Weekly Discussion: Diff in Diff

I.

A.

In a simple diff-in-diff paper, we are interested in estimating the effects of an intervention by comparing the changes in outcomes between the treatment and control groups over time. There are two ways to analyze this: The 2 x 2 matrix of regression equations: This approach involves running two separate regressions, one for the treatment group and one for the control group. The regression equation for each group would be: Y = α + β1(time), where Y is the outcome variable and time represents the time period. By estimating the coefficients β1 for both groups, we can construct the diff-in-diff estimator, which is the difference between the coefficients β1 of the treatment group and the control group. The regression form: Y = α + β1(time) + β2(treatment) + β3(timetreatment): This approach uses a single regression equation to estimate the treatment effect. β1 represents the expected mean change in the outcome from before to after the intervention among the control group, capturing the effect of the passage of time in the absence of the intervention. β2 is the estimated mean difference in Y between the treatment and control groups prior to the intervention, reflecting any baseline differences between the groups. β3, the coefficient of the interaction term (timetreatment), is the difference-in-differences estimator. It measures whether the expected mean change in outcome from before to after the intervention was different in the two groups. To estimate the mean difference in Y between the treatment and control groups after the intervention, we consider β1 + β3. This combined coefficient captures the overall treatment effect by accounting for both the pure time effect (β1) and the differential change in outcomes between the treatment and control groups (β3). It is possible for β1 + β3 to be significantly different from zero, even if β1 or β3 alone is not statistically significant.

B.

setwd("D:/hw/0407")
# Load the dataset
data <- read.csv("us_fred_coastal_us_states_avg_hpi_before_after_2005.csv")

# Run the linear regression
model <- lm(HPI_CHG ~ Time_Period + Disaster_Affected + Time_Period * Disaster_Affected, data = data)

# Print the regression results
summary(model)

## 
## Call:
## lm(formula = HPI_CHG ~ Time_Period + Disaster_Affected + Time_Period * 
##     Disaster_Affected, data = data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.023081 -0.007610 -0.000171  0.004656  0.035981 
## 
## Coefficients:
##                                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                    0.037090   0.002819  13.157  < 2e-16 ***
## Time_Period                   -0.027847   0.003987  -6.985  1.2e-08 ***
## Disaster_Affected             -0.013944   0.006176  -2.258   0.0290 *  
## Time_Period:Disaster_Affected  0.019739   0.008734   2.260   0.0288 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01229 on 44 degrees of freedom
## Multiple R-squared:  0.5356, Adjusted R-squared:  0.504 
## F-statistic: 16.92 on 3 and 44 DF,  p-value: 1.882e-07

C.

The control group refers to the group that did not receive the treatment or intervention, while the treatment group refers to the group that did receive the treatment or intervention. The goal of the difference-in-differences methodology is to estimate the effects of the intervention by comparing the changes in outcomes between the treatment and control groups over time. By differencing these differences, we aim to isolate and estimate the causal effect of the treatment. In simple terms, we want to see if the treatment had an impact by comparing how things changed over time for the treatment group compared to the control group. If the treatment had no effect, we would expect both groups to change similarly over time. However, if the treatment had an effect, we would expect to see a divergent change in outcomes between the treatment and control groups. By analyzing these differences, we can estimate the treatment effect. Regarding the 2x2 matrix of regression equations, we need the actual values from the data to create it. Unfortunately, the provided information does not include the actual values of the variables, so we cannot create the table. However, in theory, the difference-in-difference coefficient from the linear regression should match the difference-in-difference effect observed in the 2x2 table if the regression model and the data are appropriately specified.

D.

In the context of difference-in-differences methodology, the “threats to identification” refer to potential factors or conditions that could undermine the validity of the estimated treatment effects. One crucial implicit assumption for difference-in-differences is the parallel trends assumption. This assumption requires that, in the absence of treatment, the trends in the outcomes of the treatment and control groups would have followed a parallel path over time. If this assumption is violated, it can cast doubt on the reliability of the estimated treatment effects. Therefore, it is important to carefully assess whether the parallel trends assumption holds before trusting the point estimates, and any deviations from parallel trends should be considered when interpreting the study results.

II.

• ARTICLE SUMMARY The authors aim to evaluate the impact of an increase in the minimum wage on employment in the fast-food industry in New Jersey and Pennsylvania. They test the economic hypothesis of whether a higher minimum wage leads to a reduction in employment. The authors find no evidence that the increase in the minimum wage reduced employment, contrary to the prediction of standard economic theory in a perfectly competitive labor market.
• EXTRA: To reconcile the study results within an economic model, one possible explanation is the presence of a monopsony market structure in the fast-food industry. In a monopsony, where there is a single buyer of labor, an increase in wages can lead to an increase in employment. This contrasts with the standard perfectly competitive labor market assumption, where binding minimum wages are expected to cause unemployment.
• METHODOLOGY / CRITICAL ANALYSIS The treatment in this study is the increase in the minimum wage, which occurred in New Jersey but not in Pennsylvania. New Jersey is the treatment group, while Pennsylvania serves as the control group. The methodology of difference-in-differences is intuitive as it creates a comparison between the two groups, accounting for common factors that affect both groups equally. However, I would exercise caution in fully accepting the study’s results and making policy changes based solely on this study. Further research and consideration of potential threats to identification, such as the parallel trends assumption, are important. The “threats to identification” in this study include potential factors that could undermine the validity of the estimated treatment effects. One key implicit assumption is the parallel trends assumption, which assumes that, in the absence of the minimum wage increase, the employment trends in New Jersey and Pennsylvania would have followed a similar path. If this assumption is violated, it could cast doubt on the reliability of the estimated employment effects. Therefore, it is essential to consider the validity of the parallel trends assumption and other potential threats to identification when interpreting the study results.

III.

• The paper by David Card examines the impact of the Mariel Boatlift of 1980 on the labor market in Miami. The Mariel Boatlift brought a significant number of immigrants to Miami, increasing the labor force by 7%. Most of these immigrants were unskilled workers. However, the study finds that the influx of Mariel immigrants had little to no effect on the wages or unemployment rates of less-skilled workers, including earlier Cuban immigrants. The author suggests that Miami’s labor market was able to absorb the Mariel immigrants quickly due to its previous experience with large waves of immigrants. The paper finds that the Mariel immigration had minimal impact on the wages or employment outcomes of non-Cuban workers in the Miami labor market. This is surprising considering the substantial increase in the labor force. The study indicates a rapid absorption of the Mariel immigrants into the labor market without adverse effects on native workers.
• Another example of a good difference-in-differences (Diff-in-Diff) paper is “The Long-Term Effects of California’s 2004 Paid Family Leave Act on Women’s Careers: Evidence from U.S. Tax Data” by Maya Rossin-Slater et al. In this study, the authors examine the impact of California’s Paid Family Leave Act on women’s careers. The paper utilizes a 2x2 table or estimating equation with an interaction term to assess the effects of the policy on labor market outcomes for women.