Specification error is an error in estimation or inference caused by a false assumption in an econometric model. It often results in the estimators of the model parameters being biased and inconsistent. Omitted variable bias and incorrect functional form are examples of specification error. See also Ramsey regression equation specification error test.
Historical Context
The concept of specification error gained significant attention with the development of econometric methods in the mid-20th century. Early pioneers like Jan Tinbergen and Ragnar Frisch laid the groundwork for econometric modeling, where the accurate specification of models became crucial for meaningful economic inference.
Types of Specification Error
- Omitted Variable Bias: Occurs when a relevant variable is left out of the model, leading to biased and inconsistent parameter estimates.
- Incorrect Functional Form: Happens when the chosen functional form of the model does not match the true data-generating process.
- Measurement Error: Arises when the variables included in the model are measured with error, distorting the results.
Key Events
- 1944: Establishment of the Cowles Commission for Research in Economics, which emphasized the importance of model specification.
- 1961: Publication of Goldberger’s “Economic Theory of Life” which addressed issues of model specification in econometrics.
- 1983: Introduction of the Ramsey Regression Equation Specification Error Test (RESET), a diagnostic tool to detect functional form misspecification.
Detailed Explanations
Omitted Variable Bias
When a relevant variable that influences both the dependent variable and an included independent variable is omitted from the model, the estimates of the coefficients will be biased.
Incorrect Functional Form
Selecting a functional form that does not reflect the true relationship between variables results in specification error. For example, choosing a linear model when the relationship is nonlinear will lead to inaccurate estimations.
Mathematical Formulas/Models
Consider a simple linear regression model:
- Omitted Variable Bias Example: If a relevant variable \( Z \) is omitted and \( Z \) is correlated with \( X \), the estimated coefficient \( \hat{\beta}_1 \) will be biased.
Charts and Diagrams
graph TD;
A(Initial Model Assumption) --> B{Correct Specification?}
B -->|Yes| C(Accurate Inference)
B -->|No| D(Specification Error)
D --> E(Biased Estimates)
D --> F(Inconsistent Estimates)
Importance and Applicability
Accurate model specification is critical in econometrics to ensure unbiased and consistent parameter estimates. The presence of specification errors can lead to misleading inferences and incorrect policy recommendations.
Examples
- Real Estate Pricing Models: Omitting the variable ’location’ from a pricing model can lead to biased estimates of property values.
- Healthcare Studies: Using a linear model when the relationship between dose and effect is exponential will misestimate the drug efficacy.
Related Terms with Definitions
- Bias: Systematic deviation from the true parameter value.
- Consistent Estimator: An estimator that converges to the true parameter value as sample size increases.
- RESET Test: A test to detect misspecification in the functional form of a regression model.
Comparisons
- Specification Error vs. Measurement Error: Specification error relates to incorrect model assumptions, while measurement error pertains to inaccuracies in the data itself.
Interesting Facts
- The term “specification error” is not confined to econometrics and is used in other fields like machine learning, indicating its wide applicability.
Inspirational Stories
Economist Edward Leamer’s work on specification searches has inspired rigorous testing and validation methods in econometric modeling, highlighting the importance of getting the specification right.
Famous Quotes
- “All models are wrong, but some are useful.” - George Box
- “The real problem is not whether machines think but whether men do.” - B. F. Skinner, emphasizing the importance of human oversight in model specification.
Proverbs and Clichés
- “Garbage in, garbage out.”
- “You can’t make a silk purse out of a sow’s ear.”
Expressions and Jargon
- Spec Bias: Slang for specification bias.
- Model Misspec: Short for model misspecification.
FAQs
Q: How can I detect specification errors in my model? A: Use diagnostic tests like the RESET test, review model residuals, and consider theoretical knowledge to ensure all relevant variables are included.
Q: What is the impact of specification error on my results? A: It can lead to biased and inconsistent parameter estimates, undermining the credibility of your findings.
References
- Goldberger, A. S. (1961). “Economic Theory of Life.”
- Ramsey, J. B. (1969). “Tests for Specification Errors in Classical Linear Least Squares Regression Analysis.”
Summary
Specification error is a critical concept in econometrics, denoting errors arising from incorrect model assumptions. It encompasses omitted variable bias, incorrect functional forms, and measurement errors, all of which lead to biased and inconsistent parameter estimates. Accurate specification is vital for reliable econometric inference, with diagnostic tests and theoretical knowledge aiding in the identification and correction of these errors. Understanding specification error ensures more credible and valid econometric analyses.
