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Econometrics For DummiesFrom Econometrics For Dummies by Roberto PedaceYou can use the statistical tools of econometrics along with economic theoryto test hypotheses of economic theories, explain economic phenomena, andderive precise quantitative estimates of the relationship between economicvariables. To accurately perform these tasks, you need econometric model-building skills, quality data, and appropriate estimation strategies. And botheconomic and statistical assumptions are important when using econometricsto estimate models.

Econometric Estimation and the CLRM AssumptionsEconometric techniques are used to estimate economic models, whichultimately allow you to explain how various factors affect some outcome ofinterest or to forecast future events. The ordinary least squares (OLS) techniqueis the most popular method of performing regression analysis and estimatingeconometric models, because in standard situations (meaning the modelsatisfies a series of statistical assumptions) it produces optimal (the bestpossible) results.

The proof that OLS generates the best results is known as the Gauss-Markovtheorem, but the proof requires several assumptions. These assumptions, knownas the classical linear regression model (CLRM) assumptions, are the following:

The model parameters are linear, meaning the regression coefficients don'tenter the function being estimated as exponents (although the variables canhave exponents).

The values for the independent variables are derived from a random sample ofthe population, and they contain variability.

The explanatory variables don't have perfect collinearity (that is, noindependent variable can be expressed as a linear function of any otherindependent variables).

The error term has zero conditional mean, meaning that the average error iszero at any specific value of the independent variable(s).

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The model has no heteroskedasticity (meaning the variance of the error is thesame regardless of the independent variable's value).

The model has no autocorrelation (the error term doesn't exhibit a systematicrelationship over time).

If one (or more) of the CLRM assumptions isn't met (whicheconometricians call failing), then OLS may not be the best estimationtechnique. Fortunately, econometric tools allow you to modify the OLStechnique or use a completely different estimation method if the CLRMassumptions don't hold.

Useful Formulas in EconometricsAfter you acquire data and choose the best econometric model for the questionyou want to answer, use formulas to produce the estimated output. In somecases, you have to perform these calculations by hand (sorry). However, even ifyour problem allows you to use econometric software such as STATA togenerate results, it's nice to know what the computer is doing.

Here's a look at the most common estimators from an econometric model alongwith the formulas used to produce them.

Econometric Analysis: Looking at Flexibility in ModelsYou may want to allow your econometric model to have some flexibility, becauseeconomic relationships are rarely linear. Many situations are subject to the "law"of diminishing marginal benefits and/or increasing marginal costs, which impliesthat the impact of the independent variables won't be constant (linear).

The precise functional form depends on your specific application, but the mostcommon are as follows:

Typical Problems Estimating Econometric ModelsIf the classical linear regression model (CLRM) doesn't work for your databecause one of its assumptions doesn't hold, then you have to address theproblem before you can finalize your analysis. Fortunately, one of the primarycontributions of econometrics is the development of techniques to address suchproblems or other complications with the data that make standard modelestimation difficult or unreliable.

The following table lists the names of the most common estimation issues, abrief definition of each one, their consequences, typical tools used to detectthem, and commonly accepted methods for resolving each problem.

Problem Definition Consequences Detection Solution

Highmulticollinearity

Two ormoreindependentvariables inaregressionmodelexhibit aclose linearrelationship.

Large standarderrors andinsignificant t-statisticsCoefficientestimatessensitive tominor changesin modelspecificationNonsensicalcoefficient signsand magnitudes

PairwisecorrelationcoefficientsVarianceinflationfactor (VIF)

1. Collectadditionaldata.2. Re-specifythe model.3. Dropredundantvariables.

Heteroskedasticity Thevariance ofthe errortermchanges inresponse toa change inthe value oftheindependent

InefficientcoefficientestimatesBiased standarderrorsUnreliablehypothesis tests

Park testGoldfeld-Quandt testBreusch-Pagan testWhite test

1. Weightedleast squares(WLS)2. Robuststandarderrors

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variables.

Autocorrelation Anidentifiablerelationship(positive ornegative)existsbetween thevalues of theerror in oneperiod andthe values ofthe error inanotherperiod.

InefficientcoefficientestimatesBiased standarderrorsUnreliablehypothesis tests

Geary orruns testDurbin-WatsontestBreusch-Godfreytest

1. Cochrane-Orcutttransformation2. Prais-Winstentransformation3. Newey-West robuststandarderrors

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