- Email: [email protected]
Comments on “Optimal fiscal and monetary policy under imperfect competition”
Journal of Macroeconomics 26 (2004) 219–222 www.elsevier.com/locate/econbase
Discussion
Comments on ‘‘Optimal fiscal and monetary policy under imperfect competition’’ Charles T. Carlstrom Research Department, Federal Reserve Bank of Cleveland, Cleveland, OH 44101, USA Available online 25 January 2004
This paper revisits one of the long-standing questions in macroeconomics. Is the Friedman rule optimal? Given today’s near-historically low nominal interest rates this question is even more important today than it was when Friedman first proposed the idea. Friedman posited that a zero nominal interest rate was optimal because it maximized the amount of real cash-balances held by households. While policymakers have never embraced the idea, it has mostly survived the rigors of general equilibrium modeling. This paper argues that this conclusion is premature as the presence of profits will make it worthwhile to use the inflation tax as a part of a broader optimal tax policy. The optimality of the Friedman rule usually emanates from a simple public finance perspective rather than a short-run optimal cyclical monetary policy. This disconnect between what policymakers are most concerned with and the optimal taxation arguments used in establishing the optimality of the Friedman rule helps explain policymakers near universal antithesis to the idea that short-run cyclical monetary policy would be best served by setting the short-run nominal interest rate to 0. This is not to say that the optimality of the Friedman rule is a long-run concept. Chari et al. (1991) establish its optimality in a dynamic model with shocks. But typically the Friedman rule is found to be optimal in a general equilibrium model without sticky prices and sticky wages, the workhorse of modern day macroeconomic modeling. 1 Although Schmitt-Grohe and Uribe abstract from both sticky prices and sticky wages, this is but a first-step in an important and ambitious research E-mail address: [email protected] (C.T. Carlstrom). 1 An important exception is Ireland (1996) who argues that the Friedman rule is optimal in a sticky price model. Carlstrom and Fuerst (1998), however, show that there are problems with this policy conclusion. One important concern is that a zero nominal interest rate like all interest rate pegs is subject to indeterminacy. The present paper sidesteps this concern by formulating monetary policy as a money growth rule. This is in sharp contrast to an interest rate rule where money growth responds endogenously to maintain the interest rate target. Almost all present-day central banks operate off of interest rate and not money. 0164-0704/$ - see front matter Ó 2003 Elsevier Inc. All rights reserved. doi:10.1016/j.jmacro.2003.11.003
220
C.T. Carlstrom / Journal of Macroeconomics 26 (2004) 219–222
program the authors have planned to marry the Chari et al. general equilibrium public finance models to the modern sticky price/sticky wage models. One would think that the optimality of the Friedman rule in a flexible wage/price model has been extensively studied and that there is little to be gained by revisiting this issue. However, the optimality of the Friedman rule is derived in a model without profits. The authors show that by introducing profits the Friedman rule may no longer be optimal. The inclusion of profits is important given their long-run aim of redoing the analysis in a model with nominal stickiness. In modern day sticky price models marginal cost or the mark-up responds endogenously so that output is demand-determined. Thus the dynamic movement of profits is endogenous and its movement is likely to influence the optimality of the Friedman rule. Why do profits matter for the question at hand? To understand this, it is best to review the model first analyzed by Chari et al. They considered a labor only, cash– credit monetary model. An important question in determining whether or not the Friedman rule is optimal is what type of distortionary taxation can the fiscal authority levy? With a complete smorgasbord of taxes at the government’s disposal, the question of whether the Friedman rule is optimal boils down to whether a zero nominal interest rate is optimal for cyclical purposes. The answer to this question would always be yes in a model without some sort of nominal stickiness. Chari et al. assumed government has access to the inflation tax and labor tax. They do not, however, have access to consumption taxes. The important assumptions that Schmitt-Grohe and Uribe make to find that the Friedman rule is not optimal is to assume that the fiscal authority does not have access to neither consumption taxes nor a profit tax. Not being able to tax consumption is important since a CIA-constraint implies that the inflation tax or a positive nominal interest rate is equivalent to a consumption tax on cash goods. Given this equivalence the optimality of the Friedman rule is roughly equivalent to the old debate in public finance, which tax is preferable a consumption tax or a tax on labor income. In a model without capital and profits it is well known that the two are equivalent. Of course since inflation only taxes cash goods a tax on labor is preferred since it, in essence, taxes all goods. 2 This is the basis for the results of Chari et al. This equivalence breaks down, however, with capital. For example, if capital were inelastically supplied, a consumption tax is preferred to a labor tax because taxing consumption in effect taxes both labor and capital. Thus a consumption tax allows the fiscal authority to apply a lump-sum tax on the existing capital stock. The same thing occurs in a labor only economy with profits. A consumption tax allows policymakers to indirectly tax profits. While both a labor and a consumption tax distort the same labor-leisure margin a labor tax would have to be taxed at a higher rate to generate the same revenues.
