IDEAS home Printed from https://ideas.repec.org/p/red/sed017/490.html
   My bibliography  Save this paper

Cost of Inflation in Inventory Theoretical Models

Author

Listed:
  • Roberto Robatto

    (University of Wisconsin-Madison)

  • Francesco Lippi

    (Einaudi Institute (EIEF))

  • Fernando Alvarez

    (University of Chicago)

Abstract

We show that the area under the long-run demand curve for money measures the welfare cost of inflation for a very large class of inventory theoretical models of money demand. The class of inventory models considered has a general stochastic structure of the net cash expenditures as well as of the fixed/variable cost of withdrawing and depositing money. Thus, our framework includes a large number of models that have been studied in the literature as special cases. The most important feature that is responsible for our result is the fact that private agents fully internalize all the costs and benefits associated with managing their inventory of money. As a result, the social costs and benefits of holding money, which are related to the welfare cost of inflation, are equal to the private costs and benefits of holding money, which are in turn captured by the area under the money demand curve.

Suggested Citation

  • Roberto Robatto & Francesco Lippi & Fernando Alvarez, 2017. "Cost of Inflation in Inventory Theoretical Models," 2017 Meeting Papers 490, Society for Economic Dynamics.
  • Handle: RePEc:red:sed017:490
    as

    Download full text from publisher

    File URL: https://economicdynamics.org/meetpapers/2017/paper_490.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. J. Michael Harrison & Michael I. Taksar, 1983. "Instantaneous Control of Brownian Motion," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 439-453, August.
    2. André C. Silva, 2012. "Rebalancing Frequency and the Welfare Cost of Inflation," American Economic Journal: Macroeconomics, American Economic Association, vol. 4(2), pages 153-183, April.
    3. Merton H. Miller & Daniel Orr, 1966. "A Model of the Demand for Money by Firms," The Quarterly Journal of Economics, Oxford University Press, vol. 80(3), pages 413-435.
    4. Markus K. Brunnermeier & Yuliy Sannikov, 2014. "A Macroeconomic Model with a Financial Sector," American Economic Review, American Economic Association, vol. 104(2), pages 379-421, February.
    5. John Bagnall & David Bounie & Kim P. Huynh & Anneke Kosse & Tobias Schmidt & Scott Schuh, 2016. "Consumer Cash Usage: A Cross-Country Comparison with Payment Diary Survey Data," International Journal of Central Banking, International Journal of Central Banking, vol. 12(4), pages 1-61, December.
    6. Luigi Guiso & Chaoqun Lai & Makoto Nirei, 2017. "An Empirical Study of Interaction-Based Aggregate Investment Fluctuations," The Japanese Economic Review, Springer, vol. 68(2), pages 137-157, June.
    7. He, Ping & Huang, Lixin & Wright, Randall, 2008. "Money, banking, and monetary policy," Journal of Monetary Economics, Elsevier, vol. 55(6), pages 1013-1024, September.
    8. Lucas, Robert E, Jr & Stokey, Nancy L, 1987. "Money and Interest in a Cash-in-Advance Economy," Econometrica, Econometric Society, vol. 55(3), pages 491-513, May.
    9. Orazio P. Attanasio & Luigi Guiso & Tullio Jappelli, 2002. "The Demand for Money, Financial Innovation, and the Welfare Cost of Inflation: An Analysis with Household Data," Journal of Political Economy, University of Chicago Press, vol. 110(2), pages 317-351, April.
    10. Patrick Bolton & Hui Chen & Neng Wang, 2011. "A Unified Theory of Tobin's q, Corporate Investment, Financing, and Risk Management," Journal of Finance, American Finance Association, vol. 66(5), pages 1545-1578, October.
    11. Leigh A. Riddick & Toni M. Whited, 2009. "The Corporate Propensity to Save," Journal of Finance, American Finance Association, vol. 64(4), pages 1729-1766, August.
    12. Jacob A. Frenkel & Boyan Jovanovic, 1980. "On Transactions and Precautionary Demand for Money," The Quarterly Journal of Economics, Oxford University Press, vol. 95(1), pages 25-43.
    13. Ricardo Lagos & Randall Wright, 2005. "A Unified Framework for Monetary Theory and Policy Analysis," Journal of Political Economy, University of Chicago Press, vol. 113(3), pages 463-484, June.
    14. Fernando Alvarez & Francesco Lippi, 2009. "Financial Innovation and the Transactions Demand for Cash," Econometrica, Econometric Society, vol. 77(2), pages 363-402, March.
    15. Bar-Ilan, Avner & Perry, David & Stadje, Wolfgang, 2004. "A generalized impulse control model of cash management," Journal of Economic Dynamics and Control, Elsevier, vol. 28(6), pages 1013-1033, March.
