Transcript Relational Data Base Fundamentals

Chapters 1 to 4
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Outline
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The Four Questions of Public Finance
Utility maximization
Labor supply example
Efficiency
Social welfare functions
Correlation versus causation
Discounting
Question 1: When Should the
Government Intervene in the Economy?
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Normally, competitive private markets
provide efficient outcomes for the economy.
In many circumstances, it is hard to justify
government intervention in markets. Two
common justifications are:
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Market failures
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What is a market failure?
Redistribution
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Shifting resources from some groups to others.
When Should Government Intervene?
An example of market failure
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In 2003, there were 45 million people
without health insurance in the United States,
or 15.6% of the population.
Lack of insurance could cause negative
externalities from contagious disease–the
uninsured may not take account of their
impact on others.
Measles epidemic from 1989-1991, caused by
low immunization rates for disadvantaged
youth, was a problem.
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Government subsidized vaccines for low-income
families as a result.
When Should the Government
Intervene? Redistribution
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Of the uninsured, for example, roughly threequarters are in families with incomes below the
median income level in the United States.
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Society may feel that it is appropriate to redistribute
from those with insurance (who tend to have higher
incomes) to those without insurance (who tend to
have lower incomes).
Redistribution often involves efficiency losses.
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The act of redistribution can change a person’s
behavior. Taxing the rich to distribute money to the
poor could cause both groups to work less hard.
Question 2: How Might the
Government Intervene?
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If the government wants to intervene in a market,
there are a number of options:
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Using the price mechanism with taxes or subsidies.
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Tax credits that lower the “effective price” of health
insurance.
Mandate that either individuals or firms provide the
good.
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Public Provision
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“Pay-or-play” mandates that require employers to provide
health insurance, such as California’s Health Insurance Act.
The Medicare program for U.S. senior citizens.
Public Financing of Private Provision
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Medicare prescription drug cards, where private companies
administer the drug insurance.
Question 3: What Are the Effects
of Alternative Interventions?
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Much of the focus of empirical public finance is
assessing the “direct” and “indirect” effects
of government actions.
Direct effects of government actions
assume “no behavioral responses” and
examine the intended consequences of those
actions.
Indirect effects arise because some people
change their behavior in response to an
intervention. This is sometimes called the
Question 4: Why Do Governments
Do What They Do?
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Positive (as opposed to normative) question.
Governments do not simply behave as benign
actors who intervene only because of market
failure and redistribution.
Tools of political economy helps us
understand how governments make public
policy decisions.
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Just as market failures can lead to market inefficiency,
there are a host of government failures that lead to
Chapter 2:
Review (Quickly) Economics 301
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Constrained Utility Maximization is based on
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Preferences (indifference curves), and
Budget sets.
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Start with a discussion of preferences.
A utility function is a mathematical representation
U = f(X1, X2, X3, …)
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Where X1, X2, X3 and so on are the goods consumed by
the individual,
And f(•) is some mathematical function.
Bundle“C”
“C”gives
gives4 Higher utility as
“A” and “B” Bundle
both
“utils”
utility
is than
on a move toward
give 2 “utils”higher
and and
higher
either indifference
“A” or “B” northeast in the
lie on the same
quadrant.
indifference curve curve
QCD
(quantity of
CDs)
A
C
2
B
1
IC2
IC1
0
Figure 2
1
2
Utility From Different Bundles
QM (quantity
of movies)
Constrained Utility Maximization:
Marginal utility
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With the utility function, U = QMQC, the marginal
utility is:
MU QM
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U

 QC
Q M
Take the partial derivative of the utility function
with respect to QM to get the marginal utility of
movies.
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Normally, preferences exhibit diminishing marginal utility,
as would be the case if U = (QMQC)1/2 , since
MU QM
U
1 QC


