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# ECONOMETRICS ECON 240C

UCSB

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This 14 page Class Notes was uploaded by Arno Leuschke on Thursday October 22, 2015. The Class Notes belongs to ECON 240C at University of California Santa Barbara taught by Staff in Fall. Since its upload, it has received 44 views. For similar materials see /class/227171/econ-240c-university-of-california-santa-barbara in Economcs at University of California Santa Barbara.

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Date Created: 10/22/15

Econ 240C Lecture 12 1 5122009 The following Takehome Project was assigned Nov15 1994 and was due Dec 8 I Use the information in the Granfield study handed out earlier to forecast the General Fund Budget allocated to UC for scal year 199596 Report your forecast in nominal and in 1992 Attached are some sheets which reproduce the General Fund Budget allocated to UC in nominal dollars GF NOM from fiscal year 1968 69 through fiscal year 199394 as reported in Gran eld Also reproduced for the same period is the consumer price index for the US INDEX as reported in Granfield This CPI was converted to 19921 INDEX92 to calculate GFREL92 Another series reported is for California Personal Income CPYR923 This series was constructed from quarterly data for personal income in California in nominal dollars beginning in the first quarter of 1968 It was converted to real terms as listed by de ating with a Consumer Price Index for Los Angeles with the third quarter of 1992 equal to one The quarterly data was converted to annual averages and advanced two quarters to coincide with the fiscal year ie CPYR9236869 equals the average of the quarterly data for California Personal Income in real 1992 dollars for the third and fourth quarters of 1968 and the first and second quarters of 1969 The values for 1992 and 1993 for CPYR923 depend upon forecasted values since the last observation for quarterly California Personal Income was for the first quarter of 1993 Thus these figures could be updated The Legislative Analyst s Office Analysis oft16 199495 Budget BI transmitted to the California Legislature Feb 23 1994 indicates the Governor s proposed Econ 240C Lecture 12 5122009 General Fund Budget for UC was 18506 millions The estimated amount for 199394 was 17926 and the actual amount for 199293 was 18785 These latter two compare closely to the gures in Gran eld Year 6869 6970 7071 7172 7273 7374 7475 7576 7677 7778 7879 7980 8081 8182 8283 8384 8485 8586 8687 8788 8889 8990 9091 9192 9293 CPYR923 3376130 3579644 3644833 3826953 3994612 4138057 4109150 4220986 4417724 4690897 5004843 4871271 4921976 4923728 5089885 5394615 5634738 5824201 6168363 6336133 6522070 6654233 6397885 6220305 6168950 DCPY923 NA 2035138 6518921 1821201 1676590 1434448 2890686 1118359 1967380 2731729 3139462 1335721 5070496 0175201 1661569 3047299 2401233 1894629 3441620 1677698 1859369 1321631 2563477 1775800 5135498 DGFREL92 GFNOM NA 8154028 5142529 4726440 4379309 1355631 8862183 1433678 2351721 5294250 1836780 9517236 2945984 4798389 5595398 3118164 2894803 1585172 1697769 8625977 6246973 7172363 7101709 1538792 2971071 2913000 3293000 3359000 3600000 3847000 4543000 5119000 5852000 6477000 7355000 7658000 9046000 1042300 1118900 1150800 1209800 1460000 1643400 1803200 1897300 1985200 2090700 2135700 2105600 1881100 GFREL92 1205379 1286920 1235494 1282759 1326552 1462115 1470977 1614345 1637862 1690805 1672437 1767609 1797069 1749085 1693131 1724313 2013793 2172310 2342087 2333461 2395931 2403103 2332086 2178207 1881100 INDEX 3600000 3400000 3200000 3100000 3000000 2800000 2500000 2400000 2200000 2000000 1900000 1700000 1500000 1360000 1280000 1240000 1200000 1150000 1130000 1070000 1050000 1000000 0950000 0900000 0870000 INDEX92 4137931 3908046 3678161 3563218 3448276 3218391 2873563 2758621 2528736 2298851 2183908 1954023 1724138 1563218 1471264 1425287 1379310 1321839 1298851 1229885 1206897 1149425 1091954 1034483 1000000 Econ 240C Lecture 12 3 5122009 9394 6229951 6100098 1498311 1793100 1731269 0840000 0965517 9495 II The Granfield Study Michael Gran eld was a ViceChancellor at UCLA at the time he prepared his study Historical Analysis of California General Fund Budget Allocations and Related Student Workload Measures Trends and Insights 196869 through 199394 The time series GFNOM and INDEX in the table above were reproduced from the data in his study As explained in the Takehome Project Assignment INDEX92 and GFREL were derived directly from these two Granfield series DGFREL92 is the first difference of GFREL92 The only time series not from the Granfield study is