F3C1

Price increase (in %)

.9

Price net of composition effect

0 1.1

Price net of composition effect

1.15 Row price

1.2 Carat weight

1.25

1.3

1.2

Price net of composition effect

1.25

1.3 Carat weight

Row price

1

1.35

1.4

Price net of composition effect

1

786"7'&13F3C1

1

7'6"7@&13F3C1

30

7@6"7M&13F3C1

30

20

20

15

10

0

Price increase (in %)

Price increase (in %)

Price increase (in %)

20

10

0

10

5

-10 0

-20 -10

-5 1.3

1.35 Row price

1.4 Carat weight

1.45

Price net of composition effect

1.5

1.4

1.45 Row price

1.5 Carat weight

1.55

1.6

1.5

Price net of composition effect

1 1116FE;13AFCC133BC1CB1331F1456F39A6481 1115E;1?FBE1BFE3CEC13FE13BE1F1/E3C"+CE1,EB3B1ECB3EC11 1

1

1.55

1.6 Carat weight

Row price

1.65

1.7

Price net of composition effect

1

1

1

571 1 1 3951&'1*57F6AE8A+517898A78AF71D185179CE51 F3FB3EC1 2E31 .1CA3DE1 +CCAEF1 66741 1 1 >FBB31F1 6@M!1 1 1 (E3F1 667@1 1 1 .CAB1 66441 1 1 23F BCE1 66541 1 1 K31 665M1 1 1 ?E3F1 66'51 1 1 ?FBECC1 67851 1 1 33B31 66'81 1 1 9FB33F1 66681 1 1 0EF31 66@61 %EBA11B13F3C71 77@&1 .F1 1 0)EDB31ABE1P11,71 677&1 1 1 0)EDB31ABE11071 67M81 1 1 33FE1ABE1P1171 674'1 1 1 33FE1ABE11971 674'1 1 1 %ABE11(71 67841 1 1 6BA41BE1ABE11:"$71 67M'1 1 1 9BE1ABE11Q"/71 66@51 1 1 9BE1F112"O71 66741 .3FB41 1 3ECC1"1:EF3413ECC11/1"1:/71 66'51 1 1 FEF41FEF416BA41:E11FF6771 664!1 1 1 FEF41FEF416BA41:E11FF6571 67671 1 1 FEF416BA41:E11F6771 67!51 1 1 FEF416BA41:E11F6571 67!41 1 1 6BA41:E116771 67&41 1 1 6BA41:E116571 67M51 1 1 6BA41:E116871 667M1 1 1 :E11:7":871 668'1 .EFBB3E1 9EB31:CBE11+EFB3119:+71 64851 1 1 0FDE319EB31/3F3F41109/71 656!1 1 1 KAEF13F3FBEC1 66M61 ?BCA1 1 0)EE1 6'5@1 1 1 FEF411 684'1 1 1 91 67@81 1 1 3BF1"1?F1 66'!1 64EF41 0)EE1 65&81 1 1 FEF411 68&&1 1 1 91 658@1 1 1 3BF1"1?F1 66481 FECEE1 5E1 64@!1 1 1 3B1 675@1 1 1 2EB1 664!1 1 1 6F1"1EF41CF1 668!1 5EF11CEF3BC1 6FE;13AFCC133BC1CB1331F1456F39A64811 1 1 1 1

61E1 67861 6'&@1 67571 65MM1 67M51 67@&1 65671 688!1 65681 66@81 65741 6!M51 685'1 68461 684&1 684&1 68''1 68461 65551 675!1 65671 65M!1 68651 68!M1 68&61 68&!1 68M&1 67541 67!71 6''81 6'6M1 658!1 6'&'1 6'!'1 68M61 657'1 6'@@1 6'&61 6'5'1 65M71 6'5!1 68871 65M&1 67&71 7756!61

