UNC-Wilmington
Department of Economics and Finance
ECN 377
Dr. Chris Dumas
Homework 18
(Due Friday, Dec. 4th, by 12:00 noon)
Multiple Choice
1) Suppose you are thinking about an economic situation and how you should model it. You’re thinking about how you
should set up the equations. You really want to predict/forecast Y; that’s the important thing, so Y will be your dependent
variable. You think that X, Z and R affect Y, so you are planning to use X, Z and R in your equation as independent
variables. But wait! Thinking about it a little more, now you think that Y affects Z. At this point, even before you consider
any further complications in the situation, what type of model are you dealing with: a) a model with heteroskedasticity, b) a
model with autocorrelation, c) a simultaneous equations model, d) a model with multicollinearity
2) Suppose you want to use regression analysis to estimate the β’s in the demand equation for product Q, a continuous
variable. The demand and supply equations for product Q are given below:
Demand: Q = β0 + β1·PQ + β2·I + eD,
where "eD" is an error term in the Demand equation,
Supply:
Q = β3 + β4·PQ + β5·PM + eS, where "eS" is an error term in the Supply equation,
If you gather cross-section data on Q, PQ and I, and then run a regression analysis for the demand equation, what
problem will you have? a) limited dependent variable bias
b) omitted variables bias
c) the autocorrelation problem
d) simultaneous equations bias
3) Suppose you have the following data on the market quantity bought/sold (Q) and per unit price (P Q) of the latest model of
iPhone. If you ran a regression analysis on the data points, which relationship would you be estimating?
a) demand curve b) you don’t know, because of the limited dependent variables problem
c) supply curve
d) you don’t know, because of the identification problem
PQ
0
Q
4)Suppose you want to estimate a supply curve using regression analysis. In order to identify the supply curve equation, it’s
important to have enough predetermined variables in the:
a) demand curve b) supply curve c) likelihood equation d) Jarque-Bera equation
5) The equations that express the endogenous variables in a system of equations solely as functions of the predetermined
variables in the system are known as:
a) identity equations b) structural equations c) behavioral equations d) reduced-form equations
6)The equations in a simultaneous equation system that represent the structural features of the economy or behavioral aspects
of individuals in the economy are known as:
a) identity equations b) structural/behavioral equations c) rank and order conditions d) reduced-form equations
7) Suppose you are investigating the market demand and market supply equations below for product Q. You have data on Q,
PQ, I and PM.
Demand: Q = β0 + β1·PQ + β2·I + eD,
where "eD" is an error term in the Demand equation,
Supply:
Q = β3 + β4·PQ + β5·PM + eS, where "eS" is an error term in the Supply equation,
Suppose consumers’ incomes (I) begin to change significantly. This change would help you identify:
a) the demand curve b) the supply curve c) the likelihood equation d) the error term
1
UNC-Wilmington
Department of Economics and Finance
ECN 377
Dr. Chris Dumas
8) Suppose you know that the demand curve for product Q is shifting, whereas the supply curve of product Q is remaining
relatively constant, as shown in the graph below. You have data on the equilibrium quantities of Q and P Q from several points
in time, as shown by the enlarged points in the graph below. Using the data from the equilibrium points (assume that you
have data from many such points), which equation or equations would you be able to estimate using regression analysis?
a) the demand equation b) the supply equation c) both equations d) neither equation
PQ
0
Q
9) Suppose you know that the supply curve for product Q is shifting, whereas the demand curve for product Q is remaining
relatively constant, as shown in the graph below. You have data on the equilibrium quantities of Q and P Q from several points
in time, as shown by the enlarged points in the graph below. Using the data from the equilibrium points (assume that you
have data from many such points), which equation or equations would you be able to estimate using regression analysis?
a) the demand equation b) the supply equation c) both equations d) neither equation
PQ
0
Q
10) Suppose you are analyzing a system of several equations. How do you know whether you have a simultaneous system of
equations (and so, potentially, face the simultaneous equations bias problem)?
