Transcript Building and Testing a Theory Steps 1-3

Building and Testing a Theory
Steps 1-4
1.
2.
3.
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.”
4.
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
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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
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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
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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
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Hypothesis Testing – Statistical experiment used to
measure the reasonableness of a given theory or
premise
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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
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Deterministic Relation = An identity
 A relationship that is known with
certainty.
Statistical Relation – An inexact
relation
Regression Analysis
Types of Data
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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.
Regression Math
E(Y|Xi) = α + βXi
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In words…. the expected value of Y for given values of Xi is equal to a
linear function of X.
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OR….
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Y = Β0 + Β1 X1
Where
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Y = The Dependent Variable, or what you are trying to explain (or
predict).
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X = The Independent Variable, or what you believe explains Y.
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Β0 = the y-intercept or constant term.
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Β1 = the slope coefficient
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Linear vs. Non-linear equations
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The Stochastic Error Term
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Y = Β0 + Β1 X1 + 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
Sources of error term
1.
Omitted variables
2.
Measurement error
3.
Incorrect functional form
4.
Unpredictable or purely random variation
Interpretation
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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.
Estimated Regression Equation
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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.