Transcript Betting on the Future with a Cloudy Crystal Ball?

A Theory of Everything
(Adequacy, Fairness, &
Efficiency)
Spending, Taxing, Saving, and
Borrowing
A balanced budget
Portfolio management
Hedging
Self-insurance
Optimal spending rules
Fred Thompson
Atkinson Graduate School of Management
Next page
Willamette University
Deficits?
Budgets Unbalanced
The Federal Budget
State Budgets
The Oregon Case
Next page
Jump to first page
Cash Deficits
• Surplus/Deficit = Revenue - Outlays (Primary
deficit = [Revenue - Transfers] - [Exhaustive
Expenditures])
• Deficits have two components
• Cyclical = revenue shortfall due to the
business cycle
• Structural = (soft budget constraint) revenue
shortfall at full employment = (hard budget
constrain) PV revenues ≥ PV outlays
Jump to first page
The Distinction between Cyclical and
Structural Deficits is Important Because
• Governments facing a hard
budget constraint can make up
cyclical revenue shortfalls in a
variety of ways
• Real structural deficits can be
repaired only by permanent
reductions in outlays or
permanent increases in taxes.
Jump to first page
Literature on State Structural Deficits
•
Making California’s State Budget More User-Friendly and Transparent
WZ Hirsch, DJB Mitchell - California Policy Options, 2002
•
•
Making California’s State Budget More User-Friendly and Transparent:
Further Thoughts. WZ Hirsch, DJB Mitchell - California Policy Options 2003
Wisconsin's Structural Deficit: Our Fiscal Future at the Crossroads
Andrew Reshovsky, Robert M. Lafollette School of Public Affairs, University of WisconsinMadison. 8p. May 2002 (Also State Tax Notes, Vol. 25, No. 6, August 12, 2002)
•
Idaho’s Structural Deficit: A Problem that Won’t Go Away Judith Brown and
Don Reading, Idaho Center on Budget and Tax Policy, March 2005
•
It's Not Just the Recession: The Budget Crisis and Washington State’s
Structural Deficit M.P. Watkins and Jason Smith, Economic Opportunity Policy
Institute, Seattle WA, July 2003
Many analysts define a structural deficit as not having enough revenue
to meet current needs -- argument for more taxes
Some (Reshovsky, Watkins & Smith) distinguish between structural
deficits and cyclical deficits but implicitly compute the former in
terms of data series that run from peak to trough of the business
cycle -- this extrapolation is also usually an argument for more or
different taxes
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The Business Cycle
The phases of the business cycle
are:
•
•
•
•
Expansion,
Peak (or boom),
Contraction, and,
Recessionary trough.
The duration of business cycles is
irregular and the magnitude of
the swings varies.
Jump to first page
A Hypothetical Business Cycle
Real GDP
Business
peak
Trend line
Business
peak
Recessionary
trough
Recessionary
trough
Time
• In the past, ups and downs have often
characterized aggregate business activity.
• Despite these fluctuations, there has been
an upward trend in real GDP in the United
States and other industrial nations.
Jump to first page
The Business Cycle
Annual growth
rate of real GDP
8
Long-run growth rate
(approx. 3%)
6
4
2
0
-2
1960
1965
1970
1975
1980
Source: Economic Report of the President, various issues.
Jump to first page
1985
1990
1995
2000
The Economics of Revenue Growth
• Nominal increase have averaged over 10 percent per year
over the past century. However, inflation accounts for
two-thirds of the total increase.
• During the last 50 years (1950-2000), federal government
revenues grew at an average ral rate of 3.5 percent.
• Double-digit nominal occurred increases during 32 of the
50 years, while the increases were negative during only
11 of the years.
Annual
Federal Revenue Growth
20%
15%
10%
5%
0%
- 5%
- 10%
- 15%
1950
1960
mean
1970
.
Jump to first page
1980
1990
2000
The Inflation Rate, 1953-2001
Inflation rate
15
10
1973-1981 average
inflation rate = 9.2 %
1983-2001 average
inflation rate = 3.2 %
1953-1965 average
inflation rate = 1.3 %
5
0
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
Sources: Derived from computerized data supplied by FAME ECONOMICS. Also see Economic Report of the President (annual).
• Here are the annual inflation rates for the last 48 years.
• Between 1953 and 1965, the general price level
increased at an average annual rate of only 1.3%.
• In contrast, the inflation rate averaged 9.2% from 1973
to 1981, reaching double-digits during several years.
• Since 1982, the average rate of inflation has been lower
(about 3.2% from 1983-2001) and more stable.
Jump to first page
Real Federal Expenditures
Per Capita: 1792-2000
Real federal spending per person
$ 7,000
(in 2000 U.S. dollars)
$ 6,000
$ 5,000
$ 4,000
$ 3,000
$ 2,000
$ 1,000
$0
1800
1850
1900
1950
2000
• Real federal spending per person (measured in 2000 dollars)
grew slowly during the first 125 years of U.S. history, but
it soared throughout most of the 20th century.
