Empirical Analysis of Policy Interventions

Transcription

1 Empirical Analysis o Policy Interventions Eric M. Leeper and Tao Zha August 22, 2001 Abstract: We construct linear projections o macro variables conditional on hypothetical paths o monetary policy, using as an example an identiied VAR model. Hypothetical policies are restricted to ones where both the policy intervention and its impacts are consistent with history otherwise the linear projections are likely to be unreliable. We use the approach to interpret Federal Reserve decisions, modeling their requent reassessment in light o new inormation about the tradeos policymakers ace. The interventions we consider matter: they can shit projected paths and probability distributions o macro variables in economically meaningul ways. Keywords: Monetary Policy, Identiication, Forecasting, Policy Analysis, VAR JEL classiication: E52; E47; C53! 2001 by Eric M. Leeper and Tao Zha. This document may be reely reproduced or educational and research purposes provided that i) this copyright notice is included with each copy, ii) no changes are made in the document, and iii) copies are not sold, but retained or individual use or distributed ree.

2 Empirical Analysis o Policy Interventions Eric M. Leeper and Tao Zha * 1. Introduction This paper oers a ramework or interpreting the kinds o policy choices that central banks make at regular policy meetings. The approach is positive, adopting the perspective o an outside observer the econometrician to (i) address counteractual questions with linear projections o macro variables conditional on exogenous policy interventions; (ii) assess how reliable linear projections are likely to be or a given intervention; (iii) account or uncertainty about model parameters and realizations o shocks over the orecast horizon. The ramework is suited to consider interventions that would not be construed as changes in policy behavior that bring orth systematic changes in private decision rules. Our approach diers rom two dominant approaches to counteractual policy evaluation the rational expectations program that Lucas and Sargent (1981) laid out and the reduced-orm orecasting approach that Doan, Litterman and Sims (1984) developed. The rational expectations program identiies the mapping rom policy behavior to private expectations and decision rules to evaluate the impacts o adopting a new policy process. This paper does not address questions associated with changing the policy process. Instead, it analyses policy choices that are made sequentially and that are not wholly dierent rom past choices. Doan, Litterman and Sims (1984) use orecasting models to project the eects o alternative sequences o policy variables, taking private expectations and decision rules as given by history. Their approach is designed to address routine policy interventions. Like us, they argue that i the interventions do not constitute regime changes, then linear projections are likely to be reliable. * Indiana University, Department o Economics, 105 Wylie Hall, Bloomington, IN and the Federal Reserve Bank o Atlanta, 1000 Peachtree Street, N.E., Atlanta, GA eleeper@indiana.edu and tao.zha@atl.rb.org. The authors thank Ralph Bryant, Tom Cooley, Jon Faust, John Geweke, Adrian Pagan, Peter Pedroni, Tom Sargent, Anders Vredin, and especially David Gordon, Chris Sims, and Dan Waggoner or helpul suggestions. We also beneited rom Marty Eichenbaum s detailed comments. The views expressed herein are not necessarily those o the Federal Reserve Bank o Atlanta or the Federal Reserve System.

3 Unlike us, Doan, Litterman and Sims ocus on reduced-orm orecasting models in which monetary policy behavior is not identiied. We extend Doan, Litterman and Sims s methods to environments in which policy behavior is identiied, so exogenous variation in policy is separated rom systematic responses o policy to the economy. Identiication allows us to check whether the hypothetical policies we consider are consistent with linear projections, which hold estimated private decision rules ixed over the projection period. We emphasize the reliability o linear projections because we interpret Lucas s (1976) critique as pointing toward a source o nonlinearity that may be important in practice. 1 When policy interventions create sustained dynamic patterns o change in policy variables, agents may grow to believe policy regime has shited and adjust their expectations and decision rules accordingly. Learning dynamics can produce smoothly evolving private decision rules that undermine the accuracy o linear projections: a model that is linear i regime is ixed, becomes nonlinear, with the nonlinearity produced by the economic behavior that Lucas emphasizes. Linear projections will remain reliable, however, i the interventions and their eects remain in line with historical luctuations. 2 An outgrowth o identiying policy behavior is the decomposition o policy choice into two components: a deterministic unction o observable variables and an exogenous random variable. All empirical work on policy perorms a similar decomposition work ranging rom Taylor s (1993) simple rules to Romer and Romer s (1989) dummy variables to Fair s (1984) simultaneous equations, as well as identiied VARs. The presence o a random exogenous term in the policy rule implies that private agents put probability mass on more than one policy action, even though their best estimate o the action is uniquely dictated by the deterministic part o the rule. This leaves room or counteractual policy analysis even in a linear model. It takes the orm o contemplating alternative interventions that a priori agents think could occur; and i those actions are taken, agents are not shocked into thinking the underlying policy process has changed. We show that the impacts o this class o interventions can be reliably projected using a linear model. And these interventions matter: they can shit the projected paths and probability distributions o macro variables in economically meaningul ways. How much they matter 1 Sims (1998) puts orth this interpretation o the Lucas critique. 2 Leeper and Zha (2001b) explore these points in a theoretical model. 2

