Lecture 3 Understanding Inequality: Structure and Dynamics Course on Poverty and Inequality Analysis Module 5: Inequality and Pro-Poor Growth Francisco H. G. Ferreira DECRG

Roadmap 1.Distributions 2.The Determinants of Inequality: a conceptual overview 3.Inequality Decomposition Analysis 4.Income Distribution Dynamics: statistical analysis 5.Income Distribution Dynamics: towards economic decompositions 6.Summing up

3.1. Distributions Social welfare, poverty and inequality summarize different features of a distribution. Distribution of welfare indicator per unit of analysis. Discrete: y = {y 1, y 2, y 3, …., y N } Continuous: The distribution function F(y) of a variable y,defined over a population, gives the measure of that population for whom the variable has a value less than or equal to y.

The density function: f(x) The distribution function

The quantile function: y=F -1 (p)

The Lorenz curve: or

The Generalized Lorenz curve:

3.2. The Determinants of Inequality: a conceptual overview Inequality measures dispersion in a distribution. Its determinants are thus the determinants of that distribution. In a market economy, that’s nothing short of the full general equilibrium of that economy. One could think schematically in terms of: y = a.r This suggests a scheme based on assets and returns: –Asset accumulation –Asset allocation / Use –Determination of returns –Demographics –Redistribution

3.2. The Determinants of Inequality: a conceptual overview

Modeling these processes in an empirically testable way is quite challenging. –Though there are G.E. models of wealth and income distribution dynamics Historically, empirical researchers have used ‘shortcuts’, such as: –decomposing inequality measures by population subgroups, and attributing “explanatory power” to those variables which had large “between” components; –Decomposing inequality by income sources, to understand which contributed most to inequality, and why; –Decomposing changes in inequality into changes in group composition, group mean and group inequality.

3.3 Inequality Decomposition Analysis: a.By Population Subgroups Not all inequality measures are decomposable, in the sense that I = I W + I B. The Generalized Entropy class is. Examples include Theil – L Theil – T 0.5 CV 2

3.3 Inequality Decomposition Analysis: a.By Population Subgroups Let Π (k) be a partition of the population into k subgroups, indexed by j. Similarly index means, n, and subgroup inequality measures. Then if we define: where Then, E = E B + E W.

An Example from Brazil The Rise and Fall of Brazilian Inequality:

A cross-country example: Race and ethnicity decompositions. Source: WDR 2006

3.3 Inequality Decomposition Analysis: a.By Population Subgroups The methodology was developed by: Bourguignon, F. (1979): "Decomposable Income Inequality Measures", Econometrica, 47, pp Cowell, F.A. (1980): "On the Structure of Additive Inequality Measures", Review of Economic Studies, 47, pp Shorrocks, A.F. (1980): "The Class of Additively Decomposable Inequality Measures", Econometrica, 48, pp Reviewed in: Cowell, F.A.and S.P. Jenkins (1995): "How much inequality can we explain? A methodology and an application to the USA", Economic Journal, 105, pp Example from: Ferreira, F.H.G., Phillippe Leite and J.A. Litchfield (2001): “The Rise and Fall of Brazilian Inequality: ”, World Bank Policy Research Working Paper #3867.

3.3 Inequality Decomposition Analysis: b.By Income Sources Shorrocks A.F. (1982): “Inequality Decomposition by Factor Components, Econometrica, 50, pp Noted that could be written as: Correlation of income source with total income Share of income source Internal inequality of the source

3.3 Inequality Decomposition Analysis: b.By Income Sources Source: Ferreira, Leite and Litchfield, 2006.

3.4. Income Distribution Dynamics a.Scalar decompositions Mookherjee, D. and A. Shorrocks (1982): "A Decomposition Analysis of the Trend in UK Income Inequality", Economic Journal, 92, pp Pure inequality Group Size Relative means

The (obligatory) example from Brazil… The Rise and Fall of Brazilian Inequality:

3.4. Income Distribution Dynamics b.A More Disaggregated Look In practice, decompositions of changes in scalar measures suffer from serious shortcomings: –Informationally inefficient, as information on entire distribution is “collapsed” into single number. –Decompositions do not ‘control’ for one another. –Can not separate asset redistribution from changes in returns. With increasing data availability and computational power, studies that decompose entire distributions have become more common. –Juhn, Murphy and Pierce, JPE 1993 –DiNardo, Fortin and Lemieux, Econometrica, 1996

3.4. Income Distribution Dynamics b.The Oaxaca-Blinder Decomposition These approaches draw on the standard Oaxaca-Blinder Decompositions (Oaxaca, 1973; Blinder, 1973) Let there be two groups denoted by r = w, b. Then and So that Or: Caveats: (i) means only; (ii) path-dependence; (iii) statistical decomposition; not suitable for GE interpretation. “returns component”“characteristics component”

3.4.Income Distribution Dynamics b. Juhn, Murphy and Pierce (1993) Juhn, Murphy and Pierce (1993): where Define: Then: Observed charac. Component. Returns component Unobserved charac. component