Jump to first page
Federal Expenditures and Revenues
Federal Government Expenditures and Revenues
(as a share of GDP)
24
Expenditures
22
Expenditures
20
18
Revenues
1960
1965
1970
1975
1980
1985
Source: Economic Report of the President, 2001. Note, recessions are
indicated by shaded bars.
1990
1995
2000
• The federal deficit or surplus as a share of the economy is
shown here. Note the growth of budget deficits during the
1980s and the movement to surpluses during the 1990s.
Jump to first page
Budget Deficits & the National Debt
Federal deficit
as a share of GDP
2%
0%
-2%
-4%
1950
Surplus
Deficit
1960
Gross & net federal debt
as a share of GDP
80 %
60 %
40 %
20 %
1950
1970
National debt
as a % of GDP
1960
1970
1980
Other federal debt
1980
1990
2000
Privately held federal
debt as a % of GDP
1990
2001
• Through most of the 1950s & 1960s, federal budget deficits
were small as a % of GDP; occasionally there was a surplus.
• During this period, the national debt declined as a % of GDP.
Jump to first page
Budget Deficits & the National Debt
Federal deficit
as a share of GDP
2%
0%
-2%
-4%
1950
Surplus
Deficit
1960
Gross & net federal debt
as a share of GDP
80 %
60 %
40 %
20 %
1950
1970
National debt
as a % of GDP
1960
1970
1980
Other federal debt
1980
1990
2000
Privately held federal
debt as a % of GDP
1990
2001
• During 1974-1995, budget deficits were quite large, causing
the national debt to increase as a % of GDP.
• During the 1992-2002 period, the national debt fell as a
share of the economy.
Jump to first page
This is what
Happened after
2001
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Conclusions
• More than half of the federal government’s
deficits over the past fifty years were cyclical
in nature.
• Between 1976-1993, structural deficits were
between 1 and 3 percent of GDP.
• After 1994, the federal deficit was eliminated
by a combination of spending restraint,
revenue increases, and boom.
• After 2001 spending increased, taxes were cut,
and we had a slight recession, reestablishing a
structural deficit of 1 to 3 percent of GDP.
• Then came the Great Recession!
Jump to first page
State Deficits
• Most states have less volatile revenue structures than
the federal government
• Even so they often experience substantial cyclical
fiscal effects
• Because most are required to balance their budgets,
structural deficits mean something different for states:
Surpluses must equal deficits over the course of
the business cycle
See C. Hinkelmann & Steve Swidler,
• Rainy day funds (savings)
• Countercyclical borrowing
• Hedging
Jump to first page
“Macroeconomic Hedging with Existing
Futures Contracts,” Risk Letters,
forthcoming;
“State Government Hedging with
Financial Derivatives,” State and Local
Government Review, volume 37:2,
2005; “Using Futures Contracts to
Hedge Macroeconomic Risks in the
Public Sector,” Trading and
Regulation, volume 10, number 1,
2004.
ANALYTICAL FRAMEWORK
FOR STATE BBR SYSTEMS
(Hou & Smith)
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State and Local Stabilization Funds and State
Aid as Percentage of Municipal
Revenues for Fiscal Years 1995 – 2003
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Oregon’s Fiscal Gap
Primarily (but not entirely) Driven by
Revenues (actual revenues - CSB)
Budget Shortfall/Surplus over Time
Magnitude of Shortfall/Suprlus (in Millions, Real 2002$)
300
200
100
0
1980
1985
1990
1995
-100
-200
-300
-400
Year
Jump to first page
2000
2005
Oregon’s Deficits Have a
Cyclical Component
Budget Shortfall/Surplus over Time
Magnitude of Shortfall/Suprlus (in Millions, Real 2002$)
300
200
100
0
1980
1985
1990
1995
-100
-200
-300
-400
Year
Jump to first page
2000
2005
Analytical Problems
• We used negative job growth as a
recession identifier because we
lacked a formal mechanism to date
recessions at the state level.
• That’s not entirely satisfactory.
Jump to first page
Evidence of A
Structural Deficit?
