Summer School on Capability and

Multidimensional Poverty28 August-9 September, 2008

New Delhi, India

OPHIOxford Poverty & Human Development InitiativeUniversity of Oxford www.ophi.org.uk

HDCP-IRCThe Human Development, Capability and International Research CentreInstituto Universitario di Studi Superioriwww.iusspavia.it

Capability production functions

Enrica Chiappero-Martinetti

Emma Samman

5th September, 2008

Capability Approach

• Instrumental role of monetary resources in well-being

• Clear distinction between means and ends• Other factors other than lowness of income affect

capability deprivation • “The instrumental role between low income and

low capability is parametrically variable between different communities, households and individuals” (Nussbaum 1999)

Methodological requirements

– Many dimensions – Human diversity and plurality of context – Correlation among variables, dimensions and

context of analysis– Aggregation across attributes, across units of

analysis (i.e. individuals, households, groups) for determining an overall index

Most common measurement strategies

For dealing with issues (i) to (iii) – bringing multidimensionality back to a univariate

approach

– making use of multivariate techniques

For aggregation and comparison purposes (iv)– multidimensional decomposable poverty indexes

– extension of dominance stochastic conditions within a multidimensional framework

Linking means and ends: WB production process

To conceptualize the well-being process as a sort ofproduction function transforming inputs (resources, public

and private goods and commodities) into outputs (achieved functionings). Sen 1985,p.11

xi vector of commodities of individual i, b vector of functionings, c function that maps commodities into characteristics fi personal utilization or conversion function

• Kuklys (2005) :

groups conversion factors in three different categories (non-monetary constraints): personal (zi), social (zs) and environmental factors (ze)

NB: distinction between• conversion function: similarly to a production function, transforms

inputs (resources, public and private goods and commodities) into outputs (achieved functionings)

• conversion factors: internal factors, external, social and environmental circumstances

• conversion rate: the ability to transform means into achievement (“technology”)

• Ruggeri Laderchi (2008) – RL

• ECM,Salardi (2007,2008) – ECM/PS

• Ramos, Silber (2005) - RS

• Ramos (2008) -R

• Binder, Broekel (2008) - BB

Some recent literature

1. RL (2008)

A simple representation on how resources are mapped into functionings:

bi= fi (c (xi (yh, ti, to, dh, zh, l) + i

yh household resourcesti set of individual characteristicsto set of characteristics of other household members dh set of demographic characteristics of the household zh set of public goods available to the householdl a “location” variable capturing other area-specific influencesxi basket of goods and services whose characteristics (c) are combined according

an utilisation function (f)i error term

Ruggeri Laderchi (2008) II

A ‘crucial level’ bline such that

bi* = 1 if bi > bline and bi* = 0 if bi ≤ bline

• Estimation of the relationship between resources and basic capabilities with limited dependent variable techniques

• Testing for the existence, size and significance of differences between individuals with ≠ ti , to and l

• Comparison between capability based and consumption based approaches • Some relevant information for policy purposes

Empirical analysis:• Household survey, Peru, 1994 (LSMS-type)• Health (self-reported morbidity, for the overall population) and education (functional

literacy=4 years schooling for children 12-15)• Three models estimated:

– Probit (sick, non-sick)– Tobit (n° of days of illness for those who are sick)– Fixed effects associated with different departments

Ruggeri Laderchi (2008) III

Main results: • 1. Morbidity

– Monetary resources strongly and positively correlated with both health indicators– Age affects duration but not morbidity– Years of schooling play a significant role and the effect persist even controlling for

individuals and parental background education improves the “technology with which resources are transformed into health”

– Ethnicity and female head of hh do not play independent roles in determining whether people are sick or not

– access and quality of health (time to reach and to be attended in health facility) surprisingly do not play any significant role

– Effects of education and public water on morbidity (tab.6): both edu and water provision have greatest effect for the poorest;

– Policy implication: investing in the edu of the poorest would provide returns in terms of self-reported morbidity almost three times as high as those for the richest and community level: access to public water reduces

Ruggeri Laderchi (2008) IV

2. Children’s edu achievement:

• Probit model• Hh income strong and significant determinants of

children’s schooling achievement • Gender: no role; stronger effect of father years of

schooling, lower for the mother; ethnicity not significant nor the size of hh while it is the hh composition

• access and quality of schooling: not correlated with low achievements; little difference rural/urban

• Effectiveness of resources and parental edu by decile (tab 10)

