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. summarize

The variables in the Becketti and Morris study, like most economic variables, are nonstationary. When nonstationary variables
obey a stationary linear relation in the long run, the variables are said to be cointegrated, and the relationship between the
variables can conveniently be estimated in error correction form.

Take, as an example, two nonstationary variables, y_t and x_t, that follow the dynamic statistical relationship

A*(L)y_t = B*(L)x_t ⅛ e_t.

where L is the lag operator (Lx_t ≡ x_t-ι) and A*() and B* () are polynomials in the lag operator. (The lag command in the
Stata time series library can be used to mimic the lag operator.) By rearranging terms, this model can be written as

A(L)Ay_t = B(L)Ax_t - λ(y_t-₁ - ⅛⅛-ι) + e_t

where Δ is the difference operator (Ax_t ≡ x_t- x_t~₁ ≡ (1 — Z)a⅛). (The dif command in the Stata time series library can be
used to mimic the difference operator.) This latter equation is called an error correction model and (y_t-ι — <fa⅛-ι) is called the
error correction term. If y_t and x_t are cointegrated, the error correction term is the stationary linear combination of the variables.
The error correction model can be estimated consistently by least squares. The coefficients in the error correction term (1, -S)
are called the cointegrating vector. The error correction model and the error correction term generalize in a straightforward way
to models with many variables.

The error correction model has an intuitively appealing interpretation. The cointegrating vector reveals the equilibrium
(long-run) relationship between the variables. The error correction term is a measure of how far the variables have deviated from
their equilibrium relationship. The coefficient on the error correction term, λ, is a measure of how rapidly y_t responds to these
deviations. Large values of λ correspond to rapid speeds of adjustment back to equilibrium. The other coefficients in the model
measure the short-run relationship between the variables, that is, the association between their short-run fluctuations that would
occur even if the variables were in long-run equilibrium.

The error correction term contains lagged values of the nonstationary variables as regressors. The Hansen test cannot be
applied to nonstationary regressors, thus the test cannot be applied directly to the model. If the cointegrating vector is known,
the error correction term—which is stationary—can be entered as a regressor. When the cointegrating vector is not known,
Hansen (1992) recommends a two-step procedure: first estimate the cointegrating vector, then enter the estimated cointegrating
vector as a generated regressor in the error correction model.

Becketti and Morris estimate the following reduced form equation for C&I loans:

AL_t = μ ⅛ (xιAL_t~ι ⅛ a2AL_t-2 + βι,ι∆l_t-ι + β1,2ΔLt-2 + ∕⅜,χ∆⅞-ι + ∕⅜,ιΔCt-ι

+ β4,1Arμ_t-_l + β_5tlAr_m,_t-₁ + β5,2Ar_mtt-2 + ∕⅝,ι∆r3_jt-ι

— λ(L_t-ι — διl_t-ι — δ2V_t-1 — δ3C_t-1 — δ4rf_tt-1 — δ5r_m,_jt-1 —

where

Z_t = the log of bank C&I loans,

I_t = the log of business fixed investment,

T_t = the log of business inventories,

C_t = the log of corporate cash flow,
r∕_jt = the federal funds rate,
r_TOjt = the mortgage interest rate,
r_3jt = the secondary market yield on 3-month Treasury bills.

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