ECO 155 Homework Three
Show your work and explain your answers!
1. Suppose that Lemurland produces only two goods and services: stuff
and landfill services). The relevant prices and quantities are giv
Homework Ten
Show your work and explain all your answers!
Important: When answering the questions below, you do not need to submit
your graphs just explain what would happen on the graph, i.e. which
c
Aggregate Demand and Aggregate Supply
1. Suppose the economy is operating in long-run equilibrium. If a positive
demand shock hits the economy, we would expect:
1. A) a short-run increase in real GDP
ECO 155
QUIZ 2
1.
Which of the following events could shift the demand curve for gasoline to the left?
a. The income of gasoline buyers rises, and gasoline is a normal good.
b. The income of gasoline
ECO 155: QUIZ 1
1. In baseball, when one manager decides to send in a pinch hitter, the other manager often
changes pitchers. This sometimes causes the first manager to send in a new pinch hitter.
Onc
Economic Significance
0 Economic Significance asks the question: is the effect of X-
important?
a It reflects common sense and /or researchs subjective Opinion.
0 It's possible for an estimator to be
Confidence Intervals
a [mother's height, father's height] is my subjective confidence interval
for the child's adult height.
0 In econometrics, we need more rigorous confidence intervals that are
ba
Confidence Intervals
0 Let's start with the estimator B.
0 Under Assumptions MLR.1-MLR.6, we know that
SELBJ) nkla
4. _ _ _
_' 7- :
Le-:tI.Jr'r_=e E- i'-.-'iu|tir_|+.=: Fiegressirjn February 1i],
Confidence Intervals
0 Confidence Intervals are more informative.
0 Confidence intervals are interval estimators that we put a confidence
level on
0 Example: I'm 80% sure that a child's adult height
Testing M ulti ple Restrictions
o It thus make sense to compare the SSR (SSRur) from the regression
before dropping the variables in question:
log(wage) : g + 51;: + g univ + 53 exper + e
a this is ca
Economic Significance vs. Statistical Significance
:- Can a coefficient be statistically insignificant but economically
significant?
0 A better question: how to interpret a large coefficient with a
Hypothesis about a Linear Combination of the Parameters
o More generally, we want to test: Hg : 35:; + bk = 0, where a and b
are constants.
c In the above example: a:b:1, j:1, k=2.
0 Define a new para
Testing IVI ulti ple Restrictions
o The Fstatistic:
F = (SSRr SSRur)/q
SSRur/(n k 1)
o It turns out that we know the distribution of F under Ho and
Assumptions MLR.1-MLR.6:
F N Fq1nk1
o Fq1n_k_1 is a
Testing a Single Linear Combination of the Parameters
0 Regression with interaction term
log (wage) : 50 + 51 married + [32 married >< female
+53 female + B4educ + 55 exper + e
o What is the effect of
Testing M ulti ple Restrictions
a We reject Hg is F is large: if it is larger than a critical value:
C0: = q, nk1,c:
where Fq1n_k_15 is the 1 a: quantile of F 1n_k_1.
I F 4-110: can be found in statis
a In STATA:
- gen minus_married_rna|e=married*(fema|e1)
a reg log(wage) married minus_married_male female educ exper
J
44*.
I
III
I|II|
R
LE-EtlH'E ['3 f'-.-'1IJ|t'Ir_I|+.=: Flay-assign FEL1-r'ljnr
What should be Reported?
in If only a couple a regressions with a small number of regressors are
performed. you can report in equation form:
lame) : 1.47 +0.067jc +0.077univ +0.005exper
(0.021) (0.002
Testing lVl ulti ple Restrictions
a The sum or squared residuals (SSR) turns out to be very useful.
0 Dropping variables increases SSR, because more variation in Y are
left unexplained.
a Dropping uni
0 Review
0 Confidence Interval
o Hypothesis Testing
0 Setting up Hypotheses
a Test Statistic and Critical Value
0 Statistical Significance and Economic Significance
0 Testing a Single Linear Combinati
Testing the Overall Significance of a Model
o A special multiple hypotheses testing problem is testing
Hg : all the slope coefficients are zero
a When we do this, we are testing the overall signific
Trick STATA into Reporting What We Want
a Run the modified model: Y:-+d()q)+-+;(X;)+-+e
0 Then 65 and se() are reported in the modified regression.
a The null hypothesis becomes H0 : f9 : 0 can be t
Review
Confidence Interval
Hypothesis Testing
Setting up Hypotheses
Test Statistic and Critical Value
Statistical Significance and Economic Significance
Testing a Single Linear Combination of the Para
Testing the Overall Significance of a Model
a In this special case, Ftest can be formulated just the same.
0 Some special features:
in In the restricted model, we drop all the regressors, so no variat
Economic Significance vs. Statistical Significance
0 Example: when studying the participation rate (measured in
percentage point) of the retirement plan, we run the regression: reg
prate mrate age t
Confidence Interval
Hypothesis Testing
Setting up Hypotheses
Test Statistic and Critical Value
Statistical Significance and Economic Significance
Testing a Single Linear Combination of the Parameters
Testing M ulti ple Restrictions
o The Ftest uses exactly that intuition:
(555% SSRur)/q
F
SSRW/(n k 1)
o The numerator measures how much SSR increases when we drop the
regressors in question (jc and
Relationship Between Ftests and ttests
o It is possible that none of the individual coefficients are significant
(ttest fail to reject) but or variables are jointly significant (Ftest
rejects).
o It i
Statistical Significance
a An estimator, 3;, of a regression coefficient is called significant at
level a" if the following H0 is rejected by a twosided ttest of level cu:
H02 jZO.
0 Significance defi