This document contains an economics homework assignment involving calculations of rates of change, derivatives, and demand equations. It also discusses using regression analysis to examine the relationship between economic variables like interest rates and unemployment, and the percentage of votes received by incumbent presidents. The homework involves computing averages, estimating derivatives with numerical methods, finding equations of tangent lines, and using ordinary least squares regression on transformed logarithmic variables.

1. 1
Quant Tools for Bus & Econ – ECON 220-02 (11273)
Homework 6
Show your work
Section 10.4 (6 points)
1. The table below shows U.S. daily imports from Mexico, for
2001-2009 (t=1 represents
the start of 2001):
t
(year since 2000)
1 2 3 4 5 6 7 8 9
I(t)
(million barrels)
1.4 1.35 1.5 1.55 1.6 1.5 1.5 1.5 1.2
a. Use the data in the table above to compute the average rate of
change I(t) over the

2. period 2001-2006. Interpret the result (3 points)
2. The median home price in the U.S. over the perio2003-2011
can be approximated by
�(�) = −5�2 + 75� − 30 thousand dollars (3 ≤ t ≤ 11),
Where t is the time in years since the start of 2000.
a. What was the average rate of change of the median home
price from the start of
2007 to the start of 2009? (3 points)
2

3. Section 10.5 (16 points)
In the questions below, use the balanced difference quotient
method to estimate the
derivative of the given function at the indicated point. (Hint,
use h = 0.0001)
(3 points each)
3. �(�) =
1
�3
; estimate �′(−2)
4. � = 1 − �2; estimate
ⅆ�
ⅆ�
|
�=−1

4. 5. Use any method to
(a)estimate the slope of the tangent to the graph of the function
�(�) = 2� + 4 ; � = −1
at the point with the given x-coordinate (� = −1) (3 points)
3

5. (b) find an equation of the tangent line in part (a). (3 points)
6. Suppose the demand for a new brand of sneakers is given by
� =
5,000,000
�
Where � is the price per pair of sneakers, in dollars, and q, is
the number of pairs of
sneakers that can be sold at price �
a. Find �(100) (1 point)

6. b. Estimate �′(100) Using ordinary difference quotient and the
h = 0.0001 (3 points)
9-2 FINAL ECONOMETRIC ANALYSIS
9-2 FINAL ECONOMETRIC ANALYSIS 12
9 -2 FINAL ECONOMETRIC ANALYSIS
ECO 620 FINAL PROGECT THREE
“Do economic events affect the outcome of
elections in U.S?”
Description/ Introduction
I would like establish whether economic events affect the
outcome of elections in U.S. The dependent variable for this
study would be the percentage of votes garnered by incumbent.
The explanatory variables would be interest rate change and
unemployment rate change. In this study, the research question
would be, “Do economic events affect the outcome of
elections?” This particular research question is relevant since it
seeks to establish the relationship between economic events and
political outcomes. In this case, this study will of both academic
and political interest. The outcome of this study will help to fill
the knowledge gap existing in the field of political economy
whereby no appropriate study linking economic events and
political outcomes has been conducted in recent times

7. (Bateman, 2011).
The target audiences for this study would be both technical
and non-technical. These audiences would include political
decision makers, economic policy makers and the general
public. Political decision makers would be interested in
understanding what affects the outcome of elections. This
means that the outcome of this study will be of great help to the
political decision makers since it will help them to come up
with appropriate campaign manifesto in the hope of garnering
more votes. However, it is imperative to note that political
decision makers need not to exclusively use the results of this
study when making their political decisions. Other factors also
need to be considered. For example, in the event that it is
established that lower unemployment rates favor election
outcome, then an expansionary monetary policy may not be the
best solution since it has some negative consequences on the
economy. An expansionary monetary policy may cause the
country’s exchange rate to decline and hence it is not an
appropriate tool for lowering unemployment rates. Thus
political decision makers need to be cautious when applying the
results of this study.
Economic policy makers would be interested in knowing
whether the economic policies they formulate are appropriate
for the electorate. For example, a policy to lower interest rates
may be beneficial to individuals as it will create an incentive to
borrow and invest. Policy makers are appointed by the
government and hence they will be interested on the outcome of
this study so as formulate appropriate policies so as ensure that
the incumbent remains in power (Bateman, 2011). Finally, the
outcome of this study will also help to enlighten the general
public on factors to consider when electing the incumbent.
Literature Review
Some researchers have employed economic methods and
techniques such as statistical analysis, theoretical analysis and
the econometric analysis to establish the relationship between
economic events and political outcomes. Theoretical wise,

