1. 1 Power Nineteen Econ 240C

2. 2 Outline Forecast Sources Forecast Sources Ideas that are transcending Ideas that are transcending Symbolic Summary Symbolic Summary

3. 3 Outline Forecasting Forecasting Federal: Federal Reserve @ Philidelphia Federal: Federal Reserve @ Philidelphia State: CA Department of Finance State: CA Department of Finance Local Local UCSB: tri-counties UCSB: tri-counties Chapman College: Orange County Chapman College: Orange County UCLA: National, CA UCLA: National, CA

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6. 6 http://www.ucsb-efp.com

7. 7 Review 2. Ideas That Are Transcending 2. Ideas That Are Transcending

8. 8 Use the Past to Predict the Future A. Applications A. Applications Trend Analysis Trend Analysis linear trend linear trend quadratic trend quadratic trend exponential trend exponential trend ARIMA Models ARIMA Models autoregressive models autoregressive models moving average models moving average models autoregressive moving average models autoregressive moving average models

9. 9 Use Assumptions To Cope With Constraints A. Applications A. Applications 1. Limited number of observations: simple exponential smoothing 1. Limited number of observations: simple exponential smoothing assume the model: (p, d, q) = (0, 1, 1) assume the model: (p, d, q) = (0, 1, 1) 2. No or insufficient identifying exogenous variables: interpreting VAR impulse response functions 2. No or insufficient identifying exogenous variables: interpreting VAR impulse response functions assume the error structure is dominated by one pure error or the other, e.g assume   = 0, then e 1 = e dcapu assume the error structure is dominated by one pure error or the other, e.g assume   = 0, then e 1 = e dcapu

10. 10 Standard VAR (lecture 17) dcapu(t) = (        /(1-     ) +[ (    +     )/(1-     )] dcapu(t-1) + [ (    +     )/(1-     )] dffr(t-1) + [(    +      (1-     )] x(t) + (e dcapu  (t) +   e dffr  (t))/(1-     ) dcapu(t) = (        /(1-     ) +[ (    +     )/(1-     )] dcapu(t-1) + [ (    +     )/(1-     )] dffr(t-1) + [(    +      (1-     )] x(t) + (e dcapu  (t) +   e dffr  (t))/(1-     ) But if we assume    But if we assume    then  dcapu(t) =    +    dcapu(t-1) +   dffr(t-1) +    x(t) + e dcapu  (t) + then  dcapu(t) =    +    dcapu(t-1) +   dffr(t-1) +    x(t) + e dcapu  (t) + 

11. 11 Use Assumptions To Cope With Constraints A. Applications A. Applications 3. No or insufficient identifying exogenous variables: simultaneous equations 3. No or insufficient identifying exogenous variables: simultaneous equations assume the error structure is dominated by one error or the other, tracing out the other curve assume the error structure is dominated by one error or the other, tracing out the other curve

12. 12 Simultaneity There are two relations that show the dependence of price on quantity and vice versa There are two relations that show the dependence of price on quantity and vice versa demand: p = a - b*q +c*y + e p demand: p = a - b*q +c*y + e p supply: q= d + e*p + f*w + e q supply: q= d + e*p + f*w + e q

13. 13 demand price quantity Shift in demand with increased income, may trace out i.e. identify or reveal the demand curve supply

14. 14 Review 2. Ideas That Are Transcending 2. Ideas That Are Transcending

15. 15 Reduce the unexplained sum of squares to increase the significance of results A. Applications A. Applications 1. 2-way ANOVA: using randomized block design 1. 2-way ANOVA: using randomized block design example: minutes of rock music listened to on the radio by teenagers Lecture 1 Notes, 240 C example: minutes of rock music listened to on the radio by teenagers Lecture 1 Notes, 240 C we are interested in the variation from day to day we are interested in the variation from day to day to get better results, we control for variation across teenager to get better results, we control for variation across teenager

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19. 19 Reduce the unexplained sum of squares to increase the significance of results A. Applications A. Applications 2. Distributed lag models: model dependence of y(t) on a distributed lag of x(t) and 2. Distributed lag models: model dependence of y(t) on a distributed lag of x(t) and model the residual using ARMA model the residual using ARMA

20. 20 Lab 7 240 C

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22. 22 Reduce the unexplained sum of squares to increase the significance of results A. Applications A. Applications 3. Intervention Models: model known changes (policy, legal etc.) by using dummy variables, e.g. a step function or pulse function 3. Intervention Models: model known changes (policy, legal etc.) by using dummy variables, e.g. a step function or pulse function

23. 23 Lab 8 240 C

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25. 25 Model with no Intervention Variable

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27. 27 Add seasonal difference of differenced step function

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29. 29 Review Symbolic Summary Symbolic Summary

30. 30 Autoregressive Models AR(t) = b 1 AR(t-1) + b 2 AR(t-2) + …. + b p AR(t-p) + WN(t) AR(t) = b 1 AR(t-1) + b 2 AR(t-2) + …. + b p AR(t-p) + WN(t) AR(t) - b 1 AR(t-1) - b 2 AR(t-2) - …. + b p AR(t-p) = WN(t) AR(t) - b 1 AR(t-1) - b 2 AR(t-2) - …. + b p AR(t-p) = WN(t) [1 - b 1 Z + b 2 Z 2 + …. b p Z p ] AR(t) = WN(t) [1 - b 1 Z + b 2 Z 2 + …. b p Z p ] AR(t) = WN(t) B(Z) AR(t) = WN(t) B(Z) AR(t) = WN(t) AR(t) = [1/B(Z)]*WN(t) AR(t) = [1/B(Z)]*WN(t) WN(t)1/B(Z)AR(t)

