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