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Stickiness: A comment
Carnegie-Rochester Conference Series on Public Policy 49 (1998) 357-363 North-Holland
Stickiness A comment Bennett T. McCallum Carnegie Mellon University and National Bureau of Economic Research
In commenting on Chris Sims's paper, my first and most important task is to enthusiastically welcome his plunge into work concerning price level stickiness, a topic that is of central importance for the understanding of macro-monetary dynamics. There are several specific points in the paper that are not entirely convincing to me and/or deserve additional discussion, but its overall message is stimulating and of considerable promise. To some extent the paper is a criticism of some prominent "new Keynesian" specifications of price and/or wage stickiness. One aspect of this criticism is that the relevant adjustment formulae can be incorporated in models that nevertheless retain highly classical properties. Points such as this have of course been made in the past, as in Barro (1977), Hall (1980), and elsewhere, but Sims's "lean classical sticky-wage" model of Section 4.1 is new, at least to me. A more significant aspect of his criticism, however, is that prevailing specifications fail to match the facts of actual macroeconomic experience - in particular, the fact that both nominal and real variables respond sluggishly but substantially to monetary shocks. An important part of his message is that these properties may be rationalized by models that build upon the hypothesis that information-processing costs are a key feature of reality. The appropriate response to Lucas's (1972a) signal-extraction hypothesis may be to enrich and modify it, rather than to reject it--on the grounds that nominal aggregates are in reality quickly observable--as most of the profession has done. We must look forward to Sims's formal implementation of this approach in future work. In his Sections 5.1 and 5.4, Sims develops models in which individuals optimize in the face of "pervasive adjustment costs," and suggests that they possess some of the crucial properties that he indicates will be implied by models in which behavior is instead affected by limited information0167-2231/98/$ - see front matter © 1998 Published by Elsevier Science B.V. All rights reserved. PII: S0167-2231 (99)00014-7
processing capacity. In Section 2, however, he emphasizes that the former may be a misleading guide to the latter in important policy-relevant respects. For models of the former type "make the distinction between anticipated and unanticipated policy [actions] central, whereas information-based modeling would not" (p. 322). In this regard, it is not clear to me how the empirical evidence of Section 3, which is basic in his criticism of existing models, is to be interpreted. This evidence consists of impulse response functions for a 7-variable VAR system with a triangular normalization. To me it is not clear what the VAR equation residuals represent, for reasons that have been frequently (though inconclusively) discussed in the literature. My own tentative judgment is that it might be better to use autocorrelation functions of the type featured by Fuhrer and Moore (1995), instead of impulse response functions, as the basis for ascertaining a model's consistency with the time series evidence. In Section 4, Sims presents two optimizing models (with no capital or adjustment costs) in which output and employment responses to monetary shocks are basically the same--very small--although one of the models has quickly adjusting nominal wages and the other features nominal wage contracts of the form "postulated in the overlapping contract model of Taylor (1980) and the randomly-timed-adjnstment model of Calvo (1983)." He recognizes that "the essential feature of the contracts in [the wage contract] model, that leads to their not affecting neutrality, is that though they fix a 'price' they do not represent open-end commitments to sell at that price" (p. 331). In other words, the quantity of employment is not demanddetermined at the prevailing wage rate. By contrast, output and employment are demand-determined in Taylor's model, Calvo's model, and in the notable Fuhrer and Moore (1995) specification, as well as some other "new Keynesian" formulations. Consequently, this is one possibility of what one might think of as the defining characteristic of today's "Keynesian" models. It could reasonably be argued, I believe, that the assumption of demanddetermined output and employment is not theoretically objectionable, i.e., that the implied type of