econ 240 c lecture 12. 2 the big picture w exploring alternative perspectives w exploratory data...
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Econ 240 C
Lecture 12
2
The Big Picture
Exploring alternative perspectives Exploratory Data Analysis
• Looking at components
Trend analysis• Forecasting long term
Distributed lags• Forecasting short term
3The 2010-2011 CA Budget Long Run Perspectives
• Univariate trends• Bivariate relationships
Short Run
4
UC Budget in Nominal Billions $ Vs. Fiscal Year: 1968-69 - 2010-11
y = 0.0737x + 0.1305
R2 = 0.9139
0
0.5
1
1.5
2
2.5
3
3.5
4
68-6
9
70-7
1
72-7
3
74-7
5
76-7
7
78-7
9
80-8
1
82-8
3
84-8
5
86-8
7
88-8
9
90-9
1
92-9
3
94-9
5
96-9
7
98-9
9
00-0
1
02-0
3
04-0
5
06-0
7
08-0
9
10-1
1
Fiscal year
Bill
ion
s $
UC Budget $B nominal Vs. Fiscal Year
5UC Budget Billions Nominal $ Vs. Fiscal Year: 1998-09 – 2010-11
UC Budget in Billions Nominal $ Vs. Fiscal Year 1998-09 - 2010-11
y = -0.0073x + 2.9583
R2 = 0.0087
0
0.5
1
1.5
2
2.5
3
3.5
4
98-99 99-00 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11
Fiscal year
Bill
ion
s $
6
UC Budget Vs. California Personal Income, Both in $ Billions Nominal Dollars: 1968-68 - 2010-11
0
0.5
1
1.5
2
2.5
3
3.5
4
0 200 400 600 800 1000 1200 1400 1600 1800
California Personal Income
UC
Bu
dg
et
1991-2 RECESSION
2001-02 Recession?
7US Civilian Unemployment Rate
8UC’s Share of California General Fund Expenditures
UC's Share of California General Fund expenditure Vs. Fiscal Year.
y = -0.0009x + 0.0703
R2 = 0.8785
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
7.00%
8.00%
68-6
9
70-7
1
72-7
3
74-7
5
76-7
7
78-7
9
80-8
1
82-8
3
84-8
5
86-8
7
88-8
9
90-9
1
92-9
3
94-9
5
96-9
7
98-9
9
00-0
1
02-0
3
04-0
5
06-0
7
08-0
9
10-1
1
Fiscal Year
Per
cen
t
9Relative Size of California GovernmentCalifornia General Fund Expenditures as Percent of California Personal Income
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
7.00%
8.00%
68-6
9
70-7
1
72-7
3
74-7
5
76-7
7
78-7
9
80-8
1
82-8
3
84-8
5
86-8
7
88-8
9
90-9
1
92-9
3
94-9
5
96-9
7
98-9
9
00-0
1
02-0
3
04-0
5
06-0
7
08-0
9
10-1
1
Fiscal Year
Per
cen
t
10
CA Budget Crisis Estimate of the relative size of the CA
government: 5.14 % Estimate of UC’s Budget Share: 3.68% UC Bud = 0.0368*0.0514*CAPY UC Bud = 0.00189* 1597.2 $B UC Bud = 3.021 $B for 2010-11 UC Bud = 3.019 $B Governor’s proposal
11
12
Schedule 6
Fiscal Year:
CA personal
Income, CA
General Fund Expenditures
13Schedule 9: UC Budget, Gen. Fund Support
14
UC Budget and CA Personal Income, Nominal Billions, 68-69 through 08-09
1968-69
1990-01
2008-09
0
0.5
1
1.5
2
2.5
3
3.5
4
0 200 400 600 800 1000 1200 1400 1600 1800
CA Personal Income
UC
Ge
n. F
nd
. Bu
dg
et
2001-02
Recession: Dec. 1969 - Nov. 1970
Recession: Nov. 1973 - March 1975
Recession: Jan. 1980 - July 1980
Recession: July 1981- November 1982
Recession: July 1990 - March 1991
Recession: March 2001 - November 2001
15
16
17Salary by Major
18Economic Concept of a Public Good
Consumption by one person does not leave less for the next person• National Defense• Safe Streets• Public Health
• Flu shots
• Measle vaccinations
19Return to Education
20
Forecast of UC Budget ,2006-07 & 2007-08, Nominal Billions
0
0.5
1
1.5
2
2.5
3
3.5
4
0 200 400 600 800 1000 1200 1400 1600
CA Personal Income
UC
Bu
dg
et
07-08
The story based on a bivariate distributed lag model
21
fORECAST OF UC Budget, 06-07 & 07-08, Nominal Billions
0
0.5
1
1.5
2
2.5
3
3.5
4
1968
-69
1970
-71
1972
