Deck 9: Assessing Studies Based on Multiple Regression

Question 1

In the case of errors-in-variables bias,

A)maximum likelihood estimation must be used.
B)the OLS estimator is consistent if the variance in the unobservable variable is relatively large compared to variance in the measurement error.
C)the OLS estimator is consistent, but no longer unbiased in small samples.
D)binary variables should not be used as independent variables.

Answer 1

B

Question 2

Misspecification of functional form of the regression function

A)is overcome by adding the squares of all explanatory variables.
B)is more serious in the case of homoskedasticity-only standard error.
C)results in a type of omitted variable bias.
D)requires alternative estimation methods such as maximum likelihood.

Answer 2

C

Question 3

The reliability of a study using multiple regression analysis depends on all of the following with the exception of

A)omitted variable bias.
B)errors-in-variables.
C)presence of homoskedasticity in the error term.
D)external validity.

Answer 3

C

Question 4

A statistical analysis is internally valid if

A)its inferences and conclusions can be generalized from the population and setting studied to other populations and settings.
B)statistical inference is conducted inside the sample period.
C)the hypothesized parameter value is inside the confidence interval.
D)the statistical inferences about causal effects are valid for the population being studied.

Question 5

Errors-in-variables bias

A)is present when the probability limit of the OLS estimator is given by
$$\hat { \beta } _ { 1 } \rightarrow \beta _ { 1 } + \frac { \sigma _ { x } ^ { 2 } } { \sigma _ { x } ^ { 2 } + \sigma _ { w } ^ { 2 } }$$
B)arises when an independent variable is measured imprecisely.
C)arises when the dependent variable is measured imprecisely.
D)always occurs in economics since economic data is never precisely measured.

Question 6

Errors-in-variables bias

A)is only a problem in small samples.
B)arises from error in the measurement of the independent variable.
C)becomes larger as the variance in the explanatory variable increases relative to the error variance.
D)is particularly severe when the source is an error in the measurement of the dependent variable.

Question 7

A survey of earnings contains an unusually high fraction of individuals who state their weekly earnings in 100s, such as 300, 400, 500, etc.This is an example of

A)errors-in-variables bias.
B)sample selection bias.
C)simultaneous causality bias.
D)companies that typically bargain with workers in 100s of dollars.

Question 8

Applying the analysis from the California test scores to another U.S.state is an example of looking for

A)simultaneous causality bias.
B)external validity.
C)sample selection bias.
D)internal validity.

Question 9

Comparing the California test scores to test scores in Massachusetts is appropriate for external validity if

A)Massachusetts also allowed beach walking to be an appropriate P.E.activity.
B)the two income distributions were very similar.
C)the student-to-teacher ratio did not differ by more than five on average.
D)the institutional settings in California and Massachusetts, such as organization in classroom instruction and curriculum, were similar in the two states.

Question 10

By including another variable in the regression, you will

Question 11

Simultaneous causality

A)means you must run a second regression of X on Y.
B)leads to correlation between the regressor and the error term.
C)means that a third variable affects both Y and X.
D)cannot be established since regression analysis only detects correlation between variables.

Question 12

In the case of a simple regression, where the independent variable is measured with i.i.d. error,

Question 13

A study based on OLS regressions is internally valid if

A)the errors are homoskedastic, and there are no more than two binary variables present among the regressors.
B)you use a two-sided alternative hypothesis, and standard errors are calculated using the heteroskedasticity-robust formula.
C)weighted least squares produces similar results, and the t-statistic is normally distributed in large samples.
D)the OLS estimator is unbiased and consistent, and the standard errors are computed in a way that makes confidence intervals have the desired confidence
Level.

Question 14

Panel data estimation can sometimes be used

A)to avoid the problems associated with misspecified functional forms.
B)in case the sum of residuals is not zero.
C)in the case of omitted variable bias when data on the omitted variable is not available.
D)to counter sample selection bias.

Question 15

Correlation of the regression error across observations

A)results in incorrect OLS standard errors.
B)makes the OLS estimator inconsistent, but not unbiased.
C)results in correct OLS standard errors if heteroskedasticity-robust standard errors are used.
D)is not a problem in cross-sections since the data can always be "reshuffled."

Question 16

The analysis is externally valid if

A)the statistical inferences about causal effects are valid for the population being studied.
B)the study has passed a double blind refereeing process for a journal.
C)its inferences and conclusions can be generalized from the population and setting studied to other populations and settings.
D)some committee outside the author's department has validated the findings.

Question 17

Simultaneous causality bias

A)is also called sample selection bias.
B)happens in complicated systems of equations called block recursive systems.
C)results in biased estimators if there is heteroskedasticity in the error term.
D)arises in a regression of Y on X when, in addition to the causal link of interest from X to Y, there is a causal link from Y to X.

Question 18

Sample selection bias

A)occurs when a selection process influences the availability of data and that process is related to the dependent variable.
B)is only important for finite sample results.
C)results in the OLS estimator being biased, although it is still consistent.
D)is more important for nonlinear least squares estimation than for OLS.

