More useful tools for public finance

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More useful tools for public finance

• Today Size of government
• Expected value
• Marginal analysis
• Empirical tools

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Crashers?

• I should receive the waitlist from the
  Undergraduate Office on Monday
• No add codes given until next week
• Go through list of people from here on Monday
• Please let me know if you are now enrolled in the
  class
• New crashers?
• Check with me after class

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Last time

• Ground rules of this class
• If you were not here Mon., look at class website
• 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

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Today Four topics

• Size of government
• How big is it, and how has it changed?
• Expected value
• Useful in topics like health care
• Marginal analysis
• Useful in many topics in economics
• Empirical tools
• Regression analysis is the most common
  statistical tool used

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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

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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 governments
  expenditures and revenues)
• Regulatory budget (includes costs due to
  regulations)

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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 deflatorSource Calculations based on Economic Report of the President, 2006 (Washington, DC US Government Printing Office, 2006), pp. 280, 284, 323, 379 Conversion to 2005 dollars done using the GDP deflatorSource Calculations based on Economic Report of the President, 2006 (Washington, DC US Government Printing Office, 2006), pp. 280, 284, 323, 379 Conversion to 2005 dollars done using the GDP deflatorSource Calculations based on Economic Report of the President, 2006 (Washington, DC US Government Printing Office, 2006), pp. 280, 284, 323, 379 Conversion to 2005 dollars done using the GDP deflatorSource Calculations based on Economic Report of the President, 2006 (Washington, DC US Government Printing Office, 2006), pp. 280, 284, 323, 379 Conversion to 2005 dollars done using the GDP deflatorSource Calculations based on Economic Report of the President, 2006 (Washington, DC US Government Printing Office, 2006), pp. 280, 284, 323, 379
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Govt expenditures, selected countries
Source Organization for Economic Cooperation and Development 2006. Figures are for 2005.


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Federal expenditures
Note increase in Social Security, Medicare and
Income Security
Note decline in Defense
Source Economic Report of the President 2006, p. 377.
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State and local expenditures
Increase in public welfare
Decline in highways
Source Economic Report of the President 2006, p. 383.
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Federal taxes
Social insurance and individual incometax have
become more important
Corporate and othertaxes have become less
important
Source Economic Report of the President 2006, p. 377.
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State and local taxes
Individual tax more important
Property tax less important
Source Economic Report of the President 2006, p. 383.
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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

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Mathematical tools

• Two mathematical tools will be important
  throughout the quarter
• Expected value
• Marginal analysis
• Think of marginal and derivative in the same way

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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)

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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

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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

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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

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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

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Marginal analysis

• We will look at four topics related to marginal
  analysis
• Marginal utility and diminishing marginal utility
• The rational spending rule
• Marginal rate of substitution and utility
  maximization
• Marginal cost, using calculus

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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

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Example Diminishing marginal utility
Banana quantity (bananas) Total utility (utils) Marginal utility (utils/banana)
0 0
70
1 70
50
2 120
30
3 150
10
4 160
5
5 165
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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

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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)

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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

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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

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The rational spending rule

• The rational spending rule helps us derive an
  individuals demand for a good
• Example Apples
• Suppose the price of apples goes up
• Without changing spending, this persons 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

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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

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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

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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

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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

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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

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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

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Empirical tools

• There are many types of empirical tools
• Randomized study
• Not easy for economists to do
• Observational study
• Relies on econometric tools
• Important that bias is removed
• Quasi-experimental study
• Mimics random assignment of randomized study
• Simulations
• Often done when the above tools cannot be used

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Randomized study

• Subjects are randomly assigned to one of two
  groups
• Control group
• Item or action in question not done to this group
• Treatment group
• Item or action in question done to this group
• Randomization usually eliminates bias

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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?

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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

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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

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Conducting an observational study

• L a0 a1wn a2X1 anXn e
• Dependent variable
• Independent variables
• Parameters
• Stochastic error term
• Regression analysis
• Here, we assume
• changes in wn lead
• to changes in L
• Regression line
• Standard error

Slopeis a1
Interceptis a0
a0
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Regression analysis

• More confidence in the data points in diagram B
  than in diagram C
• Less dispersion in diagram B

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Interpreting the parameters

• L a0 a1wn a2X1 an1Xn e
• ?L / ?wn a1
• ?L / ?X1 a2
• Etc.

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Types of data

• Cross-sectional data
• Data that contain information on individual
  entities at a given point in time (R/G p. 25)
• Time-series data
• 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
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Pitfalls of observational studies

• Data collected in non-experimental setting
• Specification issues

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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

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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

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Quasi-experimental studies

• Quasi-experimental study
• Also known as a natural experiment
• Observational study relying on circumstances
  outside researchers control to mimic random
  assignment

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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

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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

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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

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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

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Pitfalls of quasi-experimental studies

• Assignment to control and treatment groups may
  not be random
• Researcher needs to justify why the
  quasi-experiment avoids bias
• Not applicable to all research questions
• 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

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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

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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

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What have we learned today?

• How big government is
• Composition of taxes and expenditures has changed
  since 1965
• Mathematical tools
• Expected value and marginal analysis
• Empirical tools
• When causation exists, regression analysis is a
  useful tool

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Next week

• Monday Finish Unit 1
• Welfare economics and market failure
• Pages 33-39 and 45-47
• Cost-benefit analysis
• Pages 150-157 and 160-165
• Certainty equivalent value
• Pages 175-177
• Wednesday Begin Unit 2
• Public goods

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Have a good weekend