3.4. Income Distribution Dynamics b.DFL and BFL How and why does f A (y) differ from f B (y)? One could decompose f B (y) - f A (y) into: where A similar (but distinct) decomposition would be obtained with

3.4. Income Distribution Dynamics b. DiNardo, Fortin and Lemieux (1996) Essentially, DFL propose estimating a counterfactual income distribution such as: By appropriately reweighing the sample, as follows. where

3.4. Income Distribution Dynamics b. Bourguignon, Ferreira and Lustig (2005). Partition the set of covariates T into V and W, where V can logically depend on W. Define a counterfactual distribution f s A  B (y; k s,  A ). I.e. Replace the joint distribution of covariates by the appropriate product of conditional distributions, and the joint distribution of W.* *: Note that the order of conditioning will affect interpretation.

3.4. Income Distribution Dynamics b. Bourguignon, Ferreira and Lustig (2005). For each counterfactual distribution f s, the difference between f A and f B can be decomposed as follows: And it follows that:

3.4. Income Distribution Dynamics b. Bourguignon, Ferreira and Lustig (2005). Estimate - for each country or time period - simple econometric models of earnings, occupational structure, education and fertility choices. Simulate the effects of importing the parameter estimates of each model from county A into country B (individually or jointly). Decompose distributional differences into: –Price effects –Occupational structure effects –Endowment (or population characteristic) effects

3.4. Income Distribution Dynamics b. Brazil, (Ferreira and Paes de Barros, 1999) Level 1: y = G (V, W,  ;  ) Aggregation rule: Earnings: Occupational Choice: Level 2: V = H (W,  ;  ) Education:ML E (E  A, R, r, g, n ah ;  ) Fertility:ML C ( n ch  E, A, R, r, g, n ah ;  )

Comparing g(p) and g s (p) (i): The price effect.

Comparing g(p) and g s (p) (ii): The price effect and the occupational structure effect combined.

Comparing g(p) and g s (p) (i): Price, Occupation, Education and Fertility effects.

3.5. Income Distribution Dynamics: a.towards economic decompositions? Generalized Oaxaca-Blinder decompositions such as those discussed above, whether parametric or semi-parametric, suffer from two shortcomings: –Path-dependence –The counterfactuals do not correspond to an economic equilibrium. There is no guarantee that those counterfactual incomes would be sustained after agents were allowed to respond and the economy reached a new equilibrium.

(a) Partial Equilibrium Approaches The first step towards economic decompositions, in which the counterfactual distributions may be interpreted as corresponding to a counterfactual economic equilibrium, is partial in nature. One example comes from attempts to simulate distributions after some transfer, in which household responses to the transfer (in terms of child schooling and labor supply) are incorporated. –Bourguignon, Ferreira and Leite (2003) –Todd and Wolpin (2005) –(These two papers differ considerably in how they model behavior. Todd and Wolpin are much more structural.)

(b) General Equilibrium Approaches However, a number of changes which are isolated in statistical counterfactuals – such as changes in returns to education, or in the distribution of years of schooling – are likely to have general equilibrium effects. Similarly, certain policies one might like to simulate may require a general equilibrium setting. There are two basic approaches to generate GE-compatible counterfactual income distributions (and thus counterfactual GICs): –Fully disaggregated CGE models, where each household is individually linked to the production and consumption modules. E.g. Chen and Ravallion, 2003, for China. –“Leaner” macroeconomic models linked to microsimulation modules on a household survey dataset. E.g. Bourguignon, Robilliard and Robinson, 2005, for Indonesia.

Distributional Impact of China’s accession to the WTO. (Chen & Ravallion, 2003) GE-compatible counterfactual GICs corresponding to a specific policy.

(b) General Equilibrium Approaches (continued). Macro model Linkage AggregatedVariables (prices, wages, employment levels) Household income micro-simulation model In the Macro-Micro approach, some key counterfactual linkage variables are generated in a “leaner” macro model, whose parameters may have been calibrated or estimated from a time- series, and then fed into sector-specific equations estimated in the household survey, to generate a counterfactual GIC.

The distribution of the impacts of the 1999 Brazilian devaluation (Ferreira, Leite, Pereira and Pichetti, 2004)

3.6. Summing up There has long been an interest in understanding changes in (or differences across) income distributions. Static and dynamic decompositions of certain measures of inequality (by population subgroup or income source) can shed some light on the “structure” of inequality, and on the importance of covariates. But decompositions of scalar indices are inherently informationally constrained. Disaggregated statistical decompositions based on entire counterfactual distributions (parametrically or semi-parametrically) help shed more light on changes (and to separate the effects of returns, participation and composition effects). A step beyond this sort of statistical analysis is to build counterfactual distributions that correspond to economic equilibria. If sensibly estimated, these would allow inference of causality – and hence policy simulations. –Some progress on simple partial equilibrium models. –Harder with general equilibrium approaches, where CGEs or macro models are subject to many criticisms.