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DEA expression for technical efficiency (TE)
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i
r
xxx
yyyTE
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21
i ioi
r ror
x
yu
1
i iji
r rjr
x
yu
Max
for j=1,…, n, ur, vi ≥ 0 for all i and r
Subject to
DEA framework with one input andone output
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Total spending on ART
d1
d2
d3
d4A
B
C
DE
F
•A, B, C, D, and E are efficient decision making units on the production frontier•F is inefficient and below the frontier •Efficiency score for input-oriented model equals to d1/d2
•Efficiency score for output-oriented model equals to d3/d4
Means of inputs by year
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Year Obs.Spending
(Million, $)Spending
(Million, 2007 I$)
Before 2004 41 48.6 128.2
Year 2005 34 76.2 182.3
Year 2006 45 85.8 187.6
Year 2007 31 86.5 167.0
Total 151 73.7 166.0
Mean HIV/AIDS spending by year
Obs denotes number of observations
Means of outputs by year
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Year Obs.
Unweighted coverage Weighted coverage
ARV VCT PMTCT ARV VCT PMTCT
Before 2004 41 17.99% 2.87% 18.15% 7.83% 0.92% 9.60%
Year 2005 34 23.02% 5.02% 27.15% 16.76% 1.02% 18.70%
Year 2006 46 32.73% 9.67% 30.31% 26.47% 3.62% 29.76%
Year 2007 31 39.16% 19.19% 38.77% 34.79% 10.96% 44.30%
Total 151 27.86% 8.73% 28.03% 21.58% 2.62% 23.95%
Mean coverage of VCT, PMTCT and ARV treatment
DEA models by year• Average efficiency: 49.75%
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Performance for 45 countries in 2006
6Note: One output unit is one patient on ARV or equivalent for one year
Unit cost of national programs by output
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Cautions with interpretation
• Unconditional efficiency scores may not perfectly match experts’ perception
• DEA does not account for measurement errors
• For countries that achieved 100% efficiency, the result does not mean that their efficiency cannot be improved in the future
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Pooled DEA model by year
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Component II: Determinants of efficiency of national HIV/AIDS programs
• Objective:– To indentify social and economic determinants of
efficient HIV/AIDS programs
• Methods: Random-effects Tobit model– Model:– Dependent variable: log of efficiency– Independent variables
• Governance• Political support• Financing mechanism• Economic and demographic characteristics
– t denotes time and i denotes country10
itiititititit xxxx 443322110ˆ
Regression on log efficiency(Random-effects Tobit model)
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Independent variables Coefficient P value
Voice and accountability** 0.392 0.009
Government effectiveness 0.500 0.157
Rule of law -0.333 0.333
Control of corruption -0.323 0.297
Interaction of rule of law and control of corruption** 0.602 0.008
External source as percentage of total health expenditure ** 0.030 0.004
Government source as percentage of total health expenditure* -0.014 0.023
Government commitment to health* 0.031 0.042
Interaction of control of corruption and external share of health spending* 0.022 0.013
Log (GNI per capita)* 3.485 0.016
Square of log(GNI per capita)* -0.207 0.026
Log (adult population)* 0.147 0.026
HIV/AIDS prevalence** 0.052 0.000
constant -20.497 0.000
Conclusions 1• Substantial scope for improving HIV/AIDS
programs– Output-oriented DEA: If countries performed
optimally, given the resources available, outputs would double
– Input-oriented DEA: If countries performed optimally, they would require half of the previous resources to achieve the previous level of services
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Conclusions 2
• Dollars matter, so does the efficiency of using dollars
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Service scale-up mechanism
Type of HIV/AIDS epidemic
Low or concentrated (25 countries) Generalized (20 countries)
Resource
oriented
(22 countries)
Brazil, China, Jamaica, Mali, Mauritius,
Paraguay, Peru, Thailand, Uruguay
Botswana, Cameroon, Chad, Congo Dem.
Rep., Cote d'Ivoire, Lesotho,
Mozambique, Rwanda, South Africa,
Swaziland, Togo, Uganda, Zambia
Efficiency
oriented
(23 countries)
Argentina, Belize, Cambodia, Colombia,
El Salvador, Guatemala, Honduras,
Indonesia, Iran, Lao RDR, Latvia, Nepal,
Niger, Romania, Senegal, Vietnam
Angola, Benin, Burkina Faso, Central
African Republic, Eritrea, Haiti, Tanzania
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Conclusions 3• Addressing countries’ harsh environment is
helpful in controlling HIV/AIDS– if countries achieved a notable* increase in “voice and
accountability,” the efficiency of their HIV/AIDS programs would increase by 40.8%.
– For countries in the lowest quartile of per capita gross national income (GNI), a notable* increase in GNI would increase the efficiency of their AIDS programs by 45.0%.
*A “notable” increase is defined as change from the lowest 25th percentile to the average value of a variable
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Conclusions 4
• Low-income countries with high HIV/AIDS prevalence remain the targets for controlling the spread of HIV/AIDS– Low income countries share most of HIV/AIDS
burden– Low level of governance in those countries
implies significant room for improvement of efficiency
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Relationship between gross national income and government effectiveness
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-2-1
01
Sco
re o
n g
ove
rme
nt e
ffect
iven
ess
0 5000 10000 15000Gross national income in 2007 dollar (I$)
Observed data Linear fit of data
Conclusion 5
• Controlling HIV/AIDS requires health sector actions beyond HIV/AIDS– Increase government commitment to health– Strengthen health care system
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Conclusion 6
• Controlling HIV/AIDS requires multisectoral cooperation beyond the health sector– Strengthen governance– Alleviate poverty
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Limitations
• DEA highly sensitive to data accuracy
• Input and outputs assumed representative
• Quality of services not measured
• Lag effect of inputs not considered
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Acknowledgements
• Joan Kaufman, ScD, Brandeis University• John Stover, Futures Institute
