Econ 240 C Lecture 12

2 The Big Picture w Exploring alternative perspectives w Exploratory Data Analysis Looking at components w Trend analysis Forecasting long term w Distributed lags Forecasting short term

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The story based on a bivariate distributed lag model

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8 Another Story Based On a Univariate ARIMA Model

9 Part I. CA Budget Crisis

10 CA Budget Crisis w What is Happening to UC? UC Budget from the state General Fund

11 UC Budget w Econ 240A Lab Four w New data for Fiscal Year w Governor’s Budget Summary released January

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14 CA Budget Crisis w What is happening to the CA economy? CA personal income

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16 Log Scale

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18 CA Budget Crisis w How is UC faring relative to the CA economy?

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20 CA Budget Crisis w What is happening to CA state Government? General Fund Expenditures?

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22 CA Budget Crisis w How is CA state government General Fund expenditure faring relative to the CA economy?

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24 Long Run Pattern Analysis w Make use of definitions: w UCBudget = (UCBudget/CA Gen Fnd Exp)*(CA Gen Fnd Exp/CA Pers Inc)* CA Pers Inc w UC Budget = UC Budget Share*Relative Size of CA Government*CA Pers Inc

25 What has happened to UC’s Share of CA General Fund Expenditures? w UC Budget Share = (UC Budget/CA Gen Fnd Exp)

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29 UC Budget Crisis w 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.

30 What has happened to the size of California Government Expenditure Relative to Personal Income? w Relative Size of CA Government = (CA Gen Fnd Exp/CA Pers Inc)

32 California Political History w 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 w 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 w Estimate of the relative size of the CA government: 7.00 % w Estimate of UC’s Budget Share: 3.00% w UC Bud = 0.03*0.07*CAPY w UC Bud = * $B w UC Bud = $B

34 Forecasts of UC Budget, Method Forecast Actual $ B Identity/CAPY $ B

35 Econometric Estimates of UCBUD w Linear trend w Exponential trend w Linear dependence on CAPY w Constant elasticity of CAPY

36 Econometric Estimates w Linear Trend Estimate w UCBUDB(t) = a + b*t +e(t) A lucky coincidence Usually either too low or too high!

37 A Lucky Coincidence: 2 out of 10

38 Econometric Estimates w Logarithmic (exponential trend) w lnUCBUDB = a + b*t +e(t) w simple exponential trend will over-estimate UC Budget by far

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40 Econometric Estimate w Dependence of UC Budget on CA Personal Income w UCBUDB(t) = a + b*CAPY(t) + e(t) w looks like a linear dependence on income will overestimate the UC Budget for

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42 Econometric Estimates w How about a log-log relationship w lnUCBUDB(t) = a + b*lnCAPY(t) + e(t) w Estimated elasticity w autocorrelated residual w fitted lnUCBUDB( ) = $3.78 B w actual (Governor’s Proposal) = $3.27B

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44 Is Higher Education an Inferior Good?

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48 Is Government an Inferior Good? w Elasticity = 1.073

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50 Forecasting Conclusions w Trend analysis and bi-variate regressions of UC General Fund Expenditures on California Personal Income focus on the long run w The UC budget depends on the business cycle, a more short run focus w Try Box-Jenkins Methods

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52 Econometric Estimates w 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 w Dlnucbud = h 0 *dlncapy(t) + h 1 *dlncapy(t-1) + … + e(t) w Dlnucbud(t) = h(z) dlncapy(t) + e(t) w Dlncapy = 0.709*dlncapy(t-1) + resdlncapy(t) w [ z]dlnucbud = h(z)[ z] *dlncapy(t) + [ z]*e(t) w W(t) = h(z) resdlncapy(t) + e*(t)

54 Identify dlncapy: trace

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58 Estimate ARONE Model dlncapy

59 Validate model

60 Orthogonal Residuals

61 Normal Residuals

62 Cross-Correlate w and resdlncapy

63 Distributed lag of w on resdlncapy w W =h 0 *resdlncapy + h 1 *resdlncapy(-1) + e*(t)

64 Distributed lag Model

65 Residuals

66 Also model error as arone

67 residuals

68 Estimate this model for dlnucbud

69 Estimated model

70 Diagnostics

71 Residuals

72 Fitted dlnucbud Dlnucbud (07-08) = 0.046

73 Dlnucbudf(07-08) Dlnucbudf(07-08) =

74 Forecasts of UC Budget, Method Forecast Actual $ B Identity/CAPY $ B univariate model distributed lag $3.223 B = UCBud(06- 07)*[1+dlnucbudf(07-08)]

75 Identify dlnucbud

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79 Model dlnucbud

80 Identify dlncapy Estimate model for dlnucbud

81 diagnostics

82 residuals

83 Univariate forecast dlnucbud(07-08) Dlnucbud(07-08) =

84 Forecasts of UC Budget, Method Forecast Actual $ B Identity/CAPY $ B univariate model $ B ($18 M high) distributed lag$ B = UCBud(06- 07)*[1+dlnucbudf(07-08)] ($ 47 M low) simple exp. smooth$3.083 B double exp. Smooth -HW $ B ($39 M high), trend = $226 M/yr.

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87 Efforts from earlier years

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90 Estimate ARONE Model for dlncapy

91 Satisfactory Model

92 Estimate ARONE Model for dlncapy(t) w Orthogonalize dlncapy and save residual w need to do transform dlnucbudb w dlnucbudb(t) = h(Z)*dlncapy(y) + resid(t) w dlncapy(t) = 0.72*dlncapy(t-1) + N(t) w [ Z]*dlnucbudb(t) = h(Z)* [ Z]*dlncapy(t) + [ Z]*resid(t) w i.e. w(t) = h(Z)*N(t) + residw(t)

93 Distributed Lag Model w Having saved resid as res[N(t)] from ARONE model for dlncapy w and having correspondingly transformed dlnucbud to w w cross-correlate w and res

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95 Distributed lag model w There is contemporary correlation and maybe something at lag one w specify dlnucbud(t) = h 0 *dlncapy(t) + h 1 *dlncapy(t-1) + resid(t)

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

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103 w Try a dummy for , the last recession, this is the once and for all decline in UCBudget mentioned by Granfield w There is too much autocorrelation in the residual from the regression of lnucbud(t) = a + b*lncapy(t) + e(t) to see the problem w Look at the same regression in differences

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110 Distributed lag Model w dlnucbud(t) = h 0 *dlncapy(t) + h 1 *dlncapy(t-1) + dummy ( ) + resid(t) w dlnucbud(t) = h 0 *dlncapy(t) + h 1 *dlncapy(t-1) + dummy ( ) + dummy( ) + resid(t) w dlnucbud(t) = h 0 *dlncapy(t) + dummy ( ) + resid(t)

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115 Distributed Lag Model w dlnucbud(t) = h 0 *dlncapy(t-1) + dummy ( ) + resid(t)

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120Fitted fractional change in UC Budget is (3.2%)versus Governor’s proposal of (3.3%)

121 Conclusions w Governors proposed increase in UC Budget of 3.3% is the same as expected from a Box-Jenkins model, controlling for income w The UC Budget growth path ratcheted down in the recession beginning July 1990 w The UC Budget growth path looks like it ratcheted down again in the recession beginning March 2001

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124 Try estimating the model in levels

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132 Postscript

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