Fundamentals of Econometrics-i

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FUNDAMENTALS OF ECONOMETRICS

Session I: Introduction and Basic Concepts



OBJECTIVES OF ECONOMETRIC

ANALYSES



ESSENTIAL INGREDIENTS OF GOOD

ECONOMETRIC MODELS

IntuitionTheories

StatisticsMathematics

Specificationof a function

that linksvariablestogether

Distributionassumptions

of thevariables

Explanationof results

Theoreticalfoundations

of theanalysis



STEPS IN ECONOMETRIC ANALYSES

Creating a statement of theory or hypothesis

Collecting data

Model specification

Diagnostics and Testing

Interpretation and prediction



TYPES OF DATA

Experimental Data: obtained from experiments designed toevaluate a treatment or policy to investigate a causal effect.

Observational Data: data obtained outside the experimentalsetting.

Experimental andObservational

Data

Cross-sectional Data ² Data on different entities for a singletime period.

Time-Series Data ² data for a single entity collected atmultiple time periods.

Cross-sectionaland Time-Series

Data

combination of cross-sectional and time-series data.

Panel(Longitudinal)

Data



CONCEPT I: DATA GENERATION PROCESS

AND PROBABILITY DISTRIBUTION

Stochasticprocess

ClassicExample:

Throwing a die

EconomicExample: GDP

Specifies all possible values with parameters: mean (expected value)and variance (dispersion)

Each value has certain probability tobe observed

Realized value is the observed value,i.e. the data point we collect

Possible values: 1, 2, 3, 4, 5 and 6

Each has the probability of 1/6 to beobserved

After the die is thrown, only one value weobserve. That is the data point, the realizedvalue or observed value. This value is calleda RANDOM variable.

For a given year (say 2011), there arenumerous possible levels of national

production.Mean = E(GDP)Each range or level of production has

certain probability of occurrence.

After the process completed (after 2011),the level of production measured andreported. That is the realized value.

Unlike the classic example: GDP iscontinuous.



CONCEPT II: NORMAL DISTRIBUTION

Characteristics

Bell-shaped

Symmetric

mean=mode=median

Area (probability) ² roug hly68% within one standarddeviation, 95% within 2standard deviations

Described by mean andvariance



CONCEPT III: HYPOTHESES

´ Hypothesis: supposition made as a basis for reasoning, or as astarting point for further investigation from known facts.

´ Hypothesis: A statement made concerning a particular aspect or aspects of the population under study.

´ Hypothesis: Testing of the hypotheses is an essential part in

inferential statistics ± generalizing from the statistical valuescomputed from the data to the population values.´ An example of a population value ± mean income of

households in Putrajaya.´ Why hypothesis testing?

- the value may be of interest to decision making

- the population value is unknown- estimating the value using the sample is the only way- However, in making inferences or in linking the sample meanto the population mean, a test is needed. No direct inferencescan be made



CONCEPT III: HYPOTHESES

´ Hypotheses are formulated as NULL HYPOTHESIS andALTERNATIVE (RESEARCH) HYPOTHESIS

´ Null Hypothesis: an assertion that we hold as true unless we havesufficient statistical evidence to conclude otherwise.

´ Alternative Hypothesis: the negation of the null hypothesis.´ Alternative Hypothesis: a research hypothesis that we seek to provide

supportive statistical evidence.´ Alternative Hypothesis: it can be DIRECTIONAL or EXPLORATORY´ Directional: the hypothesized population value is LESS (or MORE) than

the value stated under the null. Example: Equity ownership of theMalays is less than 30%.

´ Exploratory: the hypothesized population value is DIFFERENT fromthe null value. It is not known from theories whether it is LESS or

MORE than the null value. Example: Equity ownership of the Malays isdifferent from 30%.´ In testing, the null hypothesis is given the benefit of the doubt. That is,

the statement is held true until there is sufficient evidence to reject it.



CONCEPT III: FROM PROBLEM TO

HYPOTHESES

´ Problem: suppose a company plans to build a super store inPutrajaya. However, for the store to be viable, the mean monthlyincome of households in Puterajaya must be more than RM4,000.Problem: is the Putrajaya household mean income more thanRM4,000?

