Econometrics: Models, Variables, and Parameters
Econometrics
Econometrics combines mathematical and economic theory to build econometric models.
Model Theory
1. Models
A model is a simplified representation of economic reality, expressed in mathematical terms.
2. Requirements of Models
- Represent economic reality
- Have supporting theoretical content
- Be a simplified representation
- Be expressed mathematically
3. Elements of a Model
A model consists of three elements:
Where:
- Y = Endogenous variable
- x = Predetermined variable
- a = Intercept parameter
- b = Slope parameter
- ε = Random variable or error term
- t = Time
Equations
1. Behavioral Equations
These equations incorporate the actions of economic agents (state, companies, and individuals).
2. Institutional and Legal Equations
These equations incorporate legal standards governing a country’s economic record and its organization.
3. Technological Equations
These equations represent the combination of production factors (labor, capital) to obtain a product. Example: Cobb-Douglas Model
Where:
- Y = Product
- K = Capital
- L = Labor
- A = Technology progress
- β = Elasticity of labor
- γ = Elasticity of capital
4. Definition or Identity Equations
These are accounting equations obtained through mathematical logic (addition, subtraction, etc.) of economic variables.
5. Equilibrium Equations
These equations contain time-delayed variables.
Variables
a) Discrete Variables: Take discrete values within a certain range.
b) Continuous Variables: Can take any value within a certain range.
1. Endogenous Variables
The main variable a model tries to explain, usually found on the left-hand side of the equation.
2. Predetermined Variables
Known economic variables that influence the endogenous variable.
3. Random or Stochastic Variables
Distinguishes econometric models from purely mathematical models. Reasons for inclusion:
- Correct errors in explanatory variables
- Correct errors in model specification
- Correct errors in quantifying economic variables
4. Expectation Variables
Variables related to other observed variables.
Parameters
Numerical constants representing the statistical behavior of economic agents.
1. Structural Parameters
Found in models related to endogenous variables. Subclasses:
a) Autonomous Parameters: Found in the model and not related to predetermined variables.
b) Relational Parameters: Relate the endogenous variable to each predetermined variable.
2. Multiplier Parameters
Obtained by differentiating or manipulating equations.
3. Arbitrary Parameters
Imposed by fiscal or economic policy authorities.
Classification of Models
1. By Mathematical Correspondence
a) Linear Models: Economic variables raised to the power of one.
b) Nonlinear Models: Economic variables raised to powers other than one.
2. By Probabilistic Specification
a) Deterministic Models: Not influenced by random variables.
b) Stochastic Models: Include random variables.
3. By Number of Solutions
a) Complete Models: Have a unique solution.
4. By Domain of Investigation
1. By Number of Sectors
a) Single-Equation Models: Contain one equation and one economic sector.
b) Multi-Equation Models: Contain multiple equations representing various economic sectors.
2. By Variable Composition
a) Microeconomic Models: Contain disaggregated variables.
b) Macroeconomic Models: Contain aggregated variables.
3. By Intertemporal Causality
a) Static Models: Represent a single unit of time.
- i. Historical Models: Specific period of time.
- ii. Ahistorical Models: Individual behavior.
b) Dynamic Models: Contain time-delayed variables.
4. By Causality Between Sectors
a) Interdependent Models: Elements distributed without special features.
b) Recursive Models: Triangular coefficient matrix of predetermined variables.
c) Block Recursive Models: Block diagonal or triangular coefficient matrix.
5. By Inclusion of Foreign Trade
a) Open Economy Models: Include the external sector.
b) Closed Economy Models: Exclude the external sector.
6. By Purpose
- Predictive Models: Describe past events.
- Explanatory Models: Explain why events occurred.
- Forecasting Models: Predict future events.
- Decision Models: Incorporate scenarios and predictions for policy decisions.