4 depends on both the nature o the intervention and the elasticities o private behavior with respect to policy. The eicacy o our approach hinges on whether it can be applied without implying policy choices that would orce the economy into a new policy regime. We oer some statistical guards against this. We compute an ex-ante metric or assessing whether a contemplated intervention is consistent with the prevailing policy regime. The metric is designed to lag any hypothetical intervention that would trigger a change in private agents belies about the policy process, shit their decision rules, and undermine the linear projections. By that metric we ind that many interventions the Federal Reserve actually considers all within the prevailing regime. We also compute an ex-post version o the metric, which reports whether the choices actually taken aected macro variables in ways that are consistent with historical eects. We illustrate the approach in a small model o the U.S. economy that identiies monetary policy behavior. We assess the estimated model s in-sample and out-o-sample its, examine the model s stability, and evaluate the model s suitability or the policy questions we put to it. We ocus on two recent episodes. The irst episode is the recession, which was a time o aggressive easing o policy and one in which the Fed perceived that it aced diicult tradeos between inlation and real activity. The analysis oers a probabilistic ex-ante assessment o the tradeos, conditional on alternative policy actions. The second episode is the Fed s 1994 pre-emptive strike against inlation, during which the ederal unds rate increased 300 basis points in a year. Sequential orecasts rom the model suggest that the incremental increases in the unds rate that occurred through the year are a natural outcome when policy choices are reappraised in light o new inormation arriving in early The analysis shows how uncertainty about uture exogenous disturbances leads to conservative policymaking, as Brainard (1967) advocates, and it ormalizes Blinder (1997) description o how central banks reappraise their policy decisions. 2. An Econometric Framework or Policy Analysis This section speciies and estimates a small structural model o American monetary policy behavior. The model s it, stability, and suitability or policy analysis are scrutinized. The section also reports the model s impulse response unctions, which underlie the conditional policy projections reported below, and develops a metric or assessing policy interventions. 3

5 2.1 The Model Actual policy behavior is a complicated unction o a high-dimensional vector o variables. Policymakers choose R t, the vector o policy choices at date t, as a unction o their inormation set, " t. Actual policy behavior is a unction g such that R t % g# " $. (1) t (1) describes historical policy behavior. We assume that private agents are not privy to the details o the policymakers decision problems, including the policymakers incentives and constraints. That is, they observe the inormation set S t &" t. Agents perceive that policy is composed o a regular response to the state o the economy that they observe at time t, S t, and a random part, ' Pt. The econometric model o policy is: # $. R % S (' (2) t t Pt We take to be linear. ' Pt is exogenous to the econometric model. A policy regime is a choice o g, which implies an and a stochastic process or ' P. 3 The econometric model embeds the policy behavior in (2) in a system o equations. I y t is an ( m )1) vector o time series, the structural orm is p + Ay s t* s % ' t, (3) s% 0 where ' t is a vector o i.i.d. structural disturbances that are exogenous to the model. Those disturbances hit both nonpolicy and policy sectors o the economy, so,' Nt - ' t %., ' / 0 Pt 1 where ' Nt is the vector o nonpolicy disturbances. (4) Counteractual policy questions are addressed using the structure in (3) to project y conditional on hypothesized paths or ' P, as Marschak (1953) and the Cowles Commission 3 It is beyond the scope o this paper to rationalize randomness in policy behavior. See Sims (1987) or one detailed rationale and Leeper, Sims and Zha (1996) or urther discussion. 4

6 instructed. We impose that ' Pt is a vector o exogenous random variables, uncorrelated with all the nonpolicy exogenous disturbances in the economy. The errors are Gaussian with #'' t t t* s $ #' t t* s $ E 2 y, s 3 0 % I, E y, s 3 0 % 0, all t. (5) The A s matrices and the probability distribution o ' deine the model s structure. Assuming the matrix o contemporaneous coeicients, A 0, is non-singular, there is a representation o y in terms o the impulse responses unctions: t * 1 y % + C ' ( E y. (6) t s t* s 0 t s% 0 The elements o C s report how each variable in y responds over time to the behavioral disturbances in '. E0 y t is the projection o y t conditional on initial conditions. The reduced orm o (3) is p + Bsyt* s % ut, (7) s% 0 with B % 0 I and the covariance o the reduced-orm errors, u, is 4% * 1 A A * Expressions (3) and (7) imply a linear mapping rom the reduced-orm errors to the behavioral disturbances: u t % A ' (8) * 1 0 t. Identiication o the structural orm ollows rom imposing suicient restrictions on A 0 so that there are no more than mm ( *1) 2 ree parameters in A Identiication We estimate a version o the model in (3) that contains six variables and three sectors. The identiication scheme ollows the general approach in Gordon and Leeper (1994) and Sims and Zha (1998b). 4 Table 1 shows the restrictions placed on the contemporaneous coeicient matrix A 0. There are no restrictions on lagged variables. Three goods market variables real GDP (y), consumer prices (P), and the unemployment rate (U) compose the production sector, and are the ultimate objectives o monetary policy. 5