contract is realistic. As argued in Fischer's (1977) comment on Barro (1977), that is, many actual contracts fix a nominal wage rate (or wage schedule, specifying overtime pay, etc.) and leave firms free to determine each period's rate of output and employment with workers temporarily supplying more (or less) labor than they would on a sustained basis at the prevailing wage. Such a model does not, I am inclined to argue, have the truly undesirable features of the Keynesian models of the 1960s and of Sims's Keynesian model in 5.2. The implausible feature of these models, I suggest, is their failure to satisfy the natural-rate hypothesis (NRH). Instead, they imply that by accepting inflation a nation can keep output and employment high--i.e., keep the marginal disutility of labor above the marginal 358
product of labor--permanently. In one of his seminal papers, Lucas (1972b) defined the NRH in this way, i.e., as implying that there is n_rioinflation policy--no money creation s c h e m e - - t h a t will keep output high permanently. This is a stricter version of the NRH than one that says only that a high rate of inflation will not keep output high. If we let fh - Yt -- fh, where Yt is output and Yt is tile market-clearing value that would prevail in the absence of nominal stickiness, then Lucas's strict version of the NRH is = 0
(1)
for any monetary policy, where E is the unconditional expectation operator. In my opinion, (1) is a property that we as researchers should try to maintain while devising models that possess some nominal stickiness, permit monetary policy to have some temporary real effects on output, and match the data. Why? Well, basically for the reason stated by Lucas--that it seems a priori implausible that a nation can enrich itself in real terms permanently by any type of monetary policy, by any path of paper money creation. 1 Anyone who is attracted to this proposition should be appalled by recent discussions in the press, as well as a 1997 symposium in the Journal of Economic Perspectives, on the NRH and the NAIRU concept. In these discussions, there is a marked tendency for writers to use the NAIRU and N R H concepts as if they were the same. But in fact they are contradictory, antithetical concepts. Thus a NAIRU model is typically a version (perhaps elaborated) of a relation such as
Ap~ = a(j~ + Apt-1 + ut
a > 0
(2)
where by keeping Apt > APt-1 permanently one can keep E~t > 0 permanently. This will still be true if Apt_l is replaced with O(L)Apt_l; you just keep Apt > O(L)APt-1. The NAIRU specification (2) can also be contrasted with several popular new-Keynesian formulations. Roberts (1995) shows neatly that the nominal stickiness models of Calvo (1983) and Rotemberg (1982), and a version of Taylor (1980), can be expressed approximately as
Apt = Et/kpt+l + O~h.
(3)
Now these do not satisfy the strict NRH, because keeping A p t > /kpt_l will keep Eflt ¢ 0. However, an accelerating inflation will keep output low, not high, so a central bank that adopted this type of model would not have as lit should be emphasized that this version of the NRH does not imply monetary superneutrality, which I interpret as the proposition that different steady inflation rates do not lead to different paths for ~t itself. Nonsuperneutrality says nothing about ~)t. 359
much of a temptation to behave in an inflationary manner as would one using a NAIRU model. The Fuhrer-Moore (1995) model is one that can be represented in its two-period version as
Apt = 0.5 Apt-: + 0.5 EtApt+l + sot
(4)
so keeping Apt = Apt_: + (f with 5 > 0 gives Apt = 0.5(Apt - 5) + 0.5(Apt + ~) + s0,
(5)
so that Yt is not kept away from zero by a policy of increasing inflation by (f > 0 each period. But a policy of increasing the change in inflation, i.e., of keeping AApt > AApt_: permanently, will violate the NRH even in the Fuhrer-Moore model. The only model that I am familiar with that incorporates nominal sluggishness and still satisfies the strict NRH is the one discussed in McCallum (1994), where it is called the P-bar model. This sPecification was used by Mussa and by me in the late 1970s and was considered earlier, in a nonrational-expectations setting, by Barro and Grossman. 2 It can be expressed most compactly as Pt ---- Et-li0t + s ( p t - 1 - Pt-1),
0 < s < 1
(6)
or as
Et-lpt = Spt-1
(7)
where fit -- Pt - fit and i~t is the market-clearing price that would prevail in the same economy but in the absence of any nominal stickiness. Now by construction Pt = -t~Ot in these models, assuming linearity, so it follows that the P-bar model also has the property Et_ly t -'~ Syt-- 1.
