Understanding the gsynth Function in R: A Deep Dive into Synthetic Control Estimation

Synthetic control estimation is a powerful technique used in econometrics and statistics to estimate the effect of a treatment on an outcome variable. It involves estimating a weighted average of a non-treated group, where the weights are based on the similarity between the treated and untreated groups at each time period. In this article, we will explore the gsynth function in R, which is used for synthetic control estimation.

Introduction to Synthetic Control Estimation

Synthetic control estimation was first introduced by Abadie et al. (2010) as a way to estimate the effect of a treatment on an outcome variable when there are no comparable units available. The basic idea behind synthetic control estimation is that the treated unit can be used to create a weighted average of a non-treated group, where the weights are based on the similarity between the two groups at each time period.

Understanding the gsynth Function

The gsynth function in R is used for synthetic control estimation. It takes several arguments, including:

• Y: The outcome variable
• D: The binary treatment assignment
• data: The data frame containing the input variables
• index: A vector of indices specifying which variables to use as controls
• force: A character indicating whether to force a two-way ANCOVA or not
• CV: A logical indicating whether to perform cross-validation or not
• r: A vector of factors indicating how to handle the case where there are no comparable units available
• se: A logical indicating whether to compute standard errors for the estimates
• inference: A character indicating which inference method to use (e.g. parametric, bootstrap)
• nboots: An integer specifying the number of bootstrap iterations to perform

Common Issues with gsynth

When using the gsynth function in R, there are several common issues that can arise.

Error: attempt to set ‘rownames’ on an object with no dimensions

This error occurs when the “best” solution is r* = 0, which means that there are no comparable units available. In this case, the result will be empty.

To resolve this issue, we need to adjust the value of r in the gsynth function. The correct approach is to set r to a vector with positive values, such as c(1, 5), instead of c(0, 5).

Resolving the Issue: Adjusting the Value of r

In the given example, the error occurs because the value of r is set to c(0, 5). To resolve this issue, we need to adjust the value of r to a vector with positive values. One way to do this is by setting r to c(1, 5).

Here’s an example code snippet that demonstrates how to resolve the issue:

out <- gsynth(Y ~ D, data = data6,
             index = c("id","time"), force = "two-way",
             CV = FALSE, r = c(1, 5), se = TRUE, inference = "parametric", nboots = 1000, min.T0 = 6)

Additional Considerations

While adjusting the value of r can resolve the issue, there may be other factors that contribute to the error. For example:

• The number of factors in r should not exceed the number of unique units available.
• If there are no comparable units available, the result will be empty.

In such cases, it’s essential to carefully evaluate the data and adjust the gsynth function parameters accordingly.

Cross-Validation with gsynth

Cross-validation is an important aspect of synthetic control estimation. It involves estimating the effect of a treatment on an outcome variable multiple times, using different subsets of the data each time. The goal is to estimate the robustness of the results and account for potential overfitting.

The gsynth function in R supports cross-validation. To perform cross-validation with gsynth, we need to set CV = TRUE and specify the number of bootstrap iterations using the nboots argument.

Here’s an example code snippet that demonstrates how to perform cross-validation with gsynth:

out <- gsynth(Y ~ D, data = data6,
             index = c("id","time"), force = "two-way",
             CV = TRUE, nboots = 1000, r = c(1, 5), se = TRUE, inference = "parametric")

Conclusion

Synthetic control estimation is a powerful technique used in econometrics and statistics to estimate the effect of a treatment on an outcome variable. The gsynth function in R is widely used for synthetic control estimation. While the gsynth function can resolve common issues, it’s essential to carefully evaluate the data and adjust the parameters accordingly.

In this article, we explored the gsynth function in R, including its syntax, common issues, and additional considerations. We also demonstrated how to resolve a common error that occurs when there are no comparable units available.

Last modified on 2023-10-27