ECON321 Lecture Notes - Lecture 11: Homoscedasticity, Bias Of An Estimator, Econometrics

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blueraven607

5 Dec 2014

School

University of Waterloo

Department

Economics

Course

ECON321

Professor

Kathleen Rybczynski

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We found that the variance of our ols estimators is: Xij xj 2 1 rj because we do not know the ui, we cannot calculate. In the case of k+1 parameters, df=n-k-1: if the errors are homoskedastic, then an estimate of the var( ) using 2 is unbiased. Introduction to econometrics, notes 11 p. 2: gauss markov theorem the ols estimator is the best linear unbiased estimator (blue) 1 is the partial effect of x1 on y. So then 1 is just our estimate of the partial effect of x1 on y. But this interpretation of , and of , is not accurate in all cases. Suppose we estimate the following regression model: ln wi = 0 1educi 2experi 3experi. 1 is the partial effect of education on ln(w), if we increase education by 1 year, we believe ln(w) should increase by 1 units. It is not the partial effect of work experience on log wages!

Related Questions

For a child i living in a particular school district, let the voucher be a dummy variable equal to one if a child is selected to participate in a school voucher program, and let scores be that child's score on a subsequent standardized exam. Suppose that the participation variable, voucher, is completely randomized in the sense that it is independent of both observed and unobserved factors that can affect the test score.

i) If you run a simple regression score on vouchers using a random sample of size n, does the OLS estimator provide an unbiased estimator of the effect of the voucher program?

ii) Suppose you can collect additional background information, such as family income family structure(e.g., whether the child lives with both parents), and parents' education levels. Do you need to control for these factors to obtain an unbiased estimator of the effects of the voucher program? Explain.

iii )Why should you include the family background variables in the regression? Is there a situation in which you would not include the background variables?

pearprairie-dog202

TABLE 66 Stock Prices and Consumer Prices

CITY
Y = Rate of Change, Stock Prices, Percent Per Year
X = Rate of Change, Consumer Prices, Percent Per Year

CITY	Y	X
A	5	4.3
B	11.1	4.6
C	3.2	2.4
D	7.9	2.4
E	25.5	26.4
F	3.8	4.2
G	11.1	5.5
H	9.9	4.7
I	3.3	2.2
J	1.5	4
K	6.4	4
L	8.9	8.4
M	8.1	3.3
N	13.5	4.7
O	4.7	5.2
P	7.5	3.6
Q	4.73.	6
R	8	4
S	7.5	3.9
T	9	2.1

Table 66 gives data on percent change per year stock prices (Y) and consumer prices (X) for a cross section of 20 cities.

******************* answer in "SAS format" please********************* (if possible)

1) Plot the data in scattergram

2) Regress Y on X and examine the residuals from this regression. What do you observe?

3) Since the data for city(E) is unusual, repeat the regression in (2) dropping the data on city(E). Now examine the residuals from this regression. What do you observe?

4) If on the basis of the results in (2) you conclude that there was heteroscedasticity in the error variance but on the basis of the results in (3) you reverse your conclusion, what general conclusions do you draw?

State whether the following statements are true or false. Breifly justify your answer:

5) When autocorrelation is present, OLS estimators are biased as well as inefficient;

6) The R squared values of two models, one involving regression in the first-difference form and another in the level form, are not directly comparable.

7) In the presence of heterscedasticity the usual OLS method always overestimates the standard errors of estimators.

8) If a regression model is mis-specified (e.g., an important variable is ommitted), the OLS residuals will show a distinct pattern.

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Decide if you agree or disagree with each of the following statements. Give abrief explanation of your decision:(A)Like observations in a cross-sectional data set, it is usually okay to assume that observationsfrom time-series data are independently distributed.(B)If the rst three Gauss-Markov assumptions are satis ed, OLS is unbiased when used on time-series data.(C)A trending variable cannot be used as the dependent variable in multiple linear regression anal-ysis.(D)Seasonality is not an issue when using annual time series observations

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ECON321 Lecture Notes - Lecture 11: Homoscedasticity, Bias Of An Estimator, Econometrics

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