    16. Costas Arkolakis & Arnaud Costinot & Andres Rodriguez-Clare, 2012. "New Trade Models, Same Old Gains?," American Economic Review, American Economic Association, vol. 102(1), pages 94-130, February.
    17. J. Michael Harrison & Thomas M. Sellke & Allison J. Taylor, 1983. "Impulse Control of Brownian Motion," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 454-466, August.
    18. Sanches, Daniel & Williamson, Stephen, 2010. "Money and credit with limited commitment and theft," Journal of Economic Theory, Elsevier, vol. 145(4), pages 1525-1549, July.
    19. Luca Benati, 2018. "Long-Run Money Demand Redux," Diskussionsschriften dp1804, Universitaet Bern, Departement Volkswirtschaft.
    20. Boris Nikolov & Toni M. Whited, 2014. "Agency Conflicts and Cash: Estimates from a Dynamic Model," Journal of Finance, American Finance Association, vol. 69(5), pages 1883-1921, October.
    21. William J. Baumol, 1952. "The Transactions Demand for Cash: An Inventory Theoretic Approach," The Quarterly Journal of Economics, Oxford University Press, vol. 66(4), pages 545-556.
    22. Carlos E. da Costa & Iván Werning, 2008. "On the Optimality of the Friedman Rule with Heterogeneous Agents and Nonlinear Income Taxation," Journal of Political Economy, University of Chicago Press, vol. 116(1), pages 82-112, February.
    23. repec:oup:ecpoli:v:13:y:1998:i:26:p:261-303 is not listed on IDEAS
    24. Martin Weitzman, 1968. "A Model of the Demand for Money by Firms: Comment," The Quarterly Journal of Economics, Oxford University Press, vol. 82(1), pages 161-164.
    25. Lucas, Robert E. & Nicolini, Juan Pablo, 2015. "On the stability of money demand," Journal of Monetary Economics, Elsevier, vol. 73(C), pages 48-65.
    26. Bar-Ilan, Avner, 1990. "Overdrafts and the Demand for Money," American Economic Review, American Economic Association, vol. 80(5), pages 1201-1216, December.
    27. Agnès Sulem, 1986. "A Solvable One-Dimensional Model of a Diffusion Inventory System," Mathematics of Operations Research, INFORMS, vol. 11(1), pages 125-133, February.
    28. Raj Chetty, 2009. "Sufficient Statistics for Welfare Analysis: A Bridge Between Structural and Reduced-Form Methods," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 451-488, May.
    29. Baccarin, Stefano, 2009. "Optimal impulse control for a multidimensional cash management system with generalized cost functions," European Journal of Operational Research, Elsevier, vol. 196(1), pages 198-206, July.
    30. Blyth C. Archibald & Edward A. Silver, 1978. "(s, S) Policies Under Continuous Review and Discrete Compound Poisson Demand," Management Science, INFORMS, vol. 24(9), pages 899-909, May.
    31. Eppen, Gary D & Fama, Eugene F, 1969. "Cash Balance and Simple Dynamic Portfolio Problems with Proportional Costs," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 10(2), pages 119-133, June.
    32. Scott R. Baker & Stephanie Johnson & Lorenz Kueng, 2017. "Shopping for Lower Sales Tax Rates," NBER Working Papers 23665, National Bureau of Economic Research, Inc.
    33. Milbourne, Ross, 1983. "Optimal Money Holding under Uncertainty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 685-698, October.
    34. Alvarez, Fernando & Lippi, Francesco, 2017. "Cash burns: An inventory model with a cash-credit choice," Journal of Monetary Economics, Elsevier, vol. 90(C), pages 99-112.
    35. Robert E. Lucas, Jr., 2000. "Inflation and Welfare," Econometrica, Econometric Society, vol. 68(2), pages 247-274, March.
    36. Jovanovic, Boyan, 1982. "Inflation and Welfare in the Steady State," Journal of Political Economy, University of Chicago Press, vol. 90(3), pages 561-577, June.
    37. Jing-Sheng Song & Paul Zipkin, 1993. "Inventory Control in a Fluctuating Demand Environment," Operations Research, INFORMS, vol. 41(2), pages 351-370, April.
    38. Merton H. Miller & Daniel Orr, 1968. "The Demand For Money By Firms: Extensions Of Analytic Results," Journal of Finance, American Finance Association, vol. 23(5), pages 735-759, December.
    39. Bar-Ilan, Avner, 1990. "Trigger-Target Rules Need Not Be Optimal with Fixed Adjustment Costs: A Simple Comment on Optimal Money Holding under Uncertainty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(1), pages 229-234, February.
    40. Ricardo Lagos & Guillaume Rocheteau & Randall Wright, 2017. "Liquidity: A New Monetarist Perspective," Journal of Economic Literature, American Economic Association, vol. 55(2), pages 371-440, June.