7 We do not model the markets or reserves and a broad monetary aggregate, opting or compactness to treat the M2 money stock as the aggregate and the ederal unds rate ( R ) the monetary policy instrument as the price that clears the money market. The third sector describes an inormation variable commodity prices (CP) that is available at high requencies and reacts instantaneously to shocks rom all sectors o the economy. The data are monthly rom January 1959 to September 1998 and described in Appendix B. Monthly GDP is interpolated rom quarterly GDP using the procedure that Leeper, Sims and Zha (1996) describe. All data are logarithmic except or the ederal unds rate and the unemployment rate. We estimate with 13 lags. The identiication treats the production sector as predetermined or the rest o the system, relecting the view that production, pricing, and employment decisions do not respond immediately to shocks rom outside the sector. Production sector variables interact only with each other within the period. Money market variables and inormation variables do not enter this sector, relecting sluggishness in the goods market due to contracts and advance planning o production. Distinct behavioral equations within the production sector are not identiied; instead, the coeicients are arranged in lower triangular orm in the order y, P, and U. The monetary and inormation sectors interact simultaneously, with the strongest simultaneity determining the money stock and the ederal unds rate. The demand or nominal money balances depends on the short-term nominal interest rate, real income (proxied by real GDP), and the price level. We do not impose short-run homogeneity in prices. Changes in ' MD relect exogenous shits in money demand. We base the speciication o monetary policy behavior in (2) on the inormation available to the Federal Reserve within the month. During the month, the Federal Reserve sets its interest rate instrument based on current observations on the money stock and commodity prices. 5 We set to zero the coeicients on y, P, and U in the policy unction because within the month the 4 For urther discussion o the methods, see Christiano, Eichenbaum and Evans (1999) or Leeper, Sims and Zha (1996). Appendix A describes the Bayesian methods used to estimate the model. 5 We allow policy to choose not to react strongly to commodity prices by shrinking the prior standard deviation on the coeicient o CP toward the zero prior mean by a actor o.05. 6

8 Federal Reserve does not observe these variables directly. 6 policy equation, ' P, represents exogenous policy interventions. The error term in the monetary An eicient markets assumption guides the speciication o the inormation sector, so commodity prices may respond to all variables immediately. The error term ' I is the exogenous inormation disturbance. 2.3 Parameter Estimates and In-Sample Fit Table 2 reports the contemporaneous coeicients along with 68 percent equal-tailed probability intervals or the behavioral coeicients, estimated over the ull sample period. The money demand and monetary policy equations have reasonable economic interpretations. The interest elasticity o demand is negative and the output elasticity is positive. The price elasticity is small and imprecisely estimated. Monetary policy responds strongly to the money stock: disturbances that raise the money stock induce the Fed to increase the ederal unds rate. Although the estimates seem to suggest the Fed does not react much to inormation contained in commodity prices, this interpretation may be misleading. In the policy equation the coeicients on R and CP are highly correlated (.97), as are the coeicients on M2 and CP (.72); these correlations muddy inerences about individual coeicients. All but two coeicients are tightly estimated in the inormation sector. The coeicients on output and M2 are highly correlated with the coeicients on the price level and unemployment, so the separate inluences cannot be discerned. The estimates imply a quick reaction o commodity prices to exogenous disturbances rom elsewhere in the economy. We base a probabilistic assessment o the model s overall it on the shape o the likelihood surace, rather than on tests o whether individual coeicients are dierent rom zero [Sims and Zha (1999)]. Table 2 nonetheless displays the (marginal).68 probability intervals or individual parameters to show that they are skewed, with most o the probability mass concentrated around the maximum likelihood estimates. Because we care about the equilibrium eects o exogenous policy actions, inerences do not rest on an individual parameter in A 0. Equilibrium eects, 6 The Fed has some contemporaneous inormation about these variables. We experimented with sot zeroes on P and U and ound that the more we relaxed the zero restrictions the more likely the identiication was to produce nonsensical responses to exogenous monetary policy actions. 7

9 which section 2.4 discusses, depend on the joint distribution o all the parameters, not the marginal distribution o an individual parameter. The model is overidentiied. To evaluate whether the data avor the restricted model relative to the unrestricted (reduced-orm) model, we conduct an exact small-sample comparison using a Bayes actor. 7 Given the data, Y, we compare the probability densities o Y under the two models, denoted by pym ( R ) and pym ( U ) where M R represents the restricted model and M U the unrestricted model. Let parameter space. The Bayes actor is 5 R be the restricted parameter space and 5 U be the unrestricted # $ 8 R % # U $ 8 # $ # $ pym py6 p( 6) d6 675R, pym py6 p( 6) d6 6 75U (9) where p( 6 ) is our reerence prior probability density unction, described in Appendix A. The Bayes actor is a standard reporting procedure in Bayesian hypothesis testing. In our case, since 5 R is a lower dimensional parameter space 5 R &5 U, the Bayes actor compensates eectively or over-parameterization by integrating the likelihood py6 # $ over the two dierent parameter spaces 5 R and 5 U. Recent developments in Bayesian analysis and computer technology, surveryed in Geweke (1999), allow us to calculate the Bayes actor accurately as # R$ pym # U$ log pym * log % 0.9. (10) The data weakly avor the restricted model, suggesting that to determine the model s consistency with data it is important to compensate or over-parameterization. 8 To use the model to compute projections conditional on alternative interventions, the policy disturbances must be uncorrelated with the other shocks. We use a small-sample procedure to check whether ' Pt and ' Nt are uncorrelated. For each simulated draw rom the posterior 7 A number o statistics are used to approximate Bayes actors, including the likelihood ratio criterion and the Schwarz criterion. The method o Laplace and the Schwarz criterion are employed as higher-order corrections to the likelihood ratio criterion as an approximate Bayes actor [Schervish (1995, chapters 4 and 7) and Sims (1999b)]. 8 The Schwarz criterion computes the chi-square statistic with degrees o reedom multiplied by the log o the sample size. The chi-square statistic, which is twice the dierence in log likelihood values o the unrestricted and the restricted models at their peaks, is With a critical value o 18.11, the Schwarz criterion weakly rejects the restricted model. 8

