Introduction
Overview
Ekonometri 2013
This is a wide” introduction” to
econometrics.
Econometrics Introduction
General introduction
What you need to remember from
econometrics 101
Estimators
Properties of testing
Mathematical statistics for beginners
The Friday lecture will be longer!
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Econometrics second course
Always use more than one textbook
Use different programs
Download gretl and data for different books, inkl.
Verbeek. EVIEWS is everywhere or costs 40usd
Practice alone with the programs
Learn how to prepare data, estimate models, test
models and interpretate results.
It is your responsibility. There is plenty of exercises, if
you don’t do them you don’t learn anything.
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Econometric Software
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Software
Gretl (freeware) based on R from sourgeforce.net
JMulti (freeware)
RATS, Eviews, Gauss
TSP, Microfit, SPSS
STATA – favoured by the World Bank
SAS: Statistical Analysis System
SPSS
OXMetrics/PcGive (David Hendry & J. Doornik )
Shazam (Ken White), Ects (Davidsson), STAMP
(Harvey), LIMDEP (Green)
Matlab ... + more
Econometrics Introduction
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How to study econometrics?
1) What you should know about
econometrics and statistics
2) What you shoukld know and hopefully
remember from your first course in
econometrics
3) Econometrics basics at little higher
level
Econometrics Introduction
Econometrics Introduction
Most software is written by amatuer
programmers who learnt econometrics on
mainframe computers and requires effort to
learn. Sic
Many offers programing of the user´s own
routines.
PcGive + gretl is almost the only program with a
modern user interface
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What to do with
econometrics?
“Measurement in Economics”
Econometrics – What is it?
“The application of statistical and
mathematical methods to the analysis of
econometric data, with the purpose of
giving content to economic theories, and
verifying or refuting them.” (Maddala)
Compare: Biometrics etc…
Is Maddala’s definition realistic?
Some people think that capitalism is the
root of evil. Get rid of capitalism and all
problems will be solved.
Some thinks the same of economics, of
economists,
And some don’t like econometrics....
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Why Econometrics - 1?
• ”It is a capital mistake to theorise without
emprical observations” Sherlock Holmes
• ”Of course it might work in practice. But,
the real question is - does it work in
theory?” Unkown economist
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What is a Good Theory?
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Why Econometrics - 3?
Forecasting – yes.
Evaluation of interventions, medical, social, economic –
yes.
Scientific proof of theories? – Sorry cannot do.
Circumstancial evidence for or against at most.
o ”Nothing is as practical as a good theory”
o Some points on the topic
o A Good Theory starts from observations
o A Good Theory should have testable
hypotheses , otherwise it turns into
religion, a matter of belive
o Anecodotes are not theory or science
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Why Econometrics - 2?
“History is nothing but a pack of tricks
that we play upon the dead” (Voltaire)
For verification of economic theories logical consistency is not enough, we
need empirical research to verify the
relevance of theories.
Observation without logic. Logic without
observations?
Econometrics Introduction
Econometrics Introduction
Relevance of theories:
Describe relations, simulate, forecast, give policy
recommendations - put flesh on the bones given by theory.
Those who seek hopefully with an open mind will find
something to believe in.
Controversy: What can you really do with econometrics?
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Why Econometrics – 4
Controversies?
Look at the greater picture
The controversies are mainly related to
1) Macroeconomic policy (monetary policy?) and
2) How well are markets working, how are people behaving, are
there causes for interventions?
“Models are too simplified”
“Unrealistic assumptions”
“If you torture your data long enough it
will confess to anything”
“No econometric work has ever changed
or inspired economic theory”
Rational expectations …hmmm help?
Econometrics Introduction
’Tons of results’ support the view that when people have
to make choices they make very rational choices, given
their (limited) information, given other restrictions, given
that they maximise their welfare in the long run. The
clever economist reveals this and are able to predict
average and marginal human behavior far better than
the man on the street, politicians, poets, priests and
other social and natural scientists.
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Book Examples: Freakonomics
To improve the welfare of people, especially the
poor, politicians construct different social and
economic interventions. But, do they work?
Banerjee and Duflo (2011) Poor Economics: A
Radical Rethinking of the Way to Fight
Global Poverty.
FT:s Business Book of the Year award 2011.
Research based (scientific) evaluations
Controlled randomised experiments
Impact evaluations - A rapidly growing area
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Time Series Econometrics
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Before
Changed views during the 1980s due to
Before? Simply transfered OLS for cross section
(static) to time series. Now more based on Time
Series statistics.