2
Of course if cash goods just happened to have a lower price elasticity than credit goods an inflation tax could be optimal. This would of course assume that the fiscal authority could not apply different excise taxes to different goods.
C.T. Carlstrom / Journal of Macroeconomics 26 (2004) 219–222
221
Introducing profits into the cash–credit model analyzed by Chari et al. produces a tension. A positive nominal interest rate partially allows the lump-sum taxation of profits but at the same time the inflation tax is inefficient because it only taxes a subset of goods in the economy. It is essentially this tension that Schmitt-Grohe and Uribe analyze in their paper. Their model is a costly credit model where a fraction 1=vt 6 1 of goods is purchased with cash, while the remainder ð1 1=vt Þ purchased with non-cash (means ‘‘credit’’). Credit goods are not subject to the inflation tax. If this fraction were constant then the gross consumption tax is governed by 1 þ ðR 1Þ=v. This tax distortion governs both revenues as well as the deadweight loss. When v ¼ 1 it collapses down to the often-analyzed CIA-constraint. Assuming v entails a resource cost of csðvÞ then the tax distortion is now 1 þ sðvt Þ þ ½ðRt 1Þ=vt . 3 The resource cost sðvÞ is the extra distortion of using the inflation tax that would not be present with a consumption tax. What are the important parameters governing the result that 8% inflation is optimal? Following the logic above the important parameters are the size of the mark-up and the resource cost sðvÞ. The former governs the benefits associated with deviating from the Friedman rule while the latter governs the costs of having positive nominal interest rates. When interest rates are positive agents economize on cash and shift towards credit which entails a resource cost. Where does sðvÞ come from? Schmitt-Grohe and Uribe assume that the resource cost associated with using credit has the following form: sðvÞ ¼ Av þ B=v 2ðABÞ
1=2
:
This implies the following money demand function: B 1 R1 v2 ¼ þ : A A r A and B are then calibrated according to a simple velocity regression. But where does the assumed form of their resource cost come from? Money demand does not have the nice constant semi- or full-interest rate elasticities. But, perhaps, more importantly given their calibrations, even when agents use only cash there is still a transaction cost equal to 2.8% of consumption, sð1Þ ¼ 0:028. Given the importance sðvÞ in deriving the optimal steady state inflation rate, a more reasonable assumption is to normalize sð1Þ ¼ 0. Given the constant 2 in their transaction cost economy is arbitrary one possibility is to modify their function as follows: sðvÞ ¼ Av þ
B kðABÞ1=2 : v
The idea is that k should be chosen such that sð1Þ ¼ 0. 3 Their distortion is slightly different from this because they implicitly assume that tomorrow’s real cash-balances lower today’s transaction costs. Their choice of what Carlstrom and Fuerst (2001) refer to as cash-when-I’m-done timing is peculiar with little economic interpretation. But introducing CIA-timing would not change the central results of their paper.
222
C.T. Carlstrom / Journal of Macroeconomics 26 (2004) 219–222
The real challenge, however, lies ahead. Introducing sticky prices to this analysis is both challenging and very interesting. There will be a natural tension between stabilizing inflation as dictated by the presence of sticky prices and the desire to inflate when profits are high.
References Carlstrom, C., Fuerst, T., 1998. A note on the role of countercyclical monetary policy. Journal of Political Economy 106 (4), 860–866. Carlstrom, C., Fuerst, T., 2001. Timing and real indeterminacy in monetary models. Journal of Monetary Economics 47, 285–298. Chari, V.V., Christiano, L.J., Kehoe, P.J., 1991. Optimal fiscal and monetary policy: Some recent results. Staff Report 147, Federal Reserve Bank of Minneapolis. Ireland, P., 1996. The role of countercyclical monetary policy. Journal of Political Economy 104 (4), 704– 723.