Frequency Histogram of Budget Shortfall/Surplus
7
Normal Distn: Mean = -20, Std Dev = 140
6
Triangular Distn: Min = -350; Max = 250; ML = 69
Observed Cum Freq
Frequency
5
4
3
2
1
0
-137
-238
-163
-88
-13
63
Magnitude of Shortfall or Surplus
(in Millions, Real $ [2002 CPI=100])
Jump to first page
138
213
Problem
• Doesn’t adjust for scale, just
inflation
• Positive correlation between
budget gap and time could be
due to structural deficit or to
selection bias
Jump to first page
Analytical Solution
• Monte Carlo Simulation
• Weiner Process
• Trough to Trough Revenue
and Spending
• Trough to Trough Spending,
Peak to Peak Revenues
Jump to first page
Results of Monte Carlo Simulation
Weiner process, Peak to Peak Revenue, Trough to
Trough Outlays, Constant 2002$
r = 4%; Sigma = 260: Del t = 0.01; E-O-Y = $5,116
$6,000
$5,750
$5,500
Value
$5,250
Baseline
$5,000
$4,750
$4,500
$4,250
y = 5006.6e0.0002x
R2 = 0.2254
$4,000
0
10
20
30
40
50
Time
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60
70
80
90
100
Implications
• Other things equal, revenue growth is
faster than outlay growth
• Oregon doesn’t need to increase taxes to
offset a structural budget deficit
• Oregon could rely on a rainy day fund of
sufficient size to mitigate the adverse
consequences of cyclical revenue
shortfalls (if it had one) or mitigate them
via a program of countercyclical
borrowing
• Hedging
Jump to first page
BUDGETING IN
CHILE
• Hierarchical budget institutions
• The executive branch is solely
responsible for public financial
management
• Concentration of responsibilities
within the Executive and in the
Ministry of Finance
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BUDGETING IN
CHILE
• Reflected in:
• Initiative to initiate legislation on budget and
financial matters restricted to President
• Limited powers of the legislature to modify
the budget
• Strict deadlines for budget approval by
Congress
• Earmarking of taxes, loans from Central Bank
forbidden by the Constitution
Jump to first page
RESULTS
• Public expenditure under
control
• The budget is simple and
strictly enforced
• Budget surplus from 1986 to
1996
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MACRO EFFICIENCY I
• Structural balance fiscal rule (2000)
• Builds on studies on fiscal policy indicators
• The rule: annual structural surplus of 1% of
the GDP (changed to 0.5% of GDP for
2008)
• Strict monitoring, transparency, compliance
to secure credibility
• Improves on European convergency criteria
on stabilization, monitoring
Jump to first page
MACRO EFFICIENCY
• Medium-term financial program (2001)
• Three-year financial program, published
alongside Budget
• Aimed at identifying misadjustments in
advance, introduce corrections
• Management of assets and liabilities (2002)
• Creation of a specialized division within BO,
agreement with Treasury, State Bank
• Reduction in cash holdings, regulation of
money and investment management in
agencies, financial coverage operations
Jump to first page
STABILITY OF PUBLIC
EXPENDITURE
Central Government Expenditure 1970-2004
MM $ 2004
14.000.000
y = - 4.654.247,8 + 497.487,2*t
12.000.000
10.000.000
y = 2.523.291,7 + 195.662,2*t
8.000.000
6.000.000
4.000.000
2.000.000
-
1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004
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Lesson
• Budgetary (spending) stability is the goal
• Trying to balance budgets (match spending
to taxing) one year at a time leads to manicdepressive spending and taxing patterns
• This is costly, both directly in terms of the
expedients taken to balance budgets and
indirectly from a macroeconomic
perspective
• The problem faced by budget makers
derives from volatility in revenue growth.
Jump to first page
The Source of the
Problem
Revenue volatility
• the volatility of the tax base -underlying economy
• progressivity of the tax/transfer
regime)
We can decompose the growth path
into two components: trend & random
variance
Jump to first page
Revenue Forecasting
Mike Hand’s PPT
Next page
Principles of Forecasting
Data-Based Forecasting
In God we trust, all others bring data.
W. Edwards Deming
Michael L. Hand
Professor of Applied Statistics
and Information Systems
Atkinson Graduate School of Management
Willamette University
Principles of Forecasting
Associative Methods
 “Causal”, multiple regression models relating response
to a general set of predictors
 Data/supporting forecast requirement
Increased model complexity and development effort
 Assumes relationships among response and predictors