1

551 1 3951)'1554D3AF14A9CD341E6AF513F8AD37167"21578AC985781 1771+1B3C1 1571>FBB31B3C1 1871>FBB31B3C1 E1 CE1 E1 CE1 E1 CE1 ------.C31 &877 1 1666'71 &5&' 1 1666@71 &5@' 1 1666471 ------%EBA11B13F3C71 7&'6 1 1666771 7&M6 1 1666771 7&@! 1 1666771 --.1CA3DE1 +CCAEF1 "6'M! 1 1666'71 1 1 1 1 1 1 >FBB31F1 3E1 1 1 1 1 1 --1 1 1 1 1 1 (E3F1 "6'55 1 1666'71 --1 1 .CAB1 "6'M7 1 1666571 1 1 1 1 --1 1 23F BCE1 "6'5@ 1 1666871 1 1 1 1 --1 1 1 1 1 1 K31 "6'@8 1 1666871 --1 1 ?E3F1 "6''& 1 1666871 1 1 1 1 --1 1 ?FBECC1 "6'@4 1 1666571 1 1 1 1 --1 1 33B31 "6'4& 1 1666871 1 1 1 1 --1 1 1 1 1 1 9FB33F1 "6@6& 1 1666&71 --1 1 0EF31 "6'&4 1 1666571 1 1 1 1 .F1 1 0)EDB31ABE1P11,71 3E1 1 3E1 1 3E1 1 ------"66&7 1 1666871 "66&6 1 1666871 1 1 0)EDB31ABE11071 "66!6 1 1666571 ------1 1 33FE1ABE1P1171 "675! 1 1666571 "67'@ 1 1666871 "67'' 1 1666871 ------1 1 33FE1ABE11971 "656! 1 1666571 "655@ 1 1666871 "655@ 1 1666871 ------"6874 1 1666871 "6874 1 1666871 1 1 %ABE11(71 "6874 1 1666571 ------1 1 6BA41BE1ABE11:"$71 "6@6@ 1 1666571 "6@65 1 1666871 "6@65 1 1666871 ------1 1 9BE1ABE11Q"/71 "6!6' 1 1666871 "6!6& 1 1666871 "6!6! 1 1666871 ------"778@ 1 1666@71 "7788 1 1666@71 1 1 9BE1F112"O71 "7767 1 1666'71 .3FB41 1 3ECC1"1:EF3413ECC11/1"1:/71 3E1 1 3E1 1 3E1 1 ------1 1 FEF41FEF416BA41:E11FF6771 "676! 1 1666871 "66!6 1 1666'71 "664& 1 1666'71 ------1 1 FEF41FEF416BA41:E11FF6571 "6566 1 1666871 "6748 1 1666871 "6746 1 1666871 ------"65M7 1 1666871 "65@4 1 1666871 1 1 FEF416BA41:E11F6771 "65!5 1 1666871 ------1 1 FEF416BA41:E11F6571 "684! 1 1666871 "684M 1 1666871 "6845 1 1666871 ------1 1 6BA41:E116771 "6@5& 1 1666871 "6@8' 1 1666871 "6@5& 1 1666871 ------"6MM& 1 1666871 "6MM@ 1 1666871 1 1 6BA41:E116571 "6M4@ 1 1666871 ------"6!55 1 1666M71 "6!74 1 1666M71 1 1 6BA41:E116871 "6!'8 1 1666@71 ------1 1 :E11:7":871 "6&4M 1 1666'71 "6&47 1 1666'71 "6&M4 1 1666'71 ------6787 1 1666871 6758 1 1666871 .EFBB3E1 9EB31:CBE11+EFB3119:+71 6765 1 1666571 ------"655M 1 1666871 "658' 1 1666871 1 1 0FDE319EB31/3F3F41109/71 "67@& 1 1666571 1 1 KAEF13F3FBEC1 3E1 1 3E1 1 3E1 1 ------?BCA1 1 0)EE1 665' 1 1666771 665& 1 1666571 6654 1 1666571 ------6685 1 1666571 6658 1 1666571 64EF41 0)EE1 66'! 1 1666771 ------FECEE1 5E1 664' 1 1666871 66&7 1 1666871 66&6 1 1666871 ------1 1 3B1 66M& 1 1666871 66!' 1 1666'71 66!7 1 1666'71 ------66'6 1 1666'71 668! 1 1666'71 1 1 2EB1 668@ 1 1666871 1 1 6F1"1EF41CF1 3E1 1 3E1 1 3E1 1 --KDB31EDA11@&"M5@H71 1 1 1 1 6685 1 1666771 --KDB313E11@@"@!H71 1 1 1 1 666' 1 1666771 --.E1 1 5E1 1 1 1 1 6688 1 1666'71 --1 1 51BF3B1 1 1 1 1 665@ 1 1666'71 1 1 KAEF1 1 1 1 1 3E1 1 5EF11CEF3BC1 7756!61 1 M84741 1 M84741 1 3R1 6&4M1 1 6&441 1 6&441 1 6FE;13AFCC133BC1CB1331F1456F39A64811 ---5E;1ECB3EC1F1K/61EC1BA1C33F1EFFFC1B1F3#EC16BBB3E1EEC13FE1FECDEBE417H11 71@H11 7131 76H1 1 1 1 1 1 F3FB3EC1

