Download Demand for Local Public Goods

Demand for Local Public
Goods
© Allen C. Goodman 2008
How Responsive are LPGs?
• What are the usual suspects?
• We get pretty interested in both price and
income elasticities.
• Presumably, as Income , Q .
• Presumably, as Price , Q .
• How much is it?
– A little?
– A lot?
Let’s recall a few things from principles
EY = % Q / % Y.
EP = % Q / % P.
Why do we care?
We’d like to know (if public goods are good)
whether we might naturally get more of
them if incomes rose.
Price elasticities
Things you once learned, but you probably
wanted to forget!
How much does quantity demanded change
if price changes?
What happens to total expenditures?
Suppose EP = 0.
0 = % Q / % P
If % P is 10, % Q = 0, so total
expenditures  by 10% - that’s a lot!
Price elasticities
Suppose EP = -0.5.
-0.5 = % Q / % P
If % P is 10, % Q = -5, so total expenditures 
by 5% - Why?
What if EP = -1.5?
What happens to
total expenditures?
Suppose EP = -1.0.
-1.0 = % Q / % P
If % P is 10, % Q = -10, so total expenditures
are unchanged - Why!
Getting demand from median voter models
• Suppose median income person is median
voter.
Price
Trend Line
YA
YB>YA YC>YB
Quantity
C*
B*
tc(Yc)
tb(Yb)
A*
tA(YA)
A* B* C*
Quantity
YA
YB
YC
Income
Getting demand from median voter models
• Suppose median income person isn’t
median voter.
Price
tc(Yc)
YA
YB>YA YC>YB
tb(Yb)
Quantity
C*
A*
B*
tA(YA)
B*A* C*
Quantity
YA
YB
YC
Income
Conundrum
• If the first is the case, we can confidently
regress median income against median
expenditure and feel that we have
identified the median voter.
• If the second is the case, we cannot be
sure.
How do we examine data
• Let’s look at some
data on per capita
state/local
expenditures v.
• Per capita state
income
CT
DE
DC
ME
MD
MA
NH
NJ
NY
PA
RI
VT
PCI
42919
31955
44731
27324
35527
38944
33922
39122
35590
30240
30434
29024
PCE
7105
6834
10804
6262
6004
6698
5132
6473
8523
5999
6474
6264
Let’s draw a picture
Per Capita Expenditures
12,000
10,000
Per Capita Expenditures
• What does the
relationship look
like?
• Looks like as
income 
expenditures .
8,000
6,000
PCE
4,000
2,000
0
0
10,000
20,000
30,000
Per capita Income
40,000
50,000
Log-log Form
SUMMARY OUTPUT
Dep: ln(PC Exp)
Regression Statistics
Multiple R
0.567371
R Square
0.32191
Adjusted R Square 0.254101
Standard Error
0.163847 Goodness
Observations
12 of fit
Good thing – Elasticities are
easy to calculate
Bad thing –
1. Elasticity is constrained
to be constant
2. What do you do with 0’s?
ANOVA
df
Regression
Residual
Total
Intercept
LN(PCI)
SS
MS
F
1 0.127446 0.127446 4.747312
10 0.26846 0.026846
11 0.395906
Coefficients
Standard Error t Stat
P-value
1.650047 3.29048 0.501461 0.626901
0.685924 0.314813 2.178833 0.054353
Elasticity
Linear Form
SUMMARY OUTPUT
Dep:
Regression Statistics
Multiple R
0.606519
R Square
0.367865
Adjusted R Square
0.304651
Standard Error 1228.478
Observations
12
PCE
Good thing – Elasticities
can vary.
Bad thing –
1. Elasticity must be
calculated.
E = (PCE/PCE)/(PCI /PCI)
ANOVA
df
Regression
Residual
Total
Intercept
PCI
Elasticity
SS
1 8782402
10 15091582
11 23873984
MS
F
8782402 5.819404
1509158 E = (PCE/PCI)*(PCI /PCE)
Coefficients
Standard Error t Stat
P-value
1252.322 2360.078 0.530627 0.607259
0.160922 0.066708 2.412344 0.036537
0.818003
E = (0.161)*(PCI /PCE)
Empirical Work
• Bergstrom/Goodman (no relation) – 1973
• Already kind of dated but Fisher argues that
more recent stuff is similar.
Bergstrom/Goodman
Gen'l
Expend
Police
Expend
Parks
Recreation
Income
0.64
0.07
0.71
0.13
1.32
0.22
Tax share (price)
-0.23
0.03
-0.25
0.05
-0.19
0.08
Population
0.84
0.03
0.80
0.06
1.17
0.11
General Literature
• As income rises, quantities rise, but not by
as large a percentage. Implies that
expenditures rise.
• As price rises, quantities fall although not
by much. Also implies that expenditures
may rise.
Business Demand
• Model is one of consumer demand but how do
businesses feel?
• Application 4.1 is interesting
• On the one hand, businesses always seem to
want lower taxes.
• On the other hand,
– “without additional revenues, Colorado will be left with
little choice but to woefully under-fund areas such as
higher education, our state highways, water
resources, and vital capital construction and
maintenance projects.”