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Econ 240C

Econ 240C. Lecture 17. Part I. VAR. Does the Federal Funds Rate Affect Capacity Utilization?. 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. Preliminary Analysis.

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Econ 240C

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  1. Econ 240C Lecture 17

  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

  4. Preliminary Analysis

  5. The Time Series, Monthly, Jan uary 1967through May 2003

  6. Changes in FFR & Capacity Utilization

  7. Contemporaneous Correlation

  8. Dynamics: Cross-correlation

  9. Granger Causality

  10. Granger Causality

  11. Granger Causality

  12. Estimation of VAR

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

  14. Correlogram of DFFR

  15. Correlogram of DCAPU

  16. We Have Mutual Causality, But We Already Knew That DCAPU DFFR

  17. Interpretation • We need help • Rely on assumptions

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

  19. Primitive VAR

  20. 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

  21. DCAPU shock DFFR

  22. 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) +

  23. 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))

  24. Reality edcapu(t) DCAPU shock DFFR edffr(t)

  25. What If edcapu(t) DCAPU shock DFFR edffr(t)

  26. EVIEWS

  27. Interpretations • Response of dcapu to a shock in dcapu • immediate and positive: autoregressive nature • Response of dffr to a shock in dffr • immediate and positive: autoregressive nature • Response of dcapu to a shock in dffr • starts at zero by assumption that b1 =0, • interpret as Fed having no impact on CAPU • Response of dffr to a shock in dcapu • positive and then damps out • interpret as Fed raising FFR if CAPU rises

  28. Change the Assumption Around

  29. What If edcapu(t) DCAPU shock DFFR edffr(t)

  30. Standard VAR • 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) • if b2 = 0 • then, dffr(t) = a2 + g21 dcapu(t-1) + g22 dffr(t-1) + d2 x(t) + edffr(t)) • but, dcapu(t) = (a1 + b1 a2) + (g11+ b1 g21) dcapu(t-1) + [ (g12+ b1 g22) dffr(t-1) + [(d1+ b1 d2 ) x(t) + (edcapu(t) + b1 edffr(t))

  31. Interpretations • Response of dcapu to a shock in dcapu • immediate and positive: autoregressive nature • Response of dffr to a shock in dffr • immediate and positive: autoregressive nature • Response of dcapu to a shock in dffr • is positive (not - ) initially but then damps to zero • interpret as Fed having no or little control of CAPU • Response of dffr to a shock in dcapu • starts at zero by assumption that b2 =0, • interpret as Fed raising FFR if CAPU rises

  32. Conclusions • We come to the same model interpretation and policy conclusions no matter what the ordering, i.e. no matter which assumption we use, b1 =0, or b2 =0. • So, accept the analysis

  33. Understanding through Simulation • We can not get back to the primitive fron the standard VAR, so we might as well simplify notation • y(t) = (a1 + b1 a2)/(1- b1 b2) +[ (g11+ b1 g21)/(1- b1 b2)] y(t-1) + [ (g12+ b1 g22)/(1- b1 b2)] w(t-1) + [(d1+ b1 d2 )/(1- b1 b2)] x(t) + (edcapu(t) + b1 edffr(t))/(1- b1 b2) • becomes y(t) = a1 + b11 y(t-1) + c11 w(t-1) + d1 x(t) + e1(t)

  34. And w(t) = (b2 a1 + a2)/(1- b1 b2) +[(b2 g11+ g21)/(1- b1 b2)] y(t-1) + [ (b2 g12+ g22)/(1- b1 b2)] w(t-1) + [(b2 d1+ d2 )/(1- b1 b2)] x(t) + (b2edcapu(t) + edffr(t))/(1- b1 b2) • becomes w(t) = a2 + b21 y(t-1) + c21 w(t-1) + d2 x(t) + e2(t)

  35. Numerical Example y(t) = 0.7 y(t-1) + 0.2 w(t-1)+ e1(t) w(t) = 0.2 y(t-1) + 0.7 w(t-1) + e2(t) where e1(t) = ey(t) + 0.8 ew(t) e2(t) = ew(t)

  36. Generate ey(t) and ew(t) as white noise processes using nrnd and where ey(t) and ew(t) are independent. Scale ey(t) so that the variances of e1(t) and e2(t) are equal • ey(t) = 0.6 *nrnd and • ew(t) = nrnd (different nrnd) • Note the correlation of e1(t) and e2(t) is 0.8

  37. Analytical Solution Is Possible • These numerical equations for y(t) and w(t) could be solved for y(t) as a distributed lag of e1(t) and a distributed lag of e2(t), or, equivalently, as a distributed lag of ey(t) and a distributed lag of ew(t) • However, this is an example where simulation is easier

  38. Simulated Errors e1(t) and e2(t)

  39. Simulated Errors e1(t) and e2(t)

  40. Estimated Model

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