581 1 F3FB3EC1

3951,'1A547145FDCED7A8AD31D14A9CD34971E6AF51 +11CA3DEC1 6@13F31

713F31

7@13F3C1

%EBA11B13F3C71 "1 "1 "1 .1CA3DE1 5!5H1 86&H1 5M@H1 .F1 574H1 557H1 5M5H1 .3FB41 8M'H1 5!4H1 54&H1 .EFBB3E1 8MH1 @4H1 766H1 ?BCA1 75H1 7@H1 64H1 64EF41 57H1 5@H1 77H1 FECEE1 "67H1 67H1 68H1 3ECB31 M!H1 !@H1 48H1 931 7666H1 7666H1 7666H1 5EF11CEF3BC1 @&!@1 @@@@1 7!@M1 3R1 6&851 6&7'1 6&541 6FE;13AFCC133BC1CB1331F1456F39A6481 1 1

+1

&'4H1 6&H1 "68H1 5@H1 "6'H1 67H1 65H1 66H1 5'H1 7666H1 7756!61 6&4M1

6@13F31

"1 "1 86'H1 @'5H1 @@H1 77H1 7'H1 65H1 45H1 7666H1 '@7@1 6&5!1

>FBB31B3C1 713F31

7@13F3C1

"1 "1 87MH1 ''5H1 764H1 78H1 56H1 6'H1 &&H1 7666H1 868'1 6&651

"1 "1 8!8H1 8M4H1 7M&H1 65H1 6MH1 6@H1 M&H1 7666H1 77'81 6&871

1

+1

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5'1 1 3951-'1554D3AF14A9CD341E6AF513F8AD37163FD34A8AD391938A51578AC985781 F3FB3EC1 .C31 %EBA11B13F3C71 .1CA3DE1 1 +CCAEF1 1 1 >FBB31F1 1 1 (E3F1 1 1 .CAB1 1 1 23F BCE1 1 1 K31 1 1 ?E3F1 1 1 ?FBECC1 1 1 33B31 1 1 9FB33F1 1 1 0EF31 .F1 1 ,1 1 1 01 1 1 1 1 1 1 91 1 1 (1 1 1 :"$1 1 1 Q"/1 1 1 2"O1 .3FB41 1 /1"1:/1 1 1 FF671 1 1 FF651 1 1 F671 1 1 F651 1 1 671 1 1 651 1 1 681 1 1 :7":81 .EFBB3E11 9:+1 1 1 09/1 1 1 KAEFC1 ?BCA1 1 0)EE1 64EF411 0)EE1 FECEE1 5E1 1 1 3B1 1 1 2EB1 1 1 6F1"1CF1 5EF11CEF3BC1

S761 E1 4!8M---1 6&6!---1 "65!6---1 3E1 "67!!---1 "67!7---1 "6884---1 "6775---1 "67'4---1 "6'!8---1 "67!&---1 "6575---1 "65M6---1 3E1 "66M4---1 "6785---1 "6748---1 "6545---1 "68@4---1 "6@@&---1 "6!@5---1 3E1 666&1 "664&---1 "655@---1 "6'5'---1 "6'M!---1 "6'@!---1 "6@64---1 "6&88---1 67'7---1 6778---1 3E1 "6645---1 6655---1 66781 "667&1 "6686-1 3E1 7756!61

1 CE1 1665771 1666471 1667471 1 1665'71 1667671 1665671 1667@71 1667871 1667771 1667571 166@671 1667771 1 1667671 1667671 1667671 1667771 1667771 1667M71 1665&71 1 1667571 1667571 1667571 1667571 1667571 1667571 1665'71 1665'71 1667571 1667871 1 1666471 1666!71 1667'71 1667M71 1667471 1 1