CPYR923 a California personal income series calculated as explained in the assignment from data obtained from the UCLA and UCSB Forecasting Projects DCPYR923 is the first difference of CPYR923 Granfield used simple time series analysis including graphical methods to argue that the State General Fund appropriation to UC had suffered a permanent decline of about 05 billion dollars beginning in 199293 He argued that the shift overwhelms the impact of the recession as measured by the change in California personal disposable income In addition to forecasting the State General Fund budget allocated to UC for 199596 there are two supplementary issues raised by Granfield s analysis 1 has there been a once and for all decline or shift in the UC budget away Econ 240C Lecture 12 4 5122009 from its old trend line and 2 will the UC budget not fully recover even if California personal income recovers III A Simple Univariate Model of General Fund Expenditure on UC I used a time series GFNOMREV a revised General Fund Expenditure series which is the same as GFNOM in the table above from 196869 through 199192 and then use the information in the third paragraph of the Takehome Project assignment The value for GFNOMR for 199293 is 18785 for 199394 is 17926 and for 199495 is 18307 At the last minute the Legislature reallocated 20 million from the Govemor s proposed budget for UC to the Cal State system hence the gure 18307 for 199495 The plot for the time series GFNOMREV below indicates a series that is likely nonstationary so I used the first difference DGFNOMR whose plot appears next State General Fund Expenditures on the Universityof California 6869 throug h 9495 2500 2000 Millions of Nominal 1500 l 000 Fiscal Year196868 69 GFNOMRE Econ 240C Lecture 12 5 5122009 Annual Change in General Fund Expenditures on the University of California 300 200 Millions of Nominal 100 100 200 300 Fiscal Year1969 6970 DGFNOM quot The autocorrelation and partial autocorrelation functions for DGFNOMR indicate a rst order autoregressive structure for the time series which was used as the model IDENT DGFNOMR SMPL range 1969 1994 Number of observations 26 Autocorrelations Partial Autocorrelations ac pac oMMMM 0 l 1 0607 0607 Econ 240C Lecture 12 6 5122009 l l 2 0217 0238 O l O l 3 0008 0018 O l O l 4 0044 0164 O l l 5 0034 0113 QStatistic 5 lags 10881 SE of Correlations 0196 The model estimated was DGFNOMREVt C Vt where v0 b1 Vt 1 WNt LS Dependent Variable is DGFNOMR SMPL range 1970 1994 Number of observations 25 Convergence achieved after 2 iterations VARIABLE COEFFICIENT STD ERROR TSTAT 2TAIL SIG Econ 240C Lecture 12 7 5122009 C 60062200 37634227 15959462 0124 AR1 06079849 01655468 36725858 0001 Rsquared 0369654 Mean of dependent 6005600 Adjusted Rsquared 0342247 SD of dependent 9095471 SE of regression 7376604 Sum of squared resid 1251529 DurbinWatson stat 1690183 Fstatistic 1348789 Log likelihood 1419537 A plot of the actual and tted values of DGFNOMR along with the residuals follows The DurbinWatson statistic looks reasonable and the autocorrelation function of the residuals indicated they were white noise with a QSum statistic of 32 for 5 lags Consequently this model was used to forecast the annual change for 199596 The forecast was 467 million nominal which when added to the amount of 18307 for 199495 yields a forecast for 199596 of 18774 million ofnominal dollars The standard error of the regression was 738 million dollars This forecast amounts to a 26 increase in the nominal budget not enough to keep pace with the expected rate of in ation of30 Econ 240C Lecture 12 8 5122009 Autoregressive Model ofOrder One for Annual Changes in General Fund Budget for UC V 1970I I I I19I I I I19 0I I I I19 5I I I I19530I I I RESIDUAL DGFNOMR FITTEd IV A Model Relating California Personal Income amp the UC Budget both Nominal I used a series for California Personal Income obtained from the UCSB and UCLA forecasting projects who revise this series frequently I used their quarterly data PY to derive a series MCPYN94 that corresponded to the fiscal year for example MCPYN946869 PY683 PY684 PY691 PY6924 A comparison to the personal income series nominal reported by Granville follows in the table The values of MCPYN94 for 199495 and 199596 are forecasts from UCLNUCSB Next is a plot of General Fund Expenditure on UC GFNOMREV and California Personal Income MCPYN94 Since these series are both trended they were first differenced and the prewhitened series plotted see below Econ 240C Lecture 12 9 5122009 Year MCPYN94 CPYN Granville Year MCPYN94 CPYN Granville 6869 8263367 773 8283 3424908 3280 6970 9197045 884 8384 3781245 3524 7071 9773438 950 8485 4270260 