10 distribution o the model s parameters, we compute the sequences o exogenous disturbances consistent with the data and calculate the correlation matrix or these sequences. Table 3 reports.68 probability intervals or the correlations among the exogenous shocks, along with the correlations calculated at the maximum likelihood estimates o the parameters. ' Pt is uncorrelated with ' Nt, so restriction (5) holds well. 9 We also compute a posterior.68 probability region or the correlations o policy shocks with ive non-policy shocks. Zero values o all ive correlations all jointly inside the region. 10 With the policy disturbance uncorrelated with other shocks, it is reasonable to condition on a path o exogenous policy interventions and draw nonpolicy disturbances independently. 2.4 Dynamic Impacts o an Exogenous Monetary Policy Action Figure 1 displays the C s s in (6) over 48 months or the six variables in the model when there is a unit exogenous monetary policy contraction. The solid lines are the maximum likelihood estimates o responses and the dashed lines are equal-tailed error bands containing.68 probability, ollowing Sims and Zha (1999). The contraction raises the unds rate initially and immediately decreases the money stock and commodity prices, both o which continue to decline smoothly over the our-year horizon. Ater a brie delay, output alls and stays lower, while unemployment rises. Six months ater the exogenous action, both output and unemployment are likely to dier rom their initial levels. Consumer prices adjust more slowly and are unlikely to be appreciably lower or about a year. Ater a year prices decline smoothly and remain well below their initial level. The response o the interest rate to an exogenous policy contraction stands out. In Figure 1 the initial liquidity eect lasts about eight months, but by 18 months the unds rate lies well 9 The table suggests, however, that the model does not it the correlation between the money demand shock and the unemployment shock well, aecting some behavioral inerences, but not the ones we pursue. 10 The probability region is computed rom the small-sample distribution o the random variable # ˆ 2 * 1 9 9$ # 9 9ˆ$ * : * where 9 ˆ is the ML estimate o a vector o the ive correlations, 9, and : is the (simulated) covariance matrix o 9. Based on our simulations, ; # ˆ 2 * 1 Prob 9 9$ # 9 9ˆ < > * : * $ = 6.06?%.68 and # ˆ 2 * 0* 9$ : # $ 1 0 * 9ˆ % A 9

11 below its initial level. The decline in the unds rate then persists. Friedman (1968) and Cagan (1972) describe this path ollowing a monetary contraction as a short-lived liquidity eect ollowed by income and expected inlation eects. Ater our years the declines in inlation and the ederal unds rate are the same size, as predicted i expected inlation is the dominant source o luctuations in nominal rates over long periods. The responses in the igures suggest that to lower inlation persistently the Fed should raise the unds rate only briely. Because lower inlation is ultimately associated with a lower unds rate, the Fed must begin to reduce the rate within about a year, and then keep it lower. 2.5 Parameter Stability Because many analyses work rom the premise that U.S. monetary policy has shited substantially over the post-world War II period, some readers may object to our treating the entire sample as a ixed policy regime. We think the issue is unsettled. Bernanke and Mihov (1998a, 1998b) careully test the stability o the reduced-orm coeicients and the residual covariance matrices in VARs containing many o the same time series in our model. They conclude that the reduced-orm parameters are stable. 11 In contrast, tests o the covariance matrices o VAR innovations rom which the structural model s A 0 parameters are obtained in (8) ind evidence o breaks in late 1979 or early 1980 and between early 1982 and early The results conorm to Sims s (1999a) reaction unction estimates. Using a hidden Markov chain approach, he inds strong evidence that the Fed s responsiveness to commodity price inlation deviates rom a linear, Gaussian reaction unction. But in terms o model it, he reports that variations in the size o the errors in the policy rule are more important than variation in the coeicients o the rule. Much recent attention ocuses on the inding that coeicients in simple speciications o the Fed s policy rule shit over time [e.g., Clarida, Gali and Gertler (2000) and Taylor (1999)]. The 11 They use a Lagrange multiplier variant o Andrew s (1993) test, which checks every possible break point and tests the signiicance o the associated LM statistics. Using quarterly data, Sims and Zha (1998b) corroborate Bernanke and Mihov s results by comparing a model it rom 1964:1 to 1994:1 to one it separately to 1964:1-1979:3 and 1983:1-1994:1. Both the Akaike and Schwartz criteria avor the restricted model. 10

12 simple rules emerge rom restrictions on the policy behavior embedded in VARs. 12 For our purposes, what matters is whether the dynamic responses to exogenous policy interventions are stable. Those responses depend on the system o equations, not just the policy rule. To explore the system properties, we compute the dynamic eects o a one-period unit intervention using models estimated over a variety o sub-periods. Figure 2 reports responses to all six exogenous disturbances or models estimated over our sub-periods. The periods covered are 1959:1-1998:9 (entire sample); 1959:1-1979:9 (pre- Volcker); 1959:1-1982:12 (including non-borrowed reserves targeting); 1959:1-1998:9 with 1979: :12 eliminated (excluding non-borrowed reserves targeting). The reserves targeting period rom 1979:10 to 1982:12 is too brie to obtain reliable estimates rom just those years, so we treat the three years as potentially anomalous relative to the entire sample. Although it is popular to treat the Greenspan era (rom late 1987 on) as a distinct policy regime, we do not. The last 12 years o the sample contain only one mild recession and ew interesting exogenous disturbances, except possibly rom the stock market. The qualitative responses in Figure 2 to exogenous policy interventions are robust across sub-periods. 13 There is some tendency or the responses estimated by eliminating the reserves targeting episode to be slightly weaker and or those estimated only through the end o 1982 to be somewhat stronger. Otherwise, the responses to policy are even quantitatively very similar. Two implications low rom inding that parameters are stable. First, over the post-1959 period either monetary policy has resided in a single regime or the various regimes have been too close to be detected statistically. Second, there is no evidence that agents belies about regime have changed in ways that matter quantitatively or decision rules. This justiies our use o the entire sample period to estimate the model and to orm the history against which we evaluate whether linear projections are likely to reliably predict the impacts o an intervention. Overall, the model s it is very good. The overidentiying restrictions do not invalidate our uses o the model. Those uses rely on whether exogenous policy interventions are uncorrelated with nonpolicy disturbances. Tests conirm that this assumption holds well. An exact small- 12 Leeper and Zha (2001a) study connections between models with simple rules and identiied VARs. 13 Qualitative dierences do appear in responses to some non-policy disturbances, especially money demand and goods market shocks. This inding is consistent with Hanson (2001). 11

