Transcript April 2 - UCSB Economics

More from Chapters 1-3
Marginal analysis
Today: Government size; Marginal
analysis; Empirical tools; Edgeworth
boxes
Today: Four “mini-lectures”
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Finish Chapter 1
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Marginal analysis
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A review of what marginal means
Chapter 2
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Introduction to government size
Causation versus correlation
Statistical tools and studies
Begin Chapter 3
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Edgeworth boxes
Size of government
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The constitution gives the federal government
the right to collect taxes, in order to fund
projects
State and local governments can do a broad
range of activities, subject to provisions in the
Constitution
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10th Amendment: Limited power in the federal
government
Local governments derive power to tax and spend
from the states
Size of government
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How to measure the size of government
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Number of workers
Annual expenditures
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Types of government expenditure
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Purchases of goods and services
Transfers of income
Interest payments (on national debt)
Budget documents
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Unified budget (itemizes government’s expenditures and
revenues)
Regulatory budget (includes costs due to regulations)
(Table and figures)
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Table 1.1, p. 9
Figure 1.1, p. 10
Figures 1.2 and 1.3, p. 11
Figures 1.4 and 1.5, p. 13
Summary: Size of government
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Government spending in the US, as a
percentage of GDP, has increased in the last
50 years
Other industrialized countries spend more
than the US (as a percentage of GDP)
Composition of taxing and spending has
changed in the last 50 years
Marginal analysis
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Quick look at marginal analysis
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Important in many tools we will use this quarter
We look at “typical” cases
Marginal means “for one more unit” or “for a
small change”
Mathematically, marginal analysis uses
derivatives
Marginal analysis

We will look at four topics related to marginal
analysis
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Marginal utility and diminishing marginal utility
The rational spending rule
Marginal rate of substitution and utility
maximization
Marginal cost, using calculus
Example: Marginal utility
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Marginal utility (MU) tells us how much
additional utility gained when we consume
one more unit of the good

For this class, typically assume that marginal
benefit of a good is always positive
Example: Diminishing marginal utility
Banana quantity
(bananas)
Total utility (utils)
0
0
Marginal utility
(utils/banana)
70
1
70
50
2
120
30
3
150
10
4
160
5
5
165
Diminishing marginal utility
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Notice that marginal utility is decreasing as
the number of bananas increases
Economists typically assume diminishing
marginal utility, since this is consistent with
actual behavior
The rational spending rule
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If diminishing marginal utility is true, we can
derive a rational spending rule
The rational spending rule: The marginal
utility of the last dollar spent for each good
is equal
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Goods A and B: MUA / pA = MUB / pB
Exceptions exist when goods are indivisible or
when no money is spent on some goods (we will
usually ignore this)
The rational spending rule
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Why is the rational spending rule true with
diminishing marginal utility?
Suppose that the rational spending rule is not
true
We will show that utility can be increased
when the rational spending rule does not hold
true
The rational spending rule
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Suppose the MU per dollar spent was higher for
good A than for good B
I can spend one more dollar on good A and one less
dollar on good B
Since MU per dollar spent is higher for good A than
for good B, total utility must increase
Thus, with diminishing MU, any total purchases that
are not consistent with the rational spending rule
cannot maximize utility
The rational spending rule
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The rational spending rule helps us derive an
individual’s demand for a good
Example: Apples
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Suppose the price of apples goes up
Without changing spending, this person’s MU per dollar
spent for apples goes down
To re-optimize, the number of apples purchased must go
down
Thus, as price goes up, quantity demanded decreases
MRS and utility maximization
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Utility maximization
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Necessary condition is
that marginal rate of
substitution of two goods
is equal to the slope of
the indifference curve (at
the same point)
At point E1, the
necessary condition
holds
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Utility is maximized here
Marginal cost, using calculus
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Suppose that a firm has a cost function
denoted by TC = x2 + 3x + 500, with x
denoting quantity produced
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Note fixed costs are 500
Marginal cost is the derivative of TC with
respect to quantity
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MC = dTC / dx = 2x + 3
Notice MC is increasing in x in this example
Summary: Marginal analysis
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Marginal means “for one more unit” or “for a
small change”
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We can use derivatives for smooth functions
Marginal analysis is important in many
economic tools
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Utility
Rational spending rule
MRS
Cost functions
Empirical tools
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Economic models are as good as their
assumptions
Empirical tests are needed to show
consistency with good theories
Empirical tests can also show that real life is
unlike the theory
Causation
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Economists use mathematical and statistical
tools to try to find the effect of causation
between two events
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For example, eating unsafe food leads you to get
sick
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How many days of work are lost by sickness due to
unsafe food?
The causation is not the other direction
Causation
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Sometimes, causation is unclear
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Stock prices in the United States and temperature
in Antarctica
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No clear causation
Number of police officers in a city and number of
crimes
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Do more police officers lead to less crime?
Does more crime lead to more police officers?
Probably some of both
Empirical tools
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There are many types of empirical tools
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Randomized study
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Observational study
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Relies on econometric tools
Important that bias is removed
Quasi-experimental study
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Not easy for economists to do
Mimics random assignment of randomized study
Simulations
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Often done when the above tools cannot be used
Randomized study
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Subjects are randomly assigned to one of two
groups
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Control group
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Treatment group
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Item or action in question not done to this group
Item or action in question done to this group
Randomization usually eliminates bias
Some pitfalls of randomized studies
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Ethical issues
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Is it ethical to run experiments when only some
people are eligible to receive the treatment?
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Example: New treatment for AIDS
Technical problems
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Will people do as told?
Some pitfalls of randomized studies
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Impact of limited duration of experiment
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Often difficult to determine long-run effect from
short experiments
Generalization of results to other populations,
settings, and related treatments
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Example: Effects of giving surfboards to students
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UCSB students
UC Merced students
Observational study
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Observational studies rely on data that is not
part of a randomized study
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Surveys
Administrative records
Governmental data
Regression analysis is the main tool to
analyze observational data
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Controls are included to try to reduce bias
Conducting an observational study
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L = α0 + α1wn + α2X1 + … + αnXn + ε
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Dependent variable
Independent variables
Parameters
Stochastic error term
L
Regression analysis
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Here, we assume
changes in wn lead
to changes in L
Regression line
Standard error
Intercept
is α0
Slope
is α1
α0
wn
Regression analysis
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More confidence in the data points in diagram B
than in diagram C
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Less dispersion in diagram B
Interpreting the parameters
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L = α0 + α1wn + α2X1 + … + αn+1Xn + ε
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∂L / ∂wn = α1
∂L / ∂X1 = α2
Etc.
Types of data
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Cross-sectional data
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Time-series data
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“Data that contain information on individual entities at a
given point in time” (R/G p. 25)
“Data that contain information on an individual entity at
different points in time” (R/G p. 25)
Panel data
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Combines features of cross-sectional and time-series data
“Data that contain information on individual entities at
different points of time” (R/G p. 25)
Note: Emphasis is mine in these definitions
Pitfalls of observational studies
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Data collected in non-experimental setting
Specification issues
Data collected in non-experimental setting
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Could lead to bias if not careful
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Example: Education
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People with higher education levels tend to have higher
levels of other kinds of human capital
This can make returns to education look higher than
they really are
Additional controls may lower bias

