The Order of Acquisition of Durable Goods
and The Multidimensional Measurement of Poverty
Joseph Deutsch
and
Jacques Silber
August 2005
Department of Economics,
Bar-Ilan University, 52900
Ramat-Gan, Israel.
Incidence of poverty - ownership of durables - order of acquisition of durables
Paroush, J., 1965, "the Order of Acquisition of Consumer Durables,"
Econometrica (33(1): 225-235.
Guttman, L. 1950, “Relation of Scalogram Analysis to Other Techniques,
Measurement and Prediction”, Studies in Social Psychology in World
War II, vol. 4.
Guttman, L. 1959, “Simple Statistical Methods for Scalogram Analysis”,
Psychometrika.
Rational individual, maximizes utility given tastes and limited resources
Income increase – a change along the acquisition path of durables
Order of acquisition –permanent income
Order of acquisition- ordered logit regression- latent deprivation variable
Empirical analysis - 1995 Israeli Census of population – N= 204,098 households.
Durables Analyzed:
Share in Total Population
Ownership of dwelling
Phone
Television
VCR
Washing machine
Microwave oven
Dishwasher
Personal computer
Air-Conditioning
Dryer
Car
Total number of observations
Total
100.0
74.0
94.0
91.9
51.0
88.1
42.9
22.0
24.4
38.4
18.2
53.0
204098
Table 1: Ownership of Durable Goods by Gender of
Head of Household
Share in Total Population
Ownership of dwelling
Phone
Television
VCR
Washing machine
Microwave oven
Dishwasher
Personal computer
Air-Conditioning
Dryer
Car
Total number of observations
Male
69.3
77.4
93.8
91.6
55.3
90.3
46.7
24.6
27.4
40.0
20.5
60.9
141501
Female
30.7
66.1
94.4
92.5
41.4
83.1
34.2
16.0
17.7
34.6
13.1
35.2
62597
Total
100.0
74.0
94.0
91.9
51.0
88.1
42.9
22.0
24.4
38.4
18.2
53.0
204098
Note that quite important differences are observed (with male headed households being
evidently better endowed than female headed households)
Table 2: Ownership of Durable Goods by Household Size
1
19.5
2
23.4
3
15.6
4
17.4
5
12.9
6
6.1
Share in Total
Population
60.3 70.2 73.3 80.1 84.6 85.2
Ownership of
dwelling
92.0 94.5 94.6 95.6 95.8 93.8
Phone
88.0 92.9 93.6 95.1 94.5 90.7
Television
25.9 45.7 60.0 68.6 67.5 56.8
VCR
67.3 88.6 93.6 96.3 96.8 95.5
Washing machine
20.7 37.2 49.3 58.1 59.8 51.1
Microwave oven
7.4 19.5 22.7 31.6 36.7 26.2
Dishwasher
8.6 12.9 24.2 39.0 45.8 37.3
Personal computer
32.0 43.4 39.5 43.8 42.0 31.2
Air-Conditioning
5.2 10.1 18.8 28.7 33.3 28.4
Dryer
23.2 44.9 60.7 71.5 72.9 65.6
Car
39816 47827 31900 35432 26237 12500
Total
7
2.5
9
10 +
0.7 0.5
Total
100.0
84.3 83.6 83.3 86.2
74.0
90.6
84.9
42.7
92.5
36.6
15.2
23.7
20.9
20.3
56.5
5196
An inverted-U type of relationship is observed.
