Econ 240 c
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Econ 240 C. Lecture 12. The Big Picture. Exploring alternative perspectives Exploratory Data Analysis Looking at components Trend analysis Forecasting long term Distributed lags Forecasting short term. Schedule 6. Schedule 9. The story based on a bivariate distributed lag model. 07-08.

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Econ 240 C

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Econ 240 c

Econ 240 C

Lecture 12


The big picture

The Big Picture

  • Exploring alternative perspectives

  • Exploratory Data Analysis

    • Looking at components

  • Trend analysis

    • Forecasting long term

  • Distributed lags

    • Forecasting short term


Econ 240 c

Schedule 6


Econ 240 c

Schedule 9


Econ 240 c

The story based on a bivariate distributed lag model

07-08


Econ 240 c

Another Story Based On a Univariate ARIMA Model


Part i ca budget crisis

Part I. CA Budget Crisis


Ca budget crisis

CA Budget Crisis

  • What is Happening to UC?

    • UC Budget from the state General Fund


Uc budget

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/


Ca budget crisis1

CA Budget Crisis

  • What is happening to the CA economy?

    • CA personal income


Econ 240 c

Log Scale


Ca budget crisis2

CA Budget Crisis

  • How is UC faring relative to the CA economy?


Ca budget crisis3

CA Budget Crisis

  • What is happening to CA state Government?

    • General Fund Expenditures?


Ca budget crisis4

CA Budget Crisis

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


Long run pattern analysis

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


What has happened to uc s share of ca general fund expenditures

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

  • UC Budget Share = (UC Budget/CA Gen Fnd Exp)


Econ 240 c

07-08


Uc budget crisis

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.


What has happened to the size of california government expenditure relative to personal income

What 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)


Econ 240 c

07-08


California political history

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


Ca budget crisis5

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


Forecasts of uc budget 07 08

Forecasts of UC Budget, 07-08


Econometric estimates of ucbud

Econometric Estimates of UCBUD

  • Linear trend

  • Exponential trend

  • Linear dependence on CAPY

  • Constant elasticity of CAPY


Econometric estimates

Econometric Estimates

  • Linear Trend Estimate

  • UCBUDB(t) = a + b*t +e(t)

    • A lucky coincidence

    • Usually either too low or too high!


A lucky coincidence 2 out of 10

A Lucky Coincidence: 2 out of 10


Econometric estimates1

Econometric Estimates

  • Logarithmic (exponential trend)

  • lnUCBUDB = a + b*t +e(t)

  • simple exponential trend will over-estimate UC Budget by far


Econometric estimate

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


Econometric estimates2

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


Is higher education an inferior good

Is Higher Education an Inferior Good?


Is government an inferior good

Is Government an Inferior Good?

  • Elasticity = 1.073


Forecasting conclusions

Forecasting 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


Econometric estimates3

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


Box jenkins distributed lag

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)


Identify dlncapy trace

Identify dlncapy: trace


Estimate arone model dlncapy

Estimate ARONE Model dlncapy


Validate model

Validate model


Orthogonal residuals

Orthogonal Residuals


Normal residuals

Normal Residuals


Cross correlate w and resdlncapy

Cross-Correlate w and resdlncapy


Distributed lag of w on resdlncapy

Distributed lag of w on resdlncapy

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


Distributed lag model

Distributed lag Model


Residuals

Residuals


Also model error as arone

Also model error as arone


Residuals1

residuals


Estimate this model for dlnucbud

Estimate this model for dlnucbud


Estimated model

Estimated model


Diagnostics

Diagnostics


Residuals2

Residuals


Fitted dlnucbud

Fitted dlnucbud

Dlnucbud (07-08) = 0.046


Dlnucbudf 07 08

Dlnucbudf(07-08)

Dlnucbudf(07-08) = 0.0452


Forecasts of uc budget 07 081

Forecasts of UC Budget, 07-08


Identify dlnucbud

Identify dlnucbud


Model dlnucbud

Model dlnucbud


Estimate model for dlnucbud

Estimate model for dlnucbud

Identify dlncapy


Diagnostics1

diagnostics


Residuals3

residuals


Univariate forecast dlnucbud 07 08

Univariate forecast dlnucbud(07-08)

Dlnucbud(07-08) = 0.0696


Forecasts of uc budget 07 082

Forecasts of UC Budget, 07-08


Efforts from earlier years

Efforts from earlier years


Econ 240 c

Estimate ARONE Model for dlncapy


Econ 240 c

Satisfactory Model


Estimate arone model for dlncapy t

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)


Distributed lag model1

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


Distributed lag model2

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)


Try an ar 6 ar 8 residual for dlnucbudb

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


Econ 240 c

  • 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


Econ 240 c

05-06

92-93


Distributed lag model3

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)


Distributed lag model4

Distributed Lag Model

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


Econ 240 c

Fitted fractional change in UC Budget is 0.032 (3.2%)versus

Governor’s proposal of 0.033 (3.3%)


Conclusions

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


Try estimating the model in levels

Try estimating the model in levels


Econ 240 c

07-08


Postscript 2006 07

Postscript 2006-07


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