Expert answer:Potential Outcome Framework and Poverty Measures p
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ps1_kids.xls
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ARE/ECN 115A
Fall 2017
Problem Set 1: Potential Outcome Framework and Poverty Measures
Due: October 17, 2017
Problem 1
Migration plays an important role in development and as a strategy for poverty reduction. Burkina Faso, whose
conditions for agriculture are far from favorable, has a long history of migratory movement, and migration within West
Africa has long taken place in response to drought and low agricultural productivity. In recent decades, migration to
destinations outside the African continent and in particular to Western Europe has become more important for migrants
from Burkina Faso.
Migration affects the household in three ways:
1. When a household member migrates, the household loses labor.
2. Migration often results in remittances.
3. Migration implies a reduction in household size for consumption.
A critical question is what happens to the welfare of rural households when they engage in migration. When
households lose labor, it may be harder for them to participate in and generate income from other activities such as
agriculture. Remittances may partly compensate for these negative effects. In addition, a reduction in household size
means less consumption pressure on the household.
BEN, a famous theoretical economist, is trying to estimate the causal impact of migration on household income. Ben
took a random sample of 1,000 households where a household member has migrated and another random sample of
1,000 households where no household member has migrated.
In Ben’s final report he estimates the naive Average Treatment Effect of the program by subtracting the average
income of the 1,000 households where no one migrated from the average income of the 1,000 households where
someone migrated.
For the rest of this question, use the Table 1 below.
(Y0 | )
(Y1 | )
=0
30,000 CFA
33,000 CFA
=1
40,000 CFA
45,000 CFA
Remember that
= [ 1 | = 1] − [ 0 | = 1] + [ 0 | = 1] − [ 0 | = 0]
=
+
1.
What is Ben’s estimate of the naive Average Treatment Effect (ATE)?
2.
What is the true causal impact of migrating on household income?
3.
How large is the selection bias?
1
Problem 2
The following two countries have the same average income per capita, ̅, equal to $3.50 USD dollars (PPP) per day.
The poverty line is also z=$3.50 USD Dollars (PPP) per day.
Please complete the following tables and express the FGT measures as percentages with two decimal spaces.
1
∑( − )
=
=1
Country A
Person #
y
1
$1
2
$2
3
$3
4
$4
5
$5
6
$6
Poor
(Yes=1
No=0)
Poor*
(z-y)
(only if
poor)
Poor*
(z-y)2
(only if
poor)
Total
2
Country B
Person #
y
1
$2
2
$2
3
$2
4
$5
5
$5
6
$5
Poor
(Yes=1
No=0)
Poor*
(z-y)
(only if
poor)
Poor*
(z-y)2
(only if
poor)
Total
Final answers
Country A
Country B
0
1
2
3
Problem 3
The KwaZulu-Natal province is located on the Indian Ocean coast of South Africa and is home to approximately
20% of South Africa’s population. The KwaZulu-Natal Income Dynamics Study (KIDS) surveyed a random sample of
households in 1993. These same households were surveyed again in 1998 and 2004. The advantage of this type of
panel (or longitudinal) data is that it permits us to explore poverty and income distribution dynamics as we can see
which households get ahead over time and which fall behind. The rest of this problem set asks you to use the KIDS
data to calculate basic measures of income distribution and poverty and to explore the importance of assets in
determining the level of expenditures.
The excel spreadsheet PS1_KIDS.xls
is the KIDS data we use for this part. Use the worksheet “Per Capita
Expenditures” which contains columns representing monthly per-capita expenditures (in Rand, the South African
currency) for each KIDS household for the years 1993, 1998 and 2004. These expenditure figures have been adjusted
to the year 2000 South African price level, and they capture the value of all household expenditures, including the
value of purchased goods and services as well as home-produced foods, the rental value of owner-occupied (or
squatter) housing, etc. The data set includes information on the approximately 500 households that provided complete
information in each of the three years.
a) Fill in the table below, where ̅ denotes the sample mean of monthly per-capita expenditures; 2 is the sample
variance; ( ̅) is the variance of the sample mean; and ( ̅) is the standard error of the sample mean.
1993
2004
̅
2
( ̅)
( ̅)
95% C.I.
b) The national poverty line in South Africa in terms of monthly per-capita expenditures is 322 Rand.1 Calculate
and report in Table 2 the various poverty indices for 1993, 1998 and 2004:
Table 2. The Evolution of Poverty in South Africa
1993
1998
2004
Headcount Index
Income Gap Ratio
Poverty Gap Ratio
FGT-2
1
In the year 2000, the market exchange rate was approximately 7 Rand/$US, while the PPP exchange rate was a bit under 3
Rand/$PPP.
