Econ 240C Lecture 16
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 for total industry?
Preliminary Analysis • The Time Series, Monthly, January 1967 through April 2008
Identification of TCU • Trace • Histogram • Correlogram • Unit root test • Conclusion: probably evolutionary
Identification of FFR • Trace • Histogram • Correlogram • Unit root test • Conclusion: unit root
Dynamics: Cross-correlation Two-Way Causality?
In Levels Too much structure in each hides the relationship between them
Specification • Same number of lags in both equations • Use liklihood ratio tests to compare 12 lags versus 24 lags for example
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
Interpretation • We need help • Rely on assumptions
What If • What if there were a pure shock to dtcu • as in the primitive VAR, a shock that only affects dtcu immediately
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)
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
DTCU shock DFFR
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) +
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))
Reality edtcu(t) DTCU shock DFFR edffr(t)
What If edtcu(t) DTCU shock DFFR edffr(t)