Power Nineteen

1. Power Nineteen Econ 240C

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

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

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

7. Review • 2. Ideas That Are Transcending

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

9. Use Assumptions To Cope With Constraints • A. Applications • 1. Limited number of observations: simple exponential smoothing • assume the model: (p, d, q) = (0, 1, 1) • 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 b1 = 0, then e1 = edcapu

10. Standard VAR (lecture 17) • dcapu(t) = (a1 + b1 a2)/(1- b1 b2) +[ (g11+ b1 g21)/(1- b1 b2)] dcapu(t-1) + [ (g12+ b1 g22)/(1- b1 b2)] dffr(t-1) + [(d1+ b1 d2 )/(1- b1 b2)] x(t) + (edcapu(t) + b1 edffr(t))/(1- b1 b2) • But if we assume b1 =0, • thendcapu(t) = a1 +g11 dcapu(t-1) + g12 dffr(t-1) + d1 x(t) + edcapu(t) +

11. Use Assumptions To Cope With Constraints • A. Applications • 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

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

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

14. Review • 2. Ideas That Are Transcending

15. Reduce the unexplained sum of squares to increase the significance of results • A. Applications • 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 • we are interested in the variation from day to day • to get better results, we control for variation across teenager

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

20. Lab 7 240 C

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

23. Lab 8 240 C

25. Model with no Intervention Variable

27. Add seasonal difference of differenced step function

29. Review • Symbolic Summary

30. Autoregressive Models • AR(t) = b1 AR(t-1) + b2 AR(t-2) + …. + bp AR(t-p) + WN(t) • AR(t) - b1 AR(t-1) - b2 AR(t-2) - …. + bp AR(t-p) = WN(t) • [1 - b1 Z + b2 Z2 + …. bp Zp ] AR(t) = WN(t) • B(Z) AR(t) = WN(t) • AR(t) = [1/B(Z)]*WN(t) AR(t) 1/B(Z) WN(t)

31. Moving Average Models • MA(t) = WN(t) + a1 WN(t-1) + a2 WN(t-2) + …. aq WN(t-q) • MA(t) = WN(t) + a1 Z WN(t) + a2 Z2 WN(t) + …. aq Zq WN(t) • MA(t) = [1 + a1 Z + a2 Z2 + …. aq Zq ] WN(t) • MA(t) = A(Z)*WN(t) MA(t) A(Z) WN(t)

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

33. Distributed Lag Models • y(t) = h0 x(t) + h1 x(t-1) + …. hn x(t-n) + resid(t) • y(t) = h0 x(t) + h1 Zx(t) + …. hn Zn x(t) + resid(t) • y(t) = [h0 + h1 Z + …. hn Zn ] x(t) + resid(t) • y(t) = h(Z)*x(t) + resid(t) • note x(t) = Ax (Z)/Bx (Z) WNx (t), or • [Bx (Z) /Ax (Z)]* x(t) =WNx (t), so • [Bx (Z) /Ax (Z)]* y(t) = h(Z)* [Bx (Z) /Ax (Z)]* x(t) + [Bx (Z) /Ax (Z)]* resid(t) or • W(t) = h(Z)*WNx (t) + Resid*(t)

34. Distributed Lag Models • Where w(t) = [Bx (Z) /Ax (Z)]* y(t) • and resid*(t) = [Bx (Z) /Ax (Z)]* resid(t) • cross-correlation of the orthogonal WNx (t) with w(t) will reveal the number of lags n in h(Z), and the signs of the parameters h0 , h1 , etc. for modeling the regression of w(t) on a distributed lag of the residual, WNx (t), from the ARMA model for x(t)

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

36. VAR Model Y1(t) = h1 (t ) Y1 (t) + h2 (t) Y2 (t) +e1 (t) Y2 (t ) = h3 (t ) Y1 (t) + h4 (t) Y2 (t) +e2 (t) e1 (t) + + Y1 (t) h1 (z) Y1 (t) + With a similar schematic for Y2 (t) Note: e1 (t) and e2 (t) are each compound errors, i.e. composed of the pure shock, ey1, to Y1 and the pure shock, ey2, to Y2 h2 (z) Y2 (t)

37. Crime in California

38. 1952-2004

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

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

45. Jobs and Crime

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

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. 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)