are stable over time
 Micro-simulation is an associative method
 Best for assessing consequences of policy changes
Michael L. Hand
Professor of Applied Statistics
and Information Systems
Atkinson Graduate School of Management
Willamette University
Principles of Forecasting
Associative Models
Oregon Personal Income Tax versus Unemployment
Personal Income Tax (in $Millions)
1500
1400
1300
1200
1100
1000
900
800
700
600
3.5
4.0
4.5
5.0
Unemployment Rate (%)
Michael L. Hand
Professor of Applied Statistics
and Information Systems
Atkinson Graduate School of Management
Willamette University
5.5
6.0
Principles of Forecasting
Econometric Models
LOG(GIwages) = 20.7 + 0.93*LOG(PIwages + PIother_lab) + [AR(1)=0.85]
LOG(GIdividends) = 16.7 + 0.49*LOG(PIdir) + 0.30*LOG(MKTw5000)
LOG(GIinterest) = 19.6 + 0.34*LOG(PIwages) + 0.04* IR3mo_tbill + 0.039* IR3mo_tbill (-1) + [AR(1)=0.65]
LOG(GIcapgains) = 11.5 + 1.14*LOG(MKTw5000) + [MA(4) = -0.86]
LOG(GIretirement) = -0.12 + 1.24*LOG(POP_OR65+) + 0.97*LOG(PItotal – PIwages) + 0.32*LOG(MKTw5000) +
[AR(1)=-0.50]
LOG(GIproprietors) = -304.7 + 0.72*LOG(PIproprietors) + 2.10*LOG(EMPretail) + [AR(1)=1.0]
LOG(GIschedule_e) = 14.4 + 1.1*LOG(CORP_PROFIT) + [AR(1)=0.78]
LOG(GIother) = -2.1 + 4.14*LOG(EMPretail)
Eff_tax_rate = 0.05 + 0.005* DMYtax_rate + 0.053* FDIST1mil + 0.04*(( GIschedule_e + GIproprietors)/ GIwages) +
[AR(1)=0.58]
Personal Income Tax Model
GI - Gross Income from the source indicated
PItotal – Total Oregon Personal Income
Office of Economic Analysis
PIwages – Wage and Salary Component of Personal Income
Department of Administrative Services
PIother_lab – Other labor component of Personal Income
PIdir – Dividends, Interest and Rent component of Personal Income
PIproprietors – Proprietors’ Income component of Personal Income
MKTw5000 – Wilshire 5000 stock index
EMPretail – Oregon Retail Employment
CORP_PROFIT – U.S. Corporate Profits
POP_OR65+ – Oregon 65 and older population
IR3mo_tbill – Discount rate of 3 month Treasury Bill
FDIST1mil - Filer Distribution Model, Ratio of $1 million-plus filers to Total filers
DMYtax_rate – Dummy variable for 1982 through 1984 tax rate increase
Michael L. Hand
Professor of Applied Statistics
and Information Systems
Atkinson Graduate School of Management
Willamette University
Principles of Forecasting
Projective Methods
 Simple extrapolation in time
 Predictors are time and functions of time
Trend, seasonal, cyclical factors
 Minimal data/supporting forecast requirement
 Assumes current conditions will persist
 Best for short-term forecasts
One year out (two if we stretch) or less
Michael L. Hand
Professor of Applied Statistics
and Information Systems
Atkinson Graduate School of Management
Willamette University
1996:01
1996:02
1996:03
1996:04
1997:01
1997:02
1997:03
1997:04
1998:01
1998:02
1998:03
1998:04
1999:01
1999:02
1999:03
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2000:01
2000:02
2000:03
2000:04
2001:01
2001:02
2001:03
2001:04
2002:01
2002:02
2002:03
2002:04
2003:01
2003:02
2003:03
2003:04
2004:01
2004:02
2004:03
2004:04
2005:01
2005:02
2005:03
2005:04
2006:01
2006:02
2006:03
2006:04
2007:01
2007:02
2007:03
2007:04
Data/Forecasts/Level
Principles of Forecasting
Projective Models
Winters’ Seasonal Exponential Smoothing
Oregon Personal Income Tax Revenues (in $ Millions)
1600
1500
1400
1300
1200
1100
1000
900
800
700
Data
Forecast
Level
600
Time
Michael L. Hand
Professor of Applied Statistics
and Information Systems
Atkinson Graduate School of Management
Willamette University
Principles of Forecasting
Forecasting Process








Enterprise Understanding
Data Understanding
Alternative Model Identification
Model Estimation
Model Assessment – Adequacy, Quality
Model Selection
Model Interpretation
Forecasting
Important (oft overlooked) knowledge acquisition stages
(see Class_Tools:Hand_Outs:Forecasting:NNG_Paper.pdf)
Michael L. Hand
Professor of Applied Statistics
and Information Systems
Atkinson Graduate School of Management
Willamette University
Principles of Forecasting
Example: Oregon Personal Income Taxes,
1996 – 2005
Oregon Personal Income Tax Revenues (in $ Millions)
1500
1400
Data Understanding
Note dramatic shift in
level and nature of
seasonal variation
1300
Data/Forecast
1200
1100
1000
900
800
700
1996:01
1996:02
1996:03
1996:04
1997:01
1997:02
1997:03
1997:04
1998:01
1998:02
1998:03
1998:04
1999:01
1999:02
1999:03
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2000:01
2000:02
2000:03
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2001:02
