1. Measuring
poverty
2. Multidimensional
poverty
3. Poverty Dynamics
4. Panel Data
5. Inference with
Panel Data
6. International
Poverty
Comparisons
7. Vulnerability
8. Tackling Poverty
Module 5
Inference with
Panel Data
JONATHAN HAUGHTON
j h a u g h t o n @ S u ffo l k . e d u
JUNE 2017
Objectives
June 2017
1.
Explain the essential ideas and vocabulary of regression analysis.
2.
List and explain the main regression problems, including
i.
Measurement error
ii.
Omitted variable bias
iii.
Simultaneity bias
iv.
Sample selectivity bias
v.
Multicolinearity
vi.
Heteroskedasticity
vii.
Outliers
3.
Show how panel data can help address some of these problems
4.
Outline the key ideas underlying impact evaluation
5.
Explain how impact evaluation can be more powerful with panel data, and
illustrate this with an example from Thailand
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Regression 1
Fit a line to data
◦ As here, Vietnam 1998
◦ Engel curves
◦ Linear
◦ Food spending/cap = 1.188 + 0.22 (spending/capita)
◦ Quadratic
◦ F/cap = 0.853 + 0.30 (spend/cap) – 0.0021 (spend/cap)^2
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Vocabulary
yi  0  1 X1i  2i X 2i   i .
yi  0  1 X1i  2i X i 2 .
Intercept/constant
Coefficients
Dependent variable
Independent variables/regressors/covariates
Error (unobserved)
◦ Mean zero; identically & independently distributed
True equation; estimated equation
Residual (observed):
June 2017
ei  yi  yi
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Example
R2 = 0.47. Goodness of fit.
Coefficient signs as expected
Consumption/capita: in logs.
t-statistics shown. [>2 ≈ “significant at 5%”]
Phnom Penh variable is binary
◦ Dependency ratio: (young + old)/(prime age)
◦ Femaleness: % aged 15-60 who are female. Positive coefficient
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Regression problems:
Measurement error: y = a + bX + ε
◦ In Y: no bias, but poor fit
◦ In X: estimate of b biased toward 0
Omitted variable bias
◦ True: Child health = a + b MumEd + c MumAbility
Estimated: Child health = a + b MumEd
If ed, ability, correlated, estimate of b is too high
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More regression problems
Simultaneity bias
◦ E.g. Child health = a + b Nutrient intake
◦ But which comes first? Feed the weak or the healthy?
Sample selectivity bias
◦ E.g. Only observe wages for those who work
◦ Solution: Two steps (Heckman)
Multicolinearity
◦ Some X variables are intercorrelated
◦ Hard to get accurate coefficient estimates
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Yet more regression problems
Heteroskedasticity
◦ Errors do not have constant variance
◦ Coefficients not biased; but standard errors inefficient
Heteroskedasticity Illustrated
Panel A
Panel B
45
4
40
3.5
35
3
30
ln(y)
2.5
y
25
20
2
1.5
15
1
10
0.5
5
0
0
0
5
10
15
20
25
30
35
40
0
5
X
10
15
20
25
30
35
40
X
Source: Authors’ creation.
June 2017
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Regression Problems Again
Outliers
◦ Typo or truth?
Outliers Illustrated
Panel A
Panel B
40
90
35
80
30
70
60
y = 0.4879x + 11.182
R2 = 0.0741
50
20
y
y
25
40
y = 0.8645x + 0.6698
R2 = 0.8955
15
30
10
20
5
10
0
0
0
5
10
15
20
25
30
35
40
X
0
5
10
15
20
25
30
35
40
X
Source: Authors’ creation.
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Panel data can be helpful
Rice output = a + b fertilizer + c ability + ε
Ability unobservable, so estimate
◦ Rice output = a + b fertilizer + w
But estimate of b is likely overstated.
Use panel data:
◦
◦
June 2017
Q1  Q0  b( F1  F0 )  (1   0 )
Differencing washes out “ability”, allows an unbiased estimate of b
Very useful, but only works if ability is time-invariant.
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Impact Evaluation
Purpose: quantify the impact of a project or policy
◦ E.g. Does microcredit raise incomes
Complex; requires construction of a counterfactual
Gold standard: Randomized Controlled Trial
◦ Randomly select beneficiaries (and controls)
◦ Collect baseline data
◦ After intervention, collect data again; compare outcomes between treated and controls
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Powerful: Double Differences
Panel data with pre- and post-treatment
Outcome (Y)
◦ E.g. (30 – 10) – (21 – 14) = 13
30
30
Impact
= 13
21
17
17
14
10
10
Program
Beneficiaries
Equivalent control group
Impact
= 13
Program
Time
Beneficiaries
Time
Comparison group
Fig. 12.3. Measuring program impact under randomization (left) and
using double differences (right). The treatment sample starts with an
outcome of 10 and finishes with an outcome of 30. With random assignment,
the final level may compared with the control group (left); with a comparison
group a counterfactual must be inferred.
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Can combine with regression
Error: time-invariant and innovation components
Sweeps away effects of variables, including unobservables, that do not vary over
time
Jalan and Ravallion (1998): Poverty alleviation program in China
◦ Double differencing biased; keep variables for initial conditions that influence program
placement
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Example: Thailand Village Fund
Village-run microcredit; any impact on expenditure or income per capita?
Rural panel, Socio-Economic Surveys, 2002 and 2004
T = treatment = borrow from Village Fund
X variables include household variables (e.g. age of head, education of head,
no. of adults).
Y is log of expenditure (or income) per capita
yi,2004  yi,2002  (xi,2004  xi,2002 )  (Ti,2004  Ti,2002 )  ( i,2004   i,2002 )
Estimates of γ:
◦ Expenditure: 3.5% (s.e. 1.5%; p-value 0.02)
◦ Income: 1.4% (s.e. 1.8%; p-value 0.44)
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Extensions
There may be time-varying unobserved heterogeneity, biasing the coefficient on T
◦ E.g. Local conditions may change over time
Solution 1: Interact treatment with time-varying variables
◦ Khandker (2006): Microcredit in Bangladesh
Solution 2: Arellano-Bond dynamic lagged-dependent-variable approach
◦ See Jalan and Ravallion (1998), mentioned above
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Reading
Haughton & Khandker (2009).
◦ Handbook on Poverty and Inequality. Chapter 14; 13 (pp. 256-270). World Bank, Washington DC.
Khandker, Koolwal, & Samad (2010)
◦ Handbook on Impact Evaluation, World Bank, Washington DC.
Haughton & Haughton (2011).
◦ Living Standards Analytics, Springer, New York. Chapters 2 (Regression) and 12 (Impact Evaluation)
Boonperm et al. (2013)
◦ Does the Village Fund matter in Thailand? Evaluating the impact on incomes and spending. Journal of Asian Economics 25: 3-16.
Cameron & Trivedi (2009)
◦ Colin Cameron & Pravin Trivedi. Microeconometrics Using Stata. Stata Press.
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