Discussion
Comments on ‘‘Optimal fiscal and monetary policy under imperfect competition’’ Charles T. Carlstrom Research Department, Federal Reserve Bank of Cleveland, Cleveland, OH 44101, USA Available online 25 January 2004
This paper revisits one of the long-standing questions in macroeconomics. Is the Friedman rule optimal? Given today’s near-historically low nominal interest rates this question is even more important today than it was when Friedman first proposed the idea. Friedman posited that a zero nominal interest rate was optimal because it maximized the amount of real cash-balances held by households. While policymakers have never embraced the idea, it has mostly survived the rigors of general equilibrium modeling. This paper argues that this conclusion is premature as the presence of profits will make it worthwhile to use the inflation tax as a part of a broader optimal tax policy. The optimality of the Friedman rule usually emanates from a simple public finance perspective rather than a short-run optimal cyclical monetary policy. This disconnect between what policymakers are most concerned with and the optimal taxation arguments used in establishing the optimality of the Friedman rule helps explain policymakers near universal antithesis to the idea that short-run cyclical monetary policy would be best served by setting the short-run nominal interest rate to 0. This is not to say that the optimality of the Friedman rule is a long-run concept. Chari et al. (1991) establish its optimality in a dynamic model with shocks. But typically the Friedman rule is found to be optimal in a general equilibrium model without sticky prices and sticky wages, the workhorse of modern day macroeconomic modeling. 1 Although Schmitt-Grohe and Uribe abstract from both sticky prices and sticky wages, this is but a first-step in an important and ambitious research E-mail address: [email protected] (C.T. Carlstrom). 1 An important exception is Ireland (1996) who argues that the Friedman rule is optimal in a sticky price model. Carlstrom and Fuerst (1998), however, show that there are problems with this policy conclusion. One important concern is that a zero nominal interest rate like all interest rate pegs is subject to indeterminacy. The present paper sidesteps this concern by formulating monetary policy as a money growth rule. This is in sharp contrast to an interest rate rule where money growth responds endogenously to maintain the interest rate target. Almost all present-day central banks operate off of interest rate and not money. 0164-0704/$ - see front matter Ó 2003 Elsevier Inc. All rights reserved. doi:10.1016/j.jmacro.2003.11.003
220
C.T. Carlstrom / Journal of Macroeconomics 26 (2004) 219–222
program the authors have planned to marry the Chari et al. general equilibrium public finance models to the modern sticky price/sticky wage models. One would think that the optimality of the Friedman rule in a flexible wage/price model has been extensively studied and that there is little to be gained by revisiting this issue. However, the optimality of the Friedman rule is derived in a model without profits. The authors show that by introducing profits the Friedman rule may no longer be optimal. The inclusion of profits is important given their long-run aim of redoing the analysis in a model with nominal stickiness. In modern day sticky price models marginal cost or the mark-up responds endogenously so that output is demand-determined. Thus the dynamic movement of profits is endogenous and its movement is likely to influence the optimality of the Friedman rule. Why do profits matter for the question at hand? To understand this, it is best to review the model first analyzed by Chari et al. They considered a labor only, cash– credit monetary model. An important question in determining whether or not the Friedman rule is optimal is what type of distortionary taxation can the fiscal authority levy? With a complete smorgasbord of taxes at the government’s disposal, the question of whether the Friedman rule is optimal boils down to whether a zero nominal interest rate is optimal for cyclical purposes. The answer to this question would always be yes in a model without some sort of nominal stickiness. Chari et al. assumed government has access to the inflation tax and labor tax. They do not, however, have access to consumption taxes. The important assumptions that Schmitt-Grohe and Uribe make to find that the Friedman rule is not optimal is to assume that the fiscal authority does not have access to neither consumption taxes nor a profit tax. Not being able to tax consumption is important since a CIA-constraint implies that the inflation tax or a positive nominal interest rate is equivalent to a consumption tax on cash goods. Given this equivalence the optimality of the Friedman rule is roughly equivalent to the old debate in public finance, which tax is preferable a consumption tax or a tax on labor income. In a model without capital and profits it is well known that the two are equivalent. Of course since inflation only taxes cash goods a tax on labor is preferred since it, in essence, taxes all goods. 2 This is the basis for the results of Chari et al. This equivalence breaks down, however, with capital. For example, if capital were inelastically supplied, a consumption tax is preferred to a labor tax because taxing consumption in effect taxes both labor and capital. Thus a consumption tax allows the fiscal authority to apply a lump-sum tax on the existing capital stock. The same thing occurs in a labor only economy with profits. A consumption tax allows policymakers to indirectly tax profits. While both a labor and a consumption tax distort the same labor-leisure margin a labor tax would have to be taxed at a higher rate to generate the same revenues.