 QM 2 QM
Constrained Utility Maximization:
Marginal rate of substitution
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Marginal rate of substitution—slope of the indifference
curve is called the MRS, and is the rate at which consumer is
willing to trade off the two goods.
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Direct relationship between MRS and marginal
utility.
MRS  
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Q
MU M
  C , when U  QM QC
MU C
QM
MRS shows how the relative marginal utilities evolve
over the indifference curve.
Constrained Utility Maximization:
Budget constraints
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The budget constraint is a mathematical
representation of the combination of goods
the consumer can afford, given income.
Assume there is no saving or borrowing.
In the example, denote:
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Y = Income level
PM = Price of one movie
PC = Price of one CD
Y  PM QM  PC QC
QCD
(quantity of
CDs)
3
This bundle of goods
This
gives
indifference
the
curve gives much
highest utility, subject higher
to the budget
utility, but is not attainable.
constraint.
This indifference curve is not utilitymaximizing, because there are
bundles that give higher utility.
2
1
0
Figure 8
1
Utility Maximization
2
3
QM (quantity
of movies)
Constrained Utility Maximization:
Putting it together: Constrained
choice
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Thus, the marginal rate of substitution equals the
ratio of prices:
MU M
PM
MRS  

MU C
PC
At the optimum, the ratio of the marginal
utilities equals the ratio of prices. But this is not
the only condition for utility maximization.
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The second condition is that all of the consumer’s
money is spent
The Effects of Price Changes:
Substitution and income effects
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A change in price consists of two effects:
Substitution effect–change in consumption
due to change in relative prices, holding utility
constant.
Income effect–change in consumption due
to feeling “poorer” after price increase.
Figure 11 illustrates this.
Income and Substitution
Effects (price of rooms rises)
Meals
SE: Find a hypothetical
budget line with the new price
ratio just tangent to the
original IC.
Income
Substitution
effect
effect
Rooms
QCD
(quantity of
CDs)
Raising P
more gives another
M even
Initial
utility-maximizing
point gives
(PM,QM)Raising
combination
withanother
even less
(PM,QM)
M gives
oneP(P
M,QM) combination.
movies with
demanded.
combination
fewer movies demanded.
QM,3 QM,2 QM,1
Figure 18
QM (quantity
of movies)
Derive Demand Curves: First, Increase in the Price of
Movies
PM
PM,3
Various
of
At
a high combinations
price for
pointsdemanded
like these create
movies,
QM,3 the
demand curve.
At a somewhat lower price
for movies, demanded QM,2
At an even lower price for
movies, demanded QM,1
PM,2
PM,1
Demand
curve for
movies
QM,3
Figure 19
QM,2
QM,1
QM
Deriving the Demand Curve for Movies: Second, plot
the optimal price-quantity pairs
EQUILIBRIUM AND SOCIAL WELFARE
Elasticity of demand
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A key feature of demand analysis is the elasticity
of demand. It is defined as:
QD
D 
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P
That is, the percent change in quantity demanded
divided by the percent change in price.
Demand elasticities are:
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P
QD
Typically negative number.
Not constant along the demand curve (for a linear demand curve).
It is easy to define other elasticities (income, crossprice, etc.)
EQUILIBRIUM AND SOCIAL
WELFARE: Supply curves
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We do a similar drill on the supply side of the market. Firms
have a production technology (we might write it as)
QM  f  LM , K M 
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We can construct isoquants, which represent the ability to
trade off inputs, fixing the level of output.
Firms also have an isocost function, which represent the cost
of various input combinations.
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Firms maximize profit (minimize cost) when the marginal rate of
technical substitution equals the input price ratio.
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Also MR=MC at the profit-maximizing level of output.
EQUILIBRIUM AND SOCIAL WELFARE
Equilibrium
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In equilibrium, we horizontally sum individual
demand curves to get aggregate demand.
We also horizontally sum individual supply curves to
get aggregate supply.
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A firm’s supply curve is the MC curve above minimum
average variable cost.
Competitive equilibrium represents the point at
which both consumers and suppliers are satisfied
with the price/quantity combination.
Figure 21 illustrates this.
PM
Intersection of supply and
demand is equilibrium.
Supply
curve of
movies
PM,3
PM,2
PM,1
Demand
curve for
movies
QM,3
Figure 21
QM,2
QM,1
Equilibrium with Supply and Demand
QM
EQUILIBRIUM AND SOCIAL WELFARE
Social efficiency
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Measuring social efficiency is computing the potential
size of the economic pie. It represents the net gain
from trade to consumers and producers.
Consumer surplus is the benefit that consumers
derive from a good, beyond what they paid for it.
Each point on the demand curve represents a
“willingness-to-pay” for that quantity.
EQUILIBRIUM AND SOCIAL WELFARE
Social efficiency
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Producer surplus is the benefit derived by
producers from the sale of a unit above and
beyond their cost of producing it.
Each point on the supply curve represents
the marginal cost of producing it.
EQUILIBRIUM AND SOCIAL WELFARE
Social efficiency
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The total social surplus, also known as
