Econometrics: Economic Data and Econometric Modeling

1 Econometrics: EconomicData and Econometric ModelingBurcu EkeUC3 MWhat is econometrics ?IEconometrics Economic measurementsIIt is a discipline based on the development of probabilisticmodels and statistical inference methods for the study ofeconomic relations, the contrast of Economic theories, orthe evaluation and implementation of consists of elements from different disciplines:economics, statistics and does an econometrician do?IAn econometrician is an economist who uses statistics andmathematics to understand, explain, and predict economicvariables such as employment, supply and demand,inflation, company profits, health insurance, and manyother important Economic econometrician attempts to develop accurate economicforecasting and successful policy econometrician qualitatively and quantitativelyanalyzes how the factors of interest affect a variableassociated with an Economic question of common applications of econometrics areIprediction of macroeconomic variables such as interest rate,GDP, inflationIMacroeconomic relationships such asunemployment-inflation and inflation-moneyIMicroeconomic relationships such as wage-education,production-inputIFinance such as stock volatilityIForecasting4 Observational Data vs Experimental DataIIn anobservationalstudy.

2 Researchers simply observewhat is happening or what has happened in the past andtry to draw conclusions based on these observations. Observational dataIIn anexperimentalstudy, researchers impose treatmentsand controls and then observe characteristic and takemeasures, in a way, the researchers manipulate thevariables and try to determine how the manipulationinfluences other variables. Experimental data5 Observational Data vs Experimental DataExperimental Study:IFirst, a researcher identifies the data he/she wishes toobtain based on the research questionISecond, the researcher designs an experiment that will beused to obtain the required data. The design process isvery crucial. it needs to ensure that the experimentsmeasure what was intended to measureILast, the data analysis process takes place6 Observational Data vs Experimental DataObservational Study:IStudies the variables are observed and and effect are hard (often impossible) to associations and predictabilities among variables canbe Data vs Experimental Data,ExampleICase 1:20 people went for a flu shot to a public hospital.

3 After amonth, an independent researcher checked how many ofthem got flu. 7 of them got flu, and the others didn 2:We randomly select 20 people with similar healthcondition, and randomly assign them to two groups: A,and B. Then, we give the flu shots to group A, and placeboto group B, and observe how many got flu after a Data vs Experimental DataIExperimental studies attempt to control all factors thatmay affect the association under study, observationalstudies cannotIExperimental studies randomize assignment of factors ofinterest to subjects, this is not feasible in observationalstudiesIObservational studies are performed when experimentalstudies are infeasible due to cost, or ethical studies require more care in analysis andinterpretationIEconomic data is almost always observational9 Observational Data vs Experimental DataExperimental DataIThere are two groups: treatment and controlISubjects are randomly assigned into these groups by theexperimental designIThe difference between these two groups treatmentIHence, the different results in these two groups can beattributed to the treatment10 Observational Data vs Experimental DataNon-experimental DataIThere can still be two groups: treatment and controlIGenerally, subjects self-select themselves to the groups, ,people choose to get a flu shotIThe differences between two groups:treatmentANDthecharacteristics of those getting the treatmentIEffects of the treatment are unclear!

4 11 Observational Data vs Experimental DataRecall the flu shot example. Suppose we want to test if theaverage number of people getting the flu are different in twogroupsIThe way to test for both cases is the same, , we use thesame test statisticIOur interpretations need to be differentCorrelation versus causal relationship12 Observational Data vs Experimental DataIIn the experimental study example, the only differencebetween groups is the treatment we can conclude on acausal relationshipIIn observational data, peoplechooseto get the shot,hence, they might be more health conscious than the oneswho choose not observational data, we can only make inferences aboutwhether the results are correlated!13 Empirical AnalysisOrder of the empirical analysis1. Economic model2. Econometric model3. Data Analysis14 Empirical Analysis: Economic ModelIThe Economic theory proposes models that explainbehavior of one or more variables, sayY1,Y2.

5 ,Ym, as afunction of some other variables, sayX1,X2,..Xk, whichare determined outside of the model: Mathematical equations describing therelationship between the : utility function,U=f(c,l) orU f(c,l) = 0,where the utility (U) is a function of consumption (c) andleisure (l).IInformal model: based on the theory and more intuitiveaspects15 Empirical Analysis: VariablesIExogenousvariable: A factor in a causal model whosevalue isindependentfrom the states of other variables inthe model; a factor whose value is determined by factors orvariables outside the model under : A factor in a causal model whosevalue is determined by the states of other variables in themodel; contrasted with an exogenous general, an endogenous variable, sayYmay depend onmultiple exogenous variables in a model, For example, onemay have a model with income as endogenous variable, andeducation and experience as exogenous Analysis: Econometric modelIEconometric models are generally algebraic models that arestochastic in including random variables (as opposed todeterministic models which do not include randomvariables).