4
c) Because it is longitudinal, the KIDS data set permits us to see whether or not poverty is characterized by a lot
of churning (i.e., initially poor people tend to escape poverty while their places are taken by initially non-poor
people who fall temporarily into poverty), or whether a large element of poverty is chronic (i.e., the same
people are poor period after period).
Using the KIDS data, calculate the fraction of households that were…
i. …poor in all three periods (chronically poor):
ii. …poor in only one period (transitory poor):
5
hhid
EXPEND93 EXPEND98 EXPEND04
590010
398,37
795,75
707,99
590020
801,44
302,45
210,69
590030
694,89
202,33
826,36
590040
513,42
308,05
612,07
590050
226,73
96,88
1.037,06
590090
222,16
161,66
327,85
590100
326,37
310,59
799,54
590110
463,27
242,05
1.019,54
620030
1.228,29
1.736,91
3.028,85
620070
2.730,45
3.901,27
10.490,30
620170
2.579,03
2.760,70
2.718,50
620190
1.943,15
2.719,05
2.467,80
640010
978,76
1.789,31
2.862,19
640150
1.455,39
1.867,03
2.052,69
640190
1.013,31
1.604,84
6.698,97
643030
1.791,90
3.499,34
2.018,76
650120
603,73
631,47
785,39
650260
2.734,35
10.044,17
4.333,13
650340
712,92
1.703,66
2.587,75
660020
798,75
1.348,35
1.498,10
660050
1.965,33
963,96
2.465,84
660060
1.004,78
1.916,30
2.419,07
660090
1.101,73
1.514,55
2.555,87
660130
1.325,20
2.549,80
1.914,46
660140
1.303,87
2.054,86
2.911,35
660200
1.080,64
1.419,50
2.082,92
670010
485,51
1.048,31
976,49
670080
2.033,33
1.332,55
7.851,22
670090
535,82
786,42
1.499,47
670120
795,61
752,59
2.641,00
670150
503,59
816,77
683,87
670190
1.175,79
1.673,74
4.190,71
670210
475,08
868,01
1.224,65
670220
540,01
622,02
1.019,68
670240
486,33
957,68
1.315,89
673040
818,28
1.001,88
1.669,21
680020
1.298,72
1.598,20
1.288,52
680030
1.595,23
3.292,70
2.987,16
680060
737,22
1.509,12
1.529,62
680080
698,77
1.271,51
1.703,01
680160
838,88
384,66
476,44
680210
584,04
1.491,60
1.418,37
690030
1.191,01
2.297,81
1.211,99
690040
557,11
1.054,24
4.656,50
690060
451,83
945,87
422,55
690110
455,33
781,67
1.229,25
690160
614,37
793,89
718,17
690170
292,77
869,35
744,37
693010
398,84
701,26
919,27
700010
152,89
172,22
166,41
700290
335,97
119,12
173,66
700300
710010
710020
710040
710050
710070
710090
710120
710130
710140
710150
710190
710210
710230
730010
730060
730080
730210
733040
740100
760040
770030
770050
770210
780010
780020
780030
780050
780062
780070
780100
780110
780190
780200
780210
780220
780230
780260
790010
790040
790060
800010
800020
800030
800040
800050
800080
800090
800130
800230
1930010
1930030
224,89
410,66
307,88
363,02
432,37
107,93
245,19
186,26
152,79
256,05
177,77
112,80
178,13
380,38
5.374,51
1.139,50
1.249,33
586,53
749,89
113,47
117,68
802,50
961,72
879,53
291,18
116,19
146,91
307,40
81,98
282,25
184,19
261,63
96,04
147,69
284,00
604,13
102,16
193,42
115,87
111,74
611,85
114,32
62,30
25,12
48,00
34,48
179,84
17,12
104,79
69,32
649,12
467,55
276,15
975,30
947,74
390,09
350,84
93,14
300,59
172,90
224,61
185,87
325,44
293,30
950,86
695,63
2.994,27
1.456,16
1.683,36
1.199,86
959,01
139,57
293,68
492,28
1.482,05
1.317,56
195,69
409,35
588,59
255,99
437,50
839,69
133,23
567,28
326,35
168,53
420,73
317,08
136,09
342,88
105,95
61,66
212,98
59,83
158,44
84,64
117,57
123,02
60,39
101,84
203,40
206,26
1.242,39
335,40
244,29
1.283,09
740,20
334,62
708,01
274,67
624,95
463,58
345,42
400,05
341,80
587,63
392,88
2.271,98
2.651,61
1.026,09
988,07
1.386,16
2.827,93
138,11
895,88
1.211,47
1.727,35
2.084,33
417,95
332,37
809,62
217,99
138,38
1.376,61
582,05
407,03
583,10
337,56
377,18
459,99
286,08
288,07
551,63
252,70
362,04
37,70
92,26
71,48
105,37
620,70
155,79
81,14
43,16
125,29
679,90
93,04
1930040
1930050
1930060
1930070
1930080
1930090
1930100
1930110
1930120
1930130
1930140
1940010
1940040
1940110
1940120
1940140