8
1.3
86.8
78.7
32.1
89.2
26.3
8.5
17.5
14.0
16.1
48.8
2627
83.4
75.8
29.0
85.5
22.3
5.8
13.1
11.2
15.6
47.2
1507
81.0
94.0
73.4
91.9
24.8
51.0
80.8
88.1
18.6
42.9
4.7
22.0
11.4
24.4
11.6
38.4
15.2
18.2
46.7
53.0
1056 204098
Table 3: Ownership of Durable Goods by Age of Head of Household
Share in Total
Population
Ownership of dwelling
Phone
Television
VCR
Washing machine
Microwave oven
Dishwasher
Personal computer
Air-Conditioning
Dryer
Car
Total number of
observations
less than 30
years old
13.2
30 to 59
years old
56.4
60 to 69
years old
13.8
At least 70
years old
16.6
Total
100.0
49.9
85.7
82.5
38.5
74.6
37.6
6.7
18.3
24.5
12.3
48.7
26873
77.5
95.2
92.9
61.4
93.1
52.4
28.1
35.3
39.5
25.7
66.5
115107
77.4
95.8
94.7
49.3
89.6
36.8
22.3
10.3
42.7
9.5
42.2
28242
78.1
94.9
93.5
27.1
80.5
19.8
12.9
3.9
41.9
5.0
19.5
33876
74.0
94.0
91.9
51.0
88.1
42.9
22.0
24.4
38.4
18.2
53.0
204098
With the exeption of ownership of dwelling, we observe again an inverted-U relationship.
Table 4: Ownership of Durable Goods by Marital Status of Head of Household
Share in Total Population
Ownership of dwelling
Phone
Television
VCR
Washing machine
Microwave oven
Dishwasher
Personal computer
Air-Conditioning
Dryer
Car
Total number of observations
Married
70.1
80.1
94.5
92.6
58.4
93.9
49.9
27.1
29.2
41.6
22.7
63.1
143010
Divorced
7.5
53.5
93.5
91.9
43.1
82.4
33.9
13.0
19.0
27.6
12.6
34.1
15368
Widowed
13.7
76.3
94.0
93.1
28.7
78.9
22.0
11.1
6.1
34.9
5.9
18.0
28011
Single
8.7
38.7
90.8
84.2
34.0
60.8
26.9
5.5
19.9
26.8
6.8
43.2
17709
Total
100.0
74.0
94.0
91.9
51.0
88.1
42.9
22.0
24.4
38.4
18.2
53.0
204098
The highest degree of ownership is found among households whose head is married. With
the exception of car ownership, the lowest levels of ownership are observed either among
singles or among widow(er)s.
Table 5: Ownership of Durable Goods by Year of Immigration of Head of Household
Share in Total Population
Ownership
of dwelling
Phone
Television
VCR
Washing machine
Microwave oven
Dishwasher
Personal computer
Air-Conditioning
Dryer
Car
Total
Before
1990*
86.3
90
91
92
93
94
95
Total
4.2
3.5
1.7
1.6
1.7
1.1
100.0
78.6
94.7
92.1
52.0
89.0
46.3
24.9
26.1
41.0
20.4
56.2
176043
57.5
95.5
94.7
54.7
90.9
29.5
4.5
19.5
36.8
4.3
48.4
8473
50.4
92.0
91.8
51.3
85.7
23.0
2.9
14.9
17.7
3.0
38.6
7137
45.4
89.2
90.0
43.2
81.9
18.7
3.3
13.4
14.9
5.2
33.7
3437
40.3
86.7
89.2
37.7
78.8
15.6
3.0
9.5
13.3
5.2
21.8
3285
27.9
83.7
87.9
31.8
72.3
14.9
3.5
8.7
13.9
5.6
12.1
3460
10.7
75.0
80.4
23.2
59.7
10.3
3.0
5.1
12.5
4.9
5.7
2263
74.0
94.0
91.9
51.0
88.1
42.9
22.0
24.4
38.4
18.2
53.0
204098
In many cases the degree of ownership decreases monotonically with the year of immigration.
