X | Z | X.Z |
---|---|---|
0 | 0 | 0 |
1 | 0 | 0 |
0 | 1 | 0 |
1 | 1 | 1 |
Carolina Torreblanca
University of Pennsylvania
Global Development: Intermediate Topics in Politics, Policy, and Data
PSCI 3200 - Spring 2025
Development and Gender
Chattopadhyay and Duflo, 2004
Interaction Models
Gender gap in political representation
Gender gap in political participation:
Gender and poverty (feminization of poverty to a degree)
Gender and economic participation
Gender and violence
Gender and education
Literacy rates: 90% male vs. 83% female globally (World Bank Data, 2022)
School attendance gap (UNESCO, 2023)
The two are undoubtedly related
But could improving gender representation produce development?
Why might having more women in office improve development?
Women may want different things
Women may behave differently
Women may be better at their job
Women representatives may teach about equality
Seems like a good theory with important implications that we want to validate empirically
Imagine we have data on share of female legislators and many development outcomes
We compare places with female politicians to places with male politicians and see development differences
What is the problem with this?
Rules requiring minimum women’s representation in politics
Goal: Improve gender parity in government
Vary by country, region, and level of government
Typically set minimum thresholds (20-50%)
Started in 1990s, expanded rapidly
Now used in about 130 countries
Most common in newer democracies
Less common in older democracies (US, Japan)
Highest representation achieved in Rwanda (61%)
India reserved 1/3 of village council (panchayat) head positions for women (1993)
Reserved positions assigned by random lottery
Randomization creates natural experiment
Solves confounding problem \(\rightarrow\) can identify causal effects!
RQ: What are the policy consequences of “mandated representation of women”?
Hypothesis: In reserved villages, there is more investment in goods women prioritize
Mechanism: Heterogeneous priorities
Treatment: Village council being randomly assigned to have female head
Outcome: Investment Decisions
Data: Sample of Villages
\(Y_{ij} = \beta_1 + \beta_2 * R_j + \beta_3 D_i * R_j + \sum_{l=1}^{N} \beta_l d_{li} + \epsilon_{ij}\)
Where:
\(Y_{ij}\) is an outcome of interest
\(R_j\) takes the value of 1 if GM is reserved
\(D_i\) is differences in request about that good (women - men)
\(d_{li}\) are good Fixed Effects!
An interaction term is the product of two variables used as a covariate in a regression model
Captures how the effect of one variable depends on the value of another variable
Powerful for testing conditional hypotheses
Key Modeling Assumption
An increase in \(X\) is associated with an increase in \(Y\) only when a specific condition is met
\(Y_{i} = \alpha + \beta_1 * X_i + \beta_2 * Z_i + \epsilon_{i}\)
\(\hat{\beta_1}\) represents the change in \(Y\) when \(X\) increases by one unit
\(\hat{\beta_2}\) represents the change in \(Y\) when \(Z\) increases by one unit
Why?
A partial derivative of the equation shows how \(Y\) changes when \(X\) changes by 1:
\(Y_{i} = \alpha + \beta_1 * X_i + \beta_2 * Z_i + \epsilon_{i}\)
\(\frac{\partial Y}{\partial X} = \beta_1\)
\(\frac{\partial Y}{\partial Z} = \beta_2\)
\(Y = \alpha + \beta_1X + \beta_2Z + \beta_3(X*Z) + \epsilon\)
X | Z | X.Z |
---|---|---|
0 | 0 | 0 |
1 | 0 | 0 |
0 | 1 | 0 |
1 | 1 | 1 |
\(Y_{i} = \alpha + \beta_1 * X_i + \beta_2 * Z_i + \beta_3 * Z_i * X_i + \epsilon_{i}\)
How to interpret \(\beta_3\): Expected change in Y when the product of \(X \times Z\) increases by 1 unit.
How to interpret \(\beta_1\): Change in Y when X increases by 1 unit AND \(Z =0\)
How to interpret \(\beta_2\): Change in Y when X increases by 1 unit AND \(X =0\)
Why does the interpretation of \(\beta_1\) and \(\beta_2\) change?
\(Y_{i} = \alpha + \beta_1 * X_i + \beta_2 * Z_i + \beta_3 * Z_i * X_i \epsilon_{i}\)
\(\frac{\partial Y}{\partial X} = \beta_1 + \beta_3*Z_i\)
\(\frac{\partial Y}{\partial Z} = \beta_2 + \beta_3*X_i\)
Use for conditional hypotheses
Always include all constituent terms
Interpret \(\beta_1\) and \(\beta_2\) correctly
alpha <- 1
beta_1 <- -.5 # Coefficient for women's representation
beta_2 <- 1.5 # Coefficient for quota system
beta_3 <- 3 # Coefficient for interaction term
set.seed(12)
interaction_data <- tibble(
women_representation = runif(100, 0, 1), # any number btw 0 and 1
quota_system = sample(0:1, 100, replace = T)) %>% # either 1 or 0
mutate(policy_outcome = alpha +
beta_1 * women_representation +
beta_2 * quota_system +
beta_3 * (women_representation * quota_system) +
rnorm(n(), 0, 0.5))
Call:
lm(formula = policy_outcome ~ women_representation * quota_system,
data = interaction_data)
Residuals:
Min 1Q Median 3Q Max
-1.00935 -0.35365 -0.00404 0.34793 1.08715
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.9766 0.1348 7.245 1.09e-10 ***
women_representation -0.4865 0.2289 -2.125 0.0361 *
quota_system 1.5993 0.2084 7.673 1.39e-11 ***
women_representation:quota_system 2.8913 0.3921 7.374 5.85e-11 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.5064 on 96 degrees of freedom
Multiple R-squared: 0.8993, Adjusted R-squared: 0.8962
F-statistic: 285.8 on 3 and 96 DF, p-value: < 2.2e-16