1.
2.
3.
4.
Building and Testing a Theory
Steps 1-4
Decide on what it is you want to explain or predict.
Identify the variables that you believe are important to what you want to explain or predict.
State the assumptions of the theory.
Ceteris Paribus - A Latin term meaning “all things held constant.”
State the hypothesis

Building and Testing a Theory
Steps 5-6
5.
6.
a.
b.
Test the theory by comparing its predictions against real-world events.
If the evidence supports the theory, then no further actions is generally taken. If the evidence rejects the theory, then you can conclude the theory is incorrect.
you can conclude the data is inadequate.
Step 6 teaches a valuable lesson – We do not learn the “truth” via econometrics.

Econometrics Defined



Econometrics - the social science in which the tools of economic theory, mathematics, and statistical inference are applied to the analysis of economic phenomena.
Econometrics is defined literally as “economic measurement”
Quantitative analysis of actual economic phenomena.

Uses of Econometrics
1.
2.
3.
Describing Economic Reality
Testing Hypothesis about Economic Theory
Forecasting Future Economic Activity

Regression Analysis Defined



A statistical technique that attempts to “explain” movements in one variable as a function of movements in a set of other variables.
Dependent variable – what we wish to explain.
Independent variable – what we believe explains movements in the dependent variable.

Correlation vs .Causation




Regression analysis tells us that variables move together.
In other words, it tells us about correlation.
Regression analysis does not “prove” causation.
Causation is “established” via the combination of regression analysis and economic theory.

Hypothesis Testing



Hypothesis Testing – Statistical experiment used to measure the reasonableness of a given theory or premise

NOTE: WE DO NOT “PROVE” A THEORY
Type I Error – Incorrect rejection of a ‘true’ hypothesis.
Type II Error – Failure to reject a ‘false’ hypothesis.

Deterministic Relations vs.
Statistical Relations

Deterministic Relation = An identity

A relationship that is known with certainty.

Statistical Relation – An inexact relation

Regression Analysis
Types of Data



Time series – A daily, weekly, monthly, or annual sequence of data. i.e. GDP data for the United States from 1950 to 2005
Cross-section – Data from a common point in time. i.e. GDP data for OECD nations in 1995.
Panel data – Data that combines both cross-section and time-series data. i.e. GDP data for OECD nations from 1960 to 2000.






E(Y|X i
) = α + βX i
In words…. the expected value of Y for given values of X i linear function of X.
is equal to a

OR….

Y = Β
0
Where
+ Β
1
X
1


Y = The Dependent Variable, or what you are trying to explain (or predict).
X = The Independent Variable, or what you believe explains Y.
Β
0
Β
1
= the y-intercept or constant term.
= the slope coefficient
Linear vs. Non-linear equations





4.
Y = Β
0
+ Β
1
X
1
+ ε
Stochastic error term (ε) = disturbance term = a term that is added to a regression equation to introduce all of the variation in Y that cannot be explained by the included Xs.
Stochastic = Random
2.
3.
1.
Sources of error term
Omitted variables
Measurement error
Incorrect functional form
Unpredictable or purely random variation


Interpreting a regression coefficient

 the impact of a one unit change in X on the dependent variable Y, holding constant the other included independent variables.
This is how we do controlled experimentation in economics

If a variable is not included, then we have not controlled for this factor.






Population Regression Function (PRF) vs. a
Sample Regression Function (SRF)
True regression coefficients vs. Estimated regression coefficients.
Residual – difference between the observed
Y and the estimated regression line.
Error term – difference between the observed Y and the true regression equation.
Error term is theoretical and never observed.