More useful tools for public
finance
Today: Size of government
Expected value
Marginal analysis
Empirical tools
Crashers?
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I should receive the waitlist from the
Undergraduate Office on Monday
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Go through list of people from here on
Monday
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No add codes given until next week
Please let me know if you are now enrolled in the
class
New crashers?
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Check with me after class
Last time
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Ground rules of this class
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If you were not here Mon., look at class website
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http://econ.ucsb.edu/~hartman/
You can find syllabus and lecture slides on-line
Introduction to Econ 130
Introduction to public finance
The role of government in public finance
Today: Four topics

Size of government


Expected value


Useful in topics like health care
Marginal analysis


How big is it, and how has it changed?
Useful in many topics in economics
Empirical tools

Regression analysis is the most common
statistical tool used
Size of government


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


10th Amendment: Limited power in the federal
government
Local governments derive power to tax and spend
from the states
Size of government

How to measure the size of government


Number of workers
Annual expenditures

Types of government expenditure




Purchases of goods and services
Transfers of income
Interest payments (on national debt)
Budget documents


Unified budget (itemizes government’s expenditures and
revenues)
Regulatory budget (includes costs due to regulations)
Government expenditures, select years
1
2
3
4
Total
Expenditures
(billions)
2005 Dollars
(billions)*
2005 Dollars
per capita
Percent of
GDP
1960
123
655
3,627
24.3%
1970
295
1,201
5,858
28.4%
1980
843
1,749
7,679
30.2%
1990
1,873
2,574
10,289
32.2%
2000
2,887
3,237
11,461
29.4%
2005
3,876
3,876
13,066
31.1%
*Conversion to 2005 dollars done using the GDP deflator
Source: Calculations based on Economic Report of the President, 2006
(Washington, DC: US Government Printing Office, 2006), pp. 280, 284, 323,
379
Gov’t expenditures, selected countries
Figure 1.1: Government expenditures as a percentage of
Gross Domestic Product (2005, selected countries)
0.6
0.5
0.4
0.3
0.2
0.1
United
States
0
Sweden
France
Germany
United Kingdom
Canada
Japan
Australia
Source: Organization for Economic Cooperation and Development [2006]. Figures are for 2005.
Federal
expenditures
Figure 1.2: Composition of federal expenditures (1965
and 2005)
100%
90%
Note increase in
Social Security,
Medicare and
Income Security
80%
70%
Other
Net interest
60%
Note
Social security
decline in
Defense
Income security
50%
Medicare
Health
40%
Defense
30%
20%
10%
0%
1965
2005
Source: Economic Report of the President [2006, p. 377].
State and
local
expenditures
Figure 1.3 Composition of state and local expenditures
(1965 and 2002)
100%
90%
80%
Increase in
public
welfare
Decline in
highways
70%
60%
Other
Public welfare
50%
Highways
Education
40%
30%
20%
10%
0%
1965
2002
Source: Economic Report of the President [2006, p. 383].
Figure 1.4: Composition of federal taxes
(1965 and 2005)
Federal taxes
Social insurance
and individual income
tax have become
more important
Corporate and other
taxes have become
less important
100%
90%
80%
70%
60%
Other
Social insurance
50%
Corporate tax
40%
Individual income
tax
30%
20%
10%
0%
1965
2005
Source: Economic Report of the President [2006, p. 377].
State and
local taxes
Figure 1.5: Composition of state and local
taxes (1965 and 2002)
100%
90%
Individual tax
more important
80%
Other
70%
Grants from
federal
government
Corporation
tax
60%
50%
Inidividual
income tax
40%
Sales tax
30%
Property tax
20%
10%
Property tax
less important
0%
1965
2002
Source: Economic Report of the President [2006, p. 383].
Summary: Size of government



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
Mathematical tools

Two mathematical tools will be important
throughout the quarter


Expected value
Marginal analysis

Think of marginal and derivative in the same way
Expected value

Expected value is an average of all possible
outcomes


Weights are determined by probabilities
Formula for two possible outcomes

EV = (Probability of outcome 1)  (Payout 1) +
(Probability of outcome 2)  (Payout 2)
Expected value example






Draw cards from deck of cards
Draw heart and receive $12
Draw spade, diamond or club and lose $4
Probability of drawing heart is 13/52 = ¼
Probability of drawing spade, diamond or club
is 39/52 = ¾
EV = (1/4)($12) + (3/4)(-$4) = $0

No expected gain or loss from this game
Another example

Insurance buying



People are usually risk averse
This type of person will accept a lower expected
value in return for less risk
Numerical example


Income of $100,000 with probability 0.8
Income of $40,000 with probability 0.2
Expected income

Expected income is the weighted sum of the
two possible outcomes


$100,000  0.8 + $40,000  0.2 = $88,000
A risk averse person would be willing to take
some amount below $88,000 with certainty

How much below $88,000? Wait until Chapter 8
Marginal analysis

Quick look at marginal analysis




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

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


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


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


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



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




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


The rational spending rule helps us derive an
individual’s demand for a good
Example: Apples