2
Of course if cash goods just happened to have a lower price elasticity than credit goods an inflation tax could be optimal. This would of course assume that the fiscal authority could not apply different excise taxes to different goods.
C.T. Carlstrom / Journal of Macroeconomics 26 (2004) 219–222
221
Introducing profits into the cash–credit model analyzed by Chari et al. produces a tension. A positive nominal interest rate partially allows the lump-sum taxation of profits but at the same time the inflation tax is inefficient because it only taxes a subset of goods in the economy. It is essentially this tension that Schmitt-Grohe and Uribe analyze in their paper. Their model is a costly credit model where a fraction 1=vt 6 1 of goods is purchased with cash, while the remainder ð1 1=vt Þ purchased with non-cash (means ‘‘credit’’). Credit goods are not subject to the inflation tax. If this fraction were constant then the gross consumption tax is governed by 1 þ ðR 1Þ=v. This tax distortion governs both revenues as well as the deadweight loss. When v ¼ 1 it collapses down to the often-analyzed CIA-constraint. Assuming v entails a resource cost of csðvÞ then the tax distortion is now 1 þ sðvt Þ þ ½ðRt 1Þ=vt . 3 The resource cost sðvÞ is the extra distortion of using the inflation tax that would not be present with a consumption tax. What are the important parameters governing the result that 8% inflation is optimal? Following the logic above the important parameters are the size of the mark-up and the resource cost sðvÞ. The former governs the benefits associated with deviating from the Friedman rule while the latter governs the costs of having positive nominal interest rates. When interest rates are positive agents economize on cash and shift towards credit which entails a resource cost. Where does sðvÞ come from? Schmitt-Grohe and Uribe assume that the resource cost associated with using credit has the following form: sðvÞ ¼ Av þ B=v 2ðABÞ
1=2
:
This implies the following money demand function: B 1 R1 v2 ¼ þ : A A r A and B are then calibrated according to a simple velocity regression. But where does the assumed form of their resource cost come from? Money demand does not have the nice constant semi- or full-interest rate elasticities. But, perhaps, more importantly given their calibrations, even when agents use only cash there is still a transaction cost equal to 2.8% of consumption, sð1Þ ¼ 0:028. Given the importance sðvÞ in deriving the optimal steady state inflation rate, a more reasonable assumption is to normalize sð1Þ ¼ 0. Given the constant 2 in their transaction cost economy is arbitrary one possibility is to modify their function as follows: sðvÞ ¼ Av þ
B kðABÞ1=2 : v
The idea is that k should be chosen such that sð1Þ ¼ 0. 3 Their distortion is slightly different from this because they implicitly assume that tomorrow’s real cash-balances lower today’s transaction costs. Their choice of what Carlstrom and Fuerst (2001) refer to as cash-when-I’m-done timing is peculiar with little economic interpretation. But introducing CIA-timing would not change the central results of their paper.
222
C.T. Carlstrom / Journal of Macroeconomics 26 (2004) 219–222
The real challenge, however, lies ahead. Introducing sticky prices to this analysis is both challenging and very interesting. There will be a natural tension between stabilizing inflation as dictated by the presence of sticky prices and the desire to inflate when profits are high.
References Carlstrom, C., Fuerst, T., 1998. A note on the role of countercyclical monetary policy. Journal of Political Economy 106 (4), 860–866. Carlstrom, C., Fuerst, T., 2001. Timing and real indeterminacy in monetary models. Journal of Monetary Economics 47, 285–298. Chari, V.V., Christiano, L.J., Kehoe, P.J., 1991. Optimal fiscal and monetary policy: Some recent results. Staff Report 147, Federal Reserve Bank of Minneapolis. Ireland, P., 1996. The role of countercyclical monetary policy. Journal of Political Economy 104 (4), 704– 723.