Bigger and bigger macroeconometric models
Lucas: Rational expectations
Sargent and Sims: VAR models
Lars P Hansen: GMM to estimate ’euler equations’,
models where the right hand side contains
expectations of the future left hand variable.
Hendry: Error Correction Models, describe the data
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Evaluation
Freakonomics [Revised and
Expanded]: A Rogue Economist
Explores the Hidden Side of
Everything
Steven D. Levitt (Author)
Stephen J. Dubner (Author)
Super Freakonomics
The Undercover Economist
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Models showed bad fit, low predictability
Also relatively few observations
Spurious regression results?
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Two Principal Modeling
Strategies
Cross-section and Panel etc
During the last 30 years an explosion of methods related to
estimation related to understanding of pepole, firms, social
problems, desises etc etc. Evaluation and policy
Heckman, - Heckit model, how can you ask relevant questions as if
your sample is from a random experiment, though the data is not.
Other disciples especially in Sweden and at LiU are so far behind.
At LiU as a PhD student you are not expected to a basic course in
statistics, nor econometrics or Heckit models as an example. Since
they work behiond closed doors they don’t understand, and
students and their supervisors are lazy.
Only economists study statistical methods for evaluating social
programs.
It requires an intelletual effort to study econometrics.
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Sargent, Hansen
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Or to sum it up ...
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The other approach: Let the data speech
• Describe the Data Generating Process (DGP) of
the variables.
• Then from the DGP forecast and identify
economic behavior.
• i) Vector autoregressive models (VAR)
• ii) Structural models, single equation error
correction (ECM) or Vector error correction
models (VECM).
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Why not Statistics?
One impose theoretical restrictions from the
beginning, use econometrics to estimate specific
parameters in the model, which is calibrated to
the data.
Second, use time series statistics to describe
and forecast only
Third, use time series statistics to model welldefined statistical models from which deeper
economic paramters can be found as long as
the data supports economic theory.
Econometrics Introduction
GMM, adjust the residuals in the equation to
take care of dynamics and whatever.
The Second Approach
They worked from the perspective that you have a
intertemporal theoretical model, with expectations.
Real busines cycle models, and new Keynsian models,
Dynamic Stochastic General Equilibrium models where
you need to estimate a few parameters under specific
imposed restrictions from theory. The outcome you see
and measure is based on expectations that you don’t
measure directly. To make sense of estimates they to be
put within a theory first => consequences for
econometrics
Econometrics Introduction
Start from economic theory and impose
theory on data. Or, start from the data
and seek for theory.
1) Build a model based on much a priori
information. Examples: financial
applications + rational expectations, and
DSGE models.
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Economics - problems are interrelated with
math and statistics and probability.
To study correlation is not enough, the question
is what is the correlation representing? Can it be
understood in economic terms?
Each area forms, or has it own statistical problems.
Stochastic variables are part of economic theory (expectations,
growth, allocation over time etc.).
Bringing theory and empirics together - a discrepancy that is
best described as stochastic process.
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The ‘Special Problems’ of
Time Series Econometrics
Econometric Modelling: Start
Dependence between variables multivariate systems.
Dependence over time
Small samples
Aggregation over time and individuals
Trend and Stochastic trends
Expectations and decisions into the
future!
The sampling process cannot be
controlled. Data is given.
Econometrics Introduction
Theory gives relations and suggests parameters
of interest
Data
Transformation of data (log, differencing)
Descripitive statistics
Build an econometric model that fits the data
By testing the model - critical
Test economic hypotheses
Simulate, make predictions, draw conclusions
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Your First Course
in Statistics
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Time Series Econometricans –
Do it backwards!
• Since data is given:
Descriptive statistics of a Population
• Mean, variance (spread, dispersion)
• From a population to a sample
• Start from the sample and ask what type
of population could have generated this
data? Find the data generating process
(the DGP) of the dependent variable(s).
• You construct a model that fits the data.
• You construct a white noise residual.
• Higher level mathematical statistics.
• Sampling model is critical
• Estimation
• Mean, variance etc.
• Inference
• Hypothesis testing, significance, confidence interval
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Repetition
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Random Variables
Random Variables and their properties
Properties of OLS
When OLS breaks down
What not to do, what you should forget
from your first econometric class.