“social efficiency,” is the sum of the
consumer’s and producer’s surplus.
Figure 25 illustrates this.
PM
The
Providing
surplus the
from
first
theunit
next
Supply
gives
unit isathe
great
difference
deal of
curve of
between
surplus
the
to demand
“society.”and
movies
supply curves.
Social
The area
efficiency
between
is maximized
the supplyat
*, and iscurves
and Q
demand
the sum
from
of the
zero to
consumer
Q* represents
and producer
the surplus.
surplus.
P*
This area represents the
social surplus from
producing the first unit.
0
Figure 25
1
Social Surplus
Q*
Demand
curve for
movies
QM
EQUILIBRIUM AND SOCIAL WELFARE
Competitive equilibrium maximizes social
efficiency
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The First Fundamental Theorem of
Welfare Economics states that the
competitive equilibrium, where supply equals
demand, maximizes social efficiency.
Any quantity other than Q* reduces social
efficiency, or the size of the “economic pie.”
Consider restricting the price of the good to
P´<P*.
Figure 26 illustrates this.
PM
This triangle represents
lost surplus to society,
known as “deadweight
loss.”
The With
socialsuch
surplus
a price
from Q’
is restriction,
this area, consisting
the quantity
of a
´, and there
falls
larger
to Q
consumer
andis
smaller
excess
producer
demand.
surplus.
P*
Supply
curve of
movies
P´
Demand
curve for
movies
Q´
Figure 26
Q*
Deadweight Loss from a Price Floor
QM
EQUILIBRIUM AND SOCIAL WELFARE
The role of equity
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Societies usually care not only about how
much surplus there is, but also about how it is
distributed among the population.
Social welfare is determined by both criteria.
The Second Fundamental Theorem of
Welfare Economics states that society can
attain any efficient outcome by a suitable
redistribution of resources and free trade.
In reality, society often faces an equityefficiency tradeoff.
Chapter 3: Empirical Approaches to
Policy Analysis
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Empirical public finance is the use of data and
statistical methodologies to measure the impact of
government policy on individuals and markets.
Key issue in empirical public finance is separating
causation from correlation.
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Correlated means that two economic variables move
together.
Casual means that one of the variables is causing the
movement in the other.
THE IMPORTANT DISTINCTION
BETWEEN CORRELATION AND
CAUSATION
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One interesting, tragic example given in the
book describes some Russian peasants.
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There was a cholera epidemic. Government sent
doctors to the worst-affected areas to help.
Peasants observed that in areas with lots of
doctors, there was lots of cholera.
Peasants concluded doctors were making things
worse.
Based on this insight, they murdered the doctors.
The Problem
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In the Russian peasant example, the
possibilities might be:
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Doctors cause peasants to die from cholera
through incompetent treatment.
Higher incidence of illness caused more
physicians to be present.
Peasants thought the first possibility was
correct.
MEASURING CAUSATION WITH DATA
WE’D LIKE TO HAVE: RANDOMIZED
TRIALS
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Randomized trials are one often effective way of
assessing causality.
Trials typically proceed by taking a group of
volunteers and randomly assigning them to either a
“treatment” group that gets the intervention, or a
“control” group that is denied the intervention.
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With random assignment, the assignment of the
intervention is not determined by anything about the
subjects.
As a result, with large enough sample sizes, the treatment
group is identical to the control group in every facet but
one: the treatment group gets the intervention.
The Problem of Bias
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Bias represents differences between treatment and
control groups that is correlated with the treatment, but
not due to the treatment.
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An example of bias: in 1988 the SAT scores of Harvard
applicants who took test preparation courses were lower than
those of students who did not. This would bias straightforward
effort to study the effects of SAT classes on test scores.
By definition, such differences do not exist in a
randomized trial, since the groups, if large enough, are not
different in any consistent fashion.
Why We Need to Go Beyond Randomized
Trials
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Randomized trials present some problems:
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They can be expensive.
They can take a long time to complete.
They may raise ethical issues (especially in the context of
medical treatments).
The inferences from them may not generalize to the
population as a whole.
Subjects may drop out of the experiment for nonrandom reasons, a problem known as attrition.
Time Series Analysis
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Time series analysis documents the
correlation between the variables of interest
over time.
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It is difficult to identify causal effects when there
are slow moving trends and other factors are
changing.
Sharp changes in a policy variable over time, may
create opportunities for valid inference.
Figure 2
Cross-Sectional Regression Analysis
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Cross-sectional regression analysis is a statistical
method for assessing the relationship between two
variables while holding other factors constant.
“Cross-sectional” means comparing many individuals
at one point in time.
An example: HOURS    TANF  CONTROL  
Where the control variables account for race,
education, age, and location
i

