Modeling Poverty Martin Ravallion Development Research Group, World Bank

1. Static models 2. Dynamics: Repeated cross-sections 3. Dynamics: Panel data 4. Micro growth models

Part 1. Static models of poverty For all additive measures ("sub-group monotonicity") we can decompose the aggregate measure by sub-groups –e.g., “urban” vs “rural”, “large” vs “small” households The poverty profile can be thought of as a simple model of poverty : Prob(Y < Z)=

But this is too simple a model We would like to introduce a richer set of covariates (some continuous) to: Account better for the variance in circumstances leading to poverty Disentangle which are the key factors, given their inter- correlation. For example: poverty profile shows that rural incidence > urban incidence, and that poverty is greater for those with least education. But education is lower in rural areas. Is it lack of education or living in rural areas that increases poverty?

Multivariate poverty profiles Welfare indicator modeled as a function of multiple variables: Log(Y/Z) = πX + ε or Log Y = πX + dummy variables for location etc.,+ ε

Probits for poverty make little sense Probit regression for poverty (normally distributed error): However: This is just an inefficient way of estimating the OLS regression parameters. You do not need a probit/logit when the continuous variable is observed. You can still estimate poverty impacts: And under weaker assumptions (e.g., normality of errors is not required)

Example for Vietnam Regression for log household consumption

Part 2. Studying poverty dynamics using repeated cross-sectional data Decomposing changes in poverty Decomposition 1: Growth versus redistribution Growth component holds relative inequalities (Lorenz curve) constant; redistribution component holds mean constant Change in poverty between two dates = Change in poverty if distribution had not changed + Change in poverty if the mean had not changed + Interaction effects between growth and redistribution

Example for Brazil Poverty and inequality measures Very little change in poverty; rising inequality

Example for Brazil Poverty and inequality measures Very little change in poverty; rising inequality Decomposition No change in headcount index yet two strong opposing effects: growth (poverty reducing) + redistribution (poverty increasing). Redistribution effect is dominant for PG and SPG.

Decomposition 2: Gains within sectors vs population shifts Gains within sectors at given pop. shares; Population shift effects hold initial poverty measures constant Interaction effects.

Example: urban-rural

Example for China 75-80% of the drop in national poverty incidence is accountable to poverty reduction within the rural sector; most of the rest is attributable to urbanization of the population.

Growth Incidence Curves

Example: China in the 1990s

Measuring the rate of “pro-poor growth” Watts index for the level of poverty implies using the mean growth rate of the poor in measuring the rate of pro-poor economic growth. (Not growth rate in the mean for the poor.) Table 1: Growth rates for China

Static models on repeated cross- sections Two time periods, or two sets of households How much has the change in poverty been due to: Change in the joint distribution of the X ’s? Change in the parameters (“return to the X ’s)? Example 1: in Vietnam, returns to education are significantly higher for the majority ethnic group than minorities Example 2: in Bangladesh, returns to education are higher in urban areas. Strong geographic effects

Returns to education by ethnic group in Vietnam

Part 3. Studying poverty dynamics using panel data PROT ("Protected") = Change in proportion who fell into poverty. PROM ("Promotion") = Change in proportion who escaped poverty.

Transient vs chronic poverty Measure of poverty for household i over dates 1,2,…,D: The transient component of poverty is the part attributed to variability in consumption: The chronic component is:

Models of transient and chronic poverty Transient poverty model Chronic poverty model

Example for rural China Determinants of chronic poverty look quite similar (though not identical) to that for total poverty (chronic plus transient). However, the determinants of transient poverty measure are quite different. Low foodgrain yields foster chronic poverty, but are not a significant determinant of transient poverty. Higher variability over time in physical wealth is associated with higher transient poverty but lower chronic poverty. While smaller and better educated households have lower chronic poverty, these things matter little to transient poverty. And living in an area with better attainments in health and education reduces chronic poverty but appears to be irrelevant to transient poverty. Different models are determining chronic versus transient poverty in rural China.

Part 4: Micro growth models With panel data we can also investigate the determinants of why some households do better than others over time. Initial conditions (incl. geographic variables) Shocks Policies Examples of the questions that can be addressed: Are there geographic poverty traps? Does where you live matter independently of individual (non- geographic) characteristics? Are there genuine externalities in rural development? Does this help explain under-development (under-investment in the externality-generating activities)

Micro growth models cont., Micro model of the growth process Latent heterogeneity in growth process can be dealt with allowing for time varying effects Quasi-differencing to eliminate the fixed effect

Example for rural China Six year household panel. Consumption growth at the household level is a function of household characteristics and geographic characteristics. Consumption growth model at household level in four provinces of China (n=5,600).

Findings Publicly provided goods, such as rural roads, generate non- negligible gains in consumption relative to the poverty line. And since we have allowed for latent geographic effects, the effects of these governmental variables cannot be ascribed to endogenous program placement. Aspects of geographic capital relevant to consumption growth embrace both private and publicly provided goods and services. Private investments in agriculture, for example, entail external benefits within an area, as do “mixed” goods (involving both private and public provisioning) such as health care. Evidence of geographic poverty traps in panel data from post-reform rural China.

The results strengthen the equity and efficiency case for public investment in lagging poor areas in this setting.