3892 7172 1060843 1009 8586 4471472 4226 7273 1151184 1103 8687 4796017 4531 7374 1287205 1218 8788 5106410 4901 7475 1424412 1362 8889 5550840 5322 7576 1583612 1497 8990 5961987 5765 7677 1770997 1677 9091 6278810 6167 7778 2003873 1871 9192 6486235 6244 7879 2295016 2149 9293 6720923 6398 7980 2609174 2448 9394 6950085 6603 8081 2942671 2761 9495 6992020 8182 3250210 3087 9596 7338936 General Fund Budget for UC and California Personal Income both in Nominal Dollars 2500 2000 UC Budget Millions 1500 1000 500 1990 1955 19550 19555 1950 1995 Fiscal Year196868 69 GFNOM REV MCPYN9 Econ 240C Lecture 12 10 5122009 Annual Changes in General Fund Budget for U0 and California Personal Income both Nom39nal 50 I I I Is I II I 40 I 39 I I 39I I I l I 3o I II I 30039 1 II I 1 II Billions I z I Millions t I 3910 100 V I 390 0 1m 2w 3w I I I I I I I I I I I I I I I I I I I I 1970 1975 1980 1985 1990 1 5 Fiscal Year196868 69 SMPL range 1969 1994 Number of observations 26 CORDGFNOMRDMCPYN94i CORDGFNOMRDMCPYN94i i lag lead o l 0 l 0 0417 0417 OHM l 0 l 1 0333 0318 0 l 0 l 2 0022 0457 W l 0 l 30208 0379 gtxltgtxltgtxltgtxlt l l40293 0422 Econ 240C Lecture 12 11 5122009 0 l50l27 0195 SE of Correlations 0196 The differenced series DGFNOMR and DMCPYN94 were cross correlated as shown above DGFNOMRt depends on DMCPYN94t and DMCPYN94tl and the postulated model was DGFNOMRt C b0 DMCPYN94t b1 DMCPYN94t1 Vt where Vt a1 Vtl WNt This model is a combination of the distributed lag of the UC budget on personal income plus the rst order autoregressive univariate stucture of DGFNOMRt LS Dependent Variable is DGFNOMR SMPL range 1971 1994 Sample endpoints adjusted to exclude missing data Number of observations 24 Convergence achieved after 6 iterations VARIABLE COEFFICIENT STD ERROR TSTAT 2TAIL SIG C 67608227 74672259 09053995 0376 Econ 240C Lecture 12 12 5122009 DMCPYN94 21760785 15943904 13648342 0187 DMCPYN941 29833154 17241745 17302862 0099 AR1 06292348 01744687 36065769 0002 Rsquared 0482019 Mean of dependent 6228333 Adjusted Rsquared 0404322 SD of dependent 9221186 SE of regression 7116930 Sum of squared resid 1013014 DurbinWatson stat 1705729 Fstatistic 6203814 Log likelihood 1342281 Both of the personal income variables add to the explained variance but are not highly signi cant The standard error of the regression is only slightly smaller than it was for the univariate model The DurbinWatson statistic looks reasonable and a plot of the actual tted and residuals follows Distributed Lag Model ofthe UC Budget on Personal Income Annual Changes Plus AR1 100 V 200 300 1955 19530 19535 1950 I RESIDUAL DGFNOMR FITTEd Econ 240C Lecture 12 13 5122009 The autocorrelation function of the residuals indicated they were very white with a Q Sum statistic of 05 for five lags The forecast of DGFNOMR9596 was 381 million dollars Added to GFNOMREV94 95 of 18307 yields a forecast of the UC budget for 199596 of 18681 million dollars nominal with a standard error of 712 V A Combined Distributed Lag and Intervention Model The model in Section IV above indicates some dependence of the UC budget on California personal income To answer the question of whether there had been a once and for all change in the UC budget beginning in 199293 a dummy variable taking the value one that year and zero elsewhere was added to the regression The dummy variable indicated a once and for all decrease in the UC budget of 175 million dollars with a standard error of 51 million This is significantly less than Gran eld s estimate of a permanent reduction of 440 to 530 million The residuals were white with a QSum statistic of 1 for 5 lags LS Dependent Variable is DGFNOMR SMPL range 1971 1994 Sample endpoints adjusted to exclude missing data Number of observations 24 Convergence achieved after 8 iterations VARIABLE COEFFICIENT STD ERROR TSTAT 2TAIL SIG C 34955514 57552305 06073695 0551 DMCPYN94 22132449 12785740 17310261 0100 Econ 240C Lecture 12 14 5122009 DMCPYN941 19723526 13987550 14100772 0175 DUMMY 17528735 50522077 34695198 0003 AR1 05856715 01888902 31005923 0006 Rsquared 0683143 Mean of dependent 6228333 Adjusted Rsquared 0616436 SD of dependent 9221186 SE of regression 5710916 Sum of squared resid 6196766 DurbinWatson stat 1800633 Fstatistic 1024098 Log likelihood 1283303 The forecast for the change in the UC budget was 610 million dollars which when added to the 199495 budget of 18307 yields a forecast for 199596 of 18917 million dollars with a standard error of 571 million This is a 33 increase in the budget which should keep pace with in ation but will not make up for the losses suffered during the recession

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