8. economist Samuelson is credited for attempting to theoretically
explain how government economic decisions affect political
outcomes. Samuelson formulated the theory of optimal public
expenditure in a bid to explain how government policies affect
social welfare of the citizens (Ricardo, 2001). However, his
study lacked relevant empirical data to justify his claim.
Akerman, another economist, attempted to use statistical
analysis in finding out how economic events affect political
outcomes. He collected and analyzed the US data in order to
find out whether the fundamental economic cycles referred to as
3 ½ -year Kitchin cycles were connected with the institutional
change (Bateman, 2011). He found out that actually the 3 ½ -
year Kitchin cycles represented politico-economy cycles that
spanned the four years of presidential elections in the US
(Bateman, 2011). The results of his findings showed that indeed
changes in factors affecting real interest rates and employment
had influence on the presidential election outcome. Other
researchers have attempted to employ econometric analysis to
find out whether economic events affect political outcomes. For
instance, Gary Smith obtained a regression model linking
unemployment rate change and percentage of votes garnered by
the incumbent by using the results of the US presidential
elections for four yearly periods between 1928 and 1980
(Bateman, 2011). He used the percentage of votes garnered by
the incumbent as the dependent variable and unemployment rate
change as the dependent variable. The outcome of his study
showed that a decline in unemployment rate positively
influenced the percentage of votes garnered by the incumbent
(Bateman, 2011).
Some methods and techniques that have been used in the
past are not appropriate for this study. For instance, focusing on
the theoretical aspects without taking into consideration the
empirical evidence may lead to wrong conclusions being drawn
(Creswell & Plano Clark, 2007). Some of the empirical
techniques used also relied on obsolete data and therefore the
results of the study may not make economic sense today. But

9. nevertheless, the past studies provide great insights into the
topic. In this study, the hypothesis to be tested would be
whether interest rate change and unemployment rate change
affect the outcome of presidential elections. This hypothesis can
be translated into an empirical model by gathering data of the
specific variables and obtaining a regression linking these
variables (Baltagi, 2011).
Data ONE
The data on various variables will be used to obtain the
empirical model. The data on economic variables will be
obtained from each state in the United States. Each state in US
has an archive of data collected over the years. The advantage
of state-level data is the fact that it is more representative and
hence it is more likely to improve the statistical significance of
the results. The regression model is then estimated using this
data. The regression results to be used in explaining the
outcome of the study include the coefficients of estimates, t-
ratios, R2, F-values, standard errors and p-values (Baltagi,
2011). A priori, I expect a negative relationship unemployment
rate and the percentage of votes garnered by the incumbent.
This relationship implies that an increase in unemployment rate
will lead to a decline in votes garnered by the incumbent. How
this is just a priori expectation and not necessarily true.
The US election results data will be obtained from both
online and print resources. The online resources to be utilized
include Federal Election Commission, American Presidency
Project: Presidential Election Data, Dave Leip’s Atlas of U.S.
Presidential Elections, National Archives: Historical Election
Results and Office of the Historian websites. The print sources
to be used in the study include various book and journal articles
such as the Guide to U.S. Elections (6th ed) handbook published
in 2010 by CQ Press, The Election Book: A Statistical Portrait
of Voting in America published in 1993 by Bernan Press, A
Statistical History of the American Electorate written by Jerrold
Rusk and published in 2001 by CQ Press and the Presidential
Elections: 1789-2008 book published in 2010 by CQ Press. Both