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2002:01
2002:02
2002:03
2002:04
2003:01
2003:02
2003:03
2003:04
2004:01
2004:02
2004:03
2004:04
2005:01
2005:02
2005:03
2005:04
600
Period
(see Class Tools resource Hand_Outs:Forecasting:MultDecompPITFull.xls)
Michael L. Hand
Professor of Applied Statistics
and Information Systems
Atkinson Graduate School of Management
Willamette University
Principles of Forecasting
Example: Oregon Personal Income Taxes,
1996 – 2001
Oregon Personal Income Tax Revenues (in $ Millions)
1500
1400
For simplicity, we restrict
our initial view to the
fairly stable period from
1996 – 2001
Data Understanding
Data/Forecasts
1300
1200
1100
1000
900
800
700
2001:04
2001:03
2001:02
2001:01
2000:04
2000:03
2000:02
2000:01
1999:04
1999:03
1999:02
1999:01
1998:04
1998:03
1998:02
1998:01
1997:04
1997:03
1997:02
1997:01
1996:04
1996:03
1996:02
1996:01
600
Period
(see Class Tools resource Hand_Outs:Forecasting:MultDecompPIT.xls)
Michael L. Hand
Professor of Applied Statistics
and Information Systems
Atkinson Graduate School of Management
Willamette University
Principles of Forecasting
Example: Classical Multiplicative
Decomposition
Conceptual Decomposition:
Trend:
Cycle:
Seasonal:
Irregular:
Long-term growth/decline
Long-term slow, irregular oscillation
Regular, periodic variation w/in calendar year
Short-term, erratic variation
Conceptual Forecast:
Forecasting Model:
Michael L. Hand
Professor of Applied Statistics
and Information Systems
yt  Trend t  Cyclet  Seasonalt  Irregulart
yˆ t  Trend t  Seasonalt
 s1 
s 
yˆ t  b0  b1t   2 

 
sL 
Atkinson Graduate School of Management
Willamette University
Principles of Forecasting
Example: Classical Multiplicative
Decomposition
Conceptual Decomposition: yt  Trend t  Cyclet  Seasonalt  Irregulart
1600
1500
1400
1300
Data
1200
1100
1000
900
800
700
1996:01
1996:02
1996:03
1996:04
1997:01
1997:02
1997:03
1997:04
1998:01
1998:02
1998:03
1998:04
1999:01
1999:02
1999:03
1999:04
2000:01
2000:02
2000:03
2000:04
2001:01
2001:02
2001:03
2001:04
600
Period
Michael L. Hand
Professor of Applied Statistics
and Information Systems
Atkinson Graduate School of Management
Willamette University
Principles of Forecasting
Economic Instability Since 1945
Annual % change
in real GDP
15
Second World
War boom
First World
War boom
Change in
real GDP
10
5
0
1937-38
Recession
-5
- 10
- 15
1910
1920-21
Recession
1920
Great
Recession
1930
1940
1950
1960
1970
1980
Sources: Historical Statistics of the United States, p. 224; and Bureau of Economic Analysis, www.bea.doc.gov.
Michael L. Hand
Professor of Applied Statistics
and Information Systems
Atkinson Graduate School of Management
Willamette University
1990
2000
Principles of Forecasting
Example: Classical Multiplicative
Visual Representation
Decomposition
1.25
1600
1200
1000
1.15
Seasonal
Trend
1400
0.95
800
600
0.85
1.25
1.25
1.15
1.15
1.05
Irregular
Cyclical
1.05
1.05
0.95
0.95
0.85
0.85
Michael L. Hand
Professor of Applied Statistics
and Information Systems
Atkinson Graduate School of Management
Willamette University
Principles of Forecasting
Example: Classical Multiplicative
Decomposition, Model Interpretation
 s1 
s 
yˆ t  b0  b1t   2 ,

 
sL 
0.9794
0.9236

yˆ t  731.9291  18.5017t  
0.8913


1.2057 
Model Interpretation
Initial, time-zero (1995:Q4) level is $731.92 million
Increasing at $18.5 million per quarter
Seasonal pattern
Peak in Q4 21% over trend
Trough in Q3 11% below trend
Michael L. Hand
Professor of Applied Statistics
and Information Systems
Atkinson Graduate School of Management
Willamette University
Principles of Forecasting
Example: Classical Multiplicative
Decomposition, Forecasts
 s1 
s 
yˆ t  b0  b1t   2 ,

 
sL 
0.9794
0.9236

yˆ t  731.9291  18.5017t  
0.8913


1
.
2057


Forecasts
1996 : Q1 t  1
yˆ1  731.9291  18.5017( 1) 0.9794   750.4309  0.9794  735.00
2002 : Q1 t  25

yˆ 25  731.9291  18.5017(25) 0.9794  1194.4727  0.9794  1169.90
2002 : Q 2 t  26
yˆ 26  731.9291  18.5017(26) 0.9236  1212.9744  0.9236  1120.32
2002 : Q3 t  27 
yˆ 27  731.9291  18.5017(27) 0.8913  1231.4762 0.8913  1097.60
2002 : Q 4 t  28
yˆ 28  731.9291  18.5017(28) 1.2057  1249.9779  1.2057  1507.07
Michael L. Hand
Professor of Applied Statistics
and Information Systems
Atkinson Graduate School of Management
Willamette University
Principles of Forecasting
Forecast Model Assessment
Residual analysis: A somewhat scatological endeavor,
whereby we assess forecast quality through an analysis
of residuals or what the forecast process leaves
unexplained.