-73
1974
-75
1976
-77
1978
-79
1980
-81
1982
-83
1984
-85
1986
-87
1988
-89
1990
-91
1992
-93
1994
-95
1996
-97
1998
-99
2000
-01
2002
-03
2004
-05
2006
-07
Fiscal Year
Bil
lio
ns
$
Another Story Based On a Univariate ARIMA Model
22
Part I. CA Budget Crisis
23
CA Budget Crisis
What is Happening to UC?• UC Budget from the state General Fund
24
UC Budget
Econ 240A Lab Four New data for Fiscal Year 2008-09 Governor’s Budget Summary 2008-09
• released January 2008• http://www.dof.ca.gov/
25
UC General Fund Expenditures, $ Millions, 68-69 to 07-08
01-0207-08
0
500
1000
1500
2000
2500
3000
3500
4000
Fiscal year
$M
Logarithm of UC Budget: Changes in Growth Paths
-1.5
-1
-0.5
0
0.5
1
1.5
68-6
9
70-7
1
72-7
3
74-7
5
76-7
7
78-7
9
80-8
1
82-8
3
84-8
5
86-8
7
88-8
9
90-9
1
92-9
3
94-9
5
96-9
7
98-9
9
00-0
1
02-0
3
04-0
5
Fiscal Year
lnu
cbu
db
Fitted through 91-92
lnucbudb
27
CA Budget Crisis
What is happening to the CA economy?• CA personal income
28
California Personal Income in Billions of Nominal $
0
200
400
600
800
1000
1200
1400
1968
-69
1970
-71
1972
-73
1974
-75
1976
-77
1978
-79
1980
-81
1982
-83
1984
-85
1986
-87
1988
-89
1990
-91
1992
-93
1994
-95
1996
-97
1998
-99
2000
-01
2002
-03
2004
-05
Fiscal Year
Bil
lio
ns
$
29
California Personal Income in Billions of Nominal $
10
100
1000
10000
1968
-69
1970
-71
1972
-73
1974
-75
1976
-77
1978
-79
1980
-81
1982
-83
1984
-85
1986
-87
1988
-89
1990
-91
1992
-93
1994
-95
1996
-97
1998
-99
2000
-01
2002
-03
2004
-05
Fiscal Year
Bil
lio
ns
$
Log Scale
30
Nov 1989 Berlin Wall Down
31
CA Budget Crisis
How is UC faring relative to the CA economy?
32
UC General Fund Expenditures Vs. California Personal Income, 68-69 to 07-08
07-08
0
0.5
1
1.5
2
2.5
3
3.5
4
0 200 400 600 800 1000 1200 1400 1600
CA Personal Income, $B
UC
Ge
n F
un
d E
xp
. $B
33
CA Budget Crisis
What is happening to CA state Government?• General Fund Expenditures?
34
CA General Fund Expenditures, Nominal Millions $
07-08
0
20000
40000
60000
80000
100000
120000
68-6
9
70-7
1
72-7
3
74-7
5
76-7
7
78-7
9
80-8
1
82-8
3
84-8
5
86-8
7
88-8
9
90-9
1
92-9
3
94-9
5
96-9
7
98-9
9
00-0
1
02-0
3
04-0
5
06-0
7
Fiscal Year
$M
35
CA Budget Crisis
How is CA state government General Fund expenditure faring relative to the CA economy?
36
California: General Fund Expenditures Vs. Personal Income, 68-69 to 07-08
07-08
0
20
40
60
80
100
120
0 200 400 600 800 1000 1200 1400 1600
CA Personal Income $B
Ge
n F
un
d E
xp
. $B
37
Long Run Pattern Analysis
Make use of definitions: UCBudget = (UCBudget/CA Gen Fnd
Exp)*(CA Gen Fnd Exp/CA Pers Inc)* CA Pers Inc
UC Budget = UC Budget Share*Relative Size of CA Government*CA Pers Inc
38What has happened to UC’s Share of CA General Fund
Expenditures? UC Budget Share = (UC Budget/CA Gen
Fnd Exp)
39
UC's Share of General Fund Expenditures, 1968-69 through 2008-09
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
7.00%
8.00%
68-6
9
70-7
1
72-7
3
74-7
5
76-7
7
78-7
9
80-8
1
82-8
3
84-8
5
86-8
7
88-8
9
90-9
1
92-9
3
94-9
5
96-9
7
98-9
9
00-0
1
02-0
3
04-0
5
06-0
7
08-0
9
Fiscal Year
Pe
rce
nt
40
41
-1.5
-1.0
-0.5
0.0
0.5
1.0
2
3
4
5
6
7
8
70 75 80 85 90 95 00 05
Residual Actual Fitted
UC's Declining Budget Share: 0.1% Per Year
42
UC Budget Crisis
UC’s Budget Share goes down about one tenth of one per cent per year• will the legislature continue to lower UC’s
share? • Probably, since competing constituencies such
as prisons, health and K-12 will continue to lobby the legislature.