1940180
1950020
1950040
1950050
1950090
1950110
1950160
1950170
1950190
1950200
1960080
1960100
1960110
1960120
1960150
1960170
1970030
1970040
1970050
1970090
1970110
1970120
1970150
1980020
1980040
1980050
1980090
1980100
1980130
1980150
1980160
1980180
1980190
1980200
1990040
1990100
980,16
762,65
866,23
204,19
612,58
718,22
659,80
109,86
316,79
439,72
472,97
675,49
214,62
97,70
326,04
349,38
284,45
399,63
203,15
199,83
495,71
607,44
604,86
742,67
429,03
282,38
432,28
1.004,18
353,86
246,54
433,38
334,38
1.097,93
661,67
330,64
390,29
672,74
337,17
312,61
119,87
439,74
789,93
279,97
453,87
1.694,13
591,54
206,64
540,99
651,11
418,16
419,14
1.169,77
305,32
421,44
593,44
293,08
464,36
554,55
460,60
84,89
264,91
248,70
200,29
357,76
384,71
741,19
423,34
372,83
367,37
575,16
465,73
595,62
405,28
1.874,19
584,04
315,92
618,70
316,77
774,52
944,43
1.011,99
425,36
382,10
1.184,03
462,11
941,99
143,32
433,52
275,43
1.054,86
353,01
210,13
297,28
290,06
207,84
196,94
610,82
778,08
222,99
964,11
480,31
482,36
192,77
708,22
638,03
1.136,10
607,43
395,25
973,89
1.201,74
937,88
910,51
801,56
739,48
2.153,99
637,87
425,60
239,25
187,95
328,03
320,89
1.085,66
159,86
213,31
459,57
836,93
601,87
653,93
423,51
156,23
292,85
242,18
375,97
365,95
453,21
2.160,03
382,27
351,39
199,52
879,64
397,48
751,38
526,10
309,64
146,78
935,20
431,92
239,37
604,66
134,10
451,93
1.022,00
1.632,62
557,23
136,68
167,56
1990140
1990200
1990390
1990410
1990440
2000010
2000020
2000080
2000100
2000110
2000120
2000130
2000140
2010020
2010030
2010050
2010060
2010070
2010080
2010090
2010100
2010170
2010180
2010190
2010200
2020090
2020140
2020150
2020170
2030030
2030050
2030080
2030090
2030110
2040010
2040050
2040080
2040100
2040120
2040130
2050010
2050030
2050050
2120060
2120100
2120120
2120130
2120140
2130020
2130050
2130060
2130070
1.226,44
1.550,11
304,73
353,22
444,16
375,20
654,01
346,09
190,38
247,13
339,18
336,32
382,39
194,28
204,14
418,07
146,42
203,68
161,91
199,78
258,85
143,58
486,91
562,32
249,34
534,63
227,43
536,20
523,40
360,22
709,37
614,95
399,30
691,72
125,31
155,27
268,32
385,60
1.911,39
321,46
408,52
512,71
209,14
434,80
132,33
629,17
422,01
603,32
272,94
573,82
438,70
185,01
278,09
344,96
240,11
439,91
474,36
190,06
1.159,20
314,58
346,43
416,11
398,78
327,78
378,11
64,32
100,79
156,95
43,11
138,25
207,77
67,69
131,84
275,35
541,11
205,57
439,91
327,93
268,57
303,86
215,46
234,87
687,09
619,58
891,82
643,29
111,52
151,10
284,87
131,45
487,85
69,05
505,53
309,44
84,77
206,25
71,57
225,84
258,97
123,26
191,06
506,89
217,32
160,77
804,66
97,00
1.039,56
125,85
501,58
206,85
702,57
116,90
307,53
390,41
147,17
352,13
4.357,88
80,33
419,66
302,23
307,36
504,31
1.071,76
165,57
334,89
264,70
1.735,33
896,79
1.037,45
656,35
144,34
983,88
353,55
257,51
1.503,79
488,73
487,61
768,19
312,35
492,59
129,86
261,07
990,88
176,14
383,14
858,17
136,21
274,85
645,98
311,67
993,09
291,73
85,67
868,42
269,10
88,71
2130080
2130110
2140072
2140080
2140100
2150010
2150020
2150060
2150070
2160010
2160030
2160040
2160050
2160060
2160080
2160100
2160110
2160112
2160120
2160130
2160150
2160160
2160170
2160180
2160190
2160230
2190040
2190050
2190082
2190090
2190100
2190120
2190150
2190190
2200080
2200130
2200370
2200550
2200560
2200610
2210010
2210020
2210030
2210060
2210080
2210090
2210110
2210120
2210160
2220020
2220030
2220040
148,44
572,91
253,11
295,59
591,07
606,86
760,56
511,70
896,41
376,78
185,85
436,77
222,35
264,33
738,22
167,07
197,69
200,43
553,46
429,95
249,34
288,88
595,90
244,09
476,01
179,45
548,27
507,47
673,72
410,37
188,98
325,05
283,10
254,65
510,79
197,64
77,62
241,79
383,18
110,08
303,86
116,06
266,15
606,59
402,77
102,37
232,31
403,32
218,12
552,67
191,96
176,43
90,34
677,17
496,15
388,12
340,03
604,00
348,89
500,43
269,95
331,42