Residual (Error) = Actual – Forecast
Assessment possible for any type of forecasting process –
statistical, organizational, ad hoc, arbitrary.
Michael L. Hand
Professor of Applied Statistics
and Information Systems
Atkinson Graduate School of Management
Willamette University
Principles of Forecasting
Example: Classical Multiplicative
Decomposition, Residuals/Errors
Time
1
2
3
4
Year
1996
1996
1996
1996
Qtr
1
2
3
4
Period
1996:01
1996:02
1996:03
1996:04
Tax
700.38
694.46
731.49
933.63
Forecast
735.00
710.19
701.83
971.70
Error
-34.62
-15.74
29.66
-38.07
2001
2001
2001
2001
2002
2002
2002
2002
1
2
3
4
1
2
3
4
2001:01
2001:02
2001:03
2001:04
2002:01
2002:02
2002:03
2002:04
1075.97
1011.88
1063.42
1399.33
1097.42
1051.96
1031.64
1417.84
1169.90
1120.32
1097.60
1507.07
-21.45
-40.08
31.79
-18.50
…
21
22
23
24
25
26
27
28
Michael L. Hand
Professor of Applied Statistics
and Information Systems
Atkinson Graduate School of Management
Willamette University
Principles of Forecasting
Example: Classical Multiplicative
Decomposition, Time Series Plot of Residuals
Oregon Personal Income Tax Revenues (in $ Millions)
100
60
40
20
-40
-60
Period
Michael L. Hand
Professor of Applied Statistics
and Information Systems
Atkinson Graduate School of Management
Willamette University
2001:04
2001:03
2001:02
2001:01
2000:04
2000:03
2000:02
2000:01
1999:04
1999:03
1999:02
1999:01
1998:04
1998:03
1998:02
1998:01
1997:04
1997:03
1997:02
1997:01
1996:04
1996:03
-20
1996:02
0
1996:01
Prediction Errors (in $ Millions)
80
Lesson
• Economists cannot accurately
predict revenue growth from one
year to the next or the timing of the
business cycle, but we can make
actuarial predictions
• Mean/variance analysis: trend +
variance (systematic volatility and
unsystematic volatility or noise)
Jump to first page
Forecast Model
Assessment
Residual analysis:
Residual = Actual – Trend
Residual = Error
Trend = Forecast, mean rate of
growth
Residuals can be described in terms of
Var or SD from mean rate of growth
Var = volatility
Jump to first page
Portfolio Theory
Next page
Lesson
• Most states cannot significantly
reduce volatility in revenue growth
by substituting one tax type for
another (e.g. a broad-based goods
and services taxes for an income
tax, or vice versa).
Jump to first page
Lesson
• Unsystematic volatility in revenue
growth can in theory be reduced via a
well-designed portfolio of tax/transfer
types.
• Diversification can reduce revenue
volatility: most states rely on a portfolio
of tax types.
• How does diversification of tax portfolios
work? The answer is that portfolio
volatility is a function of the covariance
or correlation, , of its component
revenue sources
Jump to first page
Diversification of tax types
Table 1: An Illustrative, Two-Tax Portfolio
Recession
Below Average
Average
Above Average
Boom
Expected Growth
Prob.
Income
Alcohol
Portfolio
0.10
0.20
0.40
0.20
0.10
-22.0%
-2.0
10.0
18.0
30.0
8.0
8,0%
4.0
0.0
-4
-8.0
0
-7.0%
1.0
5.0
7.0
11.0
4.0
•Expected growth is the weighted average of the growth rates or four
percent.
•The volatility of the portfolio,  = 3.1 percent -- much less than the
volatility of either the income tax (13.4 percent) or the average of income
and alcohol taxes (8.9 percent). It is less even, than the volatility of the
alcohol tax alone (4.4 percent)
Jump to first page
Implications of
portfolio theory
• In general, tax sources have  0.65, so adding taxes to
the portfolio tends to reduce but not eliminate volatility.
• It is possible to construct an efficient growth frontier,
showing an efficient linear combination of growth rates and
volatilities ranging from zero volatility, to a state’s optimal
volatility at its current growth rate and beyond
• All one needs is information on the covariance of the
growth rates of each of the different tax types and designs
that obtain in different states.