43What has happened to the size of California Government Expenditure Relative to Personal Income? Relative Size of CA Government = (CA
Gen Fnd Exp/CA Pers Inc)
44
07-08CA General Fund Expenditures as Percent of Personal Income
6.36%
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
7.00%
8.00%
Fiscal Year
45
California Political History Proposition 13
• approximately 2/3 of CA voters passed Prop. 13 on June 6, 1978 reducing property tax and shifting fiscal responsibility from the local to state level
Gann Inititiative (Prop 4)• In November 1979, the Gann initiative was
passed by the voters, limits real per capita government expenditures
46
CA Budget Crisis
Estimate of the relative size of the CA government: 6.50 %
Estimate of UC’s Budget Share: 3.00% UC Bud = 0.03*0.065*CAPY UC Bud = 0.00195* 1588.5 $B UC Bud = 3.098 $B for 2008-09 UC Bud = 3.494 Governor’s proposal
47 Forecasts of UC Budget, 08-09
Method Forecast
Actual (proposed) $3.394 B
Identity/CAPY $3.098 B
48
Econometric Estimates of UCBUD
Linear trend Exponential trend Linear dependence on CAPY Constant elasticity of CAPY
49
Econometric Estimates
Linear Trend Estimate UCBUDB(t) = a + b*t +e(t)
• A lucky coincidence• Usually either too low or too high!
50
A Lucky Coincidence: 2 out of 10UCBudget, $Millions, 1968-69 through 2007-08
2007-08y = 80.259x + 37.208
R2 = 0.943
0
500
1000
1500
2000
2500
3000
3500
4000
Fiscal Year
UC
BU
D
2007-08: $3260.748plus slope: 80.259Forecast: $3341.007
51
Econometric Estimates
Logarithmic (exponential trend) lnUCBUDB = a + b*t +e(t) simple exponential trend will over-estimate
UC Budget by far
52
UC General Fund Expenditures, $ Millions, 68-69 to 07-08
01-0207-08
y = 383.78e0.0611x
R2 = 0.9047
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
68-6
9
70-7
1
72-7
3
74-7
5
76-7
7
78-7
9
80-8
1
82-8
3
84-8
5
86-8
7
88-8
9
90-9
1
92-9
3
94-9
5
96-9
7
98-9
9
00-0
1
02-0
3
04-0
5
06-0
7
Fiscal year
$M
53
Econometric Estimate
Dependence of UC Budget on CA Personal Income
UCBUDB(t) = a + b*CAPY(t) + e(t) looks like a linear dependence on income
will overestimate the UC Budget for 2007-08
54
UC General Fund Expenditures Vs. California Personal Income, 68-69 to 07-08
07-08
y = 0.0022x + 0.3674
R2 = 0.9265
0
0.5
1
1.5
2
2.5
3
3.5
4
0 200 400 600 800 1000 1200 1400 1600
CA Personal Income, $B
UC
Ge
n F
un
d E
xp
. $B
55
Econometric Estimates
How about a log-log relationship lnUCBUDB(t) = a + b*lnCAPY(t) + e(t) Estimated elasticity 0.833 autocorrelated residual fitted lnUCBUDB(2007-08) = 1.32945
• $3.78 B
actual (Governor’s Proposal) = 1.18481• $3.27B
56
57
Is Higher Education a necessary economic Good?
58
59
60
61
Is Government a luxury Good?
