Measuring Systematic Monetary Policy

Measuring Systematic Monetary Policy

Kevin D. Hoover

and

Òscar Jordà

Department of Economics

U.C. Davis

One Shields Ave.

Davis, CA95616-8578

U.S.A.

e-mail:

URL:

1. Introduction

Objective: To measure the effect of systematic monetary policy on the economy.

Background: The usual methods for evaluating VARs provide the true responses to exogenous shocks only if the economy is Lucasian in the sense that:

Policy ineffectiveness holds, and
Policy noninvariance (the Lucas Critique) holds.

Motivation: What if the economy is not Lucasian? What do VARs measure and how can we measure systematic monetary policy?

1. 1 Literature Review

Counterfactual VARs

Bernanke, Gertler and Watson (1997); Sims (1999); Boivin and Giannoni (2002).

Approach: Modify the equation for the monetary policy instrument and then recalculate the impulse response functions.

What Do VARs Mean?:

Cochrane (1998)

1. 2 A Dilemma

Horn 1: If the world is Lucasian, a “structural” VAR is, at best, quasi-structural: it remains a reduced form. The alterations to the reduced form envisaged in counterfactual experimentation violate the Lucas critique.

Horn 2: If the world in non-Lucasian, the usual methods of evaluating VARs do not provide the correct quantitative responses to exogenous shocks.

1. 3 What this Paper Does

A Path between the Horns:

Provide enough structure to the empirical model so that the data will determine the extent to which the economy is Lucasian.

Identify those elements of the structure of monetary policy that can be changed independently of nonpolicy structural elements.

Evaluate systematic monetary policy via counterfactual experimentation.

2. An Expository Model

A Version of Lucas’s Early New Classical Model

yt = (pt – ) + t, / (6)
pt= mt – yt, / (7)
mt= 1mt-1 + 2yt-1 + t, / (8)
= E(pt|t-1). / (9)
2.1 A Taxonomy of Policy is Based on the Agents:

(1) The Policymaker: is characterized by the reaction function

mt= 1mt-1 + 2yt-1 + t, / (8)

(i)Systematic Policy 1 and 2

(ii)Unsystematic Policy vt

(2) The Public: is characterized by the aggregate supply function

yt = (pt – ) + t, / (6)

(i)Unanticipated Policy .

(ii)Anticipated Policy 

2.2 Solutions for Unanticipated Shocks

Assuming that only information dated before t is included in t-1 :

Policy Non-invariance:

/ (10)

Policy Ineffectiveness:

/ (11)
2.2 Solutions for Unanticipated Shocks (Contd.)

Thus, the “structural” VAR with m ordered ahead of y is:

mt= 1mt-1 + 2yt-1 + t, / (8)
/ (10)

With MA representation (degenerate for y):

/ (11)
2.2 Solutions for Unanticipated Shocks (Contd.)

Remarks:

(1)The model generates an exact analogue to the usual “structural” VAR method and shows that it assumes that monetary policy actions are both unsystematic and unanticipated.

(2)The moving average representation is immune to the Lucas critique, not because regimes do not change, but because of the assumption that real variables respond only to monetary surprises and expectations are rational.

Solutions for anticipated shocks: Assuming that mt is known at t-1, the impulse response to vt is eliminated completely as

/ (10’)
3. A Non-Rational Model

Assume agents do not have rational expectations and have direct supply responses to money:

mt= 1mt-1 + 2yt-1 + t, / (8)
yt = mt + t. / (12)

Remarks:

(1)The distinction between anticipated and unanticipated monetary policy is moot – both have an identical effect on y.

(2)Similarly, the Lucas critique is inapplicable since expectations are not an element in the public’s supply responses.

4. A Mixed Model

Assume there are both rational and non-rational responses,

yt = bmt + (1 – )(pt – ) + t, / (13)

The solutions for y (a “structural” VAR):

mt= 1mt-1 + 2yt-1 + t, / (8)
4. A Mixed Model (Contd.)

Remarks:

(1)When  = 1, equation (14) reduces to the non-rational case. When  = 0, it reduces to the rational case.

(2) cannot be identified unless the policy regime varies.

(3)Notice that is policy is anticipated – i.e., mt is known at t-1, then the “structural” VAR equation for y becomes

/ (15)

Remarks (Contd.):

(4)Equation (15) depends on the mixing parameter , but not on the policy parameters 1 and 2 or on the policy shock vt.

(5)If  is itself invariant to regime changes, then regime changes can be sued to identify : even though the usual “structural” VAR will change with each regime change (i.e., for each change of 1 and 2), the moving average representation for an anticipated policy action will remain invariant, though dependant on .

(6)These results generalize to more complex “structural” VARs.

5. Measurement Strategy

Overview:

“Structural” VARs change as the monetary regime changes (Lucas critique), but the impulse responses to anticipated shocks remain invariant. These functions, however, depend on .

Step 1: Identify monetary policy regimes.

Step 2: Estimate regime specific “structural” VARs

Step 3: Assume  is constant across regimes and choose  that ensures responses to anticipated shocks are the same across regimes.

Step 4: Once , anticipated shock responses and regime-specific VARs have been estimated, proceed with counterfactual, Lucas-critique free, experimentation.
Cochrane (1998):

Virtue: A single parameter, , summarizes the differential dynamics in response to anticipated/ unanticipated policy.

Identifying Assumption: and A(L) and B(L) are constant across monetary regimes. Why?

The "proportion" () of Lucasian to non-Lucasian agents remains constant across monetary regimes.
The Lucasian response to monetary and non-monetary surprises is invariant to the policy regime.