• Only if we look at efficient tax portfolios is there a
necessary tradeoff between stability and growth
Jump to first page
Efficient Tax Portfolios
Expected
Portfolio
Growth
PE
PEF
Theoretically feasible
PY
OR
CY
CS
SE
Efficiency frontier
PE = Eff icient Portfolio
PEF = Eff icient and Fair Portfolio
OR = Current tax portfolio
CY = Corporate income tax
PY = Personal income tax
CS = Broad-based consumption tax
SE = Selected excises
Volatility,
Figure 6: Feasible and Efficient Tax Portfolios
Jump to first page
Lesson
• Average volatility will usually be reduced by
adding tax sources, except where the two taxes
are perfectly correlated, r = +1.0
• A two tax portfolio could in theory be combined
to eliminate revenue volatility completely, but
only if r = -1.0 and the two taxes were weighted
equally
• The portion of the volatility that cannot be
eliminated via a portfolio of revenue and
transfer types is known as systemic volatility;
the portion that can, in theory, be eliminated is
known as unsystematic volatility or noise
Jump to first page
Lesson
• Once an efficient tax-portfolio
frontier has been identified,
changes in the portfolio of tax
types and transfers to increase taxequity will also increase volatility
in revenue growth
Jump to first page
Lesson
• Even the best-designed tax portfolio
would not eliminate all volatility. In the
absence of a policy of borrowing and
lending at the risk free rate, the best taxportfolio designers could do is eliminate
the unsystematic or random portion of
the variation in revenue growth.
• The systematic portion would remain. By
systematic we mean, the portion
correlated with some underlying variable
Jump to first page
Lesson
• GNP growth is the main underlying
variable -- which has two components
• Trend (mean)
• Cyclical
• Predicting the timing and amplitude of business
cycles is no easier than predicting the growth
of the economy from one year to the next
Jump to first page
Hedging and self insurance
One way to eliminate systematic volatility in revenue
growth is with a revenue flow of equal and opposite
volatility. This is called hedging.
If we could find two tax types which produced revenue
flows of the same size that were perfectly, but inversely
correlated with each other, we could eliminate all volatility
in revenue growth. Unfortunately, there are no such tax
types.
Is it possible to design a hedge against the systematic
component of revenue volatility?
Next page
Lesson
• It is theoretically possible to do so
using forwards, futures, or options
Jump to first page
Lesson
• It is theoretically possible to do so
using forwards, futures, or options
• It is not practically feasible to do
so at this time
Jump to first page
Lesson
• It may never be politically
feasible to do so
Jump to first page
Hedging with options
& futures contracts
• Futures
• Options
See C. Hinkelmann & Steve Swidler,
“Macroeconomic Hedging with Existing
Futures Contracts,” Risk Letters,
forthcoming;
“State Government Hedging with
Financial Derivatives,” State and Local
Government Review, volume 37:2,
2005; “Using Futures Contracts to
Hedge Macroeconomic Risks in the
Public Sector,” Trading and
Regulation, volume 10, number 1,
2004.
Jump to first page
Self insurance?
• Rainy day fund
• Cooperative cash pool
Jump to first page
Lesson
Self insurance and risk pooling
• Insurance is like a put option.
• A rainy-day fund is simply a form of
self insurance.
• A rainy day fund large enough to
prevent all revenue shortfalls would be
very costly
• Risk pooling would dramatically
reduce those costs
Jump to first page
Optimal Spending
Next page
Lesson
• States can use savings and/or borrowing to smooth out
consumption over the business cycle
• Consumption smoothing implies present value balance:
PV future revenue (Taxes - Transfers) + net assets ≥ PV future
exhaustive expenditures
• Goal should be to balance budgets in a present-value sense, using
savings and debt to smooth spending
• Hence, the problem faced by budgeters is to identify the maximum
rate of growth in the spending level from one year to the next that
is consistent with present value balance, given the state’s existing
revenue/transfer structure and volatility.
• where PV future revenues + net assets < PV future exhaustive
expenditures, permanent reductions in spending or permanent
increases in taxes are necessary
Jump to first page
Lesson
• This can be done by treating revenue
growth as a random walk. In which case,
the problem faced by budget makers can
be solved mathematically by optimal
control theory or estimated via Monte
Carlo simulation.
Jump to first page
The basic question
How much should we spend next
year?
State and local governments have few
degrees of freedom but can focus on
issues of solvency and liquidity
Jump to first page
Managing spending
• Schunk and Woodward’s (S&W)
spending rule:
Increase spending no faster than the rate
of inflation plus the long-term real
growth rate of the underlying economy
(put aside the remainder for a rainy
day)
Donald Schunk and Douglas P. Woodward. Spending Stabilization Rules: A Solution to
Recurring State Budget Crises? 2005. Public Budgeting & Finance 5(4): 105-124.
Jump to first page
Managing spending 2
General Fund Budget
Figure 4: Oregon Spending, Actual and
Stabilization Rule
8,000
7,000
6,000
5,000
4,000
A
3,000
2,000
1,000
0
1
2
3
4
5
Biennium
Stabilization Rule Outlays
Jump to first page
Actual GF Outlays
Revenue growth is a
random walk
Revenue growth can be modeled as a
Wiener process:
• a continuous-time, continuous-state stochastic
process in which the distribution of future values
conditional on current and past values is identical
to the distribution of future values conditional on
the current value alone, and
• the variance of the change in the process grows
linearly with the time horizon.
