Estimating Utility Consistent Poverty Lines: With Illustrations from

Mozambique and Tanzania Channing Arndt

University of Copenhagen

Motivation for GAPP

What is happening in Africa?

Operational Foci

• Relative price differences are important • Across space • Through time • Over the income distribution

• Need to triangulate and understand outcomes • Macro, prices, terms of trade, role of agriculture ,

poverty-growth-inequality triangle etc. • Monetary and non-monetary measures

Material Drawn From

• Arndt, C. and K. Simler. “Estimating Utility Consistent Poverty Lines.” Economic Development and Cultural Change. 58(2010): 449-474.

• Variations on this approach applied to Ethiopia, Ghana, Kenya, Madagascar, Malawi, Mozambique, Tanzania, and Uganda under GAPP.

Need for Multiple Bundles?

• Tarp et al. (2002) show that poverty measures from the CBN approach based on a single national consumption bundle can be inconsistent if consumption patterns of the poor vary over space.

• Argument in favor of region-specific CBN bundles. • The same logic applies through time. • For large countries, this argument has been persuasive:

• Gibson & Rozelle – Papau New Guineau • Datt and Jolliffe – Egypt. • Owens et al. – Tanzania • Grimm – Burkina Faso

Household Surveys

• 1996-97 Household Survey (IAF 1996-97) • Divided Mozambique into 13 spatial domains • Cost of Basic Needs approach applied. • Results

• About 70% of the population lives in poverty • Rural poverty more pervasive • Poverty rates lower in the South particularly Maputo City

• 2002-03 Household Survey (IAF 2002-03)

Cost of Basic Needs Approach

• Two Choices on the Food Bundles • Fixed Food Bundles • Flexible Food Bundles

Food Poverty Line Fixed Bundle

Flexible Bundle

1996 - 1997 Σ P96 *Q96 Σ P96 *Q96 2002 - 2003 Σ P02 *Q96 Σ P02 *Q02

Fixed Bundle: Advantages and Disadvantages

Advantages: • Simplicity and clarity. • Constant quality of the bundle.

Disadvantage: • Ignores substitution effects.

Substitution Effects

C ’ ’

2 C ’

2 U = f ( Q )

0 C ’ ’

1 C ’1 C 1

- P c 2

0 2 / P c 10 2 - P c 2

9 6 / P c 19 6

Ideal Basket 2002

Fixed Basket 1996

Poverty Head Count Using Fixed Baskets from 1996-97.

1996-97 2002-03 Differença Nacional 69.4 63.2 -6.2Urbano 62.0 61.3 -0.7Rural 71.3 64.1 -7.2Niassa 70.6 61.2 -9.4Cabo Delgado 57.4 72.3 14.9Nampula 68.9 68.1 -0.8Zambezia 68.1 58.6 -9.5Tete 82.3 71.6 -10.7Manica 62.6 60.2 -2.4Sofala 87.9 48.4 -39.5Inhambane 82.6 80.1 -2.5Gaza 64.6 58.6 -6.0Maputo Prov 65.6 66.9 1.3Maputo Cid 47.8 45.5 -2.3

Provinces with reduced povertyProvinces with increased poverty

Substitution Effects

• The data indicate substantial relative price changes for almost every commodity.

• How large are these potential substitution effects?

Suppose Preferences Are Cobb Douglas

C ’ ’

2 C ’

2 U = f ( Q )

0 C ’ ’

1 C ’1 C 1

- P c 2

0 2 / P c 10 2 - P c 2

9 6 / P c 19 6

Ideal Basket 2002

Fixed Basket 1996

Poverty Head Count Assuming Cobb – Douglas Preferences

1996-97 2002-03 Differença Nacional 69.4 52.1 -17.3Urbano 62.0 55.5 -6.5Rural 71.3 50.5 -20.8Niassa 70.6 39.5 -31.1Cabo Delgado 57.4 50.1 -7.3Nampula 68.9 58.9 -10.0Zambezia 68.1 44.6 -23.5Tete 82.3 65.0 -17.3Manica 62.6 54.1 -8.5Sofala 87.9 38.1 -49.8Inhambane 82.6 69.3 -13.3Gaza 64.6 41.5 -23.1Maputo Prov 65.6 66.9 1.3Maputo Cid 47.8 45.5 -2.3

Provinces with reduced povertyProvinces with increased poverty

Flexible Bundle Approach: Advantages and Disadvantages

Disadvantages : • Difficult to maintain the same level of utility

(quality of the bundle).