Table 6: Ownership of Durable Goods by Schooling Level (Years of Schooling) of
Head of Household
0
1-8
9-12
Share in Total Population
6.4
19.9
41.4
Ownership of dwelling
76.0
80.1
75.3
Phone
81.3
91.9
94.5
Television
83.9
92.5
92.1
VCR
25.2
38.2
53.9
Washing machine
70.6
86.2
90.3
Microwave oven
15.7
29.0
46.6
Dishwasher
4.5
12.7
22.6
Personal computer
2.8
8.5
22.2
Air-Conditioning
14.1
29.8
39.5
Dryer
2.8
7.5
19.4
Car
14.8
34.4
55.4
Total number of observations 13145 40564 84483
13 or more Total
32.3
100.0
68.0
74.0
97.3
94.0
92.9
91.9
60.4
51.0
89.9
88.1
52.1
42.9
30.3
22.0
41.3
24.4
47.0
38.4
26.5
18.2
69.1
53.0
65906 204098
In most cases the degree of ownership increases monotonically with the schooling level
Table 7: Ownership of Durable Goods by Number of Months Worked by the Head of
the Household During the Last 12 Months
Share in Total Population
Ownership of dwelling
Phone
Television
Videotape
Washing machine
Microwave oven
Dishwasher
Personal computer
Air-Conditioning
Dryer
Car
Total number of observations
4 months or less
40.1
70.1
91.8
89.4
35.1
82.0
26.9
12.8
9.9
32.7
8.8
27.6
81905
5 to 8 months
4.3
62.6
91.0
89.9
47.7
84.5
37.6
16.0
21.8
29.2
14.4
49.6
8789
9 to 12 months Total
55.6
100.0
77.6
74.0
95.8
94.0
93.8
91.9
62.8
51.0
92.8
88.1
54.8
42.9
29.1
22.0
35.1
24.4
43.2
38.4
25.3
18.2
71.6
53.0
113404
204098
In most cases the greater the number of months the head of the household worked
during the last twelve months, the higher the degree of ownership of the various
durable goods.
Table 8: Ownership of Durable Goods by Status at Work of Head of Household
Share in Total Population
Ownership of dwelling
Phone
Television
VCR
Washing machine
Microwave oven
Dishwasher
Personal computer
Air-Conditioning
Dryer
Car
Total number of observations
Not working
Salaried
Self-employed
37.2
71.3
91.9
89.6
34.5
82.2
26.2
12.6
9.0
33.0
8.4
26.2
76019
51.7
74.6
94.8
92.9
59.4
91.2
51.2
25.0
32.4
39.2
22.3
66.2
105461
9.9
80.7
97.6
95.3
69.1
95.1
61.2
40.8
39.6
53.0
33.2
84.1
20252
Other
Status
1.2
75.2
95.4
92.3
58.2
80.5
50.7
28.6
33.1
47.5
22.8
60.1
2366
Total
100.0
74.0
94.0
91.9
51.0
88.1
42.9
22.0
24.4
38.4
18.2
53.0
204098
The degree of ownership is highest among self-employed individuals. Note also that
in most cases the degree of ownership is smallest when the head of the household
did not work during the last twelve months.
Table 10: Ownership of Durable Goods by Religion of Head of Household
Share in Total
Population
Ownership of dwelling
Phone
Television
VCR
Washing machine
Microwave oven
Dishwasher
Personal computer
Air-Conditioning
Dryer
Car
Total number of
observations
Jewish
85.1
Muslim
10.7
Christian
2.0
Druze
1.0
Other
1.2
Total
100.0
72.7
97.3
93.2
55.0
90.0
46.7
25.0
27.1
43.5
20.6
54.7
173668
87.1
70.7
82.8
23.9
74.2
17.9
2.9
7.1
7.6
3.3
42.1
21863
69.7
90.8
92.3
44.9
91.3
31.7
14.5
17.0
14.9
12.0
54.5
4013
97.1
82.8
82.3
31.0
88.7
39.6
6.5
11.3
6.9
5.4
54.2
2091
33.0
83.8
87.1
40.6
74.3
17.4
3.7
13.0
16.5
4.4
29.1
2463
74.0
94.0
91.9
51.0
88.1
42.9
22.0
24.4
38.4
18.2
53.0
204098
In many cases this degree of ownership is highest among Jewish heads of household
and lowest for Muslims.
