econ 4160: econometrics{modelling and systems estimation€¦ · introductioneconometric software...

Introduction Econometric software menu Review of elementary econometrics using OxMetrics

ECON 4160: Econometrics–Modelling andSystems Estimation:

Computer Class

Ragnar Nymoen, August 29th, 2011

Department of Economics, University of Oslo

Revised by André K. Anundsen, 17th August, 2012

ECON 4160: Computer Class Department of Economics, University of Oslo


Practical information

Who am I? → André K. Anundsen (PhD-student)Email: [email protected]: 1143Responsible for the CPU class + the seminar series



Aims and purpose I

I Use computer program to learn about:1. Econometric theory

I Complementary and supplementary to the lectures

2. Applied econometricsI Integrated with the seminar series



Aims and purpose II

I In the CPU class, we will demonstrate the implications of thetheoretical results established in the lectures through MonteCarlo simulations, and we will apply the methods you learn toreal-world data!

I To each seminar, you will be given a set of exercises. Theexercises are of two types:

I Applied modeling tasks, where you use your (theoretical)econometric skills in combination with the skills you acquire inthe computer class to analyze real-world data. You will thenhold a live computer presentation of your solution proposal atthe seminar

I The other type of seminar exercises will be more theoreticaland algebraic, establishing results that are extremely importantto have in mind when analyzing a data set



As noted by Greene, many powerful program packages andprogram languages are in use in econometric research and inapplied projects:

I EViews

I Gauss

I LIMDEP

I MATLAB

I NLOGIT (LIMDEP)

I RATS (including CATS in RATS)

I SAS

I Shazam

I StataI TSP



I MicroFit

I OxMetrics, which includes PcGiveI ForecastPro

I Troll

I Time Series Modelling (TSM)

and probably many more



The above programs are licensed commercial products, thoughdeveloped from research projects...

Also exist “freeware ”and “open source ”programs:

I R

I Gretl

I Scilab



How do I choose which one to use? I

I Ease and accuracy of data loading, data storage and resultreporting

I The data is often your most valuable asset, so:I Getting the data into the program is an essential step!I Basic reporting is very similar between programs, but not

standard! Reporting for typesetting (e.g., LATEX) is still rare.PcGive has some, Stata is better



How do I choose which one to use? II

I Menus, batch language and programming capabilityI Menus are good for getting started, and for demonstrationsI Batch language is important for

1. Efficient work (once you become an “expert”)2. Documentation (colleagues, yourself and journals!)3. Communication (e.g., between supervisor and yourself)

I Programming capability can be important to increaseflexibility (can’t always do “everything ”using menus andbatch language)



How do I choose which one to use? III

I The purpose of your project!I Econometric programs are like (specialized) tools: They are

designed to do specific tasks efficientlyI Each program has its strengths and weaknessesI Unless you are very specialized yourself, you will probably end

up using more than one program



Why do we use OxMetrics/PcGive in this course?

I OxMetrics is a powerful package including an option toestimate all models we consider in this course (particularlygood at simultaneous equation systems! Give = GeneralizedInstrumental Variable Estimation)

I and... the names of the models in the program are close to thenames you will see in Erik’s notes

I Fairly easy to do Monte Carlo simulations demonstrating howe.g. heteroskedasticity, autocorrelation and endogneity affectsestimated coefficients when we use OLS

I Finally, it is relatively easy to use and provides a lot of outputthat are essential to any econometric analysis!



PcGive

When you’re unsure about something (or just want to explore theoptions) in PcGive, go here:

http://pcgive.com/pcgive/index.html

Or use the help menu in the program (we’ll see later)


http://pcgive.com/pcgive/index.html


http://www.oxmetrics.net/


http://www.oxmetrics.net/


Topics for first computer class

I Loading the data into the program and get to “know”the data(always start by looking at graphs!)

I Variable transformationsI Note 1 to computer class: Use of the natural logarithm

I Simple regression and mis-specification testingI Note 2 to Computer class: Standard mis-specification tests

I Regression and mis-specification testing with the use of thebatch language

I Stability of regression models

I At last (if time) you will have the opportunity to use yournewly acquired skills to look at US housing price data from1890 to today!