Econometrics Introduction
• A random variable (X) is a variable that
can take on more than one number, or
outcomes xi. For each possible outcome xi
there is a number between zero and one
that describes the probability of observing
that particular outcome.
• Random variables = stochastic variables =
variates
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Definition cont
Random Variables
Whether a variables is random or not depend on the
available information set.
Intuition, with complete information you might be 100%
certain of the outcome. But your information set is
limited the outcome might be described in terms of
probabilities.
Remember: A random variable can always be predicted.
The outcome the value it takes on can be predicted.
Uncertainty is a different think that we do not handle
here. In fact we question the existence of uncertainty.
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Random Variables
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Continuous Random Variables
Discrete random variables take on a finite
number of values (Heads or Tails, etc).
Probability distribution function
Continuous random variables can take on
any value in a certain range.
Probability density function
Econometrics Introduction
• Random variables are described by their
moments and/or their probability
functions
• The link between observations and
probability: Mathematical function f(x;θ)
called the density function.
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For discrete RVs we can link a specific
outcome with a probability.
For continuous RVs the probability of a
specific outcome (number) is zero. We
can only state less than, greater than or
between two given numbers.
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Random Variables can be
described by their moments
Mulivariate processes
• One random variable, or a multivariate
process = several random variables
The first moment of a random variable:
The mean.
The second moment: The variance.
Higher moments:
• Joint probability density function
Skewness (Third) and kurtosis (fourth) etc.
Differ between sample moments and
population moments.
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Moments and Distributions
Distributions
In practice, we often use moments to
describe an observed random variable.
How do we know the probability of
observing an outcome?
Answer: Assumptions about the
distribution
Standard Distributions: Normal distribution
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If I know the distrubution
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Estimators
CLT - The central limit theorem
The t-distribution (small sample N)
The Chi-square Distribution (square N)
The F-distribution (ratio of two squared N)
+ more see my handout
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o The normal distribution is standard.
o It is symetrical around the mean and have only
two moments.
o Two moments are ok because we seldom need
the higher moments in practice. Only if you
have ’jumps’ in your data will the normal ’be
very bad’ [Samuelsson 196?)
o The central limit theorem says that, under
quitegeneral assumption, estimates will
asymptotically converge to the normal
distribution.
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Which Estimator?
ML is the most basic, widely used in
theoretical econometrics to derive for
instance tests and properties of estimation
under different assumptions.
OLS is the workhorse
Method of moments often when situation
calls for modelling, or restricting, the
residual process.
In Econometrics OLS is the first step
Gauss-Markov theorem = basic assumptions
Method of Moments and Maximum likelihood
estimators
MLE, FIML, IV, GMM etc.
Econometrics Introduction
The Normal Distribution (N)
The Normal Distribution
We need to know the distribution to say
something about the size, to do inference of our
estimates.
From the distribution we can construct,
estimators, or learn about estimators.
We can also create various tests
The maximum likelihood estimator is the king,
which holds the key to understand econometrics
at a higher level.
Econometrics Introduction
Joint, marginal and conditional p.d.f.
Standard probability (density) functions
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Properties of Estimators
Properties of OLS
The Gauss-Markov conditions:
yt = xt’βi + εt or matrix form y = x’ β + ε
εt is a random variable (a process)
Introduce Operators > Mean E(X), Var(X), etc.
Properties of a good estimator:
1.
2.
E{εt} = 0
E{εt εt} = σ2
Homoskedasticity
E{εt εt±/-k} = 0 for all k ≠ t No autocorrelation
E{εt | X} = 0
Var {εt | X} = 0
Unbiasedness : E(X) = µ
Efficiency
: V(X) = σ2
As small as possible, or smaller than what we use as a benchmark
BLUE (Best linear unbiased)
3.
Consistency : As the sample changes we should get the same
If these conditions are fulfilled OLS is BLUE, and the
estimated coefficients are good estimates of the true
parameters of interest.
estimates, and as the sample increases estimates should become more
unbiased and more efficient
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Three Golden Rules of
econometrics
Why?
These will not be fulfilled we must either
transform the data, change estimation method
and or respecify the statistical model. A good
econometrican knows what he or she must do
to get good estimates. Econometrics is not
about using software, it is to be able to
understand the problems at hand and how to
solve them. This requires knowledge of
properties of estimators, matrix algebra, etc.
Econometrics Introduction
Test
Test
Test
Testing is don to respicify the model so
that it fits the data chosen, and becomes
a well-defined statistical model.
