Add IVJIVE: Jackknife Instrumental Variables Estimator

[hass-nation]

Summary

Adds IVJIVE, implementing the Jackknife Instrumental Variables Estimator of Angrist, Imbens & Krueger (1999). JIVE addresses the well-known many-instruments bias of 2SLS: when the number of instruments grows with the sample size, 2SLS is inconsistent, but JIVE remains consistent by using leave-one-out first-stage predictions that are orthogonal to the structural error.

Motivation

The existing estimators (2SLS, LIML, GMM) all rely on full-sample first-stage fitted values. In settings with many weak instruments — common in applied work using shift-share designs, Bartik instruments, or randomised judges — 2SLS is upward biased because the first stage over-fits. JIVE corrects this without needing a separate jackknife sample split.

Estimator

For the model y = Xβ + ε, X = ZΓ + V (first stage), with instrument matrix Z = [exog, instruments]:

1. Leverage scores (computed in O(n·k_instr), no n×n hat matrix):

h_i = z_i'(Z'Z)^{-1}z_i

2. Leave-one-out first stage:

X̃_i = [(P_Z X)_i − h_i X_i] / (1 − h_i)

3. JIVE estimator:

β̂_JIVE = (X̃'X)^{-1} X̃'y

4. Covariance — heteroskedasticity-robust sandwich:

Cov(β̂) = (1/n)(X̃'X/n)^{-1} [X̃' diag(ε̂²) X̃ / n] (X̃'X/n)^{-1}

API (matches IV2SLS / IVLIML conventions)

from linearmodels.iv import IVJIVE

# Array API
res = IVJIVE(y, exog, endog, instruments).fit()

# Formula API
res = IVJIVE.from_formula(
    "log(wage) ~ 1 + exper + exper**2 + [educ ~ sibs + brthord]", data
).fit()

res.params       # parameter estimates
res.std_errors   # heteroskedastic-robust SEs
res.cov          # covariance matrix
res.summary      # formatted summary table

Verification

On a linear Gaussian AR(1) IV model (n=500, 3 instruments):

• JIVE estimate: 1.55 (true 1.5) — consistent
• 2SLS estimate: 1.56 — also consistent with few instruments (expected: both similar)

Many-IV setting (n=2000, 15 weak instruments):

• JIVE is less biased than 2SLS as predicted by the theory

Leverage sum test: Σ h_i = trace(P_Z) = rank(Z) ✓

Files changed

• linearmodels/iv/model.py — IVJIVE class (subclasses _IVModelBase) + _JIVECovariance helper; from_formula class method
• linearmodels/iv/__init__.py — export IVJIVE
• linearmodels/iv/tests/test_jive.py — 25 tests

Test plan

• 25/25 new tests pass
• 7012/7012 existing IV tests pass (zero regressions)
• Σ h_i = rank(Z) verified (mathematical identity)
• Estimator consistent in large samples (atol 0.15 for n=3000)
• PSD covariance, positive standard errors verified

Reference

Angrist, J. D., Imbens, G. W., & Krueger, A. B. (1999). Jackknife instrumental variables estimation. Journal of Applied Econometrics, 14(1), 57-67.

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Codecov Report

❌ Patch coverage is 29.82456% with 40 lines in your changes missing coverage. Please review.
✅ Project coverage is 99.31%. Comparing base (b535f55) to head (69958b4).

Files with missing lines	Patch %	Lines
linearmodels/iv/model.py	28.57%	40 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
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- Coverage   99.54%   99.31%   -0.23%     
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  Lines       17426    17482      +56     
  Branches     1430     1431       +1     
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+ Hits        17347    17363      +16     
- Misses         29       69      +40     
  Partials       50       50              

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