1. Econ 240C Lecture 16

2. Part I. VAR • Does the Federal Funds Rate Affect Capacity Utilization?

3. The Federal Funds Rate is one of the principal monetary instruments of the Federal Reserve • Does it affect the economy in “real terms”, as measured by capacity utilization for total industry?

6. Preliminary Analysis • The Time Series, Monthly, January 1967 through April 2008

8. Capacity Utilization Total Industry: Jan. 1967- April 2008

12. Identification of TCU • Trace • Histogram • Correlogram • Unit root test • Conclusion: probably evolutionary

17. Identification of FFR • Trace • Histogram • Correlogram • Unit root test • Conclusion: unit root

18. Pre-whiten both

19. Changes in FFR & Capacity Utilization

20. Contemporaneous Correlation

21. Dynamics: Cross-correlation Two-Way Causality?

22. In Levels Too much structure in each hides the relationship between them

23. In differences

24. Granger Causality: Four Lags

25. Granger Causality: two lags

26. Granger Causality: Twelve lags

27. Estimate VAR

28. Estimation of VAR

35. Specification • Same number of lags in both equations • Use liklihood ratio tests to compare 12 lags versus 24 lags for example

37. Estimation Results • OLS Estimation • each series is positively autocorrelated • lags 1, 18 and 24 for dtcu • lags 1, 2, 4, 7, 8, 9, 13, 16 for dffr • each series depends on the other • dtcu on dffr: negatively at lags 10, 12, 17, 21 • dffr on dtcu: positively at lags 1, 2, 9, 24 and negatively at lag 12

38. We Have Mutual Causality, But We Already Knew That DTCU DFFR

39. Correlogram of DFFR

40. Correlogram of DTCU

41. Interpretation • We need help • Rely on assumptions

42. What If • What if there were a pure shock to dtcu • as in the primitive VAR, a shock that only affects dtcu immediately

43. Primitive VAR (tcu Notation) dtcu(t) =1 + 1 dffr(t) + 11 dtcu(t-1) + 12 dffr(t-1) + 1 x(t) + edtcu (t) (2) dffr(t) = 2 + 2 dtcu(t) + 21 dtcu(t-1) + 22 dffr(t-1) + 2 x(t) + edffr (t)

44. Primitive VAR (capu notation)

45. The Logic of What If • A shock, edffr , to dffr affects dffr immediately, but if dcapu depends contemporaneously on dffr, then this shock will affect it immediately too • so assume b1 iszero, then dcapu depends only on its own shock, edcapu , first period • But we are not dealing with the primitive, but have substituted out for the contemporaneous terms • Consequently, the errors are no longer pure but have to be assumed pure

46. DTCU shock DFFR

47. Standard VAR • 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) +

48. Note that dffr still depends on both shocks • dffr(t) = (b2 a1 + a2)/(1- b1 b2) +[(b2 g11+ g21)/(1- b1 b2)] dcapu(t-1) + [ (b2 g12+ g22)/(1- b1 b2)] dffr(t-1) + [(b2 d1+ d2 )/(1- b1 b2)] x(t) + (b2edcapu(t) + edffr(t))/(1- b1 b2) • dffr(t) = (b2 a1 + a2)+[(b2 g11+ g21) dcapu(t-1) + (b2 g12+ g22) dffr(t-1) + (b2 d1+ d2 ) x(t) + (b2edcapu(t) + edffr(t))

49. Reality edtcu(t) DTCU shock DFFR edffr(t)

50. What If edtcu(t) DTCU shock DFFR edffr(t)