Assignments

• Today
  • Rozo and Grossman (2025) (download the pdf and/or watch the YouTube video)
  • Gazeaud, Jules, Eric Mvukiyehe, and Olivier Sterck (2020)
  • Sviatschi (2022)

Agenda

1. Research Design Debrief
2. Migration
3. Causal Inference with Observational Data: Difference-in-Differences

Debrief

Submissions

• You need to check what you send me…
• Read the basic instructions (quarto + html file)
• I didn’t penalize anyone, but next time I will

Research Designs

• Justify your sample
• Just “controlling for observables” will not get you full credit
• Next week, we’ll cover essentials… bring your questions!

Overview of International Migration

Economic Equilibrium

• Push factors
• Pull factors
• Costs

Economic Equilibrium: Push

Push factors: origin country factors that affect the well-being

Economic Equilibrium: Pull

Pull factors: destination country factors that affect expected well-being

Economic Equilibrium: Costs

Costs: factors that shape the costs of migrating

Economic Equilibrium Perspective

• Migration decisions are based on expected return
• Movements from poorer to richer regions will equalize wages

Migration Systems

Macro linkages between sending and receiving countries

• Migration is driven by prior links between sending and receiving countries
  • Colonization, political or cultural influence, trade, language

Micro linkages between households

• Migration is driven by prior links between individuals and households
  • Social ties to households in the destination country

Quiz

5 minutes: send me a Slack DM with something you learned from this article

Trends: Displacement

Trends: Displacement

Trends: Conflict

Trends: Conflict

Trends: Climate

• 78% of global land area has become drier over the past 30 years
• Warmer temperatures are causing extreme weather events

Trends: Research

Trends: Research

Impact on Host: Labor markets

Impact on Host: Other

Supporting Migrants

Unique challenges for forced migrants?

Supporting Migrants

Cash transfers

• Short-term increases in consumption, well-being

Labor market integration

• Increased consumption, well-being
• Reduced crime, fertility
• Kakuma vs Kalobeyei; Uganda business mentors

Supporting Migrants

• Mental health
• Social cohesion
  • Teacher bias
  • Shared aid + integration policies
  • Perspective-taking, contact

Policy Implications

Constraints to migration

• Migration causes huge income gains
• Desire for migration is extremely high
• Actual migration flows are relatively small
• Why?

Intervention

Conditional cash transfer

Findings

• Treatment households 38% more likely to migrate
• How did they measure spillovers?
• Mechanisms:
  • What were the mechanisms at play?
  • How did they reach these conclusions?

Findings

Policy Implications

How does this relate to the equilibrium model?

Policy implications

Review

• What is an interaction term?
• What are fixed effects?
• Why do we like randomization?

Identification strategy

In the real world, there are always confounders that we can’t observe (measure) or adjust for

• A research design that allows us to isolate a causal effect from observational data
• Approximates an experiment by ensuring that the treatment and untreated (control) group are similar
• These strategies rely on assumptions that we can attempt to validate

Holy Trinity of Causal Inference

1. Difference-in-Differences
2. Regression Discontinuity
3. Instrumental Variables

Difference-in-Differences

\[ Y_{it} = \alpha + \beta_1 \text{Treatment}_i + \beta_2 \text{Post}_t + \gamma (\text{Treatment}_i \times \text{Post}_t) + \epsilon_{it} \]

• \(\gamma (\text{Treatment}_i \times \text{Post}_t)\)
• Assumes measurement at two points in time

Simulation Example

# Load required libraries
library(dplyr)
library(modelsummary)

# Generate example data
set.seed(123)
data <- data.frame(
  treatment = rep(c(1, 0), each = 100),
  post = rep(c(1, 0), each = 50, times = 2),
  outcome = c(rnorm(50, mean = 10, sd = 4), # control: pre-treatment
              rnorm(50, mean = 10, sd = 4), # control: post-treatment
              rnorm(50, mean = 10, sd = 4), # treatment: pre-treatment
              rnorm(50, mean = 12, sd = 4)) # treatment: post-treatment
)

head(data)

  treatment post   outcome
1         1    1  7.758097
2         1    1  9.079290
3         1    1 16.234833
4         1    1 10.282034
5         1    1 10.517151
6         1    1 16.860260

Simulation Example

# Summarize the output
modelsummary(
  list(lm(outcome ~ treatment + post, data = data),# standard model
       lm(outcome ~ treatment * post, data = data)), # difference-in-differences model
  estimate  = "{estimate}{stars} ({std.error})",
             statistic = NULL,
  gof_omit = 'IC|RMSE|Log|F|R2$|Std.')

DiD: Assumptions

• Treatment and control units would have changed in similar ways
  • Parallel trends
• Requires at least 3 observation periods

Why can’t we just observe how units change over time?

library(ggplot2)

Year = c(0,1,2,3)
Outcome = c(NA, 1.3, 1.7, NA)
Treatment = c("Treatment", "Treatment","Treatment","Treatment")

dat = data.frame(Year, Outcome, Treatment)

ggplot(data = dat, aes(x = Year, y = Outcome, group = Treatment, color = Treatment)) +
  geom_line(aes(linetype=Treatment),size=2) +
  geom_point(size = 6) +
  xlim(0,3) + 
  ylim(0.8, 2.2) +
  scale_linetype_manual(values=c("solid", "solid")) +
  scale_color_manual(values = c("blue") ) +
  theme(legend.position = c(0.8, 0.2), text = element_text(size=20),
        legend.title=element_blank())

Why can’t we just observe how units change over time?