13 sample comparison o the restricted and unrestricted models using a Bayes actor somewhat avors the restricted model. 14 Finally, the dynamic responses o the economy to exogenous monetary policy interventions are quite stable over time. Taken together, these indicators o it and robustness lend credibility to the model s projections conditional on policy. 2.6 Measuring Policy Interventions In the VAR the K-period orecast errors, given inormation at T, that arise rom the intervention I T % {! ' PT 1,...,! ( ' PT( K} are K * 1 B ( T, K) % + C (:, i)! ', (11) P s PT( K* s s% 0 where the C (:, i ) are the impulse response matrices associated with the monetary policy s disturbance in equation i. The vector B P ( T, K) is normally distributed with mean zero and variance vector K * Cs. We transorm P ( T, K) s% 0 B to a vector o standard normal variables, B * P ( T, K) by scaling by the standard error o the B P s. Linear projections are reliable i both the intervention and its impacts are within two standard deviations o their historical luctuations. Speciically, we deem projections reliable i over a speciied orecast horizon K, or variable i, we ind that where e i is a row vector o zeros with unity in the i th column. eb * ( T, K) C 2, (12) i P * B reports how unusual a conditional projection is relative to the historical impacts o exogenous shits in policy. Large values o the statistic suggest the intervention is predicted to generate impacts on macro variables that lie outside the historical range o policy eects. When an intervention violates (12), the reliability o linear projections is called into doubt. The metric when K 3 0 is ex-ante in the sense that it assesses a hypothetical intervention. When K C 0 the metric is ex-post, computed rom the realized ˆP ' s, and it assesses actual interventions. The metric isolates exogenous policy changes as being most pertinent to evaluating policy and assessing the impact o the Lucas critique. This improves on the reduced-orm methods that 14 The model s out-o-sample it compares avorably to other econometric models [Appendix C]. 12

14 Doan, Litterman and Sims (1984) employ. The statistic at horizon K relects the ull impacts o interventions up to time T ( K. The metric emphasizes the dynamic impacts, rather than the magnitude o the intervention itsel because i policy impacts are small, even very large and unprecedented interventions that shit belies about prevailing regime may not generate signiicant changes in decision rules. 3. Some Practical Analysis o U.S. Monetary Policy This section addresses some questions that Federal Reserve oicials may have asked during the 1990s. To do so we compute policy projections under several alternative scenarios tied to actual U.S. policy experience. In each case we check the contemplated interventions to ensure that the linear projections are likely to be reliable. We ocus on two periods o aggressive policy moves: the 500 basis point drop in the unds rate rom late 1990 through 1993 and the 300 basis point increase in the rate between January 1994 and early Exogenizing Policy Can Produce Incredible Results The pure orecasting exercise that Doan, Litterman and Sims (1984) discuss, and which is implemented in many practical applications, can generate implausible results. We illustrate the point with the dramatic period beginning in September The period clariies a problem that applies generally. There are many ways to exogenize policy. One could change the systematic part o policy the unction in (11) but this can be couched as a particular ' P sequence. Bernanke, Gertler and Watson (1997) conduct the counteractual exercise o changing. Hamilton and Herrera (2000) convert the change in to a sequence o ˆP ' s and compute our metric to conclude the exercise is problematic. 15 Here we provide two more examples. We mimic conventional out-o-sample orecasting by exogenizing the ederal unds rate, orcing the actual path o R over the next 48 months to be produced solely by exogenous policy actions. For each month o the orecast period we calculate the '! Pt that produces a orecast that equals the actual unds rate, R t, given the value o '! Pt. Instead o conditioning on reduced- 15 Other recent papers that exogenize policy in this manner include Bernanke, Gertler and Watson (1997), Sims (1998), Sims and Zha (1998b), and Dungey and Pagan (2000). 13

