econ 240 c
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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
3
4
Schedule 6
5Schedule 9
6
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
7
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
8
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
9
Part I. CA Budget Crisis
10
CA Budget Crisis
What is Happening to UC?• UC Budget from the state General Fund
11
UC Budget
Econ 240A Lab Four New data for Fiscal Year 2007-08 Governor’s Budget Summary 2007-08
• released January 2007• http://www.dof.ca.gov/
12
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
14
CA Budget Crisis
What is happening to the CA economy?• CA personal income
15
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
$
16
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
17
18
CA Budget Crisis
How is UC faring relative to the CA economy?
19
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
20
CA Budget Crisis
What is happening to CA state Government?• General Fund Expenditures?
21
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
22
CA Budget Crisis
How is CA state government General Fund expenditure faring relative to the CA economy?
23
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
24
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
25What has happened to UC’s Share of CA General Fund
Expenditures? UC Budget Share = (UC Budget/CA Gen
Fnd Exp)
26
UC's Share of General Fund Expenditure, 68-69 to 07-08
3.17%
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
7.00%
8.00%
Fiscal Year
Pe
rce
nt 07-08
27
28
29
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.
30What 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)
31CA General Fund Expenditures as a Fraction of Personal Income
6.86%
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
Fiscal Year
Pe
rce
nt
07-08
32
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
33
CA Budget Crisis
Estimate of the relative size of the CA government: 7.00 %
Estimate of UC’s Budget Share: 3.00% UC Bud = 0.03*0.07*CAPY UC Bud = 0.0021* 1502.5 $B UC Bud = 3.155 $B
34 Forecasts of UC Budget, 07-08
Method Forecast
Actual $ 3.270 B
Identity/CAPY $ 3.155 B
35
Econometric Estimates of UCBUD
Linear trend Exponential trend Linear dependence on CAPY Constant elasticity of CAPY
36
Econometric Estimates
Linear Trend Estimate UCBUDB(t) = a + b*t +e(t)
• A lucky coincidence• Usually either too low or too high!
37
UC General Fund Expenditures, $ Millions, 68-69 to 07-08
01-0207-08
y = 80.323x + 36.343
R2 = 0.9431
0
500
1000
1500
2000
2500
3000
3500
4000
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
A Lucky Coincidence: 2 out of 10
38
Econometric Estimates
Logarithmic (exponential trend) lnUCBUDB = a + b*t +e(t) simple exponential trend will over-estimate
UC Budget by far
39
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
40
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
41
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
42
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
43
44
Is Higher Education an Inferior Good?
45
46
47
48
Is Government an Inferior Good?
Elasticity = 1.073
49
50Forecasting 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
51
52
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
53
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)
54
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
55
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
56
57
58Estimate ARONE Model dlncapy
59
-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
60Orthogonal Residuals
61
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
62Cross-Correlate w and resdlncapy
63
Distributed lag of w on resdlncapy
W =h0*resdlncapy + h1*resdlncapy(-1) + e*(t)
64Distributed lag Model
65Residuals
66Also model error as arone
67
residuals
68Estimate this model for dlnucbud
69Estimated model
70
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
71Residuals
72Fitted dlnucbud
Dlnucbud (07-08) = 0.046
73
Dlnucbudf(07-08)
Dlnucbudf(07-08) = 0.0452
74 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)]
75
Identify dlnucbud
-0.2
-0.1
0.0
0.1
0.2
70 75 80 85 90 95 00 05
DLNUCBUD
76
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
77
78
79
Model dlnucbud
80
Identify dlncapy
Estimate model for dlnucbud
81
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
82residuals
83Univariate forecast dlnucbud(07-08)
Dlnucbud(07-08) = 0.0696
84 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.
85
0
1
2
3
4
70 75 80 85 90 95 00 05
UCBUDGET UCBUDGSM UCBUDGSMHW
Exponential Smoothing Forecasts of UC Budget
86
87
Efforts from earlier years
88
89
90
Estimate ARONE Model for dlncapy
91
Satisfactory Model
92
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)
93
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
94
95
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)
96
97
98
99
Try an AR(6) AR(8)residual for dlnucbudb
100
101
102
103
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
104
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
105
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 $
106
107
108
109
110
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)
111
112
113
114
115
Distributed Lag Model
dlnucbud(t) = h0 *dlncapy(t-1) + dummy (1992-93) + resid(t)
116
117
118
119
120Fitted fractional change in UC Budget is 0.032 (3.2%)versusGovernor’s proposal of 0.033 (3.3%)
121
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
123
124
Try estimating the model in levels
125
126
127
128
129
130
131
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
132
Postscript 2006-07
133
-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
134
-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
135
136
137
-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
138
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