Mid-Term

Question 1

What is attrition?

Answer 1

Dropping out of an experiment or not giving full information in a questionaire. It is a form of bias.

Question 2

What is the Experimental Effect?

Answer 2

Where the researcher’s cognitive bias impacts the experiment.

Question 3

What is internal validity?

Answer 3

It is where there is an issue with the random sample such as having too small sample or failing to randomize your results.

Question 4

What is randomised assignment rule?

Answer 4

It assumes that all of the treated and non-treated are equal in all aspects (apart from treatment status).

Question 5

What is a social experiment method?

Answer 5

It is where you carry out a theory free experiment, it will mimic a clinical trail.

Question 6

What is the formula for the estimate of B1?

Answer 6

(sum of (x-xbar)(y-ybar))/sum(x-xbar)^2

Question 7

What are the formulas for;

Total Sum of Squares (TSS)

Explained Sum of Squares (ESS)

Residual Sum of Squares (RSS)

Answer 7

TSS: sum(yi-ybar)^2

ESS: sum( yhat-ybar)^2

RSS: sumU^2

Question 8

What does it mean if the error variance is larger?

What does it mean if there is larger variability in Xi?

Answer 8

It will mean that the variance of the slope estimate will be higher.

It means that the variance of the slope estimate will be smaller.

Question 9

What is the adjusted coefficient of determination?

When will R^2bar increase?

Answer 9

It is adjusted R^2 it is Rbar^2.

It measures the goodness of fit but penalizes for every extra regressor.

It will only increase if the new value has a t-ratio which is greater than unity in absolute value.

Question 10

What is the formula for the f-statistic when testing exclusion restrictions?

Answer 10

F = ((SSRr-SSRu)/q)/(SSRur/n-k-1)

Q is the number of restrictions.

n-k-1 is the no. of deg free of unrestricted.

Question 11

What is the formula for the test of overall significance?

Answer 11

F=(R^2/k)/(1-R^2)/(n-k-1)

Where H0= b1=b2=bk.

Question 12

When asked a question about finding the real log hourly wage what must you do to it to earn full marks?

Answer 12

You must find the exponential of your answer.

Question 13

What should you mention in a question about dummy variables?

Answer 13

You should mention that there needs to be one omitted category to prevent multicollinearity.

Question 14

What must you remember about the ramsay reset test?

Answer 14

You must always mention that it has weak power.

Question 15

What is the formula for the Chow Test?

Answer 15

(RRSS-(RSS1+RSS2)/(K))/(RSS1+RSS2)/(n-2k)

F(k,n-2k)

Question 16

What is the formula for testing exclusion restrictions?

Answer 16

F = ((R^2Ur-R^2r)/q)/((1-R^2ur)/(n-k-1))

Question 17

Imagine you have done a ramsey reset test and the prob>F=0.1012, do you reject the null?

Answer 17

You do not reject the null as 0.1012 is greater than 0.05.

Question 18

Explain the meaning and consequences of:

Omitting relevant variables.

Answer 18

• Omitting a relevant variable is known as under fitting the model.
• This will result will result when you do not include enough variables.
• This will result in the OLS estimates being biased.
• The direction of this bias is determined by E(b1)-b1=B2gamma1

B2 is the marginal effect of the wrongly omitted variable.

Gamma1 is the correlation between the regressor and the omitted variable.

Direction of Bias:

If the signs are the same then positive bias.

If the signs are different then there is negative bias.

E(b1)=b1+B2((cov(xt,zt))/Var (xt))

Question 19

Explain the meaning and consequences of:

Including Irrelevant Variables.

Answer 19

• This is know as ‘overfitting the model’ you are including unnecessary variables.
• it is when you include variables which are unnecessary for the explanatory power of the model.
• It will cause the standard errors to be too large and the t-ratios will be too small.

This means some coefficients will be found to be insignificant, despite truly being significant.

Question 20

Discuss the relevance of the following two terms in the context of the Classical Linear
Regression Model:

Heteroscedasticity & Homoscedasticity.

Answer 20

Heteroscedasticity:

Is a model where the variance of the error, conditional on the explanatory variables, is non-constant.

• The effect that this has on the OLS is that the presence will cause the standard errors in the regression to be biased. In turn this will result in us not being able to use them for t-tests and f-tests.

It will also mean that the variances are no longer a minimum hence the regression is not Best Linear Unbiased Estimator (BLUE).

You can have what is known as a heteroscedastic robust procedure. This simply means that it will work in the presense of heteroscedastic variance. (in large samples).

You can test for heteroscedasticity using a
breusch-pagan test Ho: the model has constant varience. If 0.05 is > P you know to reject.

To Deal with Heteroscedasticity you can;

• try to respecify the model
• try weighted least squares.

Question 21

Discuss the relevance of the following two terms in the context of the Classical Linear
Regression Model:

Autocorrelation

Answer 21

• Autocorrelation is correlation between the errors within a model. Corr(Ut,Us)=0

for all t=s.

Informal tests:
-Plot residuals across time,
if they follow each other you can see autocorrelation.

• Plot them in a scatter graph. From there you can see if there is any positive or negative correlation.

Formal Tests:

• Durbin Watson test is one example of a formal test.
• T-test by regressing Ut on Ut-1 then test significance of rho.
• Breusch Godfrey Test: Run an auxiliary regression for each of the lagged residuals (u) and regress them on U.

You are then testing to see if r1=r2=r3=r4=0.

Question 22

What are the assumptions for a MLR (Multiple Linear Regression Model)

Answer 22

1) The population regression is linear in it’s parameters.
2) We will randomly sample n observations, following the population model in MLR1.
3) Zero Conditional Mean: U is independent of the x variables . (X are deterministic, non stochastic)

4) No Perfect Collinearity (none of the independent variables in the sample is a linear combination of the other independent variables. .
5) U has a constant variance (homoscedastic)

6) u is normally distributed

Question 23

What is the null for the Durbin Watson test and when would you reject the null from the Stata readout?

What is the null and rejection condition for a Breusch-Godfrey test.

Answer 23

The null Ho: is there is no serial correlation.

h1: rho > 0

Reject if 0.05 > P

Question 24

What effect does Autocorrelation actually have on the OLS?

How do you deal with Autocorrelation?

Answer 24

It will cause the OLS to underestimate the true variance.

This will result in incorrect T-Ratios.

This will cause us to reject the null when it is true. (TYPE 1 ERROR).

It will also cause the OLS parameter estimates to be biased.

In order to deal with Autocorrelation, you can either;

1) Estimate using a different estimator. (such as the Cochrane-Orcutt estimator.

2) Respecify the model.
It may have the wrong functional form
omitted variables
misspecified a dynamic model as a static one.

Question 25

How does the Cochrane-Orcutt estimator work?

Answer 25

You have the model;

Yt=B1+B2Xt+Ut

ut=rhout-1 +et

say that:
yt=yt-rhoyt-1

xt=xt-rhoxt-1

Re-run the OLS on the transformed data.

Y’t=B1’+B2x’t+et

B1’=(1-rho)B1

Question 26

What are the OLS effects of non-normality?

Answer 26

If the error term is non-normal, the OLS estimators will also be non-normal. This means that we cannot use hypothesis testing as we will not have a distribution with which to compare the t-distribution.

If the sample size is under 30, you can still hypothesis test due to the CLT, however; it is still not appropriate to F-Test.

Question 27

How do you test for normality?

When should you reject the test in Stata?

Answer 27

You run a test for the kurtosis and skewness in stata.

Ho: y normally distributed, x normally distributed, e7- normally distributed.

Then look at Prob> CHI2

If P<0.05 reject the null.