Order of acquisition of durable goods - Paroush (1965):
For the case with 3 durables: A,B and C. Sample space - 23=8 possible outcomes
Table 11: List of possible orders of acquisition when there are 3 goods
Ownership
Profile
1
2
3
4
5
6
7
8
The
household
owns good A
0
1
1
1
0
0
0
1
The
household
owns good B
0
0
1
1
1
1
0
0
The
household
owns good C
0
0
0
1
1
0
1
1
With k=11 durables the number of possible profiles is 211=2048. In fact we found just 695
different profiles for the 204,000 households. 22 profiles account for more than 50% of the
households.
Distribution of Profiles Ranked by Number of Households
Prof.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Phone
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
T.V
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Wash
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
Dwell.
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
VCR
0
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
Car
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
0
0
0
1
1
Microw
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
1
AirCon
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
Dish
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
P.C.
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
Dryer N
N%
0
14021
6.9
1
8911 11.2
0
8522 15.4
0
5662 18.2
0
5652 21.0
0
5444 23.6
0
5271 26.2
0
4519 28.4
0
4456 30.6
0
4090 32.6
0
4067 34.6
0
3805 36.5
0
3754 38.3
0
3481 40.0
0
3391 41.7
1
3256 43.3
0
2816 44.6
0
2562 45.9
0
2549 47.1
0
2471 48.4
0
2426 49.5
0
2280 50.7
Assume that the order of acquisition is A,B and C, then all the consumers will be
distributed along the path of acquisition with profiles, 1-4 and there will be no
consumers with profiles 5-8. In this case we say that there is a perfect scale. When
comparing actual figures, some consumers may deviate from the path of acquisition.
For practical purpose, we will conclude that there is an order of acquisition if 90% of
the profiles are reproducible.
Table 11: List of possible orders of acquisition when there are 3 goods
Ownership
Profile
1
2
3
4
5
6
7
8
The
household
owns good A
0
1
1
1
0
0
0
1
The
household
owns good B
0
0
1
1
1
1
0
0
The
household
owns good C
0
0
0
1
1
0
1
1
Guttman developed the index of reproducibility as:
R 1
 N i Si
i
k  Ni
i
Where Si is the minimum distance of the profile of individual i to the closest profile pj in the
acquisition path. That is, suppose a consumer with the profile 0,1,0. If the order of
acquisition is A,B,C then the closest profile in the path of acquisition to the consumer’s
profile are profiles 1 or 3 with a deviation S=1.
List of possible profiles with
acquisition order A,B,C
Consumer’s Profile, X
Good A Good B Good C
0
1
0
The household owns
Profile, P Good A Good B Good C
1
0
0
0
2
1
0
0
3
1
1
0
4
1
1
1
Deviation
S=xi-pi
1*
2
1*
2
We then calculate de minimum deviation for each consumer in the sample, Ni is the number
of consumers with deviation Si and k is the number of commodities.
Guttmans showed that the coefficient R is bounded between 0.5 and 1.
0.5  R  1 
 N i Si
i
k  Ni
1
i
When there is a perfect scale Si=0 for all consumers and R=1.
When the profile is randomly determined,the maximum deviation will be obtained when
the consumer’s profile is a series of consecutives 0,1. In this case the value of Si=k/2.
Household’s Profile
Closest Profile
Commodity 1 2 … k-1 k
Profile X
0 1 … 0 1
-
Maximal Deviation
Commodity 1 2 … k-1 k
Profile P
1 1 … 1 1
If all the consumers have the same profile then R=0.5.
R 1
 N i Si
i
k  Ni
i
1
 Ni k / 2
i
k  Ni
i
 0.5
S=X-P=xi-pi=k/2
R 1
 N i Si
i
k  Ni
i
The calculation of the index of reproducibility assumes a given order of acquisition. Paroush
suggested to find the coefficient of reproducibility for all the possible orders of acquisition and
estimate the population order of acquisition as the order of acquisition with the highest
coefficient R provided that it is greater than 0.9.
Estimating the order of acquisition requires a very high number of computations. For a given
order of acquisition with k commodities, the path of acquisition has k+1 possible profiles.