´ The statement that the Puterajaya household mean income is morethan RM4,000 CAN NOT be the null hypothesis. If it is, there isno need for testing since it is assumed to be TRUE. In other words, it must be the alternative hypothesis.

´ The null hypothesis would be: the mean income is equal or less

than RM4,000.´ Note that the alternative hypothesis is directional

´ The burden of proof is on the researcher to provide evidence for the alternative hypothesis.



FLOW CHART: PUTRAJAYA

SUPERSTORE

Problem: Is Putrajaya meanhousehold income more than

RM4000?

Let Q = mean income

And X = income

DATACOLLECTION:

* Population ² all

putrajaya households

* Sample ² a subset of the

population

FORMULATION OF HYPOTHESES:

Null: Q e 4000

Alternative:Q

> 4000

ESTIMATION:

Aformula used to estimate Q .The example is the mean income

of the households in the sampleor sample mean,

TESTING:

* How to use the sample mean

to make inferences regarding Q.

* This requires the distributionof X or of sample mean

INFERENCES:

The conclusion made from thetest

X



CONCEPT III: FROM PROBLEM TO

HYPOTHESES

´ Problem: inflation in one of the main variable focused by policymakers and economists. Over the past years, the role of money supply growth in affecting inflation has received muchattention. However, there seems to be an increasing concern thatthe inflation in Malaysia is imported due to its pegged exchangerate system. Perhaps, changes in the US inflation and the Ringgitvalue exert significant effect on inflation.

´ Null: US inflation has no impact on Malaysia¶s inflation

´ Alternative: US inflation has significant impact on Malaysia¶sinflation.

´ The same can be stated for the effect of exchange rate changes.

(FLOWCHART In Session II)



CONCEPT IV: ESTIMATION

´ Estimation: A formula used to estimate population parameters using the information.

´ Point Estimation: A single value computed from a

given formula using sample data. Margin of Error =1.96 of the standard error of the estimator.

´ Interval Estimation: Lower and Upper Bound thatwill likely include the true parameter in the interval

with some level of confidence. The confidence levelis always expressed as (1 - E)100%, where E is thesignificance level.



CONCEPT V: HYPOTHESIS TESTING

Elements

Null and AlternativeHypotheses

Test Statistics

Critical Values of the Testand Significance Level

One-Tailed V. Two-Tailed Tests

Type I Error and Type IIError.



HYPOTHESIS TESTING

STEP 1: STATE HYPOTHESES

´ Null Hypothesis: A statement about the value of the population parameter It is an assertion aboutthe value of the parameter. It is an assertion that

we hold as TRUE unless we have sufficientstatistical evidence to conclude otherwise.

´ Alternative Hypothesis: A Statement that isaccepted if the sample data provide enoughevidence that the null hypothesis is false. It is thecomplement of the Null.



HYPOTHESIS TESTING

STEP 2: SELECT A LEVEL OF SIGNIFICANCE

STEPS 3: SELECT THE TEST STATISTICS´ Level of Significance: the probability of rejecting the

null hypothesis when it is true.´ Errors in testing:´ (a) Type I Error: Rejecting the Null Hypothesis

when it is TRUE´ (b) Type II Error: Accepting the Null

Hypothesis when it is false

´ Test Statistic: A Value, determined from sampleinformation, used to determine whether to reject thenull hypothesis.



HYPOTHESIS TESTING

STEP 4: FORMULATE THE DECISION RULE

STEPS 5: MAKE DECISION´ Critical Value: The dividing point between the region

where the null hypothesis is rejected and the region where it is not rejected.

´ P-value: the probability of observing a sample value as

extreme as, or more extreme than, the value observed,given that the null hypothesis is true.

´ Reject the Null Hypothesis if the test statistic exceedsthe critical value [in ABSOLUTE VALUE].

OR ´ Reject the Null Hypothesis if the p-value is less than

the significance level.



END OF SESSION I

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