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

Utility maximization


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

Utility is maximized here
Marginal cost, using calculus

Suppose that a firm has a cost function
denoted by TC = x2 + 3x + 500, with x
denoting quantity produced



Variable costs are x2 + 3x
Fixed costs are 500
Marginal cost is the derivative of TC with
respect to quantity


MC = dTC / dx = 2x + 3
Notice MC is increasing in x in this example
Summary: Mathematical tools


Expected value is the weighted average of all
possible outcomes
Marginal means “for one more unit” or “for a
small change”


We can use derivatives for smooth functions
Marginal analysis is important in many
economic tools, such as utility, the rational
spending rule, MRS, and cost functions
Empirical tools



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

Economists use mathematical and statistical
tools to try to find the effect of causation
between two events

For example, eating unsafe food leads you to get
sick


How many days of work are lost by sickness due to
unsafe food?
The causation is not the other direction
Causation

Sometimes, causation is unclear

Stock prices in the United States and temperature
in Antarctica


No clear causation
Number of police officers in a city and number of
crimes



Do more police officers lead to less crime?
Does more crime lead to more police officers?
Probably some of both
Empirical tools

There are many types of empirical tools

Randomized study


Observational study



Relies on econometric tools
Important that bias is removed
Quasi-experimental study


Not easy for economists to do
Mimics random assignment of randomized study
Simulations

Often done when the above tools cannot be used
Randomized study

Subjects are randomly assigned to one of two
groups

Control group


Treatment group


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

Ethical issues

Is it ethical to run experiments when only some
people are eligible to receive the treatment?


Example: New treatment for AIDS
Technical problems

Will people do as told?
Some pitfalls of randomized studies

Impact of limited duration of experiment


Often difficult to determine long-run effect from
short experiments
Generalization of results to other populations,
settings, and related treatments

Example: Effects of giving surfboards to students


UCSB students
UC Merced students
Observational study

Observational studies rely on data that is not
part of a randomized study




Surveys
Administrative records
Governmental data
Regression analysis is the main tool to
analyze observational data

Controls are included to try to reduce bias
Conducting an observational study

L = α0 + α1wn + α2X1 + … + αnXn + ε





Dependent variable
Independent variables
Parameters
Stochastic error term
L
Regression analysis



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

More confidence in the data points in diagram B
than in diagram C

Less dispersion in diagram B
Interpreting the parameters

L = α0 + α1wn + α2X1 + … + αn+1Xn + ε



∂L / ∂wn = α1
∂L / ∂X1 = α2
Etc.
Types of data

Cross-sectional data


Time-series data


“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


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


Data collected in non-experimental setting
Specification issues
Data collected in non-experimental setting

Could lead to bias if not careful

Example: Education



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

Does the equation have the correct form?

Incorrect specification could lead to biased results

Example: The correct form is a quadratic equation, but
you estimate a linear regression
Quasi-experimental studies

Quasi-experimental study


Also known as a natural experiment
Observational study relying on circumstances
outside researcher’s control to mimic random
assignment
Example of quasi-experimental study

A new college opens in a city

Will this lead to more people in this city to go to
college?



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

Three methods




Difference-in-difference quasi-experiments
Instrumental variables quasi-experiments
Regression-discontinuity quasi-experiments
We will focus only on the first one

These topics are covered more extensively in the
econometrics sequence
Difference-in-difference method



Find two similar groups of people
One group gets treatment; the other does not
Compare the differences in the two groups
Difference-in-difference example

Example: Two groups of college freshmen






Assume both groups have similar characteristics
One group is induced to exercise more
The other group is not induced to exercise more
Exercise group: Average weight gain of 2 pounds in
freshman year
Non-exercise group: Average weight gain of 7 pounds in
freshman year
Difference-in-difference estimate: 2 – 7 = –5

Interpretation: Additional exercise leads to average of 5
fewer pounds gained per person in freshman year
Pitfalls of quasi-experimental studies

Assignment to control and treatment groups
may not be random


Not applicable to all research questions


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

As before: Surfboards to UCSB students and UC
Merced students
Simulations



Sometimes, there is no good data set to
statistically analyze an economic problem
Some economists use simulations to “do their
best” to mimic real life in their models
Example: Given a model of the economy,
what will happen in my model if I change the
federal minimum wage from $9 per hour to
$10 per hour

A computer will analyze the parameters of the
model to estimate the impact
Summary: Empirical tools




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
What have we learned today?

How big government is


Mathematical tools


Composition of taxes and expenditures has
changed since 1965
Expected value and marginal analysis
Empirical tools

When causation exists, regression analysis is a
useful tool
Next week

Monday: Finish Unit 1

Welfare economics and market failure


Cost-benefit analysis


Pages 150-157 and 160-165
Certainty equivalent value


Pages 33-39 and 45-47
Pages 175-177
Wednesday: Begin Unit 2

Public goods
Have a good weekend