(S)
C o n s e q u e n t l y , E ( E t _ l Y t ) -- s E y t - 1 , which implies E~t - 0, so (7) does satisfy the NRH. Thus if combined with the assumption of demand-determined output it yields temporary effects of monetary policy on Yt without permitting any permanent effect. My 1994 attempt to study this relation empirically was rather unsuccessful, but more recent attempts, in McCallum and Nelson (1998, 1999), are more encouraging (and include an improved derivation as well). Be that as it may, the point at hand is that, in models incorporating nominal stickiness, satisfaction of the NRH seems a desirable property--one that I would encourage Sims to consider in his future work. 2For references, see McCallum (1994).
360
One quibble that is of no substantive importance in terms of Sims's current paper, but is worth making (I believe) for possible application elsewhere, concerns his statement that the paper's models "are formulated in continuous time to avoid the need to use the uninterpretable 'one period' delays that plague the discrete time models in their literature" (p. 318). My objection here is to the apparent contention that there is some form of error that requires a continuous-time formulation to be avoided. This seems mistaken to me, as there is apparently no compelling reason for adopting a continuoustime setup (or vice-versa) except for the convenience of the analyst and his or her readers. After all, one can use discrete time with the proviso that time periods are to be interpreted as minutes, in which case the models would need to be related to quarterly or monthly empirical analysis in the same way as is required with continuous-time formulations. More fundamentally, all continuous-time setups are inherently just limiting cases of discrete-time formulations in which the time period approaches zero. The foregoing points and reservations should not be permitted to obscure my agreement with Sims's basic messages: (i) that various models with nominal stickiness can be quite different in terms of their policy-relevant dynamic properties, (ii) that it is important to look among the formulations for ones that match actual data, (iii) that sluggish responses to shocks seem to characterize both nominal and real variables, a n d - - m o r e provisionally--(iv) that costs of information processing may provide a fruitful area of investigation.
361
References
Barro, R.J., (1977). Long-Term Contracting, Sticky Prices, and Monetary Policy. Journal of Monetary Economics, 3: 305- 316. Calvo, G.A., (1983). Staggered Prices in a Utility-Maximizing Framework. Journal of Monetary Economics, 12: 383-398. Fischer, S., (1977). Long-Term Contracting, Sticky Prices, and Monetary Policy: A Comment. Journal of Monetary Economics, 3: 317-324. Fuhrer, J.C., and Moore, G.R., (1995). Inflation Persistence. Journal of Economics, 109: 127-159.
Quarterly
Hall, R.E., (1980). Employment Fluctuations and Wage Rigidity. Brookings Papers on Economic Activity. No. 1, 91-123. Lucas, R.E., Jr., (1972a). Expectations and the Neutrality of Money. Journal of Economic Theory, 4: 103-124. Lucas, R.E., Jr., (1972b). Econometric Testing of the Natural Rate Hypothesis. O. Eckstein (ed.), The Econometrics of Price Determination. Washington; Board of Governors of the Federal Reserve System. McCallum, B.T., (1994). A Semi-Classical Model of Price Level Adjustment. Carnegie-Rochester Conference Series on Public Policy, 41: 251-284. McCallum, B.T. and Nelson, E., (1998). Nominal Income Targeting in an Open-Economy Optimizing Model. NBER Working Paper 6675. McCallum, B.T. and Nelson, E., (1999). Performance of Operational Policy Rules in an Estimated Semi-Classical Structural Model. J.B. Taylor (ed.), Monetary Policy Rules. Chicago: University of Chicago Press, forthcoming. Roberts, J., (1995). New Keynesian Economics and the Phillips Curve. Journal of Money, Credit, and Banking, 27: 975-984. Rotemberg, J.J., (1982). Monopolistic Price Adjustment and Aggregate Output. Review of Economic Studies, 44: 517-531.
362
Taylor, J.B., (1980). Aggregate Dynamics and Staggered Contracts. Journal of Political Economy, 88: 1-23.