Advantages : • Accommodates changes in consumption

patterns.

Utility Consistency C ’ ’

2 C ’

2 U = f ( Q )

0 C ’ ’

1 C ’1 C 1

- P c 2

0 2 / P c 10 2 - P c 2

9 6 / P c 19 6

Ideal Basket 2002

Fixed Basket 1996

Revealed Preference Conditions

1. ∑i p02ir * q96ir ≥ ∑i p02ir * q02ir

2. ∑i p96ir * q02ir ≥ ∑i p96ir * q96ir

3. ∑i p02ir * q02irq ≥ ∑ip02ir * q02ir

Where: r spatial domain i product rq comparator spatial domain

Revealed Preference Conditions 1 2 3 4 5 6 7 8 9 10 11 12 13

1 4756 6397 3991 4472 4007 5621 5508 6330 5580 6250 6536 8436 99842 5903 7717 4501 5490 4922 6601 6420 7599 7090 7972 8791 10409 103003 3500 4470 2752 3660 2907 4713 3041 2492 4703 3539 3499 4820 70994 4879 5853 3542 3749 3058 5232 4471 5956 5816 5429 5216 7833 73975 4589 6167 3663 4399 3548 5459 4768 5090 5041 5080 5691 7033 91246 5730 7402 4216 5358 4446 5902 6180 7006 6331 6811 8102 8177 93897 6770 8770 4741 7210 5090 7741 6937 9584 9608 10260 12430 15311 113618 7737 9813 5646 7079 6058 8910 7863 9657 9087 10128 12221 13032 117709 4454 5813 3389 4014 3577 5601 4587 4950 5438 5932 10243 8752 8969

10 5090 6728 3943 5048 4303 6753 5580 6419 6458 6613 9812 9279 945111 7102 10317 5677 7657 6376 9478 7291 9532 9663 10422 12584 13772 1381612 8158 10971 5860 8153 7482 11599 9158 11329 10938 11580 13881 13741 1370013 7866 10626 5653 7837 7146 11458 8921 11179 10766 11433 13501 13270 13211

Revealed pref satisfied Revealed pref not satisfied Food poverty line (pre-adj)

Region-specific prices

Familiar Juncture in Empirical Science

• National Accounts. • Physics. • Image processing. • Common element: Despite best efforts at

observations, we often end up with data that is inconsistent with what is required to be true.

Information Theory

“The intention is to give a way of extracting the most convincing conclusions implied by given data and any prior knowledge of the circumstance.”

Buck and McAuley (1991).

Information Theory: Minimum Cross Entropy

∑∑ S

SS flex

ri

ent

ri

r i

ent

ri,

,, ln

Choose new baskets that preserve, to the greatest degree possible, the information inherent in the original shares, satisfy revealed preferences, and meet calorie needs.

Min Subject to:

1) revealed preference conditions

2) some accounting constraints

3) calorie requirements

Mozambique- Adjusted Baskets

1 2 3 4 5 6 7 8 9 101 5434 7541 4471 5146 4424 6679 6137 7573 6614 78082 5642 7541 4471 5290 4746 6591 6190 7355 6627 77073 5988 8912 4471 5762 4502 7804 5628 7145 7856 82974 7014 8900 5067 4853 4155 7312 6603 9937 7936 83595 5816 8340 4600 5486 4155 7162 5772 7145 6614 72646 6060 8209 4471 5836 4673 6591 6411 7564 6790 76667 6087 10244 4471 8629 4182 8286 5628 9806 11301 108108 6118 7541 4648 5786 4935 7003 6039 7145 7435 80109 5823 7553 4471 5380 4920 7954 5937 7145 6614 8936

10 5564 7541 4471 5605 4713 7468 5990 7145 6839 7264

RP satisfied RP constraint binding Food poverty line (post-adj)

