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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

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

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

- If you were not here Mon., look at class website
- Introduction to Econ 130
- Introduction to public finance
- The role of government in public finance

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

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)

- Types of government expenditure

Federal expenditures

Note increase in Social Security, Medicare and Income Security

Note decline in Defense

Social insurance and individual incometax have become more important

Corporate and othertaxes have become less important

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
- 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

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

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

MRS and utility maximizationMarginal 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

- For example, eating unsafe food leads you to get sick

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

- Stock prices in the United States and temperature in Antarctica

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

- Randomized study

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

- Control 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

- Is it ethical to run experiments when only some people are eligible to receive the treatment?
- 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

- Example: Effects of giving surfboards to 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

L = α0 + α1wn + α2X1 + … + αnXn + ε

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

L

wn

Conducting an observational studySlopeis α1

Interceptis α0

α0

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
- “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

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

- Example: Education
- 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

- Incorrect specification could lead to biased results

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

- Will this lead to more people in this city to go to 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
- 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

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
- 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

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

- Welfare economics and market failure
- Wednesday: Begin Unit 2
- Public goods

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