450,55
221,43
201,77
94,51
177,65
42,37
181,07
69,92
89,13
362,19
421,84
177,92
306,31
97,03
312,63
78,90
182,91
113,42
175,49
186,48
222,19
222,18
316,69
124,04
185,35
120,51
181,94
402,98
266,73
147,46
90,15
232,23
633,00
343,16
295,40
155,26
99,35
443,96
235,38
686,03
88,45
89,69
98,42
337,38
327,66
279,71
719,31
852,35
519,77
4.733,93
689,99
656,67
108,49
261,57
448,60
213,29
123,52
100,71
625,44
111,89
228,08
300,31
239,64
279,24
742,75
231,48
163,26
256,69
64,37
260,15
139,96
226,93
156,37
222,92
213,93
26,60
710,30
205,87
198,74
341,42
255,88
106,99
30,58
375,15
523,81
61,97
603,16
78,17
134,81
670,64
257,29
366,52
199,82
371,96
2220090
2220100
2220110
2220120
2220140
2220142
2220143
2230020
2230090
2230110
2230120
2230130
2240020
2240040
2240050
2240080
2240090
2240100
2240120
2240210
2240240
2240250
2250010
2250020
2250030
2250040
2250060
2250080
2250090
2250100
2250110
2250120
2250150
2250170
2250180
2250190
2250200
2250210
2260140
2260200
2260240
2260300
2260310
2260620
2260660
2260830
2260832
2260890
2270010
2270030
2270040
2270050
639,95
283,86
448,69
224,16
237,63
270,92
272,43
541,57
375,32
777,56
134,92
292,11
214,03
170,89
113,26
208,57
272,15
285,53
588,62
396,64
900,48
285,42
218,98
221,57
223,58
220,42
170,16
176,97
89,46
295,41
261,15
216,94
404,98
372,85
353,72
106,82
115,19
160,81
343,58
550,77
740,36
156,04
510,40
386,10
153,11
403,57
405,12
528,50
154,42
144,66
421,95
352,77
365,01
49,30
158,17
315,40
384,83
512,04
146,01
570,11
207,18
123,04
47,34
100,98
387,75
223,53
154,25
142,51
177,48
288,09
779,10
392,15
623,86
143,67
52,93
126,80
282,11
156,91
135,44
117,40
454,33
167,50
413,11
366,26
218,56
431,54
216,36
113,48
124,63
164,48
153,25
284,84
390,10
323,77
299,63
291,75
44,22
687,19
846,64
501,50
65,26
245,02
134,51
182,02
260,25
69,43
593,31
386,35
975,52
455,06
377,66
840,91
41,89
138,04
290,83
259,90
481,27
71,86
230,26
210,99
212,88
344,87
148,56
619,62
938,88
169,74
86,22
277,28
467,35
323,69
154,48
189,63
117,46
242,02
159,32
400,18
119,81
344,34
215,76
90,44
141,97
644,66
286,26
378,03
846,25
561,79
147,62
132,71
149,38
414,24
1.068,30
498,65
183,58
29,54
358,01
109,97
2270060
2270110
2270120
2270130
2270140
2270150
2270200
2280010
2280020
2280060
2280070
2280080
2280140
2280150
2280200
2290010
2290020
2290050
2290060
2290070
2290090
2290100
2290110
2290112
2290120
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159,33
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2320150
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57,60
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143,01
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605,40
196,06
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273,43
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207,64
313,95
802,90
1.447,82
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370,68
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520,70
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186,41
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313,29
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112,77
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502,91
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347,95
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108,24
66,18
109,43
201,92
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2410010
2410020
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2440120
2440152
354,12
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233,36
261,09
260,81
572,25
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760,81
165,85
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120,72
147,16
205,47
217,18
366,39
102,40
333,14
358,13
179,83
302,21
159,18
287 …
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