Elasticity = 1.073
62
63Forecasting Conclusions
Trend analysis and bi-variate regressions of UC General Fund Expenditures on California Personal Income focus on the long run
The UC budget depends on the business cycle, a more short run focus
Try Box-Jenkins Methods
64
Econometric Estimates
Try a distributed lag Model of lnUCBUDB(t) on lnCAPY(t)• clearly lnUCBUDB(t) is trended (evolutionary)
so difference to get fractional changes in UC Budget
• likewise, need to difference the log of personal income
65
Box-Jenkins Distributed Lag
Dlnucbud = h0*dlncapy(t) + h1*dlncapy(t-1) + … + e(t)
Dlnucbud(t) = h(z) dlncapy(t) + e(t) Dlncapy = 0.709*dlncapy(t-1) + resdlncapy(t) [1-0.709z]dlnucbud = h(z)[1-0.709z]
*dlncapy(t) + [1-0.709z]*e(t) W(t) = h(z) resdlncapy(t) + e*(t)
66
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
70 75 80 85 90 95 00 05
DLNCAPY
trace of dlncapy
Identify dlncapy: trace
67
0
2
4
6
8
0.02 0.04 0.06 0.08 0.10 0.12 0.14
Series: DLNCAPYSample 1969 2007Observations 39
Mean 0.074725Median 0.074927Maximum 0.133703Minimum 0.010863Std. Dev. 0.032209Skewness -0.029624Kurtosis 2.366026
Jarque-Bera 0.658830Probability 0.719344
Histogram of dlncapy
68
69
70Estimate ARONE Model dlncapy
71
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.00
0.05
0.10
0.15
70 75 80 85 90 95 00 05
Residual Actual Fitted
Validate model
72Orthogonal Residuals
73
0
2
4
6
8
10
12
-0.06 -0.04 -0.02 0.00 0.02 0.04
Series: ResidualsSample 1970 2007Observations 38
Mean -1.05E-14Median 0.003422Maximum 0.037503Minimum -0.063393Std. Dev. 0.022969Skewness -0.838009Kurtosis 3.560656
Jarque-Bera 4.945341Probability 0.084359
Normal Residuals
74Cross-Correlate w and resdlncapy
75
Distributed lag of w on resdlncapy
W =h0*resdlncapy + h1*resdlncapy(-1) + e*(t)
76Distributed lag Model
77Residuals
78Also model error as arone
79
residuals
80Estimate this model for dlnucbud
81Estimated model
82
Diagnostics
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
-0.2
-0.1
0.0
0.1
0.2
75 80 85 90 95 00 05
Residual Actual Fitted
83Residuals
84Fitted dlnucbud
Dlnucbud (07-08) = 0.046
85
Dlnucbudf(07-08)
Dlnucbudf(07-08) = 0.0452
86 Forecasts of UC Budget, 07-08 Method Forecast
Actual $ 3.270 B
Identity/CAPY $ 3.155 B
univariate model
distributed lag $3.223 B = UCBud(06-07)*[1+dlnucbudf(07-08)]
87
Identify dlnucbud
-0.2
-0.1
0.0
0.1
0.2
70 75 80 85 90 95 00 05
DLNUCBUD
88
0
2
4
6
8
10
-0.10 -0.05 0.00 0.05 0.10 0.15 0.20
Series: DLNUCBUDSample 1969 2007Observations 39
Mean 0.062005Median 0.058792Maximum 0.187981Minimum -0.114127Std. Dev. 0.073377Skewness -0.442336Kurtosis 2.920772
Jarque-Bera 1.281995Probability 0.526767
89
90
91
Model dlnucbud
92
Identify dlncapy
Estimate model for dlnucbud
93
diagnostics
-0.2
-0.1
0.0
0.1
0.2
-0.2
-0.1
0.0
0.1
0.2
70 75 80 85 90 95 00 05
Residual Actual Fitted
94residuals
95Univariate forecast dlnucbud(07-08)
Dlnucbud(07-08) = 0.0696
96
Univariate forecast for 2008-09
Fit AR(1) to dlnucbud, 68-69 though 07-08 Forecast dlnucbud for 08-09 = 0.059 with
sef =0.064 Governor’s proposed increase is 0.069
97
-0.2
-0.1
0.0
0.1
0.2
70 75 80 85 90 95 00 05
DLNUCBUD DLNUCBUDF
Dlnucbud, 69-70 through 08-09 with forecast from AR(1) model through 07-08
proposed
Actual
2004-05 wasScwarzenegger’sFirst budget
98 Forecasts of UC Budget, 07-08 Method Forecast
Actual $ 3.270 B
Identity/CAPY $ 3.155 B
univariate model $ 3.298 B ($18 M high)
distributed lag $ 3.223 B = UCBud(06-07)*[1+dlnucbudf(07-08)]
($ 47 M low)
simple exp. smooth $3.083 B
double exp. Smooth -HW $ 3.309 B ($39 M high), trend = $226 M/yr.
