Econometrics Guides

8/10/2019 Econometrics Guides

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1. Research Question

A research question must be an interesting puzzle which can be understood through some

theory and accepts falsifiable hypotheses to explain the phenomenon.

2. What ind of data!methodology will allow you to answer it"

#$en using perfect data or being able to obser$ed and accurately measured all the data for the whole population statistical analysis has some limitations. %ome limitations come from inherent

assumptions in the processes while others will be consequence of noise in reality. %ome tools to

analysis effects of certain factors are descripti$e or comparati$e statistics& modeling& experimental&

in $itro analysis& regression analysis& agent'based modeling& spacial analysis& etc. (hese methods

are the quantitati$e part of possible analysis as opposed to qualitati$e analysis.

Regression analysis allows for hypothesis testing& i.e.& test assumption against empirical data

and pro$ide an indicator of the li elihood the assumption is true gi$en the obser$able outcomessuch as a p'$alue. )i$en the nature of the analysis and importance of certainty the researcher can

choose a le$el at which to re*ect the null hypothesis therefore being able to re*ect null hypothesis if

the significance le$el pro$ided by the data is abo$e said threshold. +astly& consideration is gi$en to

the practical significance which calls into consideration effect size in order to *udge whether the

possible $ariation in the outcome predicted by the factor is rele$ant within the context. Rele$ance

can be a consideration of the relati$e possible de$iation in the outcome gi$en how manipulable the

explanatory $ariable can be.

,. Regression analysis -%tandard #conometrics

Regression analysis is a set of tools that allow for hypotheses testing through comparati$e statics.

(he basic idea is to use an economic model or mathematical equations as a base to fit data gi$en

said structure and unco$er estimates for the $ariables that can best sol$e the problem. (hese

estimators represent the $alue that best fit the data gi$en the specifications and operator employed.

(hese estimates with their associated certainty and effect size considerations can be used for

hypotheses testing& prediction& and other purposes such as strategy design. )enerally& these

applications come from the analysis at mean $alues and at ceterus paribus& i.e.& where we would

obser$ed it most of the time and when e$erything else is held constant.

(heory and empirical analysis are both compliments as it is borderline absurd to do one

without the other. (heory is the underlying description of how something wor s. Any strategy or

policy that is based on science follows some understanding that comes from theory. +i ewise&

theory until it has been supplemented and re$ised through empirical analysis can and should not be

applied unless necessary as it carries high uncertainty. As it is in science& theory is not to be ta en as

true& but carries its worth on it practical usefulness and resistance to ha$e been dispro$ed. (heory

which has not been tested cannot be fails in credentials regardless of its practical usefulness.


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/. (heory

A theory must be a proposed explanation of a phenomenon obser$ed or belie$ed to be

possible. 0t must be of practical usefulness and it must be falsifiable. )oods theories also must wor

gi$en a domain which is set by wor ing assumptions. (he mechanism or processes that ma e up the

theory must also be consistent with logic or obser$able beha$ior. +astly& the best theories also allowfor expansions of the theoretical realm to a model that can be used to better understand the

wor ings of the phenomenon and operationalized its arguments with measurable indicators.

odel %pecification for #mpirical Analysis

A good model operationalizes the theory in ways that allow to test its $alidity through

empirical analysis. 0n the case of regression analysis that includes to protect the economic model

from omitted $ariables. A good economic model must ha$e present all rele$ant factors according to

the theory including an error term if the model is stochastic and not deterministic. (he equation or series of equations used in the economic model must also ha$e the correct nature. or example&

linear regressions where there is a single outcome $ariable as opposed to non'linear regression

models.

3. 4ata and ethodology

(he data and methodology depends on your economic model& but are also constrained by

what data is both attainable and feasible. (he methodology employed will most li ely be a function

of the data which in turn is influenced by both the research question& theory& and chosen model. 0n

practice& the ultimate decision will depend on all factors and not necessarily in the order proposed.

(wo aspects that largely influence the methodology are going to be the pre$ious approaches to the

issue in the literature and the quality and nature of the data.