Education example: If we had human capital
characteristics, we could include them in our
regression analysis
Specification issues
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Does the equation have the correct form?
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Incorrect specification could lead to biased results
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Example: The correct form is a quadratic equation, but
you estimate a linear regression
Quasi-experimental studies
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Quasi-experimental study
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Also known as a natural experiment
Observational study relying on circumstances
outside researcher’s control to mimic random
assignment
Example of quasi-experimental study
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A new college opens in a city
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Will this lead to more people in this city to go to
college?
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Probably
These additional people go to college by the
opening of the new school
We can see the earnings differences of these
people in this city against similar people in
another city with no college
Conducting a quasi-experimental study
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Three methods
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Difference-in-difference quasi-experiments
Instrumental variables quasi-experiments
Regression-discontinuity quasi-experiments
Difference-in-difference method
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Find two similar groups of people
One group gets treatment; the other does not
Compare the differences in the two groups
Instrumental variables (IV) method
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Assignment to treatment group is not always
random
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This can lead to bias
IV analysis finds a third variable that has two
characteristics
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Directly affects entry into the treatment group
Is not directly correlated with the outcome variable
Regression-discontinuity method
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Have a strict cut-off point to get into treatment
group
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Examples: Income, test score
Compare those that are very close to the cutoff point
Pitfalls of quasi-experimental studies
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Assignment to control and treatment groups
may not be random
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Not applicable to all research questions
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Researcher needs to justify why the quasiexperiment avoids bias
Data not always available for a research question
Generalization of results to other settings and
treatments
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As before: Surfboards to UCSB students and UC
Merced students
Summary: Empirical tools
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Empirical tools can be useful to test
economic theory
Bias can be problematic in studies that are
not randomized
Controls in observational studies may lower
bias
Quasi-experimental studies can act like
randomized experiments
Edgeworth boxes
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Begin study of welfare economics
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Pure exchange economy
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R/G chapter 3
For an in-depth look, see also Varian’s Intermediate
Micro book, chapters 30-33
We begin today with Edgeworth boxes
Edgeworth boxes
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Simple study of distribution
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We will make extensive use of Edgeworth boxes,
Pareto efficiency, and Pareto improvements
Edgeworth boxes are used for a two-person
economy
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Bottom left of Edgeworth box is origin for one person
Top right of Edgeworth box is origin for other person
See Figure 3.1, p. 34
Indifference curves
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See Figure 3.2, p. 35
Pareto efficiency
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Nobody can be made better off without
making another person worse off
In cases with “standard” indifference curves
(ICs), the two ICs will be tangent to each
other when Pareto efficiency is achieved
Pareto improvement
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Reallocation of goods or resources that
meets the following requirement
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At least one person is made better off without
anybody else being made worse off
See Figures 3.3-3.6 (p. 35-37)
Contract curve
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The set of all Pareto efficient points
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Usually goes from one person’s origin to the
other person’s origin
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See Figure 3.7, p. 38
Origin of each person is Pareto efficient
Note that efficient points may or may not be
“fair” in your mind
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Fairness is often not a topic brought up by
economists
More on “fairness” later
Pareto Efficiency in Consumption
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At each point on the contract curve, the
marginal rates of substitution for both Adam
and Eve are equal
Adam
MRSaf
Eve
= MRSaf
Summary: Edgeworth boxes
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Two-person exchange economy
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Edgeworth box is the main tool used
Pareto efficiency and Pareto improvements
Contract curve
What have we learned today?
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Size of government
Some tools that are useful
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Marginal analysis
Empirical tools to test theory
Edgeworth boxes