a) each equation has endogenous variables, b) each equation has predetermined variables, c) each equation has lagged
endogenous variables, d) the equations have no endogenous variables in common, e) the equations share two or more
endogenous variables
11) Suppose the value of a variable in a simultaneous equations model is determined outside the model; that is, its values are
“given,” and you don’t solve for them using the model. That type of variable is known as a/an:
a) endogenous variable b) predetermined variable c) structural/behavioral variable d) reduced-form variable
12) Suppose a variable in a simultaneous equations model is not an endogenous variable and has never been an endogenous
variable. That type of variable is known as a/an:
a) exogenous variable b) lagged endogenous variable c) structural/behavioral parameters d) reduced-form variable
13) Suppose a predetermined variable in a simultaneous equations model is an endogenous variable from an earlier time
period. This type of variable is known as a/an:
a) exogenous variable b) lagged endogenous variable c) structural/behavioral variable d) reduced-form parameters
14) OMITTED
15) OMITTED
2
UNC-Wilmington
Department of Economics and Finance
ECN 377
Dr. Chris Dumas
16) When working with simultaneous equation models, which type of equation does not suffer from the problem of
simultaneous equations bias?
a) reduced form equations b) structural/behavioral equations c) exogenous equations d) endogenous equations
17) What is the purpose of indirect least squares (ILS) regression analysis?
a) to solve the simultaneous equations bias problem by doing regression analysis on reduced-form equations
b) to solve the autocorrelation problem
c) to solve the heteroskedasticty problem
d) to solve the multicollinearity probblem
e) to solve the limited dependent variables problem
18) When working with simultaneous equations models, the “rank and order conditions” are:
a) a set of rules that determine whether it is possible to solve for the original reduced-form coefficients from the
structural/behavioral coefficients.
b) a set of rules that determine whether it is possible to solve for the original structural behavioral coefficients from the
reduced-form coefficients.
c) a set of rules for determining whether you should use probit analysis
d) a set of rules for determining whether you should use ILS or 2SLS analysis
e) a set of rules for determining whether you should use probit or 2SLS analysis
f) a and c g) a and e h) b and c i) b and d j) a and d k) c and e
19) When doing indirect least squares (ILS) regression analysis, you first find estimates of the reduced-form parameters, and
then you use the reduced-form parameters to solve back for the parameters of the original structural/behavioral equations.
Does the “solve back” step always work?
a) yes, why else would we learn about ILS?
b) no, it never works. (stupid ILS method!)
c) it sometimes works, you need to check the rank and order conditions to determine whether it will work
d) it works when the equation of interest is under-identified
e) both c and d
20) Suppose that you are working with a simultaneous equations model, and you want to use regression analysis to estimate
one of the equations in the model, the so-called “equation of interest.” As you should, you check the rank and order
conditions for the “equation of interest,” and you find out that the equation is “over-identified.” What does this mean?
a) you should use ordinary least squares (OLS) regression to estimate the equation
b) you should use weighted least squares (WLS) to estimate the equation
c) you should use indirect least squares (ILS) regression to estimate the equation
d) you should use two-stage least squares (2SLS) regression to estimate the equation
e) you should use probit regression to estimate the equation
f) you can’t estimate the equation in its present form—you need to go “back to the drawing board” and add more variables or
more equations to the model
21) Suppose that you are working with a simultaneous equations model, and you want to use regression analysis to estimate
one of the equations in the model, the so-called “equation of interest.” As you should, you check the rank and order
conditions for the “equation of interest,” and you find out that the equation is “exactly-identified.” What does this mean?
a) you should use ordinary least squares (OLS) regression to estimate the equation
b) you should use weighted least squares (WLS) to estimate the equation
c) you should use indirect least squares (ILS) regression to estimate the equation
d) you should use two-stage least squares (2SLS) regression to estimate the equation
e) you should use probit regression to estimate the equation
f) you can’t estimate the equation in its present form—you need to go “back to the drawing board” and add more variables or
more equations to the model
3
UNC-Wilmington
Department of Economics and Finance
ECN 377
Dr. Chris Dumas
22) Suppose that you are working with a simultaneous equations model, and you want to use regression analysis to estimate
one of the equations in the model, the so-called “equation of interest.” As you should, you check the rank and order
conditions for the “equation of interest,” and you find out that the equation is “under-identified.” What does this mean?
a) you should use ordinary least squares (OLS) regression to estimate the equation
b) you should use weighted least squares (WLS) to estimate the equation
c) you should use indirect least squares (ILS) regression to estimate the equation
d) you should use two-stage least squares (2SLS) regression to estimate the equation
e) you should use probit regression to estimate the equation
f) you can’t estimate the equation in its present form—you need to go “back to the drawing board” and add more variables or
more equations to the model
23) Suppose you are working with a simultaneous equations model, and you attempt to estimate each equation in the model
separately, using ordinary least squares (OLS) regression. Which problems would you face?