363
Stickiness A comment Bennett T. McCallum Carnegie Mellon University and National Bureau of Economic Research
In commenting on Chris Sims's paper, my first and most important task is to enthusiastically welcome his plunge into work concerning price level stickiness, a topic that is of central importance for the understanding of macro-monetary dynamics. There are several specific points in the paper that are not entirely convincing to me and/or deserve additional discussion, but its overall message is stimulating and of considerable promise. To some extent the paper is a criticism of some prominent "new Keynesian" specifications of price and/or wage stickiness. One aspect of this criticism is that the relevant adjustment formulae can be incorporated in models that nevertheless retain highly classical properties. Points such as this have of course been made in the past, as in Barro (1977), Hall (1980), and elsewhere, but Sims's "lean classical sticky-wage" model of Section 4.1 is new, at least to me. A more significant aspect of his criticism, however, is that prevailing specifications fail to match the facts of actual macroeconomic experience - in particular, the fact that both nominal and real variables respond sluggishly but substantially to monetary shocks. An important part of his message is that these properties may be rationalized by models that build upon the hypothesis that information-processing costs are a key feature of reality. The appropriate response to Lucas's (1972a) signal-extraction hypothesis may be to enrich and modify it, rather than to reject it--on the grounds that nominal aggregates are in reality quickly observable--as most of the profession has done. We must look forward to Sims's formal implementation of this approach in future work. In his Sections 5.1 and 5.4, Sims develops models in which individuals optimize in the face of "pervasive adjustment costs," and suggests that they possess some of the crucial properties that he indicates will be implied by models in which behavior is instead affected by limited information0167-2231/98/$ - see front matter © 1998 Published by Elsevier Science B.V. All rights reserved. PII: S0167-2231 (99)00014-7
processing capacity. In Section 2, however, he emphasizes that the former may be a misleading guide to the latter in important policy-relevant respects. For models of the former type "make the distinction between anticipated and unanticipated policy [actions] central, whereas information-based modeling would not" (p. 322). In this regard, it is not clear to me how the empirical evidence of Section 3, which is basic in his criticism of existing models, is to be interpreted. This evidence consists of impulse response functions for a 7-variable VAR system with a triangular normalization. To me it is not clear what the VAR equation residuals represent, for reasons that have been frequently (though inconclusively) discussed in the literature. My own tentative judgment is that it might be better to use autocorrelation functions of the type featured by Fuhrer and Moore (1995), instead of impulse response functions, as the basis for ascertaining a model's consistency with the time series evidence. In Section 4, Sims presents two optimizing models (with no capital or adjustment costs) in which output and employment responses to monetary shocks are basically the same--very small--although one of the models has quickly adjusting nominal wages and the other features nominal wage contracts of the form "postulated in the overlapping contract model of Taylor (1980) and the randomly-timed-adjnstment model of Calvo (1983)." He recognizes that "the essential feature of the contracts in [the wage contract] model, that leads to their not affecting neutrality, is that though they fix a 'price' they do not represent open-end commitments to sell at that price" (p. 331). In other words, the quantity of employment is not demanddetermined at the prevailing wage rate. By contrast, output and employment are demand-determined in Taylor's model, Calvo's model, and in the notable Fuhrer and Moore (1995) specification, as well as some other "new Keynesian" formulations. Consequently, this is one possibility of what one might think of as the defining characteristic of today's "Keynesian" models. It could reasonably be argued, I believe, that the assumption of demanddetermined output and employment is not theoretically objectionable, i.e., that the implied type of contract is realistic. As argued in Fischer's (1977) comment on Barro (1977), that