Year = c(0,1,2,3)
Outcome = c(0.9, 1.3, 1.7, 2.1)
Treatment = c("Treatment", "Treatment","Treatment","Treatment")

dat = data.frame(Year, Outcome, Treatment)

ggplot(data = dat, aes(x = Year, y = Outcome, group = Treatment, color = Treatment)) +
  geom_line(aes(linetype=Treatment),size=2) +
  geom_point(size = 6) +
  xlim(0,3) + 
  ylim(0.8, 2.2) +
  scale_linetype_manual(values=c("solid", "solid")) +
  scale_color_manual(values = c("blue") ) +
  theme(legend.position = c(0.8, 0.2), text = element_text(size=20),
        legend.title=element_blank())

Why can’t we just compare units without randomization?

Year = c(0,1,2,3)
Outcome = c(NA, 1.2, 1.4, NA, 
            NA, 1.3, 1.7, NA)
Treatment = c("Control", "Control","Control","Control", 
              "Treatment", "Treatment", "Treatment", "Treatment")

dat = data.frame(Year, Outcome, Treatment)
dat$Treatment = factor(dat$Treatment, levels = c("Treatment", "Control"))

ggplot(data = dat, aes(x = Year, y = Outcome, group = Treatment, color = Treatment)) +
  geom_line(aes(linetype=Treatment),size=2) +
  geom_point(size = 6) +
  xlim(0,3) + 
  ylim(0.8, 2.2) +
  scale_linetype_manual(values=c("solid", "solid")) +
  scale_color_manual(values = c("blue", "red") ) +
  theme(legend.position = c(0.8, 0.2), text = element_text(size=20),
        legend.title=element_blank())

Why can’t we just compare units without randomization?

Year = c(0,1,2,3)
Outcome = c(1, 1.2, 1.4, 1.6, 
            0.9, 1.3, 1.7, 2.1)
Treatment = c("Control", "Control","Control","Control", 
              "Treatment", "Treatment", "Treatment", "Treatment")

dat = data.frame(Year, Outcome, Treatment)
dat$Treatment = factor(dat$Treatment, levels = c("Treatment", "Control"))


ggplot(data = dat, aes(x = Year, y = Outcome, group = Treatment, color = Treatment)) +
  geom_line(aes(linetype=Treatment),size=2) +
  geom_point(size = 6) +
  xlim(0,3) + 
  ylim(0.8, 2.2) +
  scale_linetype_manual(values=c("solid", "solid")) +
  scale_color_manual(values = c("blue", "red") ) +
  theme(legend.position = c(0.8, 0.2), text = element_text(size=20),
        legend.title=element_blank())

Why can’t we just compare units without randomization?

Year = c(0,1,2,3)
Outcome = c(NA, 1.3, 1.5, NA,
            1, 1.2, 1.4, NA,
            1.1, 1.3, 1.7, NA)
Treatment = c("Comparison","Comparison","Comparison","Comparison",
              "Control", "Control","Control","Control",
              "Treatment", "Treatment", "Treatment", "Treatment")

dat = data.frame(Year, Outcome, Treatment)
dat$Treatment = factor(dat$Treatment, levels = c("Treatment", "Comparison", "Control"))

ggplot(data = dat, aes(x = Year, y = Outcome,  color = Treatment)) +
  geom_line(aes(linetype=Treatment),size=2) +
  geom_point(size = 6) +
  ylim(0.8, 2.2) +
  scale_linetype_manual(values=c("solid", "dotted", "solid")) +
  scale_color_manual(values = c("blue", "black", "red"  ) ) +
  theme(legend.position = c(0.8, 0.2), text = element_text(size=20),
        legend.title=element_blank())

Why can’t we just compare units without randomization?

Year = c(0,1,2,3)
Outcome = c(NA, 1.3, 1.5, 1.7,
            1, 1.2, 1.4,1.6,
            1.1, 1.3, 1.7, 1.9)
Treatment = c("Comparison","Comparison","Comparison","Comparison",
              "Control", "Control","Control","Control",
              "Treatment", "Treatment", "Treatment", "Treatment")

dat = data.frame(Year, Outcome, Treatment)
dat$Treatment = factor(dat$Treatment, levels = c("Treatment", "Comparison", "Control"))

ggplot(data = dat, aes(x = Year, y = Outcome,  color = Treatment)) +
  geom_line(aes(linetype=Treatment),size=2) +
  geom_point(size = 6) +
  ylim(0.8, 2.2) +
  scale_linetype_manual(values=c("solid", "dotted", "solid")) +
  scale_color_manual(values = c("blue", "black", "red"  ) ) +
  theme(legend.position = c(0.8, 0.2), text = element_text(size=20),
        legend.title=element_blank())

Sviatschi (2022)

• What is the effect of mass deportations on the root causes of migration?

Three sources of variation

1. Geography (birth municipality)
2. Time (policy change)
3. Age (recruitment age)

Identifying assumption

• Municipalities where gang-deportees were born would have changed in similar ways to other municipalities in the absence of a policy change

Findings

Policy Implications

• Addressing pull factors can have unintended affects on push factors in complex ways

Threats to Inference

• Confounders
• Colliders
• Mechanisms
• Reverse Causality

Adjusting on Observables

• Matching
• Weighting
• Synthetic Control (very fancy weighting)

Validity

Irregular Migration Evidence Review

Objective:

• Review evidence efficacy of interventions designed to target the root causes of irregular migration

Root causes: social and political conditions that induce departures

1. Lack of economic opportunity
2. Lack of capacity to adopt to shocks
3. High levels of violence
4. Lack of regular migration channels

Irregular Migration Evidence Review

What is irregular migration?

Why is it different from regular migration?

Findings

Studies reporting migration outcomes are concentrated on 3 intervention categories:

1. Human capital strengthening
2. Active labor market policies
3. Information campaigns

Conclusions

• Some evidence on interventions that address the root causes of irregular migration
• Almost no evidence looking at irregular migration as a primary outcome
• A number of studies are ongoing