Sum up:

individual, household and community characteristics, in ≠ degrees and to varying degrees do affect the way resources are translated into individual achievement (a monetary indicator is not sufficient or appropriate)

2. ECM/PS (2007, 2008)

Empirical evidence on conversion factors/conversion rates:

• Disaggregated results by subgroups of population • Regression analysis controlled by a range of socio-demographic characteristics (Anand,

van Hees, 2006; Zaidi, Burchardt, 2005; Kuklys, 2005, Ruggeri-Laderchi 2008);• Equivalence scales literature. Zaidi and Burchardt (2005), Lelli (2005), • Latent variable models (factor analysis, structural equation models and multiple

indicators and multiple causes model). Kuklys (2005), Addabbo et al (2004) and Krishnakumar (2007)

In most cases: evidence of the (ambiguous) correlation between income and functionings, impact of personal and socio-environmental features, measure of cost differences related to individual or household conditions.

In none of these cases, an estimation of the rate of conversions is produced

Figure 2 – A diagrammatic representation of the well-being process: the functioning “being healthy”

THE “MICRO”SIDE OF IQUAL THE “MACRO” SIDE OF IQUAL

Inputs for the public provisions of health services (proxy: n. of doctors and nurses, n. of hospital beds, etc.)

a) public health services b) private health services (proxy: available income)

Internal conversion factors (age, gender, abilities and disabilities)

EXTERNAL FACTORS (INSTITUTIONS, SOCIO-ECONOMIC CONTEXT, ETC.)

Technical production coefficients

choices

Public services production function Well-being production function

Capability set (vector of functionings, including “to be healthy”)

Achieved functioning (“being in a good health”

ECM/PS (2007, 2008)

Empirical Analysis (2008). Data: both macro-data and HH multiporpose survey (Italy, 2006)

“Inputs”:• A composite index for public resources:

– Public services for health (Indicatori socio sanitari - ISTAT, 2006)– Public services for environmental (Ecosistema Urbano - Ambiente Italia, 2008)– Public services for security and public order (Compendio Statistico Eventi

Criminosi – Ministero dell’Interno, 2003)

• Private resources:– Problems: no income information in our dataset; possible reversal causality

between income and the selected achievements; income instability and fluctuations– Solution: to build up a Wealth index via the principal component analysis by using

variables on housing characteristics, durables and affordability

“output”

• Three achievements:1. “being healthy” : a subjective indicator for health status (very good, good, fair, bad, very bad) 2. “living in a healthy and safe environment”: a subjective indicator of satisfaction for the environmental quality, e.g pollution, parking public transport, traffic, noise, etc (bad, not much, fair, good)3. “feeling secure”: a subjective indicator of satisfaction of public security (bad, not much, fair, good)

• Conversion rates estimated for six subgroup of population (by gender and by age: young, adult, elderly) and controlling by individual characteristics: gender, age, levels of attained education, marital status, occupational status and external/geographical characteristics (macro-area, regions)

• Econometric strategy: an ordered probit model (due to the categorical nature of the dependent variables) for each functioning, for the overall population and for subgroups of population: how these groups differ in converting resources into functioning (more efficient or more critical groups)

ijijklijkjijoij CCGWBprob ...5,...1 121

Bij the achieved functioning Wij, the wealth index, proxy for private resources Gj, the variable of public services, proxy for public resources for the individual i, i=1…n, living in the geographical area j, j=1…m.Cijk, the k internal conversion factors with k=1…l, that varies across individuals or the geographical areas where they live.

• Main results:

– Pooled estimation: positive and statistically significant impact of:

• both private and public resources for health

• Private resources only for environment

• Public resources only for security

• individual characteristics provide information in line with one could expect :

– H= worst health reported conditions for F, elderly, unemployed

– E=lower perceived achievement for F, elderly and better educated people

– S = similar pattern as before

Empirical findings (I): “Being healthy”Pooled estimations

– Subgroups estimations: statistically significant estimations only for adult and elder female and male

• F are more efficient to convert public resources while M convert better private resources

• Elderly are less able to convert public as well as private resources

Empirical findings (II): “Living in a safe and healthy environment”

Pooled estimations

Ramos and Silber 2005

- EFFICIENCY ANALYSIS

-They use distance functions to estimate the standard of living (inputs or resources), the quality of life (outputs or capabilities) and the efficiency in transforming resources into functionings

They compare four different wb approaches, measuring 1) an index of achievements reached by the individual in each dimensions2) An overall index of well-being/ human development.