is, many actual contracts fix a nominal wage rate (or wage schedule, specifying overtime pay, etc.) and leave firms free to determine each period's rate of output and employment with workers temporarily supplying more (or less) labor than they would on a sustained basis at the prevailing wage. Such a model does not, I am inclined to argue, have the truly undesirable features of the Keynesian models of the 1960s and of Sims's Keynesian model in 5.2. The implausible feature of these models, I suggest, is their failure to satisfy the natural-rate hypothesis (NRH). Instead, they imply that by accepting inflation a nation can keep output and employment high--i.e., keep the marginal disutility of labor above the marginal 358
product of labor--permanently. In one of his seminal papers, Lucas (1972b) defined the NRH in this way, i.e., as implying that there is n_rioinflation policy--no money creation s c h e m e - - t h a t will keep output high permanently. This is a stricter version of the NRH than one that says only that a high rate of inflation will not keep output high. If we let fh - Yt -- fh, where Yt is output and Yt is tile market-clearing value that would prevail in the absence of nominal stickiness, then Lucas's strict version of the NRH is = 0
(1)
for any monetary policy, where E is the unconditional expectation operator. In my opinion, (1) is a property that we as researchers should try to maintain while devising models that possess some nominal stickiness, permit monetary policy to have some temporary real effects on output, and match the data. Why? Well, basically for the reason stated by Lucas--that it seems a priori implausible that a nation can enrich itself in real terms permanently by any type of monetary policy, by any path of paper money creation. 1 Anyone who is attracted to this proposition should be appalled by recent discussions in the press, as well as a 1997 symposium in the Journal of Economic Perspectives, on the NRH and the NAIRU concept. In these discussions, there is a marked tendency for writers to use the NAIRU and N R H concepts as if they were the same. But in fact they are contradictory, antithetical concepts. Thus a NAIRU model is typically a version (perhaps elaborated) of a relation such as
Ap~ = a(j~ + Apt-1 + ut
a > 0
(2)
where by keeping Apt > APt-1 permanently one can keep E~t > 0 permanently. This will still be true if Apt_l is replaced with O(L)Apt_l; you just keep Apt > O(L)APt-1. The NAIRU specification (2) can also be contrasted with several popular new-Keynesian formulations. Roberts (1995) shows neatly that the nominal stickiness models of Calvo (1983) and Rotemberg (1982), and a version of Taylor (1980), can be expressed approximately as
Apt = Et/kpt+l + O~h.
(3)
Now these do not satisfy the strict NRH, because keeping A p t > /kpt_l will keep Eflt ¢ 0. However, an accelerating inflation will keep output low, not high, so a central bank that adopted this type of model would not have as lit should be emphasized that this version of the NRH does not imply monetary superneutrality, which I interpret as the proposition that different steady inflation rates do not lead to different paths for ~t itself. Nonsuperneutrality says nothing about ~)t. 359
much of a temptation to behave in an inflationary manner as would one using a NAIRU model. The Fuhrer-Moore (1995) model is one that can be represented in its two-period version as
Apt = 0.5 Apt-: + 0.5 EtApt+l + sot
(4)
so keeping Apt = Apt_: + (f with 5 > 0 gives Apt = 0.5(Apt - 5) + 0.5(Apt + ~) + s0,
(5)
so that Yt is not kept away from zero by a policy of increasing inflation by (f > 0 each period. But a policy of increasing the change in inflation, i.e., of keeping AApt > AApt_: permanently, will violate the NRH even in the Fuhrer-Moore model. The only model that I am familiar with that incorporates nominal sluggishness and still satisfies the strict NRH is the one discussed in McCallum (1994), where it is called the P-bar model. This sPecification was used by Mussa and by me in the late 1970s and was considered earlier, in a nonrational-expectations setting, by Barro and Grossman. 2 It can be expressed most compactly as Pt ---- Et-li0t + s ( p t - 1 - Pt-1),
0 < s < 1
(6)
or as
Et-lpt = Spt-1
(7)
where fit -- Pt - fit and i~t is the market-clearing price that would prevail in the same economy but in the absence of any nominal stickiness. Now by construction Pt = -t~Ot in these models, assuming linearity, so it follows that the P-bar model also has the property Et_ly t -'~ Syt-- 1.
