ECONOMETRICS 3A EXAM STUDY NOTES
LECTURE 1: METHODOLOGY OF ECONOMETRICS
Follows classical methodology consisting of 8 steps:
1. Statement of theory/ hypothesis
2. Specification of the mathematical model of the theory
3. Specification of the econometric model
4. Obtaining the data
5. Estimation of the parameters of the econometric model
6. Hypothesis testing
7. Forecasting
8. Using the model for policy/control purposes
CHAPTER 1: THE NATURE OF THE REGRESSION ANALYSIS
o Regression analysis- concerned with the study of the dependence of one variable
on another variable, with the view to estimating the mean value of the former into
the known values of the latter
o Scatter plot- used to identify the relationship between two variables
o Regression is concerned with statistical relationships
Statistical relationships
Deterministic relationships
Deals with random variables
Variables are exact, not random
REGRESSION VS. CAUSATION
Regression doesn’t imply causation
o Causality- the relationship between cause and effect
o Causality is the agency that connects the cause with the effect, where the
first is understood to be partly responsible for the second, and the second
is dependent on the first
o Regression- examines how the change in the dependent variable is
explained by the change in the explanatory variable
o Causation between variables must come from economic theory
o Regression explains association
o Theory explains causation
REGRESSION VS. CORRELATION
o Correlation theory deals with measuring the degree of relationship between
two variables (strength of linear association)
o Correlation between variables can be positive, negative, strong, weak
o In regressions, we distinguish between the dependent and independent
variables, while with correlation they are treated the same
TERMINOLOGY
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ECONOMETRICS 3A EXAM STUDY NOTES
o Dependent variable- (Y) variable that is explained by the (X) independent variable
o Independent variable- (X) variable that explains the change in the dependent
variable
o Simple regression- regression where the dependent variable is explained by a
single (one) independent (explanatory variable).
o Multiple regression- regression where the dependent variable is explained by
more than one explanatory variable
o Regressors- explanatory variables
So, simple(single) regression= one regressor
Multiple regression= multiple regressors
TYPES OF DATA
o Time series data- is a set of observations on the values that a variable takes at
different times
o Cross-sectional data- data on one or more variables collected at the same point
in time
o Pooled data- data are elements of both time series and cross-sectional data
o Panel data- a special type of a pooled data in which the same cross-sectional unit
is surveyed over time.
MEASUREMENT SCALE OF VARIABLES
o Nominal level- gender, marital status. Aspects with categories
o Ordinal level- income class / grading systems, sovereign credit ratings. Ordering
exists but the distance between the categories cannot be quantified
o Interval level- temperature. Distance between two points make sense but not the
ratio
o Ratio level- most economic variables belong in this category, e.g. GDP. The ratio
and distance between two variables are meaningful quantities
CHAPTER 2: TWO-VARIABLE REGRESSION ANALYSIS
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ECONOMETRICS 3A EXAM STUDY NOTES
Two-variable regression analysis consists of one dependent variable with one explanatory
variable
Regression analysis is concerned with the estimation of the mean value of the dependent
variable based on the known values of the explanatory variable
SIGNIFICANCE OF THE STOCHASTIC ERROR TERM
Disturbance term includes all variables that are omitted from the model but collectively
explain Y
Reasons why these variables are not included:
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Vagueness of theory
Unavailability of data
Wrong functional form
Poor proxy of variables
Principle of parsimony
CHAPTER 3:
OLS ASSUMPTIONS
1. Linear regression model (linear in variables or parameters)
2. Fixed X values (X values independent of the error term)
3. Zero mean value of disturbance (no specification error)
4. Homoscedasticity or constant variance of µi
5. No autocorrelation between the disturbances
6. The number of observations must be greater than the number of parameters to be
estimated
7. The X values must not be the same
PROPERTIES OF OLS ESTIMATORS UNDER CLRM