31. 31 Moving Average Models MA(t) = WN(t) + a 1 WN(t-1) + a 2 WN(t-2) + …. a q WN(t-q) MA(t) = WN(t) + a 1 WN(t-1) + a 2 WN(t-2) + …. a q WN(t-q) MA(t) = WN(t) + a 1 Z WN(t) + a 2 Z 2 WN(t) + …. a q Z q WN(t) MA(t) = WN(t) + a 1 Z WN(t) + a 2 Z 2 WN(t) + …. a q Z q WN(t) MA(t) = [1 + a 1 Z + a 2 Z 2 + …. a q Z q ] WN(t) MA(t) = [1 + a 1 Z + a 2 Z 2 + …. a q Z q ] WN(t) MA(t) = A(Z)*WN(t) MA(t) = A(Z)*WN(t) WN(t)A(Z)MA(t)

32. 32 ARMA Models ARMA(p,q) = [A q (Z)/B p (Z)]*WN(t) ARMA(p,q) = [A q (Z)/B p (Z)]*WN(t) WN(t)A(Z)/B(Z)ARMA(t)

33. 33 Distributed Lag Models y(t) = h 0 x(t) + h 1 x(t-1) + …. h n x(t-n) + resid(t) y(t) = h 0 x(t) + h 1 x(t-1) + …. h n x(t-n) + resid(t) y(t) = h 0 x(t) + h 1 Zx(t) + …. h n Z n x(t) + resid(t) y(t) = h 0 x(t) + h 1 Zx(t) + …. h n Z n x(t) + resid(t) y(t) = [h 0 + h 1 Z + …. h n Z n ] x(t) + resid(t) y(t) = [h 0 + h 1 Z + …. h n Z n ] x(t) + resid(t) y(t) = h(Z)*x(t) + resid(t) y(t) = h(Z)*x(t) + resid(t) note x(t) = A x (Z)/B x (Z) WN x (t), or note x(t) = A x (Z)/B x (Z) WN x (t), or [B x (Z) /A x (Z)]* x(t) =WN x (t), so [B x (Z) /A x (Z)]* x(t) =WN x (t), so [B x (Z) /A x (Z)]* y(t) = h(Z)* [B x (Z) /A x (Z)]* x(t) + [B x (Z) /A x (Z)]* resid(t) or [B x (Z) /A x (Z)]* y(t) = h(Z)* [B x (Z) /A x (Z)]* x(t) + [B x (Z) /A x (Z)]* resid(t) or W(t) = h(Z)*WN x (t) + Resid*(t) W(t) = h(Z)*WN x (t) + Resid*(t)

34. 34 Distributed Lag Models Where w(t) = [B x (Z) /A x (Z)]* y(t) Where w(t) = [B x (Z) /A x (Z)]* y(t) and resid*(t) = [B x (Z) /A x (Z)]* resid(t) and resid*(t) = [B x (Z) /A x (Z)]* resid(t) cross-correlation of the orthogonal WN x (t) with w(t) will reveal the number of lags n in h(Z), and the signs of the parameters h 0, h 1, etc. for modeling the regression of w(t) on a distributed lag of the residual, WN x (t), from the ARMA model for x(t) cross-correlation of the orthogonal WN x (t) with w(t) will reveal the number of lags n in h(Z), and the signs of the parameters h 0, h 1, etc. for modeling the regression of w(t) on a distributed lag of the residual, WN x (t), from the ARMA model for x(t)

35. 35 Distributed Lag Model X(t) H(z) Y(t) + Residual(t) + Remember to Model the Residual!

36. 36 VAR Model Y 1 (t) = h 1 (t ) Y 1 (t) + h 2 (t) Y 2 (t) +e 1 (t) Y 2 (t ) = h 3 (t ) Y 1 (t) + h 4 (t) Y 2 (t) +e 2 (t) Y 1 (t) h 1 (z) Y 1 (t) + e 1 (t) + + h 2 (z) Y 2 (t) With a similar schematic for Y 2 (t) Note: e 1 (t) and e 2 (t) are each compound errors, i.e. composed of the pure shock, e y1, to Y 1 and the pure shock, e y2, to Y 2

37. 37 Crime in California

38. 38 1952-2004

39. 39 Use the California Experience Crime rates Have Fallen. Why Haven’t Imprisonment rates? Crime rates Have Fallen. Why Haven’t Imprisonment rates? Apply the conceptual tools Apply the conceptual tools Criminal justice system schematic Criminal justice system schematic crime control technology crime control technology

40. 40 Crime Generation Crime Control Offense Rate Per Capita Expected Cost of Punishment Schematic of the Criminal Justice System: Coordinating CJS Causes ?!! (detention, deterrence) Expenditures Weak Link “The Driving Force”

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45. 45 Jobs and Crime

46. 46 Model Schematic Crime Generation: California Index Offenses Per Capita Causality: California Misery Index Crime Control: California Prisoners Per Capita

47. 47 CA Crime Index Per Capita (t) = 0.039 + 0.00034*Misery Index (t) – 3.701*Prisoners Per Capita (t) + e(t) where e(t) = 0.954*e(t-1)

48. 48 Ln CA Crime Index Per Capita (t) = -5.25 + 0.17*ln Misery Index (t) -0.22 ln Prisoners Per capita (t) +e(t) where e(t) = 0.93 e(t-1)