Region-specific prices

Poverty Headcounts 1996-97 Difference

Fixed Bundles Adj.-Orig.Original Adjusted

National 69.4 63.2 48.0 54.1 6.1Urban 62.0 61.3 52.4 51.5 -0.9Rural 71.3 64.1 45.9 55.3 9.4Niassa 70.6 61.2 45.6 52.1 6.5Cabo Delgado 57.4 72.3 57.1 63.2 6.1Nampula 68.9 68.1 30.5 52.6 22.1Zambezia 68.1 58.6 35.1 44.6 9.4Tete 82.3 71.6 70.8 59.8 -11.0Manica 62.6 60.2 58.5 43.6 -15.0Sofala 87.9 48.4 30.9 36.1 5.2Inhambane 82.6 80.1 75.1 80.7 5.6Gaza 64.6 58.6 47.1 60.1 13.1Maputo Prov 65.6 66.9 75.9 69.3 -6.6Maputo City 47.8 45.5 58.0 53.6 -4.4

Flexible Bundles2002-03

Comparison with Tanzania

Tanzania: Spatial Domains (9)

• Rukwa, Tabora, Mbeya, Singida (R+U)

• Dodoma, Morogoro, Iringa, Ruvuma, Lindi, Mtwara (R+U)

• Kigoma, Kagera, Shinyanga, Mwanza, Mara (R+U)

• Arusha, Kilimanjaro, Manyara, Tanga (R+U) plus rural Pwani.

• Dar Es Salaam & urban Pwani.

Final Revealed Preference Matrix (adjusted food poverty lines)

1 2 3 4 5 6 7 8 9

1 U: Ruk-Tab-Mbe-Sin 144 120 184 163 156 127 183 183 2112 R: Ruk-Tab-Mbe-Sin 144 117 190 157 156 120 189 183 2143 U: Dod-Mtw-Ruv-Iri-Lin-Mor 158 127 183 166 169 138 183 184 2024 R: Dod-Mtw-Ruv-Iri-Lin-Mor 150 122 183 151 153 121 184 183 2055 U: Kig-Shi-Kag-Mwa-Mar 146 124 183 167 146 124 188 185 2066 R: Kig-Shi-Kag-Mwa-Mar 148 119 188 160 150 117 188 179 2187 U: Aru-Kil-Tan 154 125 183 166 167 135 183 184 2098 R: Aru-Kil-Tan-Pwa 148 117 184 152 159 124 183 179 2239 Dar Es Salaam & Urban Pwa 173 137 194 178 184 151 194 191 202

Region Specific Prices

Revealed Preference Conditions 2000/01

• Five mutually consistent pairs out of 36 possible.

1 2 3 4 5 6 7 8 91 U: Ruk-Tab-Mbe-Sin 148 123 189 167 160 130 187 187 2162 R: Ruk-Tab-Mbe-Sin 130 106 172 142 141 108 173 168 1953 U: Dod-Mtw-Ruv-Iri-Lin-Mor 176 143 205 187 187 154 202 206 2234 R: Dod-Mtw-Ruv-Iri-Lin-Mor 144 117 176 146 147 116 178 177 1975 U: Kig-Shi-Kag-Mwa-Mar 141 120 176 161 141 120 182 179 1996 R: Kig-Shi-Kag-Mwa-Mar 143 115 182 155 145 113 182 173 2117 U: Aru-Kil-Tan 182 147 216 195 196 159 215 217 2468 R: Aru-Kil-Tan-Pwa 124 99 156 130 134 105 157 153 1909 Dar Es Salaam & Urban Pwa 201 161 229 210 214 175 226 225 238

Region Specific Prices

Poverty Rates in 2000/01

• Similar national result is a happy coincidence. • Similar pattern of poverty across space based on

different methods.

Mainland Rural Other Urban Dar Es SalaamOfficial 35.7 38.7 25.8 17.6Util. Cons. 35.2 37.6 26.7 21.5Note: Correlation between official and new results at regional level is 0.67.

Conclusions

• It is often desirable to develop multiple bundles to reflect variations in relative prices and hence consumption patterns through space or time.

• These bundles should satisfy revealed preference conditions.

• The entropy adjustment procedure suggested is attractive once all other information has been exhausted.

Thank you