5. +east %quares ethod - ost used linear regression approach

+east %quares method is a technique in which equations are modeled with a single outcome

$ariable on the left and some right side parameters. (he most common form is a multiple linear

regression with an intercept coefficient&

-#quation 1

where y is the outcome $ariable -which by theory is a dependent $ariable & 6 7 is an intercept

which best fits the data when all $ariables ta e on the $alue of zero& 6 1 is the sub'$ector containing

the coefficient for the $ariables of interest which are denoted V.I. & the 62 is the remaining sub'$ector

which includes the coefficients for the remaining explanatory $ariables denoted X & and lastly&u is

the stochastic normally distributed error term by assumption

8nce the model is estimated the $alues theoretical $alues become data'estimated

parameters&

-#quation 2


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9. 8rdinary +east %quares -8+%

8+% is the most popular regression analysis method gi$en its characteristics:

a ;omputationally feasible

(he parameters are estimated using only calculus and algebra. odern technologyand matrices allow for statistical software to easily and promptly compute these

estimations using $ast amount of data.

b Applicable to many linear models

As long as the model has a single obser$able outcome $ariable in each equation and

the parameters are linear 8+% can be employed.

#xamples of +inear Right'%ide owe$er& the full potential of the 8+% method is when the )auss' ar o$ Assumptions are

met and through the )auss' ar o$ (heorem it can be pro$ed that the estimates are both efficient

and unbiased& i.e.& the ?est +inear @nbiased #stimates -?+@# . (he fi$e )auss' ar o$

Assumptions are:

a +inearity in the functional form

(he economic model must ha$e linearity in the right'side parameters.

b %pherical #rrors -or White =oise

0n order to ha$e White =oise there most be

>omoscedasticity: uniform $ariance and uncorrelated with the error termi.

ii.

=onautocorrelation: the errors are uncorrelated between obser$ations:

i. .

c ero ;onditional ean

0t follows that the distribution of the error term has mean zero - and theexplanatory $ariables are not correlated with the error term - .


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d =o


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(he true nature of the model must be linear in nature. 4ata considerations

%ample must be representati$e of the population. 0ndependent 0dentically 4istributed -iid allows for this.

%ur$ey data might be collected in non'random sampling ways. >eteroscedasticity: non'uniform $ariance

What it does: Ciolates White Noise Assum tion ;onsequence: #stimator is no longer efficient (est: )raph the residuals& WhiteDs (est for heteroscedasticity -a$oid ?< + 'test

0n %tata: !hitetst %olutions: Attempt to find what is causing the heteroscedasticity. 0t might be one or

more $ariables. 0dentify the source of heteroscedasticity and which $ariables.

@se theory and $isual interpretation or -)Q test to identify possible culprits

and causes. Respecify the odel!(ransform the Cariables

0f the source of heteroscedasticity is of a scalar multiplier then transform

$ariable to a per unit measure -income per capita . 0f the $ariable is not

normally distributed attempt a standardization -use z'scores . or outcome

$ariable or $ariables with large $alues attempt a natural log transformation

-lnEpopulationF . ;hec whether the sample is homogenous and if not run separated restricted

regressions.


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a e sure the model is correct -unit root test for 4 ;ontrol for seasonality effects )eneralized +east %quaress

0n %tata: prais y x& ssesearch

(echnical ;onsiderations easurement errors may affect the independent $ariables. ulticollinearity

What it does: a es the errors unreliable ;onsequence: ;annot be used for hypotheses testing (est: ;o$ariance matrix& C0 and ;onditional =umber (est

0n %tata: cor &vif &collin x !

%ol$e: %pecify and code $ariables such that the explanatory $ariables are linearly

independent and not too strongly correlated. %ample size

#nough obser$ations. 4o not o$er do with high le$el of unnecessary obser$ations

Cariation on $ariables Cariables should ha$e some $ariation across the sample

G. )eneralized +east %quares

(he idea is to con$ert the $ariance co$ariance matrix of a non spherical error regression to

an equi$alent with White =oise.

H. +atent 8utcome Cariable

When the outcome $ariable is unobser$able through a mathematical model an equation can

be used to described how explanatory $ariables push the unobser$able $alue until a threshold is met

and an outcome is obser$able. (wo common ways to regress latent $ariable models are probit and

logit. (he results for both are usually consistent& but each one forces the underlying distribution to

the data. 8ther methods are cox relati$e hazard and the li es which allows for panel analysis.

+ogistic regressions ha$e the ad$antage that the estimators can be interpreted as odd ratios as

opposed to marginal effect intensities with the probit. (he li elihood functions are sol$ed not

through an analytical solution& but through numerical analysis.

While there are not formal tests as there are for 8+%& it can be useful to run reg on the

model to see whether there might be some indications of complications while using the latent

$ariable methods.

0n %tata some useful commands are: ro#it &mfx&logistic or logit$ or%rr.

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