10. the online and print resources will provide crucial election
results data to be used in the study.
Data-TWO
The data to be used in this study will be obtained from the
secondary sources. Secondary data is readily available from
various sources (Creswell & Plano Clark, 2007). However,
secondary data may impose some limitations on the choice of
empirical method. First, secondary data is mainly collected for a
general purpose and thus inappropriate for a specific study
(Özerdem & Bowd, 2010). This means that secondary data may
not answer our specific research question. For example, if we
intend to conduct a study by relying on secondary data collected
over the past forty years and the only relevant data available is
for the past thirty years then this means that we our results of
the study will be compromised. Second, secondary data is
subject to errors or misinterpretation based on data collection
methods that were used (Özerdem & Bowd, 2010). The errors in
secondary data will have a negative impact on the results of the
study
Finally, secondary data collected may be lacking the
required quality and sometimes the variables are expressed in an
inappropriate form (Creswell & Plano Clark, 2007). Quality
data refers to the data that is reliable and relevant. Reliability in
this case means having an appropriate definition of the variable.
In essence, the variables should be expressed in a form that can
be easily utilized by the researcher. Absence of quality
secondary data may lead to poor estimation of the regression
model. In general, weaknesses of secondary data will have a
negative impact on the overall regression results.
To address this issue, I intend to use the most reliable
secondary sources of information. In this regard, I will utilize a
variety of both online and print resources especially when
obtaining the US election results data. Examples of online
resources that I intend to use include Federal Election
Commission, American Presidency Project: Presidential
Election Data, Dave Leip’s Atlas of U.S. Presidential Elections,

11. National Archives: Historical Election Results and Office of the
Historian websites. I will also make use of print sources such as
the Guide to U.S. Elections (6th ed) handbook. I intend to
obtain data for the other variables from each state in the United
States. The advantage of state-level data is the fact that they are
reliable and hence they are likely to produce statistically
significant results.
Empirical Approach
I intend to use the ordinary least squares (OLS) estimation
technique to estimate my empirical model. The ordinary least
square (OLS) regression shows the relationship between the
dependent variable and explanatory variables (Baltagi, 2011). In
this case, the assumption made when using the OLS technique is
that the dependent variable is a linear function of explanatory
variables (Baltagi, 2011). Therefore it would be appropriate to
use this method since it would enable us to establish the linear
relationship between interest rate change, unemployment rate
change and percentage of votes garnered by the incumbent.
However, OLS estimation technique has got some
disadvantages. First, presence of outliers, i.e., extremely high or
small values for the dependent variable in comparison to the
values of explanatory variables may lead to poor estimation of
the regression model (Baltagi, 2011). Second, sometimes the
explanatory variables are correlated and this may lead to a
biasness and inconsistency of estimated coefficients (Baltagi,
2011). The estimated coefficients may have wrong signs which
do not make economic sense. Finally, OLS estimation technique
assumes that dependent and explanatory variables are always
linearly related (Baltagi, 2011). This is not always true in
reality since most systems are non-linear. Other possible
alternative methods that can be used include the logit and probit
models (Baltagi, 2011). These models are preferred over OLS in
certain circumstances. For example, the logit model allows the
properties of a linear regression model to be exploited. The
model specification is as follows:
-The independent variable (Y) is the percentage of votes

12. garnered by the incumbent.
- The explanatory variables are:
a) Interest rates (X2) and
b) Unemployment rate (X3).
Percentage of votes garnered by the incumbent is taken to
be the dependent variable since it is influenced by the other two
variables.
Since the above variables are expressed in levels, I have
converted each of them into a log to obtain the log-transformed
model shown below:
InYt = B1+B2 InX2t +B3 InX3t + ut
Note that:
InYt = natural log of Y
InX2t = natural log of X2
InX3t = natural log of X3
A log-transformed model helps to produce more consistent
results since it eliminates heteroskedasticity. Heteroskedasticity
refers to the inequality in variability of variables across a range
of data values (Baltagi, 2011). Converting variables into logs
helps to eliminate heteroskedasticity. The coefficients of
variables in the log-transformed model can also be interpreted
as elasticities. In this case, since we are regressing Y on X2 and
X3 , the coefficient on X2 is interpreted as a percent change in
Y holding X3 . Similarly, the coefficient on X3 is interpreted
as a percent change in Y holding X2 .
Results and Robustness Check
-The preliminary results are as follows:
InYt = 1.54- 0.023InX2t -0.075 InX3t
The interpretation of each coefficient is as follows:
· The coefficient on X2 tells us that one percent increase in
interest rates holding X3 constant leads to 2.3% decline in
votes garnered by the incumbent.
· The coefficient on X3 tells us that one percent increase in
unemployment rate holding X2 constant leads to 7.5% decline