99
0
1
2
3
4
70 75 80 85 90 95 00 05
UCBUDGET UCBUDGSM UCBUDGSMHW
Exponential Smoothing Forecasts of UC Budget
100
101
Efforts from earlier years
102
103
104
Estimate ARONE Model for dlncapy
105
Satisfactory Model
106
Estimate ARONE Model for dlncapy(t)
Orthogonalize dlncapy and save residual need to do transform dlnucbudb dlnucbudb(t) = h(Z)*dlncapy(y) + resid(t) dlncapy(t) = 0.72*dlncapy(t-1) + N(t) [1 - 0.72Z]*dlnucbudb(t) = h(Z)* [1 -
0.72Z]*dlncapy(t) + [1 - 0.72Z]*resid(t) i.e. w(t) = h(Z)*N(t) + residw(t)
107
Distributed Lag Model
Having saved resid as res[N(t)] from ARONE model for dlncapy
and having correspondingly transformed dlnucbud to w
cross-correlate w and res
108
109
Distributed lag model
There is contemporary correlation and maybe something at lag one
specify dlnucbud(t) = h0 *dlncapy(t) + h1
*dlncapy(t-1) + resid(t)
110
111
112
113
Try an AR(6) AR(8)residual for dlnucbudb
114
115
116
117
Try a dummy for 1992-93, the last recession, this is the once and for all decline in UCBudget mentioned by Granfield
There is too much autocorrelation in the residual from the regression of lnucbud(t) = a + b*lncapy(t) + e(t) to see the problem
Look at the same regression in differences
118
UCBudget Vs. CA Personal Income, 68-69 through 05-06
0
0.5
1
1.5
2
2.5
3
3.5
4
0 200 400 600 800 1000 1200 1400
CAPY Nominal Billions
UC
Bu
dg
et N
om
inal
Bil
lio
ns
05-06
92-93
119
UC Budget In Billions of Nominal $
0
0.5
1
1.5
2
2.5
3
3.5
4
0 5 10 15 20 25 30 35 40
Fiscal year
Bil
liu
on
s $
120
121
122
123
124
Distributed lag Model dlnucbud(t) = h0 *dlncapy(t) + h1 *dlncapy(t-
1) + dummy (1992-93) + resid(t) dlnucbud(t) = h0 *dlncapy(t) + h1 *dlncapy(t-
1) + dummy (1992-93) + dummy(2002-03) + resid(t)
dlnucbud(t) = h0 *dlncapy(t) + dummy (1992-93) + resid(t)
125
126
127
128
129
Distributed Lag Model
dlnucbud(t) = h0 *dlncapy(t-1) + dummy (1992-93) + resid(t)
130
131
132
133
134Fitted fractional change in UC Budget is 0.032 (3.2%)versusGovernor’s proposal of 0.033 (3.3%)
135
Conclusions Governors proposed increase in UC Budget
of 3.3% is the same as expected from a Box-Jenkins model, controlling for income
The UC Budget growth path ratcheted down in the recession beginning July 1990
The UC Budget growth path looks like it ratcheted down again in the recession beginning March 2001
Logarithm of UC Budget: Changes in Growth Paths
-1.5
-1
-0.5
0
0.5
1
1.5
68-6
9
70-7
1
72-7
3
74-7
5
76-7
7
78-7
9
80-8
1
82-8
3
84-8
5
86-8
7
88-8
9
90-9
1
92-9
3
94-9
5
96-9
7
98-9
9
00-0
1
02-0
3
04-0
5
Fiscal Year
lnu
cbu
db
Fitted through 91-92
lnucbudb
137
138
Try estimating the model in levels
139
140
141
142
143
144
145
Forecast of UC Budget ,2006-07 & 2007-08, Nominal Billions
0
0.5
1
1.5
2
2.5
3
3.5
4
0 200 400 600 800 1000 1200 1400 1600
CA Personal Income
UC
Bu
dg
et
07-08
146
Postscript 2006-07
147
-0.4
-0.2
0.0
0.2
0.4
0.6
0 20 40 60 80 100 120
DCAPY
DU
CB
UD
GE
T
148
-0.4
-0.2
0.0
0.2
0.4
0.6
70 75 80 85 90 95 00 05
DUCBUDGET
0
20
40
60
80
100
120
70 75 80 85 90 95 00 05
DCAPY
Changes in California Personal Income and Changes in the UC Budget
149
150
151
-0.2
-0.1
0.0
0.1
0.2
0.3
-0.4
-0.2
0.0
0.2
0.4
0.6
80 85 90 95 00 05
Residual Actual Fitted
152
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