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  • Implementing Wild Bootstrap T Standard Errors in Regression Output

    Hello everyone

    I am investigating the effects of an exogenous economic shock on the unsecured credit market. I have a panel data set consisting of 6 states and monthly data over a period of five years resulting in 360 observations.
    So far I have used the Generalized Difference in Difference approach (see regression below).

    Code:
    reg marketsize interaction_term
    Dstate2 Dstate3 Dstate4 Dstate5 Dstate6
    Dyear2 Dyear3 Dyear4 Dyear5, robust
     
    Ssc clustse
    Ssc install unique
    Ssc install boottest
     
    reg marketsize interaction_term
    Dstate2 Dstate3 Dstate4 Dstate5 Dstate6
    Dyear2 Dyear3 Dyear4 Dyear5
    boottest interaction_term, boottype(wild) weight (webb) cluster(state) level(95)
    However, in investigating and testing the OLS assumptions, I found the model to have problems with heteroskedasticity and autocorrelation of one lag in the residuals. After reading the implications of autocorrelation and heteroskedasticity for inference in Bertrand, Duflo and Mullainathan (2004), I found it necessary to use the appropriate standard errors.

    I originally thought to correct for this using clustered standard errors. However, after reading Angrist and Pischke (2008) on the topic, I understood robust clustered standard errors to potentially perform worse than standard robust errors when clusters are small. A minimum of 42 clusters was suggested for it to be appropriate to use cluster-robust standard errors, which is significantly higher than the 6 clusters in my model.

    After further investigating potential solutions, I came across the Wild bootstrap-t method for standard errors as described by A. Colin Cameron, Jonah B. Gelbach and Douglas L. Miller (2008), which seems to be generally accepted as the best method for clustered standard errors for few clusters, even as low as 6, which is our case.

    I have currently found the boottest command to test individual factors with wild bootstrapped-t standard errors following a regression estimation. However, I am struggling to implement wild bootstrap-t standard errors in the STATA regression output for the remaining variables. Does anyone know how do this?

    Any help would be greatly appreciated.

    I read the bootstrap pdf entry in STATA but I did not feel it answered my question as there mention of the wild bootstrap method.

    Bertrand, M., E. Duflo, and S. Mullainathan, “How Much Should We Trust Differences-in-Differences Estimates?” Quarterly Journal of Economics 119 (2004), 249–275
    Angrist and Pischke, Mostly Harmless Econometrics: An empiricist’s companion (2008)
    A. Colin Cameron, Jonah B. Gelbach and Douglas L. Miller, “Bootstrap-Based Improvements for Inference with Clustered Errors” The Review of Economics and Statistics, (2008)

  • #2
    It might be too late, but this Twitter discussion offers pointers on how to include boottest results into a regression table using esttab/estout:
    https://twitter.com/jacob_econ/statu...06608217182209

    As a side note, boottest does not offer SEs for the coefficients, only p-value and confidence interval; my intuition is that SEs are only relevant information when something is distributed symmetrically, which is not necessarily the case when bootstrapping on a small number of clusters. (See the graphs generated by boottest to convince yourself.)

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