Question 19

Sample selection bias occurs when

A)the choice between two samples is made by the researcher.
B)data are collected from a population by simple random sampling.
C)samples are chosen to be small rather than large.
D)the availability of the data is influenced by a selection process that is related to the value of the dependent variable.

Question 20

The components of internal validity are

Question 21

Your textbook used the California Standardized Testing and Reporting (STAR)data set
on test student performance in Chapters 4-7.One justification for putting second to
twelfth graders through such an exercise once a year is to make schools more
accountable.The hope is that schools with low scores will improve the following year
and in the future.To test for the presence of such an effect, you collect data from 1,000
L.A.County schools for grade 4 scores in 1998 and 1999, both for reading (Read)and
mathematics (Maths).Both are on a scale from zero to one hundred.The regression
results are as follows (homoskedasticity-only standard errors in parentheses): (a)Interpret the results and indicate whether or not the coefficients are significantly different
from zero.Do the coefficients have the expected sign and magnitude?

Question 22

Possible solutions to omitted variable bias, when the omitted variable is not observed, include the following with the exception of

A)panel data estimation.
B)nonlinear least squares estimation.
C)use of instrumental variables regressions.
D)use of randomized controlled experiments.

Question 23

A possible solution to errors-in-variables bias is to

A)use log-log specifications.
B)choose different functional forms.
C)use the square root of that variable since the error becomes smaller.
D)mitigate the problem through instrumental variables regression.

Question 24

A study of United States and Canadian labor markets shows that aggregate
unemployment rates between the two countries behaved very similarly from 1920 to
1982, when a two percentage point gap opened between the two countries, which has
persisted over the last 20 years.To study the causes of this phenomenon, you specify a
regression of Canadian unemployment rates on demographic variables, aggregate demand
variables, and labor market characteristics.
(a)Assume that your analysis is internally valid.What would make it externally valid?

Question 25

Your professor wants to measure the class's knowledge of econometrics twice during the
semester, once in a midterm and once in a final.Assume that your performance, and that
of your peers, on the day of your midterm exam only measure knowledge imperfectly and
with an error,

Question 26

You have been hired as a consultant by building contractor, who have been sued by the
owners' representatives of a large condominium project for shoddy construction work.In
order to assess the damages for the various units, the owners' association sent out a letter
to owners and asked if people were willing to make their units available for destructive
testing.Destructive testing was conducted in some of these units as a result of the
responses.Based on the tests, the owners' association inferred the damage over the entire
condo complex.Do you think that the inference is valid in this case? Discuss how proper
sampling should proceed in this situation.

Question 27

Until about 10 years ago, most studies in labor economics found a small but significant
negative relationship between minimum wages and employment for teenagers.Two labor
economists challenged this perceived wisdom with a publication in 1992 by comparing
employment changes of fast-food restaurants in Texas, before and after a federal
minimum wage increase.
(a)Explain how you would obtain external validity in this field of study,

Question 28

Assume that a simple economy could be described by the following system of equations,

Question 29

The Phillips curve is a relationship in macroeconomics between the inflation rate (inf)
and the unemployment rate (ur).Estimating the Phillips curve using quarterly data for
the United States from 1962:I to 1995:IV, you find (a)Explain why, at first glance, this is a surprising result.

Question 30

You have decided to analyze the year-to-year variation in temperature data.Specifically
you want to use this year's temperature to predict next year's temperature for certain
cities.As a result, you collect the daily high temperature (Temp)for 100 randomly
selected days in a given year for three United States cities: Boston, Chicago, and Los
Angeles.You then repeat the exercise for the following year.The regression results are as
follows (heteroskedasticity-robust standard errors in parentheses): (a)What is the prediction of the above regression for Los Angeles if the temperature in the
previous year was 75 degrees? What would be the prediction for Boston?

Question 31

Macroeconomists who study the determinants of per capita income (the "wealth of
nations")have been particularly interested in finding evidence on conditional
convergence in the countries of the world.Finding such a result would imply that all
countries would end up with the same per capita income once other variables such as
saving and population growth rates, education, government policies, etc., took on the
same value.Unconditional convergence, on the other hand, does not control for these
additional variables.
(a)The results of the regression for 104 countries was as follows, Interpret the results and point out the difference with regard to unconditional
convergence.

Question 32

Sir Francis Galton (1822-1911), an anthropologist and cousin of Charles Darwin, created
the term regression.In his article "Regression towards Mediocrity in Hereditary Stature,"
Galton compared the height of children to that of their parents, using a sample of 930
adult children and 205 couples.In essence he found that tall (short)parents will have tall
(short)offspring, but that the children will not be quite as tall (short)as their parents, on
average.Hence there is regression towards the mean, or as Galton referred to it,
mediocrity.This result is obviously a fallacy if you attempted to infer behavior over time
since, if true, the variance of height in humans would shrink over generations.This is not
the case.
(a)To research this result, you collect data from 110 college students and estimate the
following relationship: where Studenth is the height of students in inches and Midparh is the average of the
parental heights.Values in parentheses are heteroskedasticity-robust standard errors.
Sketching this regression line together with the 45 degree line, explain why the above
results suggest "regression to the mean" or "mean reversion."