15 orm errors, our interpretation o Doan, Litterman and Sims derives the sequence o exogenous policy actions consistent with the R path. Table 4 reports the central tendencies or the paths o the unds rate, output growth, inlation, and unemployment over the our-year orecast horizon. The actual unds rate ell dramatically over the period, rom an annual average o almost 8 percent in 1990 to an average o less than 3 percent in It takes a sequence o same-signed exogenous impulses to generate that decline solely rom exogenous policy actions. The impulses drive output growth and inlation into double digits and the unemployment rate down to 3.5 percent. Given the actual path or the policy instrument, the implausible paths or macro variables suggest that much o the movement in R over the period was an endogenous response o policy to nonpolicy disturbances. 16 The results in Table 4 come rom hypothesizing policy behavior that deviates substantially rom any behavior observed over the sample. The orecast errors or each variable are extremely unlikely, as shown by the statistics below: Variable B * P (90 : 9, 48) R y P 9.64 U The metric warns against placing much conidence in the linear projections. It is commonplace or central banks to condition orecasts on an unchanged path o the policy instrument. The Bank o England (2000), or example, projects GDP growth and inlation over horizons exceeding two years, under the assumption that the oicial interest rate is constant. 17 As the state o the economy is orecasted to change, however, an unchanged path o the instrument always requires some pattern o intervention. Whether that intervention is likely to shit private decision rules depends both on how persistent the intervention is and on how large the dynamic impacts are. 16 Altig, Carlstrom and Lansing (1995) assume a path o exogenous monetary policy disturbances to use their general equilibrium model to simulate the eects o reducing inlation by a percentage point over a two-year period and holding it at the lower value or three more years. The model predicts implausible paths or the nominal interest rate and output growth. 17 Central banks requently interpret a constant instrument path an unchanged stance o policy [Board o Governors o the Federal Reserve System (1999) or Sveriges Riksbank (1999)]. 14

16 In September 1990, the ederal unds rate stood at 8.20 percent. Suppose the Fed were to hold the rate ixed at 8.20 percent over the next 4 years. Doing this requires a sequence o positive '! P s that increase nearly monotonically over the orecast horizon, and average 1½ standard deviations in year 3 and over 2 in the last year. This intervention implies large orecast errors: Variable * B # 90 :9,48$ y P U 6.69 P Linear orecasts are unlikely to be reliable. 3.2 Routine Policy Interventions Can Matter We now address whether conditioning on the class o interventions we consider is inormative about routine policy decisions. It turns out that this class o interventions is rich: it can generate economically meaningul shits in the distributions o orecasted macro variables and clariy the tradeos acing policymakers. The analysis demonstrates that a complete probability model, which quantiies the uncertainties that Brainard (1967) emphasizes, can answer complex joint probability questions about those tradeos. We conduct the analysis through the eyes o an econometrician who has inormation about the economy through September Minutes o the October 2, 1990 FOMC meeting reveal that the Fed predicted a mild downturn in economic activity ollowed by a rapid resumption o moderate growth. The minutes report that insoar as could be judged on the basis o traditional indicators, the available data did not point to cumulating weakness and the onset o a recession. 18 Political developments in the Middle East, however, generated concerns about uture oil prices and created uncertainty about the outlook or inlation. Although the domestic policy directive that emerged rom the meeting sought to maintain the existing degree o pressure on reserve position, several FOMC members dissented. One member avored immediate easing and three members opposed the FOMC s perceived leaning in avor o easing. 18 Board o Governors o the Federal Reserve System (1990, p. 135). 15

17 In light o the dissension among FOMC members, we consider two scenarios. The irst scenario conditions orecasts on the actual path o the ederal unds rate rom October 1990 to January An alternative scenario considers tighter policy over those our months. Figure 3 reports the actual time series, the out-o-sample orecasts conditional on the actual path o the unds rate, and 68 percent probability bands or the orecasts. The actual unds rate was 8.11 percent in October, 7.81 percent in November, 7.31 percent in December, and 6.91 percent in January. With that path o the unds rate, there is substantial probability that inlation will rise above 5½ or 6 percent through 1993, real growth will all below 1 percent in 1991, and unemployment will rise to near 7 percent through Based on the path o the unds rate, it may appear that the Fed was concerned primarily about recession. As it happened, inlation ell to 3 percent by 1992, a recession occurred rom July 1990 to March 1991 (according to the NBER dating), and unemployment hit 7½ percent in O course, as the model s orecasts conirm, policymakers were unaware in October that the recession began three months earlier. The FOMC minutes report that some policymakers were concerned about higher inlation. Those FOMC members might want to see orecasts conditional on tighter policy. The orecasts assume an intervention that raises the unds rate by 50 basis points in October (to 8.70 percent) and an additional 25 basis points over the period rom November 1990 to January Ex-ante it appears that tighter policy would reduce the likelihood o higher inlation, but at the cost o raising the probability o negative real growth in 1991 (Figure 4). The point orecasts o output growth and unemployment, conditional on tighter monetary policy, come very close to the actual paths o the variables in 1991 and In spite o the sharp decline in the projected unds rate in , the intervention exerts a contractionary inluence. 19 Debate during the October 1990 FOMC meeting centered on the tradeos associated with alternative policy choices. The tradeos can be ramed as joint probability statements. To 19 To hit the actual path o the unds rate the intervention is I T %{0.5,0.1, * 0.7, * 0.7,0,...,0} and or tightening it is I T % {2.3,1.7,1.0,0.9,0,...,0}. The resulting metrics are * * B P # 90 :9,48$ B P 90 :9,48 Variable Actual R # $ Tighter Policy y P U

