More useful tools for public finance Today: Size of government Expected value Marginal analysis Empirical tools
Jan 04, 2016
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