(S)
C o n s e q u e n t l y , E ( E t _ l Y t ) -- s E y t - 1 , which implies E~t - 0, so (7) does satisfy the NRH. Thus if combined with the assumption of demand-determined output it yields temporary effects of monetary policy on Yt without permitting any permanent effect. My 1994 attempt to study this relation empirically was rather unsuccessful, but more recent attempts, in McCallum and Nelson (1998, 1999), are more encouraging (and include an improved derivation as well). Be that as it may, the point at hand is that, in models incorporating nominal stickiness, satisfaction of the NRH seems a desirable property--one that I would encourage Sims to consider in his future work. 2For references, see McCallum (1994).
360
One quibble that is of no substantive importance in terms of Sims's current paper, but is worth making (I believe) for possible application elsewhere, concerns his statement that the paper's models "are formulated in continuous time to avoid the need to use the uninterpretable 'one period' delays that plague the discrete time models in their literature" (p. 318). My objection here is to the apparent contention that there is some form of error that requires a continuous-time formulation to be avoided. This seems mistaken to me, as there is apparently no compelling reason for adopting a continuoustime setup (or vice-versa) except for the convenience of the analyst and his or her readers. After all, one can use discrete time with the proviso that time periods are to be interpreted as minutes, in which case the models would need to be related to quarterly or monthly empirical analysis in the same way as is required with continuous-time formulations. More fundamentally, all continuous-time setups are inherently just limiting cases of discrete-time formulations in which the time period approaches zero. The foregoing points and reservations should not be permitted to obscure my agreement with Sims's basic messages: (i) that various models with nominal stickiness can be quite different in terms of their policy-relevant dynamic properties, (ii) that it is important to look among the formulations for ones that match actual data, (iii) that sluggish responses to shocks seem to characterize both nominal and real variables, a n d - - m o r e provisionally--(iv) that costs of information processing may provide a fruitful area of investigation.
361
References
Barro, R.J., (1977). Long-Term Contracting, Sticky Prices, and Monetary Policy. Journal of Monetary Economics, 3: 305- 316. Calvo, G.A., (1983). Staggered Prices in a Utility-Maximizing Framework. Journal of Monetary Economics, 12: 383-398. Fischer, S., (1977). Long-Term Contracting, Sticky Prices, and Monetary Policy: A Comment. Journal of Monetary Economics, 3: 317-324. Fuhrer, J.C., and Moore, G.R., (1995). Inflation Persistence. Journal of Economics, 109: 127-159.
Quarterly
Hall, R.E., (1980). Employment Fluctuations and Wage Rigidity. Brookings Papers on Economic Activity. No. 1, 91-123. Lucas, R.E., Jr., (1972a). Expectations and the Neutrality of Money. Journal of Economic Theory, 4: 103-124. Lucas, R.E., Jr., (1972b). Econometric Testing of the Natural Rate Hypothesis. O. Eckstein (ed.), The Econometrics of Price Determination. Washington; Board of Governors of the Federal Reserve System. McCallum, B.T., (1994). A Semi-Classical Model of Price Level Adjustment. Carnegie-Rochester Conference Series on Public Policy, 41: 251-284. McCallum, B.T. and Nelson, E., (1998). Nominal Income Targeting in an Open-Economy Optimizing Model. NBER Working Paper 6675. McCallum, B.T. and Nelson, E., (1999). Performance of Operational Policy Rules in an Estimated Semi-Classical Structural Model. J.B. Taylor (ed.), Monetary Policy Rules. Chicago: University of Chicago Press, forthcoming. Roberts, J., (1995). New Keynesian Economics and the Phillips Curve. Journal of Money, Credit, and Banking, 27: 975-984. Rotemberg, J.J., (1982). Monopolistic Price Adjustment and Aggregate Output. Review of Economic Studies, 44: 517-531.
362
Taylor, J.B., (1980). Aggregate Dynamics and Staggered Contracts. Journal of Political Economy, 88: 1-23.
363