    41. George M. Constantinides & Scott F. Richard, 1978. "Existence of Optimal Simple Policies for Discounted-Cost Inventory and Cash Management in Continuous Time," Operations Research, INFORMS, vol. 26(4), pages 620-636, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Martin Brown & Nicole Hentschel & Hannes Mettler & Helmut Stix, 2020. "Financial Innovation, Payment Choice and Cash Demand - Causal Evidence from the Staggered Introduction of Contactless Debit Cards," Working Papers on Finance 2002, University of St. Gallen, School of Finance.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alvarez, Fernando & Lippi, Francesco, 2013. "The demand of liquid assets with uncertain lumpy expenditures," Journal of Monetary Economics, Elsevier, vol. 60(7), pages 753-770.
    2. Arango-Arango, Carlos A. & Bouhdaoui, Yassine & Bounie, David & Eschelbach, Martina & Hernandez, Lola, 2018. "Cash remains top-of-wallet! International evidence from payment diaries," Economic Modelling, Elsevier, vol. 69(C), pages 38-48.
    3. Yi Wen, 2009. "When does heterogeneity matter?," Working Papers 2009-024, Federal Reserve Bank of St. Louis.
    4. Patrick Bolton & Neng Wang & Jinqiang Yang, 2020. "Leverage Dynamics and Financial Flexibility," NBER Working Papers 26802, National Bureau of Economic Research, Inc.
    5. Carlos Arango & Yassine Bouhdaoui & David Bounie & Martina Eschelbach & Lola Hernández, 2013. "Cash Management and Payment Choices: A Simulation Model with International Comparisons," Staff Working Papers 13-53, Bank of Canada.
    6. Bar-Ilan, Avner & Marion, Nancy, 2013. "Demand for cash with intra-period endogenous consumption," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2668-2678.
    7. Pedro Teles & Harald Uhlig & João Valle e Azevedo, 2016. "Is Quantity Theory Still Alive?," Economic Journal, Royal Economic Society, vol. 126(591), pages 442-464, March.
    8. Adão, Bernardino & Silva, André C., 2020. "The effect of firm cash holdings on monetary policy," European Economic Review, Elsevier, vol. 128(C).
    9. Francisco Salas-Molina & David Pla-Santamaria & Juan A. Rodriguez-Aguilar, 2018. "A multi-objective approach to the cash management problem," Annals of Operations Research, Springer, vol. 267(1), pages 515-529, August.
    10. García Cabello, Julia, 2017. "The future of branch cash holdings management is here: New Markov chains," European Journal of Operational Research, Elsevier, vol. 259(2), pages 789-799.
    11. Alvarez, Fernando & Lippi, Francesco, 2017. "Cash burns: An inventory model with a cash-credit choice," Journal of Monetary Economics, Elsevier, vol. 90(C), pages 99-112.
    12. Stephen D. Williamson & Randall Wright, 2010. "New monetarist economics: methods," Review, Federal Reserve Bank of St. Louis, vol. 92(May), pages 265-302.
    13. André C. Silva, 2012. "Rebalancing Frequency and the Welfare Cost of Inflation," American Economic Journal: Macroeconomics, American Economic Association, vol. 4(2), pages 153-183, April.
    14. Williamson, Stephen & Wright, Randall, 2010. "New Monetarist Economics: Models," Handbook of Monetary Economics, in: Benjamin M. Friedman & Michael Woodford (ed.), Handbook of Monetary Economics, edition 1, volume 3, chapter 2, pages 25-96, Elsevier.
    15. John R Graham & Mark T Leary, 2018. "The Evolution of Corporate Cash," Review of Financial Studies, Society for Financial Studies, vol. 31(11), pages 4288-4344.
    16. Martin Brown & Nicole Hentschel & Hannes Mettler & Helmut Stix, 2020. "Financial Innovation, Payment Choice and Cash Demand – Causal Evidence from the Staggered Introduction of Contactless Debit Cards," Working Papers 230, Oesterreichische Nationalbank (Austrian Central Bank).
    17. Tamas Briglevics & Scott Schuh, 2013. "U.S. consumer demand for cash in the era of low interest rates and electronic payments," Working Papers 13-23, Federal Reserve Bank of Boston.
    18. repec:bof:bofrdp:urn:nbn:fi:bof-201511251450 is not listed on IDEAS
    19. Francisco Salas-Molina, 2020. "Risk-sensitive control of cash management systems," Operational Research, Springer, vol. 20(2), pages 1159-1176, June.
    20. Yashar Blouri & Maximilian v. Ehrlich, 2017. "On the optimal design of place-based policies: A structural evaluation of EU regional transfers," Diskussionsschriften dp1702, Universitaet Bern, Departement Volkswirtschaft.
    21. Ben A. Chaouch, 2018. "Analysis of the stochastic cash balance problem using a level crossing technique," Annals of Operations Research, Springer, vol. 271(2), pages 429-444, December.

    More about this item

    JEL classification:

    • E41 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Demand for Money
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:red:sed017:490. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christian Zimmermann). General contact details of provider: https://edirc.repec.org/data/sedddea.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.