Ec 120B ECONOMETRICS B LECTURE NOTES
Foster, UCSD April 10, 2014
TOPIC 11. SIMPLE OLS REGRESSION
A. Overview of Econometrics
a) Econometrics – the application of mathematical/statistical methods to economic data to investigate
relationships among economic variables and processes.
b) Methods of econometrics.
1) Correlation analysis – shows if 2 variables have a linear relationship, without exactly specifying
2) Regression analysis – estimates exact mathematical (linear or nonlinear) relationships among
variables. Regression is the backbone of econometrics and is more powerful than mere
2. Estimation with Regression Analysis:
a) GOOD ECONOMETRICS ALWAYS BEGINS WITH A THEORY OR HYPOTHESIS!
1) Example – Keynesian macro theory says that personal consumption expenditure is a function of
disposable personal income: C = c(I).
2) The theory also asserts that the marginal propensity to consume (MPC = dC/dI) is between 0 and
1, while “autonomous consumption” C =0c(0) is positive.
3) We can use econometric regression methods to examine this theory.
b) For simplicity, we assume that the relationship is linear: C =1β 2 β I.
1) β 1= intercept = c(0); 2 = slope c’(I)
2) These parameters are unknown and will have to be estimated.
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c) We begin by gathering sample data.
1) Crosssection data C, i,ii = 1…500, from 500 CA households in 2004.
2) Timeseries C, t,tt = 1…57, for the state of California over years 19552011.
3) A scatter plot might look like Fig. 1.
d) Using an Ordinary Least Squares (OLS) regression program, we obtain the equation of the straight
line which has the best fit to the data points in the scatter diagram. Ec 120B SIMPLE REGRESSION Page 2 of
1) β 1 and β2 are OLS estimates of parameters β and 1 . 2
2) SE(β ) and SE(β ) are estimates of the standard errors of the OLS estimators.
2 1 2
3) R is a measure of how well the line fits the scatter plot of data.
4) Suppose the equation of the bestfitting line is C = 3.7 + 0.7 I.
3. Uses of Econometrics:
a) Measuring (estimating) relationships.
1) We have obtained point estimates β 1 = 3.7 and β2 = 0.7.
̂ ̂ ̂
2) With the SÊ, we can construct interval estimates like β 1 ± 1.96 SE(β ) 1 .
3) With the R measure, we can decide if our estimated linear consumption function has a good or
poor “fit” to the data points in the scatter diagram.
b) Hypothesis testing.
1) Keynes said that 0 20 and H : 0 ≥21; H : 1