5.1 A Structural VAR and Anticipated Effects

Combine Cochrane (1998),

with the usual Structural MA (Impulse Response) representation of a monetary VAR:

to get:

Remarks

If  = 0 (rational expectations), the response of the economy to monetary shocks should have been invariant to the policy regime.
B(L) is the response of output to non-policy shocks. A(L)Cmw (L) is the endogenous response of monetary policy to non-policy shocks. If  = 0 (rational expectations) then the Cyw(L) would be invariant to the policy regime.
Notice that if there is only one regime, there is a lack of identification problem.

6. Recovery of Structural Model – Application

Christiano, Eichenbaum and Evans (1996), Evans and Marshall (1998)

Data:

EM: log of non-agricultural payroll employment
P:log of personal cons. Expenditures deflator
PCOM:annual growth rate index of sensitive commodities
FF:Federal Funds Rate
NBRX: ratio of non-borrowed reserves to total reserves
M2: annual growth rate of M2

Sample:

Monthly, January 1960 to January 1999

6.1 Testing for Structural Breaks

Bai and Perron (1998)

Let

then

Table 2. Structural Break Tests of the Monetary-Policy Equation

Number of breaks under the alternative, H / sup F(H|0) / 5% Critical value / sup F(H+1|H) / 5% Critical value / AIC / BIC
1 / 106.59 / 64.69 / - / - / 0.232 / 0.302
2 / 125.92 / 58.56 / 119.92 / 68.12 / 0.132 / 0.224
3 / 117.20 / 55.52 / 96.80 / 70.21 / 0.125 / 0.279
4 / 106.32 / 53.16 / 96.80 / 71.09 / 0.122 / 0.354
5 / 123.22 / 50.93 / 90.20 / 71.84 / 0.118 / 0.445
6 / 124.74 / 48.77 / 70.62 / 72.59 / 0.119 / 0.588
7 / 102.92 / 46.29 / 46.76 / 73.83 / 0.127 / 0.815
8 / 88.84 / 42.83 / 52.22 / 74.83 / 0.140 / 1.171
Breaks / Dates
1 / 1980:6
2 / 1978:6 / 1982:4
3 / 1970:4 / 1978:6 / 1982:4
4 / 1970:4 / 1978:6 / 1982:4 / 1986:2
5 / 1970:6 / 1974:6 / 1978:6 / 1982:4 / 1986:2
6 / 1965:5 / 1970:9 / 1974:5 / 1978:6 / 1982:4 / 1986:2
7 / 1965:5 / 1970:9 / 1974:5 / 1978:6 / 1982:4 / 1986:2
8 / 1965:5 / 1970:9 / 1974:5 / 1978:6 / 1982:4 / 1986:2 / 1989:12 / 1994:8

Break Dates and Estimation

5 Break Dates:

1970:6 / 1974:6 / 1978:6 / 1982:4 / 1986:2

 = 0.57; SD = 0.14

7. Evaluating Systematic Monetary Policy

7.1 Systematic Monetary Policy Component

Response of EM to a 1% shock in the Fed Funds rate: A(L)Cmm
Response of EM to a –1% shock in EM: A(L)Cmy

Figure 2

Comments:

Reasonably homogeneous response of EM to unexpected tightening in the usual direction.
The systematic response of policy to a shock in EM is important and differs significantly across regimes.

Measuring Systematic Monetary Policy
Kevin Hoover and Oscar Jordá
U.C. Davis

7.2 The Sims and Zha Counterfactual Revisited

Sims-Zha (1998)/Bernanke, Gertler and Watson (1997):

Assume the Lucas critique is ineffectual in the short run ( = 1)
Modify the policy rule while keeping other equations unchanged.
Compare the responses of the VAR relative to the experiment.

Figure 3

Measure Systematic Policy response to a -1% shock to EM

Results:

Generally smaller responses with Cochrane’s than with Sims-Zha but similar in shape (except 1986-1999 regime)

7.3 Historical Performance of Fed Chairmen

Sims (1999) reruns the Great Depression with Postwar monetary policies. However, his simulations are subject to the Lucas Critique.

To the degree that our identifying assumptions are correct, our model is sufficiently structural to avoid the Lucas critique.

We generate simulations using the actual shocks from the model and the reaction function from two other Fed Chairmen:

(1)The Burns-Miller regime

(2)The Greenspan regime.

8. Extensions

Direct estimation of systematic monetary policy in a VAR.
Allow for learning mechanisms so that  is not constant nor a constant fraction of agents are forced to remain non-rational.

Recall Cochrane (1998)

and rewrite in VAR form as

Taking inverses

with C(L) = -B(L)A(L) and (L) = B(L)-1

Special cases

Case 1: Fully Non-rational  = 1

Notice the monetary coefficients (L) and(L) do not enter the monetary block.

Case 2: Fully Lucasian,  = 0

which is the typical VAR.

8.1 Estimation

Notice that for , then

An for the term

8.1 Estimation (Contd.)

Let t = Th denote the date of the hth shift in policy regime so that and as and . A specific functional form for  that meets these criteria is, for example,

Estimate the “structural” VAR with the EM algorithm to obtain direct estimates of:

Time varying t
Systematic Monetary Policy

Remarks:

Estimates will be more efficient because we do not have generated regressors.

9. Conclusions

This paper shows:

Cochrane (1998) is right! The interpretation given in the VAR literature to impulse responses is likely to be incorrect because the economy is not fully Lucasian.
New methods to estimate the relative importance of the Lucasian paradigm
New methods to estimate systematic monetary policy.
New methods to conduct counterfactual experimentation. Lucas-critique free.

Measuring Systematic Monetary Policy
Kevin Hoover and Oscar Jordá
U.C. Davis