Jump to first page
Monte Carlo simulation of Oregon’s future
spending and revenues, given the adoption
of S&W’s spending rule
y = 2.6215x
R2 = 0.5876
$1,000
$800
Value
$600
$400
$200
$0
0
10
20
30
40
50
-$200
Time
Jump to first page
60
70
80
90
100
A better spending rule
Given that we can model revenue growth as
a Wiener process, it is possible to calculate
a spending rule directly using optimal
control theory.
By comparing proposed spending levels
(including tax expenditures and debt
service) against the optimum spending
level calculated using this rule, one can say
whether or not the specified spending level
is sustainable and implicitly assess a state’s
saving and borrowing policies as well.
Jump to first page
Findings
• Budgetary Growth = to
geometric mean of revenue
growth is closer to optimum
than Budgetary Growth equal
to arithmetic mean of nominal
growth of the underlying
economy
Jump to first page
Practical Implications
• Oregon cannot significantly reduce volatility in
revenue growth by tinkering with its tax structure -at least not without also reducing progressivity
• Hedging -- probably not practical
• Oregon could rely on a rainy day fund of sufficient size
to mitigate the adverse consequences of cyclical
revenue shortfalls (if it had one) or meliorate them via
a program of countercyclical borrowing
• Other things equal, Oregon’s revenue growth trend is
faster than outlay growth under the S&W rule
• Oregon doesn’t need to increase taxes to offset a
structural budget deficit -- it could adopt an optimal
spending rule that would allow it to smooth
consumption
Jump to first page
RANKING THE
STATES
Next page
Ranking State &
Local Tax Systems
• Finding a way to rank
fairness, adequacy, and
efficiency is difficult
• There are a lot of outliers
Jump to first page
Fairness
How does my state
compare?
Jump to first page
Method
• Found the log/log
slope using the 7
groups in “Who
Pays?”
• Weighted OLS
Least regressive
New York
Vermont
South Carolina
Wisconsin
Delaware
Oregon
Montana
Kansas
Kentucky
Maryland
1.078
1.055
1.052
1.038
1.011
1.010
1.004
1.003
0.995
0.989
1.815
1.567
1.529
1.387
1.099
1.082
1.019
1.005
0.923
0.858
1
2
3
4
5
6
7
8
9
10
Most regressive
New Hampshire
Alabama
Nevada
Arizona
Texas
Wyoming
Florida
South Dakota
Tennessee
Washington
Alaska
Jump to first page
0.855
0.838
0.806
0.792
0.776
0.769
0.749
0.741
0.733
0.709
0.705
-0.585
-0.762
-1.115
-1.257
-1.429
-1.505
-1.724
-1.810
-1.893
-2.158
-2.198
40
41
42
43
44
45
46
47
48
49
50
Caveat 1: ITEP Treats
every tax the same, but not
all states have same taxes
Table 1: Oregon’s Tax Structure, the ITEP Version 2007
Jump to first page
Table 2: Oregon’s Tax Structure, with Adjustments for Implicit Excises,
for Business and Property Taxes and for Reported Income and Taxes Paid 2007
Jump to first page
Ranking vs. Slope
Data Source: Who Pays?
Jump to first page
Efficiency
How hard is it?
Jump to first page
Method
• Data source: census • Squared MTRs
data for each state.
• Weighted average
• Calculated
squared percentages
administrative costs
• Deadweight losses
Alaska
Oregon
Washington
Florida
Wyoming
Tennessee
South Dakota
Massachusetts
New York
Hawaii
Lowest
10
Kentucky
Alabama
Illinois
Vermont
Pennsylvania
Michigan
Louisiana
New Mexico
West Virgina
North Dakota
Oklahoma
Jump to first page
Highest
10
Ranking vs. Efficiency
Jump to first page
Adequacy
Paying the bills.
Jump to first page
Method
• Data Source:
Book of the
States
• 1940-2008 data
• Geometric mean
per-capita S&L
revenue growth
• Auto-regressive
moving average
Top 10
Florida
Alaska
Nevada
Wisconsin
Ohio
Arizona
Iowa
Indiana
Utah
Kentucky
Washington
Jump to first page
Bottom 10
Pennsylvania
North Carolina
Alabama
Louisiana
South Dakota
Minnesota
West Virginia
North Dakota
Mississippi
Tennessee
Arkansas
Rank vs. Sum of Z
scores
Jump to first page
Visual Comparison Tool
Making comparisons quick
& painless.
Jump to first page
Alabama
Jump to first page
Arizona
Jump to first page
New York
Jump to first page
Washington
Jump to first page
Oregon
Jump to first page
Conclusion
• Adjustments to current calculations
need to be evaluated
• Ideally an optimum in each category
would be found and the distance from
the optimum would be used to
calculate the ranking.
• Unified scale.
Jump to first page
Caveat 2
We ought to treat transfers as negative taxes.
Taxes are not the locus of redistribution. Instead, transfers are.
Cash and noncash transfers go far more to the poor than to the rich.
Transfers do most of the redistributive work in all states.
Major source of volatility in state/local systems of taxing and
spending
Jump to first page