OLS estimators are BLUE (best linear unbiased estimator)
o Linear (linear function of a random variable)
o Unbiased (expected value is equal to the true value)
o Efficient (unbiased estimator with least variance)
THE COEFFICIENT OF DETERMINATION: R2
o Measure of the goodness of fit
o Tells us well the sample regression fits the data
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ECONOMETRICS 3A EXAM STUDY NOTES
o Measures the proportion of variation in Y (dependent variable) that is explained by
X (explanatory variable)
o TSS = ESS + RSS
𝐸𝑆𝑆
o R2 = 𝑇𝑆𝑆
𝑅𝑆𝑆
o R2 = 1 - 𝑇𝑆𝑆
o R2 = 0: no relationship
o R2 =1: perfect fit
CORRELATION COEFFICIENT
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Measures the degree of association between two or more variables
Can be positive or negative
Ranges between -1 and +1
Correlation between x and y is the same as correlation between y and x,
symmetrical
o Does not imply causality
o Measures linear association
o Zero correlation doesn’t imply independence
CASES TO NOT TRUST OLS ESTIMATORS
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Heteroscedasticity
Omitted variables
Reverse causality
Measurement error
Structural breaks
CHAPTER 4
PROPERTIES OF OLS ESTIMATORS UNDER NORMALITY ASSUMPTION
o They are unbiased
o They have minimum variance
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ECONOMETRICS 3A EXAM STUDY NOTES
o They are consistent
o Slope coefficients are normally distributed
CHAPTER 5: INTERVAL ESTIMATION AND HYPOTHESIS TESTING
CONFIDENCE INTERVALS
o The width of the confidence interval is proportional to the standard error of the
estimator
o Large standard error- wide interval
o Small standard error- narrow interval
o Wide interval means we are less certain about the parameter estimate
o The standard error is therefore the measure of precision
HYPOTHESIS TESTNG
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State the null hypothesis
State the alternative hypothesis
Formulate the decision rule
Make a decision
Conclusion
Rejecting the null hypothesis means the finding is statistically significant
Not rejecting the null hypothesis means the finding is statistically insignificant
2-t rule of thumb- if the number of degrees of freedom is 20 or more, and at α=0.05, the
null hypothesis is rejected if the t-value exceeds 2 in absolute value
TYPE I ERROR
o Probability of rejecting the null hypothesis when it is true
TYPE II ERROR
o Probability of accepting the null hypothesis when it is false
THE P-VALUE (EXACT LEVEL OF SIGNIFICANCE)
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ECONOMETRICS 3A EXAM STUDY NOTES
o Exact probability of committing a type I error
o As t-value increases, the p-value decreases, we reject the null hypothesis with
increasing confidence
o Small p-value: strong evidence to reject the null hypothesis
o P-value<0.05: reject the null hypothesis and conclude that the finding is statistically
significant
TESTING FOR NORMALITY OF THE DISTURBANCE TERM
1. Histogram of the residuals
2. Anderson-Darling normality test
o H0: residuals are normally distributed
o If p-value is higher than 0.05, do not reject the null hypothesis, residuals are
normally distributed
3. Jarque-Bera test of normality
o H0: residuals are normally distributed
o If p-value is higher than 0.05, do not reject the null hypothesis, residuals are
normally distributed
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CHAPTER 6
REGRESSION THROUGH THE ORIGIN
Regression model with no intercept
YI = β2Xi +µi
Makes R2 negative
Makes R2 inappropriate for the regression
Used only when there is a very strong priori expectation
Intercept is omitted only if it is statistically insignificant
Omission of the intercept result in specification error
REGRESSION ON STANDARDIZED VARIABLES
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ECONOMETRICS 3A EXAM STUDY NOTES
o A variable is standardized if we subtract the mean value of the variable from
its induvial values and divide by the standard deviation of that variable
o Y* =
𝑌𝑖− Ȳ
𝑆𝑦
o The mean value of the standard variable is always zero and its standard
deviation is always zero
o The intercept is always zero
REGRESSION FORMS OF REGRESSION MODELS
REGRESSION MODELS THAT ARE NONLINEAR IN THE VARIABLES
BUT LINEAR IN PARAMETERS:
o The log-linear model (double log model)-measures elasticity
o Semi-log model- measures the growth rate
o Reciprocal model- shows trade-offs
o The logarithmic reciprocal model
CHAPTER 8
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