a) the estimates of the β's would be biased
b) the estimates of the β's would be inconsistent
c) the estimates of the s.e.’s would be biased
d) the estimates of the SER would be biased
e) both a and b
f) a, b and c
g) a, b, c and d
24) Suppose you want to estimate the growth rate of GDP (Y) over time (T). Which functional form would be best for
estimating the growth rate r (which could be calculated from parameter Β1)?
a) Y = β0 + β1D1 + β2T + e
b) Y = β0 + β1T + β2D1T + e
c) Y = β0 + β1(1/T) + e
d) Y = β0 + β1T + β2T2 + e
2
3
e) ln(Y) = β0 + β1ln(T) + e f) Y = β0 + β1T + β2T + β3T + e
g) ln(Y) = β0 + β1T + e
25) Some of the graphs in the questions above are non-linear. Is it a mistake to use “linear regression analysis” to analyze
such relationships?
a) Yes, you must use some other type of analysis, such as contingency tables
b) No, linear regression analysis refers to relationships that are linear in the parameters, not linear in the variables
c) No, linear regression analysis refers to relationships that are linear in the variables, not linear in the parameters
d) No, due to the Central Limit Theorem
e) Yes, due to the Gauss-Markov Theorem
26) When does the simultaneous equations bias problem occur?
(a) when one X variable is linearly correlated with another X variable
(b) when an X variable is correlated with u, causing bias due to feedback among model equations
(c) when the variance in the errors is not constant
(d) when the error from one observation (one row of data) affects the error from another observation (another row of data)
(e) when an X variable has been INCORRECTLY included in, or omitted from, a regression
27) If you discover that you have the autocorrelation problem, what should you do to correct it?
a) drop one of the two X variables that are correlated with one another
b) use rho (ρ) to weight the Y and X variables and run a weighted least squares regression
c) create a weight variable (w) equal to 1/sqrt(X) or 1/sqrt(X2) to weight the Y and X variables and run a weighted least
squares regression
d) log or square one of the two X variables that are correlated with one another
e) either c or d
28) When might simultaneous equations bias cause problems in regression analysis?
a) when there are two or more equations in a model and each variable is found in either one equation or the other, but not
both
b) when there are two or more equations in a model and only one variable is present in both equations (the remaining
variables are in one equation or the other, but not both)
c) when there are two or more equations in a model and two or more variables are present in both equations (the remaining
variables are in one equation or the other, but not both)
d) both b and c
29) When an economic model contains two or more equations, _________ variables are those found in both equations,
whereas ________ variables are those found in just one of the two equations.
a) endogenous, predetermined b) predetermined, endogenous
c) endogenous, reduced-form d) reduced-form, lagged endogenous
4
UNC-Wilmington
Department of Economics and Finance
ECN 377
Dr. Chris Dumas
30) When working with simultaneous equations models, what are the “Rank and Order Conditions?”
a) smelly, but well-organized rules
b) rules that determine whether one should check for heteroskedasticity or autocorrelation
c) conditions used to determine whether probit model estimates are biased
d) rules that determine whether an equation in the system is under-identified, just/exactly-identified, over-identified.
31) In a simultaneous equations model, "under-identified" refers to a situation in which _____,
a) an equation cannot be estimated because the other equations in the system do not have enough predetermined variables
b) an equation can be estimated using Ordinary Least Squares (OLS)
c) an equation can be estimated using Indirect Least Square (ILS) because the other equations in the system have just enough
predetermined variables
d) an equation can be estimated using Two-Stage Least Squares (2SLS) because the other equations in the system have more
than enough predetermined variables
32) In a simultaneous equations model, "exactly-identified" refers to a situation in which _____,
a) an equation cannot be estimated because the other equations in the system do not have enough predetermined variables
b) an equation can be estimated using Ordinary Least Squares (OLS)
c) an equation can be estimated using Indirect Least Square (ILS) because the other equations in the system have just enough
predetermined variables
d) an equation can be estimated using Two-Stage Least Squares (2SLS) because the other equations in the system have more
than enough predetermined variables
33) In a simultaneous equations model, "over-identified" refers to a situation in which _____,
a) an equation cannot be estimated because the other equations in the system do not have enough predetermined variables
b) an equation can be estimated using Ordinary Least Squares (OLS)
c) an equation can be estimated using Indirect Least Square (ILS) because the other equations in the system have just enough
predetermined variables
d) an equation can be estimated using Two-Stage Least Squares (2SLS) because the other equations in the system have more
than enough predetermined variables
34) When an economic model contains two or more equations, either ordinary least squares (OLS), indirect least squares
(ILS), or two-stage least squares (2SLS) may be the appropriate regression methodology. If each equation has one
endogenous variable, then simply estimate each equation separately using _____. If the equations share two or more
endogenous variables in common, then use _____ to correct simultaneous equations bias if the equations are _____identified, but _____ is needed if the equations are _____-identified.