Question 33

The guidelines for whether or not to include an additional variable include all of the following, with the exception of

A)providing "full disclosure" representative tabulations of the results.
B)testing whether additional questionable variables have nonzero coefficients.
C)determining whether it can be measured in the population of interest.
D)being specific about the coefficient or coefficients of interest.

Question 34

(a)Specify a linear consumption function.Show that the assumption of a falling APC
implies the presence of a positive intercept.

Question 35

Several authors have tried to measure the "persistence" in U.S state unemployment rates
by running the following regression: (a)Explain why finding a slope estimate of one and an intercept of zero is typically
interpreted as evidence of "persistence."

Question 36

One of the most frequently used summary statistics for the performance of a baseball
hitter is the so-called batting average.In essence, it calculates the percentage of hits in the
number of opportunities to hit (appearances "at the plate").The management of a
professional team has hired you to predict next season's performance of a certain hitter
who is up for a contract renegotiation after a particularly great year.To analyze the
situation, you search the literature and find a study which analyzed players who had at
least 50 at bats in 1998 and 1997.There were 379 such players.
(a)The reported regression line in the study is and the intercept and slope are both statistically significant.What does the regression
imply about the relationship between past performance and present performance? What
values would the slope and intercept have to take on for the future performance to be as
good as the past performance, on average?

Question 37

Your textbook gives the following example of simultaneous causality bias of a two
equation system:

Question 38

You try to explain the number of IBM shares traded in the stock market per day in 2005. As an independent variable you choose the closing price of the share.This is an example of

A)simultaneous causality.
B)invalid inference due to a small sample size.
C)sample selection bias since you should analyze more than one stock.
D)a situation where homoskedasticity-only standard errors should be used since you only analyze one company.

Question 39

In the case of errors-in-variables bias, the precise size and direction of the bias depend on

Question 40

The errors-in-variables model analyzed in the text results in so that the OLS estimator is inconsistent.Give a condition involving the variances of X
and w, under which the bias towards zero becomes small.

Question 41

Your textbook uses the following example of simultaneous causality bias of a two
equation system:

Question 42

Your textbook has analyzed simultaneous equation systems in the case of two equations, where the first equation might be the labor demand equation (with capital stock and
technology being held constant), and the second the labor supply equation (X being the
real wage, and the labor market clears).What if you had a a production function as the
third equation where Z is output.If the error terms, u, v, and w, were pairwise uncorrelated, explain why
there would be no simultaneous causality bias when estimating the production function
using OLS.

Question 43

Give at least three examples where you could envision errors-in-variables problems.For
the case where the measurement error occurs only for the explanatory variable in the

Question 44

Consider a situation where Y is related to X in the following manner:
Draw the deterministic part of the above function. Next add, in the same graph, a hypothetical Y, X scatterplot of the actual observations. Assume that you have misspecified the functional form of the regression function and estimated the relationship

between Y and X using a linear regression function. Add this linear regression function to your graph. Separately, show what the plot of the residuals against the X variable in your regression would look like.

Question 45

Your textbook states that correlation of the error term across observations "will not
happen if the data are obtained by sampling at random from the population." However, in
one famous study of the electric utility industry, the observations were listed by the size
of the output level, from smallest to largest.The pattern of the residuals was as shown in
the figure.
What does this pattern suggest to you?

Question 46

In the simple, one-explanatory variable, errors-in-variables model, the OLS estimator for
the slope is inconsistent.The textbook derived the following result

Question 47

In macroeconomics, you studied the equilibrium in the goods and money market under
the assumption of prices being fixed in the very short run.The goods market equilibrium
was described by the so-called IS equation Show that there is simultaneous causality bias in this situation.

Question 48

Consider the one-variable regression model,
assumptions from Chapter 4 are satisfied. However, suppose that both Y and X are
measured with error,
and independent of both Y and X respectively. If you estimated the regression model
\quad using OLS, then show that the slope estimator is not consistent.

Question 49

Your textbook only analyzed the case of an error-in-variables bias of the type
What if the error were generated in the simple regression model by entering data that always contained the same typographical error, say where a and b are constants. What effect would this have on your regression model?

Question 50

Explain why the OLS estimator for the slope in the simple regression model is still
unbiased, even if there is correlation of the error term across observations.

Question 51

A professor in your microeconomics lectures derived a labor demand curve in the lecture.
Given some reasonable assumptions, she showed that the demand for labor depends
negatively on the real wage.You want to put this hypothesis to the test ("show me")and
collect data on employment and real wages for a certain industry.You try to estimate the
labor demand curve but find no relationship between the two variables.Is economic
theory wrong? Explain.

Question 52

To analyze the situation of simultaneous causality bias, consider the following system of
equations:

Question 53

Think of three different economic examples where cross-sectional data could be
collected.Indicate in each of these cases how you would check if the analysis is
externally valid.

Question 54

Assume that you had found correlation of the residuals across observations.This may
happen because the regressor is ordered by size.Your regression model could therefore
be specified as follows:

Question 55

The textbook derived the following result:
Show that thisis sthe same as