13. in votes garnered by the incumbent.
I had earlier predicted a negative relationship between the
dependent variable and the explanatory variables and the
preliminary results indicate that indeed the explanatory
variables negatively influence the dependent variable. Hence
the regression results are significant.
I had also anticipated existence of correlation between
the two explanatory variables. Usually, OLS estimation
technique assumes that there is absence of multicollinearity
between the explanatory variables. To test for the presence and
severity of multicollinearity, we compute the variance inflation
factor (VIF) of various explanatory variables (Baltagi, 2011). If
the variance inflation factor lies between 1 and 10 then there is
no multicollinearity. If the variance inflation factor is less than
1 or greater than there is multicollinearity (Baltagi, 2011).
Recommendations on study and Results
Just like the results of studies that have been conducted before,
the results of this study can be a potential or a pitfall to the
entire research. The primary objective of this study is to
establish the role played by sensitivity analysis in future
success of a business. However, the results of the study may not
be accurate enough to help us make the right judgment about the
study. It is therefore important to present some of the
recommendations to the results of this study so that I can draw
right conclusions from the study.
The first recommendation has to do with making a
decision on which results should be offered for the study and
eligibility of participants. For this study, it will be important to
keep in mind that the study is on sensitivity analysis and most
of the issues in the study can only be identified during the
review process (Doubilet et al., 1984). When the results of the
sensitivity analysis are not affected by different decisions made
during the research, then the researcher needs to consider those

14. results to significant or have a high degree of certainty. In case
of missing information, there will be need to find the missing
information from other resources. In case this fails to work out,
the results will have to be interpreted with a lot of caution.
Furthermore, the reporting of the results should be done with
the help of a summary table (Doubilet et al., 1984). This makes
it easier to interpret the results and avoid confusion which could
be risky for the business.
Comparing these recommendations to those presented in
literature review reveals a very slight difference. From
literature on the concept of sensitivity analysis, it is evident
that sensitivity analysis can be approached in different ways.
The brute force method is suitable for a small model
(Caracotsios & Stewart, 1985). Basically using method involves
changing initial data and solving the model again to see a
change a change in the results.
References
Baltagi, B. (2011). Econometrics. Berlin: Springer.
Bateman, B. (2011). Tocqueville's Political Economy. History
Of Political Economy, 43(4), 769. 770.
http://dx.doi.org/10.1215/00182702-1430319
Baltagi, B. (2011). Econometrics. Berlin: Springer.
Caracotsios, M., & Stewart, W. E. (1985). Sensitivity analysis
of initial value problems with mixed ODEs and algebraic
equations. Computers & Chemical Engineering, 9(4): 359-
365.
Creswell, J., & Plano Clark, V. (2007). Designing and
conducting mixed methods research.
Thousand Oaks, Calif.: SAGE Publications.

15. Decision Making, 5(2): 157- 177
Doubilet, P., Begg, C. B., Weinstein, M. C., Braun, P., &
McNeil, B. J. (1984). Probabilistic sensitivity analysis
using Monte Carlo simulation. A practical approach. Medical
decision making: an international journal of the Society
for Medical
Ricardo, D. (2001). On the principles of political economy and
taxation. London: Electric Book
Özerdem, A., & Bowd, R. (2010). Participatory research
methodologies. Farnham,
England: Ashgate.
.