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GLS and FGLS (or EGLS)
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GLS
In you first course you learn how to understand the
coefficients in a mutivariate linear regression model
You focus on ”the problems” of heteroscedasticity and
autocorrelation.
These ”problems” can be analysed and ’solved’ with
Generalized Least squares GLS.
Since GLS assumes that we know the covariance matrix,
it must be replaced by a estimates, which leads to
Feasible Generalized Least Squuares (FGLS) or
Estimated Generalized Least Squares (EGLS).
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You want E{ε’ ε} = σ2I
Where I is the identity matrix
But got E{ε’ ε} = σ2 Ω
To get what you want find P’P = Ω -1
So that Ω -1 Ω = I, find P use it to
Py = Px’ β + Pε
y* = x*‘ β + ε* where V{ε* } = σ2I
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GLS and FGLS
When OLS Breaks down
Autocorrelation in combination with lagged dependent
variable
Is mostly an illusion
It show how you can manipulate models
Works quite fine for heteroscedasticity
Works very rarely for autocorrelation
No longer consistent
Measurment error in variables
A matter of degree
Omitted variables
Omitting a relevant variable is always bad for the interpretation
of the estimated parameters – the model might still be fine
though
Including an irrelvant (insignificant) variable is harmless
Simulataneity and reversed causality
Simulataneity bias. Again, the model might be ok but the
parameter estimates might be wrong.
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What Not to DO!
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• Linear regression, OLS estimator and assumptions,
properties of OLS
• Multiple linear regression
• Interpretation of a multiple regression
• Understand that multicollinearity is not really a problem, it is all
about understanding model specification.
• First two basic textbook problems:
• Heteroscedasticity: consequences, testing, solution
• Autocorrelation: consequences, testing, solutions (Warning
most textbook solutions are usually not applicable)
• Generalised least squares
• Simultaneity problems: consequences, solutions,
two- or three-step, FIML etc. There are no tests!
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Advanced cont...
More advanced econometrics
Dependent variable is a probability. Probit and
Logic models.
More general: the dependent variable is an
ordered variable, 1, 2, ... K. Ordered data
models.
Dependent variable is censored. Say that it
cannot be zero. ”Tobit models”. Censored
models.
Dependent variable is truncated. Implies that
the right-hand variables cannot be observed
either. Truncated models.
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First Econometrics Course
Don’t use the DW test for autocorrelation!
It is biased against 2.0 with lagged dependent variables,
there i an inconclusive region and there are better
alternatives around.
Do not use Cochrane-Orcutt and similar procedures to
cure first order autocorrelation. It will not work!
Don’t use partial adjustment models, so-called almon
lags, or polynomial lag restrictions. Parameter
restrictions should never be imposed on the data
without tests that confirms that the restriction is valid.
You cannot really test for multicollinearity!
You cannot really test for exogeneity! The proof is in the
pudding.
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Observations on the dependent variable depend on
some underlying deterministic process. It is not really
random. Sample selection models. (Heckit models)
Dependent variable measures the duration of something
going on, or the length in time before something will
happen, conditional on X:s. Duration models.
Pooled cross section and time series models
Panel data models – originally many cross section
units and relatively few time series observations
Data Envelopment Analysis DEA. Not stochastic in
their basic form, but can be viewed as stochastic.
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Advanced cont...
Advanced ...Time Series
Testing procedures
Improving estimated variances, jack-knife,
bootstrapping
Simulating the distributions of estimates
to learn about properties and find better
critical values.
Econometrics Introduction
OLD Dynamic models
Partial adjustment models
Restricted lag structures
Now: work with unrestricted lag structures
Econometric Time series Modelling differs from cross-section and
classical econometrics
Modern econometric time series is based on statistical time series
analysis.
Your models should describe and fit the data.We will develop this more
during course, and discuss the limitations (financial econometrics)
Start from ARIMA, VAR models
Assume that data is generated from an unknown data generating
process.
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Cont..
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This course ...
Replicate the Data Generating Process
DGP contains different components such as trend, seasonality, irregular
components etc.which must be identified
All components in the DGP must be modelled correctly, and in the right
order, to get inference right
We will look at:
ARIMA models
Time series processes in general
VAR, SVAR or VECM models etc.
Integrated variables, unit roots and cointegration
ARCH and GARCH models
Non-linear models
Dealing with (rational) expectations
....Starts here
Exercise
MLE and GMM
+ more and more....
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