Parallel Trends Assumptions: Sensitivity To Functional Form Matters

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The concept of parallel trends has been a cornerstone of econometric analysis, particularly in the context of difference-in-differences (DiD) estimation. The basic idea is to assume that the trend in the treatment group would have been the same as the trend in the control group, had the treatment not occurred. This assumption allows researchers to identify the causal effect of the treatment by comparing the observed outcome in the treatment group to the counterfactual outcome that would have occurred in the absence of treatment.

However, recent research has highlighted the importance of considering the sensitivity of parallel trends assumptions to functional form. In other words, the validity of the parallel trends assumption can depend crucially on the specific functional form used to model the trends. This is a critical issue, as the choice of functional form can have significant implications for the estimated treatment effect.

One of the primary concerns is that the parallel trends assumption may not hold under certain functional forms. For example, if the true trend is non-linear, but the researcher assumes a linear trend, the parallel trends assumption may be violated. This can lead to biased estimates of the treatment effect, as the researcher is essentially comparing apples to oranges.

The Importance of Functional Form

The choice of functional form is critical in DiD estimation, as it can significantly impact the estimated treatment effect. Researchers often rely on simple linear models, but these may not always capture the underlying trends in the data. In some cases, non-linear models or models with time-varying coefficients may be more appropriate.

For instance, consider a scenario where the treatment effect is increasing over time. A linear model may not capture this non-linear trend, leading to biased estimates of the treatment effect. In contrast, a non-linear model or a model with time-varying coefficients may be better suited to capture the underlying trend.

Sensitivity to Functional Form

The sensitivity of parallel trends assumptions to functional form can be evaluated using a variety of methods. One approach is to use a flexible functional form, such as a non-parametric or semi-parametric model, to estimate the trends in the treatment and control groups. This can provide a more robust estimate of the treatment effect, as it is less reliant on specific functional form assumptions.

Another approach is to use a model selection criterion, such as the Akaike information criterion (AIC) or the Bayesian information criterion (BIC), to evaluate the fit of different functional forms. This can help researchers to identify the most appropriate functional form for their data, which can in turn help to ensure the validity of the parallel trends assumption.

Empirical Applications

The importance of considering sensitivity to functional form can be illustrated using empirical applications. For example, a recent study on the impact of a minimum wage increase on employment outcomes used a non-linear model to capture the trend in employment rates. The results showed that the estimated treatment effect was highly sensitive to the choice of functional form, highlighting the importance of careful model selection.

Practical Implications

The sensitivity of parallel trends assumptions to functional form has important practical implications for researchers. It highlights the need for careful consideration of the functional form used to model trends, as well as the importance of evaluating the robustness of the results to different functional forms.

In practice, researchers can use a variety of methods to evaluate the sensitivity of parallel trends assumptions to functional form. These include using flexible functional forms, model selection criteria, and sensitivity analyses to evaluate the robustness of the results.

Conclusion and Future Directions

In conclusion, the sensitivity of parallel trends assumptions to functional form is a critical issue in DiD estimation. Researchers must carefully consider the functional form used to model trends, as well as evaluate the robustness of the results to different functional forms.

Future research should continue to explore the importance of functional form in DiD estimation, including the development of new methods for evaluating sensitivity to functional form. Additionally, researchers should prioritize the use of flexible functional forms and model selection criteria to ensure the validity of parallel trends assumptions.

We invite readers to share their thoughts on the importance of functional form in DiD estimation and to suggest future directions for research. Please leave a comment below or share this article on social media to continue the conversation.

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