i
i
i
Quasi-Experiments
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Economists typically cannot set up randomized trials for
many public policy discussions. Yet, the time-series and
cross-sectional approaches are often unsatisfactory.
Quasi-experiments are changes in the economic
environment that create roughly identical treatment and
control groups for studying the effect of that environmental
change.
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This allows researchers to take advantage of randomization created
by external forces.
An Example of a QuasiExperiment
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New Jersey raises their state minimum wage.
Pennsylvania does not.
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We are interested in the effect of the minimum wage on
employment.
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We could look at the employment of low-skilled workers in NJ
before and after the minimum wage increase.
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But other things in the economy might be occurring.
So, we can see how employment changed in PN over the same
interval.
The difference in employment in NJ, before and after,
compared to the difference in employment in PN, before
and after, may reveal the causal effect of minimum wages
changes, if NJ and PN are identical (similar?) in other
respects.
Structural Modeling
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Both randomized trials and quasi-experiments suffer from
two drawbacks:
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First, they only provide an estimate of the causal impact of a
particular treatment. It is difficult to extrapolate beyond the changes
in policy.
Second, the approaches often do not tell us why the outcomes
change. For example, the approaches do not separate out income
and substitution effects in the TANF example used in the book.
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Structural estimation attempt to estimate the underlying parameters of the
utility function.
Chapter 4: A Couple Tools and
Definitions
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Government debt is the amount that a government
owes to others who have loaned it money.
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It is a stock variable; the debt is an amount owed at any
point in time.
Government deficit is the amount by which
spending exceeds revenues in a given year.
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It is a flow variable; the deficit flow is added to the
previous year’s debt stock to produce a new stock of debt
owed.
Real vs. Nominal
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The debt and deficit are often expressed in nominal
values–that is, in today’s dollars.
Inflation changes the real value of the debt or deficit,
however, because prices change.
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The consumer price index (CPI) measures the cost of
purchasing a typical bundle of goods. It increased 91% between
1982 and 2003.
Inflation reduces the burden of the debt, as long as that debt is a
nominal obligation to borrowers.
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Rising prices leads to what is known as the “inflation tax” on the holders
of the debt–the payments are worth less because of rising prices.
In 2003, the national debt was $3.91 trillion and inflation was 1.9%. The
inflation tax was therefore $74 billion, which would reduce the
conventionally measured deficit from $375 billion to $301 billion.
Background: Present Discounted Value
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To understand budgeting, you must understand the
concept of present discounted value (PDV).
Receiving a dollar in the future is worth less than
receiving it today, because you have foregone the
opportunity to earn interest.
PDV takes future payments and expresses them in
today’s dollars.
It does so by discounting payments in some future
period by the interest rate.
Background: Present Discounted Value
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A stream of payments would be discounted as:
B1
B2
Bt
PDV  B0 

...
2
1  r  1  r 
1  r t
Where B0 through Bt represent a stream of benefit
obligations, r is the interest rate, and t is the number of
periods.
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For example, $1,000 received 7 years from now is only worth $513
with a 10% interest rate:
51316
. 

1000
. 
1  010
7
1000

1948
.
A constant payment received indefinitely has the PDV=P/r