More useful tools for public finance

Today: Size of governmentExpected valueMarginal analysisEmpirical 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

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)

Government expenditures, select years1 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

Source: Organization for Economic Cooperation and Development [2006]. Figures are for 2005.

Figure 1.1: Government expenditures as a percentage of Gross Domestic Product (2005, selected countries)

0

0.1

0.2

0.3

0.4

0.5

0.6

Sweden France Germany United Kingdom Canada Japan Australia

UnitedStates

Gov’t expenditures, selected countries

Figure 1.2: Composition of federal expenditures (1965 and 2005)

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1965 2005

Other

Net interest

Social security

Income security

Medicare

Health

Defense

Source: Economic Report of the President [2006, p. 377].

Note decline in Defense

Note increase in Social Security, Medicare and

Income Security

Federal expenditures

Figure 1.3 Composition of state and local expenditures (1965 and 2002)

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1965 2002

Other

Public welfare

Highways

Education

Source: Economic Report of the President [2006, p. 383].

Decline in highways

Increase in public

welfare

State and local expenditures

Figure 1.4: Composition of federal taxes (1965 and 2005)

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1965 2005

Other

Social insurance

Corporate tax

Individual incometax

Source: Economic Report of the President [2006, p. 377].

Social insurance and individual income

tax have become more important

Corporate and othertaxes have become

less important

Federal taxes

Figure 1.5: Composition of state and local taxes (1965 and 2002)

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1965 2002

Other

Grants fromfederalgovernmentCorporationtax

Inidividualincome tax

Sales tax

Property tax

Source: Economic Report of the President [2006, p. 383].

Individual tax more important

Property tax less important

State and local taxes

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

Example: Diminishing marginal utilityBanana 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

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

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

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

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

Regression analysis Here, we assume

changes in wn leadto changes in L

Regression line Standard error

wn

L

α0

Interceptis α0

Slopeis α1

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

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 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

Wednesday: Begin Unit 2 Public goods

Have a good weekend