a) ILS, OLS, under, 2SLS, over
b) OLS, ILS, exactly, 2SLS, over
c) 2SLS, OLS, over, ILS, under
d) OLS, 2SLS, over, ILS, exactly
35) Suppose you have a simultaneous equations model with two equations, demand and supply. Suppose that the
endogenous variables are Q and PQ, and both of these variables are in both equations. Suppose that the demand equation has
the additional predetermined variables I and Z, and the supply equation has the additional predetermined variables R and G.
Demand: Q = β0 + β1·PQ + β2·I + β3·Z + eD,
where "uD" is the error term in Demand
Supply:
Q = β4 + β5·PQ + β6·R + β7·G + eS,
where "uS" is the error term in Supply
You decide that you need to use two-stage least squares (2SLS) to estimate the supply equation. Put the following steps
of 2SLS in the correct order, 1 to 4, with 1 being the first step.
___ Replace PQ on the right-hand-side of the supply equation with its instrumental variable P Qhat.
___ Predict PQ using the regression of PQ on I, Z, R and G. Name the prediction “PQhat” (note that PQhat is
the instrumental variable for PQ)
___ Use OLS to estimate the β's in the supply equation, with PQhat in place of PQ.
___ Regress PQ on I, Z, R and G.
5
UNC-Wilmington
Department of Economics and Finance
ECN 377
Dr. Chris Dumas
36) Suppose you have a two equation model and you need to correct for simultaneous equations bias. In SAS, you should
use: a) PROC CORR
b) PROC SYSLIN 2SLS c) PROC REG d) DATA step
e) PROC AUTOREG
37) Suppose that you are estimating a simultaneous equations model using SAS. SAS uses a different term for the
predetermined variables in the model. In SAS, predetermined variables are called:
a) endogenous variables b) reduced-form variables c) instrument variables d) structural/behavioral variables
38) Which of the following situations require the use of a limited dependent variable model (such as probit)?
a) the Y variable indicates a category, such as male or female, or green or blue
b) the Y variable indicates a qualitative choice, such as yes or no
c) the Y variable is a binary variable, with values 0 or 1
d) an X variable indicates a category, such as male or female
d) all of the above
e) only a, b and c above
f) only a and d above
39) Limited Dependent Variable Models should be used when which of the following assumptions of OLS regression analysis
is violated?
a) The variance of the population error e is the same for all individuals in the population.
b) Each population error e is uncorrelated with (independent of) every other population error.
c) The dependent (Y) variable is a continuous, measurement variable.
d) The population error e is uncorrelated (is independent of) the X and Y variables in the model.
e) There is no perfect linear correlation between any two X variables in the model.
f) The model is correctly “specified.” (That is, all X variables that affect Y are included in the regression model equation, and
all X variables that do not affect Y are excluded from the regression equation.)
g) The distribution of the population error e is normal (bell-shaped) with a mean value of zero.
40) In the Probit regression model, the regression equation is used to predict:
a) the dependent variable, Y
b) one of the independent variables, X
d) the probability that the error term = 0
e) the probability that X = 0
c) the probability that Y = 1
41) In the Probit regression model, which function is used to translate the value of β0 +β1X1+β2X2+... into a value between 0
and 1?
a) the equation for the normal, bell curve (called “f”)
b) the integral of the equation for the normal, bell curve (called “F”)
c) the probability density function (p.d.f.) of the normal bell curve (called “f”)
d) the cumulative distribution function (c.d.f.) of the normal bell curve (called “F”)
e) both a and c
f) both b and d
42) In the Probit model, suppose that Prob(Y = 1) is given by F(Xindex). What, then, is Prob(Y = 0)?
