Econ 240 C

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

Fiscal Year:

CA personal

Income, CA

General Fund Expenditures

5Schedule 9: UC Budget, Gen. Fund Support

6

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

7

8

9Salary by Major

10Economic 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

11Return to Education

12

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

13

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

14

Part I. CA Budget Crisis

15

CA Budget Crisis

What is Happening to UC?• UC Budget from the state General Fund

16

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/

17

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

19

CA Budget Crisis

What is happening to the CA economy?• CA personal income

20

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

$

21

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

22

Nov 1989 Berlin Wall Down

23

CA Budget Crisis

How is UC faring relative to the CA economy?

24

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

25

CA Budget Crisis

What is happening to CA state Government?• General Fund Expenditures?

26

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

27

CA Budget Crisis

How is CA state government General Fund expenditure faring relative to the CA economy?

28

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

29

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

30What has happened to UC’s Share of CA General Fund

Expenditures? UC Budget Share = (UC Budget/CA Gen

Fnd Exp)

31

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

32

33

-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

34

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.

35What 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)

36

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

37

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

38

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

39 Forecasts of UC Budget, 08-09

Method Forecast

Actual (proposed) $3.394 B

Identity/CAPY $3.098 B

40

Econometric Estimates of UCBUD

Linear trend Exponential trend Linear dependence on CAPY Constant elasticity of CAPY

41

Econometric Estimates

Linear Trend Estimate UCBUDB(t) = a + b*t +e(t)

• A lucky coincidence• Usually either too low or too high!

42

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

43

Econometric Estimates

Logarithmic (exponential trend) lnUCBUDB = a + b*t +e(t) simple exponential trend will over-estimate

UC Budget by far

44

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

45

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

46

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

47

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

48

49

Is Higher Education a necessary economic Good?

50

51

52

53

Is Government a luxury Good?

Elasticity = 1.073

54

55Forecasting 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

56

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

57

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)

58

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

59

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

60

61

62Estimate ARONE Model dlncapy

63

-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

64Orthogonal Residuals

65

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

66Cross-Correlate w and resdlncapy

67

Distributed lag of w on resdlncapy

W =h0*resdlncapy + h1*resdlncapy(-1) + e*(t)

68Distributed lag Model

69Residuals

70Also model error as arone

71

residuals

72Estimate this model for dlnucbud

73Estimated model

74

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

75Residuals

76Fitted dlnucbud

Dlnucbud (07-08) = 0.046

77

Dlnucbudf(07-08)

Dlnucbudf(07-08) = 0.0452

78 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)]

79

Identify dlnucbud

-0.2

-0.1

0.0

0.1

0.2

70 75 80 85 90 95 00 05

DLNUCBUD

80

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

81

82

83

Model dlnucbud

84

Identify dlncapy

Estimate model for dlnucbud

85

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

86residuals

87Univariate forecast dlnucbud(07-08)

Dlnucbud(07-08) = 0.0696

88

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

89

-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

90 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.

91

0

1

2

3

4

70 75 80 85 90 95 00 05

UCBUDGET UCBUDGSM UCBUDGSMHW

Exponential Smoothing Forecasts of UC Budget

92

93

Efforts from earlier years

94

95

96

Estimate ARONE Model for dlncapy

97

Satisfactory Model

98

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)

99

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

100

101

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)

102

103

104

105

Try an AR(6) AR(8)residual for dlnucbudb

106

107

108

109

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

110

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

111

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 $

112

113

114

115

116

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)

117

118

119

120

121

Distributed Lag Model

dlnucbud(t) = h0 *dlncapy(t-1) + dummy (1992-93) + resid(t)

122

123

124

125

126Fitted fractional change in UC Budget is 0.032 (3.2%)versusGovernor’s proposal of 0.033 (3.3%)

127

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

129

130

Try estimating the model in levels

131

132

133

134

135

136

137

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

138

Postscript 2006-07

139

-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

140

-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

141

142

143

-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

144