Therefore, for each individual household i in the sample, the determination of the minimum
distance Si from his profile to one of the possible profiles in the path of acquisition is based on
12 comparisons. As our sample is based on 204,098 household, 2,449,176 comparisons are
needed in order to determine the reproducibility index R for a given order of acquisition. This
procedure has to be repeated 11! =39,916,800 times which is the total number of possible
order of acquisition resulting from 11 durable goods.
As a result, the total number of iterations needed to find the order of acquisition with the
highest index of reproducibility R is 2,449,176  39,916,800 = 9.771013.
Table 12: Order of acquisition with highest proximity coefficient R (R = 0.92)
Rank Durable Good
1
2
3
4
5
6
7
8
9
10
11
Ownership
(%)
Telephone
94.0
Television
91.9
Washing machine
88.1
Apartment (or house)
74.0
VCR
51.0
Car
53.0
Microwave oven
42.9
Air-Conditioner
38.4
Dishwasher
22.0
Computer
24.4
Dryer
18.2
The order of acquisition is similar but does not completely coincide with the rank of the
durables ordered by the percentage of ownership.
Also, the proportion of households with a profile of acquisition of durable goods
corresponding to the different stages of the order of acquisition is 32% (65,333
households).
Let Di denote the continuous level of deprivation of household i such that a higher value of Di corresponds
to higher degrees of deprivation . The deprivation score is assumed to be a function of H factors whose
value for household i are Xih , h = 1 to H. We may therefore express this latent variable Di as
k
Di    h X ih   i
h 1
where  is assumed to be a random logistic variable. We assume that this deprivation level is
related to the stage of acquisition of durable goods where the household is located. We define
the observed variable Yi as the number of durables not owned by household i. That is:
Yi  1
if
Di  1
the household owns all the 11 durable goods
(the lowest level of deprivation)
Yi  2
if
1  Di   2
the household owns only the first 10 durables
in the acquisition path

Yi  j if

Yi  12 if

 j 1  Di   j the household owns only the first j-1 durables
in the acquisition path

the household does not own any of the durable goods
11  Di
(the highest level of deprivation)
Table 13: Results of Ordered Logit Regression
(Dependent Variable = Latent deprivation index)
Explanatory Variable
Schooling
H.Size
H. Size2
Age
Age2
Jew
Muslim
Christian
Druze
Imm> 1989
Married
Divorced
Single
Jerusalem
Tel Aviv
Haifa
Working
Male
Male  married
Male divorced
Male  single
Male works
Coefficient St. Error
-0.1395 0.0018
-0.9191 0.0175
0.0751 0.0019
-0.1582 0.0029
0.0014 0.0000
-0.9890 0.0673
0.4683 0.0728
0.1951 0.0840
0.0977 0.0989
2.2979 0.0216
-0.3625 0.0364
0.9756 0.0394
1.6400 0.0489
0.6370 0.0273
0.2305 0.0264
0.0289 0.0278
-0.9153 0.0314
-0.1908 0.0477
0.3704 0.0565
0.4170 0.0819
0.1486 0.0785
-0.1179 0.0353
Number of observations: 65333
Pseudo R-square: 0.1726
Log-Likelihood: -123827.97
t-value P-value
-77.42
0.000
-52.62
0.000
40.38
0.000 Turning point=6
-54.61
0.000
51.04
0.000 Turning point=57
-14.69
0.000
6.43
0.000
2.32
0.020
0.99
0.323
106.50
0.000
-9.97
0.000
24.74
0.000
33.55
0.000
23.33
0.000
8.73
0.000
1.04
0.299
-29.17
0.000
-4.00
0.000
6.55
0.000
5.09
0.000
1.89
0.058
-3.34
0.001
Table 14: Estimated Boundaries of the Deprivation Levels
Deprivation
Level
Y=1
Y=2
Y=3
Y=4
Y=5
Y=6
Y=7
Y=8
Y=9
Y=10
Y=11
Y=12
Ownership
Level
All 11
First 10
First 9
First 8
First 7
First 6
First 5
First 4
First 3
First 2
Owns 1
Owns 0
Latent Value
From
To
-11.299
-11.299 -10.633
-10.633 -10.061
-10.061 -9.515
-9.515 -8.997
-8.997 -8.404
-8.404 -7.786
-7.786 -6.191
-6.191 -4.716
-4.716 -3.315
-3.315 -2.396
-2.396
St. Observed
Error Probabil.