18 answer the concerns over economic slowdown and higher inlation, Table 5 reports a variety o joint probabilities involving real GDP growth in 1991 or 1992 or 1993 and inlation in 1992 and 1993, conditional on two alternative policies. Tighter policy assumes the same counteractual policy behavior as in Figure 4, while Actual R adjusts policy to be consistent with Figure 3. The probabilities put a sharp point on the tradeos Federal Reserve oicials perceived they aced. In terms o the marginal probabilities, tighter policy makes it very likely that inlation will remain low in 1992 and 1993 (below 5½ percent), but it also produces a better than 50 percent chance o a recession in 1991 (negative real GDP growth or the year). More relevant to policymakers is the apparent tradeo: tighter policy creates a one-third chance o a recession in 1991 or 1992 or 1993 and low inlation in 1992 and For an intervention to generate the actual path o the unds rate, the Fed would have to tighten slightly in October and November and then ease in December and January. The column in the table labeled Actual R reports these results. This policy reduces by hal the marginal probability o a recession in 1991 while lowering the marginal likelihoods o low inlation in 1992 and It also greatly reduces the joint probability o a recession in 1991 or 1992 or 1993 and low inlation in 1992 and Again the tradeo is clear: the probability o no recession coupled with inlation over 5½ percent now exceeds 40 percent, compared to 18 percent when policy is tighter. 3.3 Appraising and Reappraising Policy with Sequential Interventions Blinder s (1997) description o the appraisal/reappraisal process inherent in routine policymaking is echoed by Kohn (1995, p. 235) who observes that policymakers must be lexible in revising orecasts and the policy stance in response to new inormation. This perspective helps to understand the Federal Reserve s preemptive strike against inlation in Our analysis shows that in February the tighter policy looked to be suicient to oset higher inlation in 1996 and 1997; it was not suicient by April, once three months o new inormation arrived. When we reappraise policy in April, a urther tightening appears necessary to preempt inlation. The analysis puts empirical lesh on Brainard s (1967) argument or gradualism. Figure 5 displays actual data and out-o-sample orecasts made in January under two alternative policy scenarios or February through May. Given that the ederal unds rate had 17

19 been nearly constant at 3 percent over the previous year, a natural baseline maintains this constancy through May. The irst intervention holds the unds rate constant or 4 months. That policy portends rising inlation over the next several years, exceeding 3½ percent in 1996 and 1997; but policymakers do not seem to ace an unpleasant tradeo between inlation and real activity. Real GDP is expected to grow at least 3 percent annually rom 1995 to 1997, while the unemployment rate is projected to continue to decline. Key policy questions at the time were when to raise the rate and how much to raise it. To address these questions we consider an alternative policy o moderate tightening that raises the unds rate along its actual path. Although the actual unds rate rose a ull percentage point rom January to May, that path requires a relatively small exogenous intervention. 20 Even moderate tightening in January shits the projected inlation path down without severely aecting real activity (Figure 5). The Fed reappraises policy in April with three additional months o news about the economy. Now the baseline o a constant unds rate at 3.75 percent leads policymakers to expect inlation will once again drit toward the 3½ to 4 percent range in 1996 and 1997 (Figure 6). The outlooks or output and unemployment remain promising, so the Fed still does not ace a diicult tradeo. A somewhat stronger tightening move to match the actual path o the unds rate rom May through August pushes the unds rate to 4.47 percent in August. Tighter policy shits the mean orecast o inlation down below 3 percent through 1997 without risking recession Holding the unds rate constant requires the intervention I T %{*.3, *.2,*.2, *.2,0,...,0}, while * tracking the actual unds rate calls or the intervention I T % {.5,0,.5,1.1,0,...,0}. The B statistics associated with the interventions are: Variable * * B P # 94 :1, 48$ B P # 94 :1, 48$ Constant R Actual R y P U A constant R requires I T %{.1, *.3,0,...,0} and the actual path o * I % {.8,.4,.1,.8,0,...,0}. The associated B s are: T R requires 18

20 By reappraising their decisions in light o updated orecasts, policymakers move cautiously against inlation. So long as orecasts extend ar enough into the uture to capture monetary policy s lagged eects, the gradual approach can be successul. This analysis ormalizes Blinder s (1997) description o policymaking. It also illustrates why uncertainty about uture exogenous disturbances may lead policymakers to move cautiously, as Brainard (1967) instructs. Some readers might worry that i policy makers use the kind o on-going policy analysis that we describe as a basis or policy decisions, agents belies about regime might shit. We perorm an ex-post check o how likely this situation was in January We estimate the model through January 1994, back out the realized policy disturbances, ˆP ' s, over the preceding 48 months, and compute an ex-post metric using the realized disturbances. The metric yields Variable * B # 90 : 2, * 48$ P Ex-post y P U 1.94 or orecasts beginning in February 1990 and ending in January These values or * B warn that over this period agents belies may have shited in avor o a new, tighter monetary policy regime. This result would be consistent with Taylor s (1999) inding that during the Greenspan era the Federal Reserve responded more strongly to inlation than in previous periods. Although this ex-post metric raises a warning lag, we judge that the conditional projections o interventions in January and April 1994 are reliable. The judgment call is based on three considerations. First, a change in belies about regime is necessary but not suicient or undermining the reliability o the linear approximation. Second, as Appendix D shows, the responses to policy disturbances are extremely stable across estimation periods ending in September 1990, January 1994, and April I changes in belies generated quantitatively important shits in decision rules, one would expect to observe greater instability in the response Variable * * P # 94 : 4, 48$ B P # 94 : 4, 48$ Constant R Actual R B y P U