a) F(Xindex)2
b) 1 - F(Xindex)
c) F(Xindex) – 1
d) log [F(Xindex)]
43) In the Probit model, which method is used to find the estimates of the coefficients (the β's) in the model equation?
a) Ordinary Least Squares (OLS) b) Weighted Least Squares (WLS) c) Indirect Least Squares (ILS)
d) Two-Stage Least Squares (2SLS)
e) Maximum Likelihood Estimation (MLE)
44) In the Probit model, why is the Maximum Likelihood Method (MLE) called “Maximum Likelihood”?
a) because it finds the β's that maximize the chances that Y = 1
b) because it finds the β's that maximize the chances that Y = 0
c) because it finds the β's that maximize the chances of obtaining the actual Y values in the dataset
d) because it finds the β's that maximize the changes of obtaining the actual X values in the dataset
45) In the Maximum Likelihood Method (MLE) equations of the Probit model, what does the capital Greek letter “pi” mean?
a) add together b) multiply together
c) it’s a constant, 3.14159
d) take a logarithm of a logarithm
6
UNC-Wilmington
Department of Economics and Finance
ECN 377
Dr. Chris Dumas
46) Suppose variable Y is an indicator variable with just two possible values, 0 and 1. Suppose that you use ordinary least
squares (OLS) to estimate a regression equation in which Y is the dependent variable and several other variables are the
independent (X) variables. Which problems could arise?
a) the estimates of the β's are biased
b) the estimates of the β's are inconsistent (the bias remains even when we increase sample size)
c) the error term (ehats) is heteroskedastic (the heteroskedasticity problem)
d) when we use the OLS model to make predictions, we can obtain predictions greater than 1 or less than 0, which makes no
sense, given that Y is supposed to be either 1 or 0
e) all of the above
47) Suppose we want to use a Probit model to predict the chances that the value of dependent variable Y will equal one (that
is, Prob(Y=1) ). Put the following steps of the Probit model prediction process in the correct order, 1 to 4, with 1 being the
first step:
____ plug Xindex into the F function to find F(Xindex)
____ note that Prob(Y=1) is equal to F(Xindex)
____ plug our (given) X values into Xindex = β0 + β 1X1+ β 2X2+...
____ find the MLE estimates of the β's
48) In the Probit model, what is meant by “the marginal effect of X”?
a) the change in Y due to a unit change in X
b) the change in Prob(Y=1) due to a unit change in X
c) the change in X due to a unit change in Y
d) the change in Prob(Y=1) due to a unit change in Prob(Y=0)
49) Suppose that you have estimated a Probit model. Now you want to find the marginal effect of X1 on Prob(Y=1). What is
the formula for the marginal effect?
a) β1 (that’s all; β1 is the marginal effect)
b) β1*Prob(X1=1)
c) β1*Prob(Y=1)
d) β1*[slope of F(Xindex)]
e) R2McFadden = 1 – (LU/LR)
50) In the Probit model, we cannot use an F-test to test the statistical significance of the model as a whole. Instead, we use
the _____________ test. a) McFadden b) Rank and Order c) Durbin-Watson d) Likelihood Ratio
51) Suppose you conduct a Likelihood Ratio test for a Probit model and find that LR test > LRcritical. What do you conclude?
a) the X’s in the model help to predict Prob(Y=1)
b) the X’s in the model don’t help to predict Prob(Y=1)
c) all β's in the model are zero
d) one or more of the β's in the model is not zero
e) both a and c
f) both b and c
g) both a and d
52) In the Probit model, which of the following measures how well the model fits the data (“Goodness of Fit”)?
a) the F-test b) the Likelihood Ratio test c) Adjusted R2 d) McFadden’s R2
Short Answer / Calculation Problems
1) Suppose you are estimating a Probit model and you would like to do a Likelihood Ratio (LR) test to determine the
statistical significance of the model as a whole. You have the following information n = 70, k = 6, P = 0.62 and
ln(LU) = -12.43.
(a) What are the null and alternative hypotheses for this test?
(b) Calculate the value of ln(LR) for this test. SHOW YOUR WORK.
(c) Calculate the value of LRtest for this test. SHOW YOUR WORK.
(d) Calculate the value of LRcritical for this test for a significance level of α = 0.05. SHOW YOUR WORK.
(e) What is the result of the LR test for a significance level of α = 0.05? SHOW YOUR WORK.
2) For the problem above, calculate the value of McFadden’s R2? SHOW YOUR WORK
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