0.111 0.1364
0.110 0.0626
0.109 0.0623
0.109 0.0682
0.108 0.0692
0.108 0.0807
0.107 0.0867
0.106 0.2146
0.105 0.1304
0.106 0.0582
0.108 0.0167
0.000 0.0141
We calculated for each household i in the sample the value of its latent deprivation variable
Di and defined as “poor” the top 25%.
k
Dˆ i   ˆh X ih
h 1
Table 15: Incidence of Poverty by Gender of Head of Household
Percentage
Male
Female
Total
67.6
32.4
100.0
in Sample
15.8
44.2
25.0
Poor
44150
21183
65333
Total
by Household Size
Percentage
1
2
3
4
5
6
7
8
9 +10 Total
20.4 23.0 15.1 17.5 13.6 5.9
2.4 1.1 0.6 0.4 100.0
in Sample
67.2 29.3 13.9 5.5
3.6 4.5
8.4 13.6 24.4 59.9 25.0
Poor
13340 14999 9868 11427 8892 3842 1553 743 390 279 65333
Total
by Age of Head of Household
Percentage <30 30 - 59 60 -69 70+
8.9
56.2
16.1 18.8
in Sample
51.8 11.4
27.4 51.0
Poor
5834 36716 10521 12262
Total
Percentage
in Sample
Poor
Total
Total
100.0
25.0
65333
by Marital Status of Head of Household
Married
Divorced Widowed
Single
69.3
7.5
16.2
7.0
10.0
53.8
52.1
80.2
45265
4903
10585
4580
by Year of Immigration of Head of Household
Percentage >90
90
91
92
93
94
83.5
4.3
4.3
2.0
2.1
2.2
in Sample
18.3
50.2
56.7
60.6
62.8
68.1
Poor
54539 2816 2780 1325 1364 1428
Total
Percentage
in Sample
Poor
Total
95
1.7
68.5
1081
by Years of Schooling of Head of Household
0
1-8
9-12
13+
8.1
21.8
39.4
30.7
71.1
31.1
17.8
17.7
5283
14215
25758
20077
Total
100.0
25.0
65333
Total
100.0
25.0
65333
Total
100.0
25.0
65333
by Number of Months Worked by the Head of the Household
During the Last 12 Months
Percentage
>4
5-8
9-12
Total
44.2
4.0
51.8
100.0
in Sample
44.8
22.2
8.3
25.0
Poor
28895
2600
33838
65333
Total
by Status at Work of Head of Household
Not
Salaried Self
Other
Percentage working
Empl.
Status
41.5
48.0
9.5
1.0
in Sample
45.7
11.6
3.3
15.5
Poor
27112
31369
6193
659
Total
Total
100.0
25.0
65333
by Place of Residence of Head of Household
Percentage Jerusalem Tel-Aviv Haifa 100-200 20-100 2-20 Other Total
7.6
8.6
7.0
26.9
32.0 13.4 4.4 100.0
in Sample
40.1
34.0
26.5
22.8
23.4 21.2 15.5 25.0
Poor
4985
5617
4563 17597 20932 8769 2870 65333
Total
by Religion of Head of Household
Percentage Jewish Muslim Christian Druze
86.8
9.1
1.9
0.9
in Sample
23.7
29.4
33.6
13.4
Poor
56706 5957
1248
559
Total
Other Total
1.3
100.0
73.8
25.0
863 65333

(1  Rˆ )( Rˆ  0.5)
(1  Rˆ )( Rˆ  0.5) 
ˆ

ˆ
Pr R  z
 R Rz
 1
N
N