21 unctions. Finally, the large * B s arise rom only a ew positive interventions larger than one standard deviation and there is no clear sign pattern in the interventions that might systematically shit belies. These observations underscore the bias that can arise rom mechanically applying the metric without actoring in the dynamic patterns an intervention implies Concluding Remarks Our ramework uniies identiication and orecasting. Identiying exogenous variation in policy is essential or addressing counteractual questions. A careul examination o both insample and out-o-sample its and the model s stability allow the econometrician to assess the model s statistical properties. We showed how the approach can address practical counteractual policy questions. The approach rames answers in probabilistic terms, quantiying uncertainty about the model and about uture exogenous events. This is a ramework or interpreting actual central bank behavior. We illustrated the approach with an identiied VAR model o U.S. monetary policy. We probed the range o policy interventions or which an identiied linear model is likely to be reliable. We checked that this range o policies is consistent with an unchanged policy regime and showed that it is suiciently rich to address questions considered by central banks at regular policy meetings. The interventions studied matter: they can shit the projected paths and probability distributions o macro variables in economically meaningul ways. In line with recent work, the paper has not ound compelling evidence that Federal Reserve behavior has been unstable over the past 40 years. Although some readers may dispute our inerence that the Fed has operated in approximately one regime since 1959, this does not diminish the useulness o our approach. Researchers can simply estimate the model over any sample period they deem constitutes a single regime, and then apply our approach to compute linear projections. The approach assesses the projections reliability conditional on policy 22 For the 4 years preceding September 1990, the example in section 3.2, the ex-post metrics or the three variables are below 0.5 in absolute value. 20

22 regime: i two researchers can agree that a data sample constitutes a single regime, they should also agree on whether a linear projection is reliable. Our methodology has broad applicability. We have stressed its useulness or the kinds o practical analyses central banks conduct. Closely related techniques are being used to study the behavior o the central bank o Sweden as it implements inlation targeting [Jansson and Vredin (2000)]. Our method also yields insights about the plausibility o answers to counteractual questions. Hamilton and Herrera (2000) apply the methodology to assess the plausibility o Bernanke, Gertler, and Watson s (1997) counteractual analysis o the Federal Reserve s response to oil price shocks. 21

23 Table 1. Structure o Contemporaneous Variables Money demand am2 ( ar ( ay( ap %' MD Monetary policy ar ( am2( acp %' P Inormation sector a CP( a M2 ( a R ( a y( a P( a U %' I Production sector This subsystem is arranged in the lower-triangular order y, P, and U. Table 2. Maximum Likelihood Estimates o Contemporaneous Coeicients Money demand M2 ( R * y ( 6.84 P %' MD (49.65, ) (45.33, ) (* 36.44, * 9.11) (* 23.95, 36.95) Monetary policy R * M2 * 3.10 CP % ' P (* 12.08, ) (* , * 40.42) (* 11.29, 4.90) Inormation CP * M 2 ( R * 7.09 y * P ( U % ' I (45.85, 50.83) (* 65.95, 36.56) (6.60, 51.59) (* 19.57, 3.40) (* 65.79, * 15.82) (21.31, 85.24) 68 percent probability intervals or the maximum likelihood estimates are reported in parentheses. Those intervals are based on exact inite-sample results computed by a Gibbs sampler algorithm with 360,000 Monte Carlo draws. See Waggoner and Zha (1998) or details. 22

24 Table 3. Correlations Among Exogenous Disturbances Maximum likelihood estimates and 68% probability intervals, in parentheses, based on 360,000 draws rom the posterior distribution o the model coeicients ' P ' MD ' I ' y ' CPI ' U ' P ' MD ' I ' y ' CPI ' U 1.0 (1,1) (-.048,.052) (1,1) (-.064,.032) (-.060,.032) (1,1) (-.056,.084) (-.052,.044) (-.048,.044) (1,1) (-.004,.052) (-.056,.044) (-.060,.036) (-.052,.040) (1,1) (-.140,.068) (-.192,.-088) (-.048,.044) (-.052,.044) (-.048,.044) (1,1) (grouped into bins o size.002 to keep storage demands manageable) Table 4. Out-o-Sample Forecasts Conditional on Actual Path o R Forecasts assume the path o R is produced by exogenous policy actions only Forecasts rom October 1990 to September 1994 Maximum likelihood estimates; annual average growth rates or percentage points. R y DE U orecast (actual) orecast (actual) orecast (actual) (1.2) 5.4 (5.4) 5.6 (5.6) (-0.9) 6.0 (4.2) 6.7 (6.9) (2.7) 7.2 (3.0) 6.0 (7.5) (2.3) 12.7 (3.0) 3.5 (6.9) 23

25 Table 5. Joint and Marginal Probabilities Conditional on Alternative Policies Outcomes Based on Out-o-Sample Forecasts rom September Tighter policy raises R to 8.70% in October and to 8.95% in November 1990-January 1991 and is produced by the sequence o exogenous actions! ' P % (2.3,1.7,1.0,0.9). Actual R sets R at 8.11% in October, 7.81% in November, 7.31% in December, 6.91% in January 1991 and is produced by the sequence o exogenous actions! ' % (0.5,0.1,-0.7,-0.7). Tighter P Actual Plow ( D in1992 ) Plow ( D in1993 ) Plow ( D in1992 and 1993 ) P( recession in 1991 ) P( recession in 1992 ) P( recession in 1993 ) P( recession and low D ) P( recession and high D ) P( no recession and low D $ P( no recession and high D ) P( recession) is the probability o negative real GDP growth in 1991 or 1992 or Plow ( D ) is the probability o inlation below 5½ percent in 1992 and P( recession and low D ) is the probability o negative real GDP growth in 1991 or 1992 or 1993 and inlation below 5½ percent in 1992 and R 24