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