ISOQUANT: all possible combinations of inputs (x) that allow to produce a given output L(y)The distance between an inefficient and an efficient amount of inputs lying onto the isoquant for the corresponding output level – is measured by an (input) distance function. Din (y,x) = OA/OB >1 (=1 if x is on L(y): how much input vector may be proportionally contracted given an output vector

Production possibility frontier PPF(x): various combinations of output (y1,y2) that can be produced using an input vector x

The distance between any output vector inside PPF and an efficient combination of output lying onto the PPF – is measured by an output distance function. Dout (y,x) = OA/OB <1 (=1 if x is on PPF (x); extent to which the output vector may be proportionally expanded given an input vector

ESTIMATING ACHIEVEMENT FOR GIVEN DIMENSION OF WELLBEING

Let x = (x1,…,xN) RN++ denote the vector of the n

elements that are considered as inputs in the production of achievement levels in the various domains and u=(u1,… ,uM) RM

++ denote the vector of achievement levels.

Then an individual’s endowment of inputs and levels of achievement are denoted by the pair (xi, ui), i =1, …I individuals

They estimate a standard of achievement SA using an input quantity index:

SA(u, xs, xt) = Din(u, xs)/Din(u, xt)

where xs and xt are two different input vectors and Din is an input distance function.

Similarly, they estimate an output distance function

WB(x, us, ut) = Dout(x, us)/Dout(x, ut)

where us and ut are two achievement vectors and x is an input vector

Problem: Production functions compare two inputs based on their relative prices. But how do we value e.g., education versus health in our capability production function? => reference point

Level of achievements:They assume each individual has the same vector e of achievement e.g one unit of achievement for each of M dimensions. L(e) is called “reference set” and bounds the input vectors from below. Individuals with input vectors onto L(e) share the lowest level of achievement (with an index value = 1) whereas individuals with large input vectors will have higher levels of achievement (index values > 1)

Overall wb:As above assuming that each individual is endowed with one unit of each input PPF (e). If individual has a vector of achievements that places her on PPF(e) => max WB (=1) while if it is lower the index values will be <1.

Empirical analysis:

British Household Panel Survey, 1997Input variables (long and broader set of subj/obj var)Four lists of functionings:

•Allardt 1993: Having (material resources, working conditions, health and education), Loving (contacts w/ local community, family, friends etc) and Being (self determination, leisure, meaningful work etc)• Cummin, 1996: material wellbeing, health, productivity, intimacy/friendship, safety, the community and emotional wellbeing• Narayan, 2000: material wb, bodily wb, social wb, security, freedom of choice & action, psychological wb• Sen 1985; list of indicators they feel compatible with CA

-Inequality and poverty analysis in achievements and overall wb (CA: higher inequality for the right environment and health vs ability to undertake mental or physical tasks or to socialize).

- WB domains weakly correlated with income; Correlation between dimensions is also quite low whatever approach is used

- They conclude: “It might therefore not matter too much which of these approaches we select given that we make sure that aspects of wellbeing that have not much to do with resources, such as emotional wellbeing, friendship etc. are taken into account”.

Binder, Broekel, 2008

-They also refer to efficiency analysis and use BHPS- Three functioning:

- being happy (mental wb in the General Health Quest)- being educated (highest level of edu)- being healthy (subj reported)

-I as a proxy for commodity vector

-Two steps: 1.identify the “best practice” individuals in terms of achievements (no other individuals with lower or equal I shows a higher level of achiev.) =>reference group. Individuals with = I and lower achievm is “inefficient” (euclidean distance between obs and efficiency frontier).

-Problem: outliers-Solution: robust non parametric frontier techniques. Instead of comparing the efficiency of each person with respect the efficiency of all other obs, the comparison is made with a random subsample of observations. 2nd step: influence of individual conversion factors (gender, age, job and marital status) on the “efficiency scores”.

To concludeAt what extent the production theory/production function approach is “coherent”

with the theoretical foundation of the CA a) Common problem: to summarize or collapse a large amount of information

into only one dimensionb) Production economics as well-consolidated theory and tools

c) Similarities with Gary Becker’s household production function

But see Sen’s (1985) critique about the appropriateness of seeing functionings as fundamental commodities produces by the household:

• the former are not just a simple commodity but a state of existence of a person and

• many of the functionings are produced outside the household (e.g. through public policy)

• rather restrictive assumptions regarding the existence of shadow prices and implicit markets