Regression with experimental and non-experimental data

Consider the modelling task with experimental/lab data:

Yiresult

= g(Xi )input

+ vishock

(1)

and compare with the situation with non-experimental, real-worlddata:

Yiobserved

= f (Xi )explained

+ ε iremainder

(2)



Clearly, we know much less about the match between f (Xi ) and Yiin the non-experimental case: We simply can’t control the inputand then study the output. Often, we may not even know allvariables that are included in the vector Xi ! Thus, our choice offunctional form, f (·), and explanatory variables, Xi , will bereflected in the remainder ε i :

ε i = Yi − f (Xi ) (3)

However, we will follow custom and refer to ε i as the disturbanceand the estimated counterpart ε̂ i as the residual.



I We will then need to keep in mind that the assumptions thatwe make about the disturbances , e.g., the “classicalassumptions” are only tentative, and that we need to test thatthey are valid after estimation

I This is called residual mis-specification testing



Residual mis-specification overview

Disturbances ε i are:Xi heteroscedastic autocorrelated

β̂1 V̂ar(β̂1) β̂1 V̂ar(β̂1)

exogenousunbiased

consistentwrong

unbiased

consistentwrong

predeterminedunbiased

consistentwrong

biased

inconsistentwrong



Test battery in PcGive I: Non-normalityNormality, Jarque and Bera (1980): (Note: Small samplecorrection in Give)Test the joint hypothesis of no skewness and no excess kurtosis(3rd and 4th moment of the normal distr.):

JB =n

6

(Skewness2 +

1

4Excess kurtosis2

)(4)

The sample skewness and excess kurtosis (skewness = 0 andkurtosis = 3 for normal distr. is defined as follows):

Skewness =1n ∑

ni=1 (ε̂ i − ¯̂ε)

3(1n ∑

ni=1 (ε̂ i − ¯̂ε)

2) 3

2

=1n ∑

ni=1 ε̂

3i(

1n ∑

ni=1 ε̂

2i

) 32

(5)

Excess kurtosis =1n ∑

ni=1 (ε̂ i − ¯̂ε)

4(1n ∑

ni=1 (ε̂ i − ¯̂ε)

2) 4

2

=1n ∑

ni=1 ε̂

4i(

1n ∑

ni=1 ε̂

2i

)2 (6)Null is normality.



Test battery in PcGive II: HeteroskedasticityHeteroskedasticity, White (1980):Auxiliary regression:

ε̂2i = β0 + β1Xi + β2X2i + ui (7)

Test that β1 = β2 = 0 against non-zero using an F-test.Hetero X (two or more regressors), White (1980)Auxiliary regression:

ε̂2i = β0 + β1Xi + β2Zi + β3XiZi + β4X2i + β5Z

2i + ui (8)

Test that β1 = β2 = β3 = β4 = β5 = 0 against non-zero using anF-test.In both cases the null is homoskedasticity.



Test battery in PcGive III: Autocorrelation

Autocorrelation, Godfrey (1978):Auxiliary regression (note, i is now time unit! Call it t):

ε̂t = β0 +p

∑i=1

βi ε̂t−i + βpXt + ut (9)

A test for pth order autocorrelation is then to test thatβ1 = β2 = · · · = βp = 0 against non-zero using an F-test.Null is no autocorrelation.



Test battery in PcGive IV: Autoregressive conditionalheteroskedasticity

ARCH, Engle (1982):Auxiliary regression:

ε̂t = β0 +p

∑i=1

βi ε̂2t−i + ut (10)

A test for pth order ARCH is then to test thatβ1 = β2 = · · · = βp = 0 against non-zero using an F-test.Null is no ARCH.



Test battery in PcGive V: Regression Specification Test

RESET, Ramsey (1969):Auxiliary regression (Note 2,3 in PcGive means squares andcubes!):

ε̂t = β0 + β1Xt + β2Ŷt + β3Ŷ2t + ut (11)

A test for pth order ARCH is then to test that β1 = β2 = 0against non-zero using an F-test.Null is no specification error.


IntroductionEconometric software menuReview of elementary econometrics using OxMetrics

econ 4160: econometrics{modelling and systems estimation€¦ · introductioneconometric software...

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