S5@1 E1 !858---1 747&---1 "65M4---1 3E1 "68!'---1 "67@7---1 "688'---1 "67MM---1 "6557---1 "6@78---1 "6577---1 "68'8---1 "65@4---1 3E1 "66MM---1 "6686--1 "66M5---1 "67!&---1 "688M---1 "64M7---1 "7768---1 3E1 "66M'---1 "678'---1 "65'7---1 "68'@---1 "6'78---1 "6'55---1 "6@@@---1 "6&&4---1 675'---1 66M8---1 3E1 "665!---1 "66641 667&1 "66@8---1 "66741 3E1 7756!61

1 CE1 1665!71 1666!71 1665571 1 1665!71 1667571 1665671 1665671 1667471 1667771 1667M71 166@471 1667'71 1 1667871 1667571 1667571 1667871 1667871 1667!71 1665!71 1 1665671 1667&71 1667!71 1667!71 1667!71 1667!71 1668771 1665@71 1667'71 1667@71 1 1666!71 1666&71 1667471 1667&71 1665671 1 1

S@61 E1 !&55---1 74!4---1 "68@4---1 3E1 "6'4@---1 "6'5M---1 "6'8&---1 "6'!6---1 "6'!'---1 "6848---1 "6@7'---1 "6'&!---1 "6'7'---1 3E1 "66@5---1 "66'8---1 "66@@---1 "657&---1 "6'57---1 "6M@!---1 "6&87---1 3E1 "677@---1 "67M'---1 "67!4---1 "658!---1 "6888---1 "6'&!---1 "6!54---1 "6!M&---1 66&@---1 "66MM---1 3E1 6684---1 666M1 6758---1 66&5---1 66'@---1 3E1 7756!61

1 CE1 1665771 1666@71 1665671 1 1667&71 1667671 1667@71 1667M71 1667871 1666471 1667871 166'771 1667571 1 1666&71 1666&71 1666&71 1666&71 1666&71 1667571 1667&71 1 1667'71 1667'71 1667871 1667871 1667871 1667'71 1665871 1667471 1667771 1667571 1 1666M71 1666M71 1667871 1667'71 1667@71 1 1

S4@1 E1 76687---1 5MM8---1 "6!6&---1 3E1 "6M'6---1 "6&64---1 "6M67---1 "6!66---1 "644&---1 "6@54---1 "6!88---1 "647!---1 "6!47---1 3E1 "66!8---1 "675'---1 "65M@---1 "68&6---1 "6M!@---1 "76@4---1 "75&7---1 3E1 "6786---1 "65'7---1 "685@---1 "68&7---1 "6M67---1 "6&@7---1 "756M---1 "76&'---1 67!5---1 "6548---1 3E1 6775---1 678&---1 674!---1 67&M---1 675M---1 3E1 7756!61

1 CE1 1668671 1666471 1665!71 1 1665471 1667'71 1665771 1665771 1667471 1667771 1667471 166M!71 1667!71 1 1667571 1667571 1667871 1667871 1667871 1667!71 1665&71 1 1665771 1665771 1665671 1665671 1665671 1665671 1668571 1665@71 1667@71 1667471 1 1666!71 1666&71 1667!71 1665671 1665771 1 1

S&61 E1 7758@---1 5@&!---1 "647&---1 3E1 "6@45---1 "6447---1 "6@5'---1 "647!---1 "646M---1 "6@67---1 "6467---1 "6!57---1 "6!M!---1 3E1 "677&---1 "654M---1 "6'@'---1 "6@5&---1 "64!6---1 "6&4!---1 "75'5---1 3E1 "67@@---1 "65M8---1 "65&&---1 "6''!---1 "64!6---1 "6&&@---1 "776&---1 "6&64---1 66'M--1 "6@84---1 3E1 66@M---1 66!@---1 66'8-1 6765---1 66M6--1 3E1 7756!61

6FE;13AFCC133BC1CB1331F1456F39A64811 ---5E;1ECB3EC1F1K/61EC1BA1C33F1EFFFC1B1F3#EC16BBB3E1EEC13FE1FECDEBE417H11 71@H11 7131 76H1 1 1

1 CE1 166''71 1667871 166'771 1 1668571 1667&71 1665M71 1665!71 1665771 1667'71 1665@71 166!871 1665'71 1 1667M71 1667471 1667!71 1667&71 1667!71 1665@71 1668471 1 1668771 1668771 1665&71 1668671 1665&71 1668671 166'771 1668871 1665571 1665'71 1 1667771 1667871 1665@71 1665!71 1668671 1 1

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