Description
covariance = meanProduct-instrumentMean*regressorMean; gap = covariance-referenceCovariance.
Instrumental-variable and moment calculations compare supplied regressors, instruments, residuals and first-stage quantities. A local moment or relevance statistic does not establish exclusion, exogeneity, identification or a complete estimator.
covariance = meanProduct-instrumentMean*regressorMean; gap = covariance-referenceCovariance.
When to use this tool
Use Instrument Relevance One Moment Gap when checking one supplied first-stage or moment contribution.
How to use the tool and how it works
- Enter instrumentMean, regressorMean, meanProduct, referenceCovariance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read covariance, gap. Use the output convention below.
covariance = meanProduct-instrumentMean*regressorMean; gap = covariance-referenceCovariance.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| instrumentMean | Instrument Mean | Required. Finite number. |
| regressorMean | Regressor Mean | Required. Finite number. |
| meanProduct | Mean Product | Required. Finite number. |
| referenceCovariance | Reference Covariance | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| covariance | Covariance | Required. Finite number. |
| gap | Signed difference from the stated reference, using compatible units. | Required. Finite number. |
{
"input": {
"instrumentMean": 2,
"regressorMean": 3,
"meanProduct": 8,
"referenceCovariance": 1
},
"output": {
"covariance": 2,
"gap": 1
}
}Limitations and assumptions
- The supplied means must come from a compatible sample and normalization. This algebraic moment gap does not establish instrument relevance, statistical significance or exclusion validity.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Fit an appropriate full model and examine identifying assumptions and diagnostics before interpreting an IV result.
References
Similar or alternative tools
- Instrument Intercept Exclusion Flag
When excludeIntercept is true, remove instrumentNames that occur literally in interceptNames; otherwise select all names.
- Weak Instrument First Stage Partial Ratio
Calculate nested first-stage partial R-squared and an ordinary homoskedastic partial F statistic from supplied sums of squares.