1. Regression Analysis
Chapters 1-2

2. Econometrics : Econo + Metrics
It means “economic measurement”.
“The application of mathematical statistics to economic data to lend empirical support to the models constructed by mathematical economics.”
It provide numerical estimates to most economic theory.

3. Economic statistics is mainly concerned with collecting, processing, and presenting economic data in the form of charts and tables.
In econometrics the modeler is often faced with observational as opposed to
experimental data.

4. Traditional econometric methodology proceeds as:
1. Statement of theory or hypothesis;
2. Specification of the mathematical model of the
theory;
3. Specification of the statistical, or econometric,
model
4. Obtaining the data
5. Estimation of the parameters of the
econometric model
6. Hypothesis testing
7. Forecasting or prediction
8. Using the model for control or policy purposes.

5. <Example>
Statement of theory or hypothesis
Keynes postulated that the marginal propensity to consume (MPC), the rate of change of consumption for a unit (say, a dollar) change in income, is greater than zero but less than 1.
Specification of the mathematical model of consumption
Economist might suggest:

7. Single-equation model vs. multiple-equation model.
Dependent variable vs. independent, or explanatory variable(s).
Specification of the Econometric Model of Consumption
An example of an econometric model, more technically, a linear regression model:
where u, known as the disturbance, or error term, is a random (stochastic) Variable, may well represent all those factors that affect consumption but are not taken into account explicitly.

9. Obtaining Data

11. Estimation of the Econometric Model:
Statistical inference (hypothesis testing):
Q: “Is statistically less than 1 and greater than 0?”
Forecasting or Prediction
If the chosen model does not refute the hypothesis or theory under consideration, we may use it to predict the future value(s) of the dependent, or forecast variable Y on the basis of known or expected future value(s) of the explanatory, or predictor variable X.

12. Predict the mean consumption expenditure for 1997
Predict the mean consumption expenditure for The gdp value for 1997 was billion dollars.
The actual value was billion dollars.
Forecast error is about billion dollars, which is about 0.76 percent of the actual gdp value for 1997
Suppose the president decides to propose a reduction in the income tax. What will be the effect of such a policy on income and thereby on consumption expenditure and ultimately on employment?

13. A dollar’s worth of change in investment expenditure is given by the income multiplier M, which is defined as
If we use the MPC of 0.70, this multiplier becomes about M=3.33
An increase (decrease) of a dollar in investment will eventually lead to more than a threefold increase (decrease) in income.

14. Use of the model for control or policy purposes
Suppose the government believes that consumer
expenditure of about 4900 will keep the unemployment
rate at its current level of about 4.2 percent. What level
of income will guarantee the target amount of
consumer expenditure?
Which gives X=7197
The government can manipulate the control variables
X to produce the desired level of the target variable Y

15. The anatomy of classical econometric modeling

16. 1 The Nature of Regression Analysis
The term Regression was introduced by Francis Galton:
“Although there was a tendency for tall parents to have tall children and for short parents to have short children, the average height of children born of parents of a given height tended to move or “regress” toward the average height in the population as a whole.”

17. The Modern Interpretation:
Regression analysis is concerned with the study of the dependence of one variable, the dependent variable, on one or more other variables, the explanatory variables, with a view to estimating and/or predicting the (population) mean or average value of the former in terms of the known or fixed (in repeated sampling) values of the latter.

18. Examples regression line shows how the average height of sons
increases with the father’s height.
studying the dependence of crop yield on temperature, rainfall, amount of sunshine, and fertilizer. enable the forecasting of the average crop yield, given information about the explanatory variables

19. Statistical vs. Deterministic Relationships
Regression vs. Causality
Regression vs. Correlation
In correlation analysis, X and Y are random variables; whereas in regression analysis, one variable (e.g., Y) is treated as a random variable and the other (X) is treated as deterministic.

20. Types of Data The Sources of Data
Time series, cross-section, and pooled (i.e., combination of time series and cross section) data.
Panel, Longitudinal, or Micropanel Data: a special type of pooled data in which the same cross-sectional unit (say, a family or a firm) is surveyed over time.
The Sources of Data

21. 2 Two-Variable Regression Analysis: Some Basic Ideas
<Example> A total population of 60 families in a hypothetical community and their weekly income (X) and weekly consumption expenditure (Y), both in dollars.

24. Unconditional expected value of weekly consumption expenditure, E(Y):
Add the weekly consumption expenditures for all the 60 families in the population and divide this number by 60 = $
What is the expected value of weekly consumption expenditure of a family,” we get the answer $
“What is the expected value of weekly consumption expenditure of a family whose monthly income is, say, $140,” we get the answer $101.

25. population regression curve is simply the locus of the conditional means of the dependent variable for the fixed values of the explanatory
variable(s).
Figure 2.2
Population Regression Function
“Conditional expectation function (CEF) or population regression function (PRF) or population regression (PR).”
it tells how the mean or average response of Y varies with X.

27. Linear population regression function:
“Linearity in the Variables” and not “Linearity in the Parameters”.
If , for income X = $80 (see Table 2.1), it can be expressed as

28. The deviation of an individual around its expected value.
Thus, the assumption that the regression line passes through the conditional means of Y (see Figure 2.2) implies that the conditional mean values of (conditional upon the given X’s) are zero.

29. The disturbance term is a surrogate for all those variables that are omitted from the model but that collectively affect Y.
1. Vagueness of theory
2. Unavailability of data
3. Core variables versus peripheral variables
4. Intrinsic randomness in human behavior
5. Poor proxy variables
6. Principle of parsimony
7. Wrong functional form

30. THE SAMPLE REGRESSION FUNCTION (SRF):
In most practical situations we have only a sample of Y values corresponding to some fixed X’s. Therefore, our task now is to estimate the PRF on the basis of the sample information.

33. Analogously to the PRF that underlies the population regression line, the sample regression function (SRF) is:
For individual observation:

34. Estimator, also known as (sample) statistic, is a rule or formula or method that tells how to estimate the population parameter from the information provided by the sample at hand.
A particular numerical value obtained by the estimator in an application is known as an estimate.