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Econ 240 C

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Econ 240 C

Lecture 12

- 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

Another Story Based On a Univariate ARIMA Model

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

- 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/

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

Log Scale

- How is UC faring relative to the CA economy?

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

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

- 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

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

07-08

- 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.

- Relative Size of CA Government = (CA Gen Fnd Exp/CA Pers Inc)

07-08

- 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

- 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

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

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

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

- 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

- 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

- Elasticity = 1.073

- 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

- 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

- 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)

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

Dlnucbud (07-08) = 0.046

Dlnucbudf(07-08) = 0.0452

Identify dlncapy

Dlnucbud(07-08) = 0.0696

Estimate ARONE Model for dlncapy

Satisfactory Model

- 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)

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

- There is contemporary correlation and maybe something at lag one
- specify dlnucbud(t) = h0 *dlncapy(t) + h1 *dlncapy(t-1) + resid(t)

- 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

05-06

92-93

- 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)

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

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

Governor’s proposal of 0.033 (3.3%)

- 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

07-08