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Jackknife Inference for Fixed Effects Models

Ayden Higgins

Abstract

This paper develops a general method of inference for fixed effects models which is (i) automatic, (ii) computationally inexpensive, and (iii) highly model agnostic. Specifically, we show how to combine a collection of subsample estimators into a self-normalised jackknife $t$-statistic, from which hypothesis tests, confidence intervals, and $p$-values are readily obtained.

Jackknife Inference for Fixed Effects Models

Abstract

This paper develops a general method of inference for fixed effects models which is (i) automatic, (ii) computationally inexpensive, and (iii) highly model agnostic. Specifically, we show how to combine a collection of subsample estimators into a self-normalised jackknife -statistic, from which hypothesis tests, confidence intervals, and -values are readily obtained.
Paper Structure (13 sections, 4 theorems, 133 equations, 1 figure, 2 tables)

This paper contains 13 sections, 4 theorems, 133 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Related literature
  3. Jackknife Inference
  4. Minimum Variance Unbiased Jackknife Estimator
  5. Jackknife $t$-Statistic
  6. Jackknife $t_q$-Statistic
  7. Further Matter
  8. Multi-dimensional Fixed Effects
  9. Higher-order Bias Corrections
  10. Numerical Examples
  11. Linear Regression with Individual Effects
  12. Probit Model with Interactive Effects
  13. Conclusion

Key Result

Theorem 2.1

Under Assumptions AAD and AJK the programme prog admits at least one solution $\boldsymbol{v}^\ast \in \mathcal{V}$.

Figures (1)

  • Figure 1: Subsamples for $\ell = 2$.

Theorems & Definitions (19)

  • Remark 1
  • Remark 2
  • Example 1: One-way Effects
  • Example 2: Two-way Effects
  • Remark 3
  • Remark 4
  • Remark 5
  • Theorem 2.1
  • proof
  • Theorem 2.2
  • ...and 9 more