6 IThe random variables that are included, typically asadditive stochastic disturbance terms, account in part forthe omission of relevant variables, incorrect specification ofthe model, errors in measuring variables, the utility function example, the Econometric modelwould beU=f(c,l) + orU f(c,l) = 17 Empirical Analysis: Econometric modelIIn general, the mathematical equations are written for thewhole population, and in Econometric analysis, we almostalways deal with sample data. in order to account for this,and possible measurement errors, or incorrect specificationof the model Econometric models include a stochasticcomponent that satisfy the following equation:E[Y f(x1,x2,..xk)] =E[ ] = 0, whereYis theendogenous variable in the model18 Empirical Analysis: Econometric modelIIn order to quantify the relationship between economicvariables, it is necessary to propose afunctional formthat depends on some variables and unknown Econometric model can be expressed as follows:Y=f(x1,x2.)

7 ,xk; ) + , where is a vector of unknownparameters and is theerror termIThe nature of the model and the interpretation of theparameters depend on the assumptions on the error term19 Empirical Analysis: ExampleConsider the following modelIEconomic model:Wage is a function of educational attainment, andexperience W=f(Ed,Ex)IEconometric model:W= 0+ 1Ed+ 2Ex+ 3Ex2+ 20 Empirical Analysis: Data AnalysisIAfter determining an Economic model, and correspondingeconometric model to answer the questions of interest, weanalyze the data, , estimate the unknown parametersIWe answer some questions based on the estimatedparameters, such as are the estimates s different from 0?,what sign do the have? and so of Econometric modelsISingle variable versus multiple variablesISingle equation versus simultaneous equations22 Types of dataIn econometrics there are three main types of data (notnecessarily mutually exclusive)ICross-sectional dataITime series dataIPanel (longitudinal) dataAll these different data types require specific Econometric andstatistical techniques for data analysis23 Cross-SectionIA type of one-dimensional data setICollected by observing many subjects (such as individuals,firms or countries/regions) at the same point of time, orwithout regarding the differences in timeIIn general used to compare the differences among thesubjectsIOrder doesnotmatterIExamples: Explaining people s wages by reference to theireducation level24 Cross-SectionExample.

8 Data for a sample of individuals in a countryIndividual Income Marital Status Educational Attainment11500singleuniversity degree22500marriedgraduate degree32000separatesuniversity SeriesIA sequence of data points, measured typically at successivetimes spaced at uniform time intervals , annual,semi-annual, quarterly, monthly, daily and so series models often make use of the natural one-wayordering of time so that values for a given period will beexpressed as deriving in some way from past values, ratherthan from future valuesIHave a natural temporal orderingIExamples: Annual inflation rates, daily closing value of acertain stock26 Time SeriesA time series data exampleTime Inflation (Longitudinal)IDate that involve repeated observations of the same itemsover long periods of timeINot necessarily cohort study Different cohorts may havedifferent subjectsIPanel data (Longitudinal) studies track the same subject(people, countries, same set of stocks)IMeasurements are observed or taken on the same subjectsrepeatedly28 Panel (Longitudinal)

9 Company YearProfit12000 billion12001 billion120022 billion22000 billion22001 billion22002 billion320003 billion32001 billion320024 and ceteris paribus in EconometricsIWe sometimes study causality between two variables, notjust correlationICorrelation does not guarantee causalityThis is because our data is Economic data, not experimentalThis prevents us from inferring causality from co-movement,since we have not controlled from other factors that mightinfluence the variables30 Causality and ceteris paribus in EconometricsIIn the rare case that our data fits exactly the experimentwe test for, we can infer causalityIThus, when studying an empirical case, it may be worth toquestion what the right experiment should be and howour data can address and/or mimic itIWhen looking for causality, the ceteris paribus concept(all other factors remain constant) plays a crucial role: itallows us to infer the partial effect of one variable onanother oneIEconometric techniques allow us to estimate ceterisparibus effects and infer causal relations betweenvariables, by simulating a situation close to the experimentwe are interested in31