Introduction
In econometrics, especially dynamic econometric models, a predetermined variable is a variable whose current and lagged values are uncorrelated with the current error term, though its future values might not share this property. This characteristic makes predetermined variables crucial in addressing the endogeneity problem by serving as instrumental variables.
Historical Context
The concept of predetermined variables has evolved alongside the development of econometric models. During the mid-20th century, econometricians began to identify the need to distinguish between different types of variables based on their relationships with error terms, leading to a better understanding and categorization of predetermined variables.
Types/Categories
- Lagged Dependent Variables: These are past values of the dependent variable itself and often used in autoregressive models.
- Exogenous Variables: External factors whose current and past values influence the system but are not influenced by the system’s endogenous variables.
- Instrumental Variables: Used to correct for endogeneity, their values are set prior to the model period under study.
Key Events
- Introduction of Instrumental Variable Techniques: The utilization of predetermined variables became more pronounced with the development of instrumental variable techniques.
- Advancements in Panel Data Analysis: Panel data methods further cemented the role of predetermined variables in accounting for unobserved heterogeneity.
Detailed Explanations
Predetermined variables are characterized by their temporal attributes relative to the error term. Formally, a variable \( Z_t \) is predetermined if \( E(u_t | Z_t, Z_{t-1}, Z_{t-2}, …) = 0 \). This relationship ensures that while past and current values are independent of the current error term \( u_t \), future values are not guaranteed this property.
Mathematical Models/Formulas
Consider a simple dynamic model:
- \( Y_t \) is the dependent variable at time \( t \)
- \( X_t \) is a predetermined variable
- \( Y_{t-1} \) is a lagged dependent variable, often predetermined
- \( u_t \) is the error term
In this context, \( X_t \) and \( Y_{t-1} \) are predetermined with respect to \( u_t \).
Charts and Diagrams
flowchart TD
A[Current Period (t)] --> |X_t and Y_{t-1}| B[Uncorrelated with Error Term (u_t)]
C[Future Period (t+1)] --> |X_{t+1} and Y_{t}| D[Not Necessarily Uncorrelated with u_t]
Importance
Predetermined variables are pivotal in mitigating bias in parameter estimates, making them essential in regression analysis where endogeneity poses a threat to inference accuracy.
Applicability
- Instrumental Variable Regression: To deal with endogeneity in explanatory variables.
- Dynamic Panel Data Models: In methods such as the Arellano-Bond estimator, which rely on lagged dependent variables as instruments.
Examples
- Macroeconomic Indicators: Lagged values of GDP used in forecasting models.
- Financial Time Series: Past stock prices used in predicting future trends.
Considerations
- Instrument Validity: The choice of predetermined variables must ensure they meet the relevance and exogeneity conditions for valid instruments.
- Model Specification: Correct model specification is crucial to accurately account for the role of predetermined variables.
Related Terms with Definitions
- Endogeneity: Situation where an explanatory variable is correlated with the error term.
- Instrumental Variables (IV): Variables that are used to account for endogeneity by replacing problematic predictors.
Comparisons
- Exogenous vs. Predetermined: While both are not influenced by current error terms, predetermined variables do not assume independence of future values from the error term.
Interesting Facts
- The concept dates back to early econometric pioneers like Haavelmo and was later expanded through the works of Simons and others.
Inspirational Stories
Economist James Heckman, Nobel laureate, utilized predetermined variables effectively in his research on labor economics, enhancing our understanding of human capital development.
Famous Quotes
“Statistics are no substitute for judgment.” – Henry Clay
Proverbs and Clichés
- “Data never lies, but it can mislead.”
- “Past is prologue.”
Expressions, Jargon, and Slang
- Granger-Causality: Testing if past values of one variable help in forecasting another.
- Lagged Instrument: Using past values as instruments.
FAQs
What distinguishes a predetermined variable from an exogenous variable?
A predetermined variable is specifically uncorrelated with current errors but not necessarily future ones, while an exogenous variable is uncorrelated with both current and future errors.
Why are predetermined variables important in econometrics?
They help tackle endogeneity issues, providing unbiased and consistent parameter estimates.
References
- Stock, J.H., & Watson, M.W. (2019). “Introduction to Econometrics.” Pearson.
- Wooldridge, J.M. (2010). “Econometric Analysis of Cross Section and Panel Data.” MIT Press.
Summary
Predetermined variables play a critical role in econometrics by addressing endogeneity and ensuring accurate parameter estimates in dynamic models. Their correct identification and application enhance the reliability of statistical inferences and econometric modeling, proving indispensable in the realms of economics and finance.
