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Maintenance and investment: complements or substitutes? A reappraisal

Author

Listed:
  • Raouf Boucekkine
  • Giorgio Fabbri
  • Fausto Gozzi

Abstract

A benchmark AK optimal growth model with maintenance expenditures and endogenous utilization of capital is considered within an explicit vin- tage capital framework. Scrapping is endogenous, and the model allows for a clean distinction between age and usage dependent capital deprecia- tion and obsolescence. It is also shown that in this set-up past investment profile completely determines the size of current maintenance expendi- tures. Among other findings, a closed-form solution to optimal dynam- ics is provided taking advantage of very recent development in optimal control of infinite dimensional systems. More importantly, and in con- trast to the pre-existing literature, we study investment and maintenance co-movements without any postulated ad-hoc depreciation function. In particular, we find that optimal investment and maintenance do move to- gether in the short-run in response to neutral technological shocks, which seems to be more consistent with the data.

Suggested Citation

  • Raouf Boucekkine & Giorgio Fabbri & Fausto Gozzi, 2009. "Maintenance and investment: complements or substitutes? A reappraisal," Working Papers 2009_21, Business School - Economics, University of Glasgow.
  • Handle: RePEc:gla:glaewp:2009_21
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    References listed on IDEAS

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    1. Boucekkine, R. & Fabbri, G. & Gozzi, F., 2010. "Maintenance and investment: Complements or substitutes? A reappraisal," Journal of Economic Dynamics and Control, Elsevier, vol. 34(12), pages 2420-2439, December.
    2. repec:kap:jeczfn:v:78:y:2003:i:1:d:10.1007_s00712-002-0554-9 is not listed on IDEAS
    3. Ellen R. McGrattan & James A. Schmitz, 1999. "Maintenance and repair: too big to ignore," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 2-13.
    4. Feldstein, Martin S & Rothschild, Michael, 1974. "Towards an Economic Theory of Replacement Investment," Econometrica, Econometric Society, vol. 42(3), pages 393-423, May.
    5. Askenazy, Philippe & Le Van, Cuong, 1999. "A Model of Optimal Growth Strategy," Journal of Economic Theory, Elsevier, pages 24-51.
    6. Faggian, Silvia & Gozzi, Fausto, 2010. "Optimal investment models with vintage capital: Dynamic programming approach," Journal of Mathematical Economics, Elsevier, pages 416-437.
    7. Nickell, Stephen, 1975. "A closer look at replacement investment," Journal of Economic Theory, Elsevier, vol. 10(1), pages 54-88, February.
    8. Boucekkine, Raouf & Licandro, Omar & Puch, Luis A. & del Rio, Fernando, 2005. "Vintage capital and the dynamics of the AK model," Journal of Economic Theory, Elsevier, pages 39-72.
    9. Pantelis Kalaitzidakis & Sarantis Kalyvitis, 2005. "“New” Public Investment and/or Public Capital Maintenance for Growth? The Canadian Experience," Economic Inquiry, Western Economic Association International, vol. 43(3), pages 586-600, July.
    10. Karl Whelan, 2002. "Computers, Obsolescence, And Productivity," The Review of Economics and Statistics, MIT Press, pages 445-461.
    11. Cagri Saglam & Vladimir M. Veliov, 2008. "Role of Endogenous Vintage Specific Depreciation in the Optimal Behavior of Firms," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(3), pages 381-410.
    12. Omar Licandro & Luis A. Puch & J. Ramón Ruiz-Tamarit, 2001. "Optimal growth under endogenous depreciation, capital utilization and maintenance costs," Investigaciones Economicas, Fundación SEPI, vol. 25(3), pages 543-559, September.
    13. Kalaitzidakis, Pantelis & Kalyvitis, Sarantis, 2004. "On the macroeconomic implications of maintenance in public capital," Journal of Public Economics, Elsevier, pages 695-712.
    14. Raouf Boucekkine & Ramón Ruiz-Tamarit, 2003. "Capital Maintenance and Investment: Complements or Substitutes?," Journal of Economics, Springer, pages 1-28.
    15. Raouf Boucekkine & Fernando del Río & Blanca Martínez, 2009. "Technological progress, obsolescence, and depreciation," Oxford Economic Papers, Oxford University Press, pages 440-466.
    16. Fabbri, Giorgio & Gozzi, Fausto, 2008. "Solving optimal growth models with vintage capital: The dynamic programming approach," Journal of Economic Theory, Elsevier, vol. 143(1), pages 331-373, November.
    17. Hartl, Richard, 1983. "Optimal maintenance and production rates for a machine : A nonlinear economic control problem," Journal of Economic Dynamics and Control, Elsevier, vol. 6(1), pages 281-306, September.
    18. repec:adr:anecst:y:2000:i:58:p:05 is not listed on IDEAS
    19. Collard, Fabrice & Kollintzas, Tryphon, 2000. "Maintenance, Utilization, and Depreciation along the Business Cycle," CEPR Discussion Papers 2477, C.E.P.R. Discussion Papers.
    20. Sarantis Kalyvitis, 2006. "model: an empirical analysis of aggregate business capital spending with maintenance expenditures," Canadian Journal of Economics, Canadian Economics Association, vol. 39(4), pages 1282-1315, November.
    21. Fabbri, Giorgio & Gozzi, Fausto, 2006. "Vintage Capital in the AK growth model: a Dynamic Programming approach. Extended version," MPRA Paper 7334, University Library of Munich, Germany.
    22. Goetz, Renan-Ulrich & Hritonenko, Natali & Yatsenko, Yuri, 2008. "The optimal economic lifetime of vintage capital in the presence of operating costs, technological progress, and learning," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 3032-3053, September.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Fabbri, Giorgio, 2017. "International borrowing without commitment and informational lags: Choice under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 103-114.
    2. Raouf Boucekkine & Bruno De Oliveira Cruz, 2015. "Technological Progress and Investment: A Non-Technical Survey," Working Papers halshs-01145485, HAL.
    3. d’Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2014. "Multiple solutions in systems of functional differential equations," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 50-56.
    4. Diego Romero-Avila & DIEGO ROMERO-ÁVILA & ILASKI BARAÑANO, 2012. "Long-Term Growth and Persistence with Endogenous Depreciation: Theory and Evidence," EcoMod2012 3757, EcoMod.
    5. Raouf Boucekkine & David De la Croix & Omar Licandro, 2011. "Vintage Capital Growth Theory: Three Breakthroughs," Working Papers 565, Barcelona Graduate School of Economics.
    6. Albonico, Alice & Kalyvitis, Sarantis & Pappa, Evi, 2014. "Capital maintenance and depreciation over the business cycle," Journal of Economic Dynamics and Control, Elsevier, pages 273-286.
    7. Mauro Bambi & Cristina Girolami & Salvatore Federico & Fausto Gozzi, 2017. "Generically distributed investments on flexible projects and endogenous growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 521-558, February.
    8. BOUCEKKINE, Raouf & FABBRI, Giorgio & PINTUS, Patrick, 2012. "On the optimal control of a linear neutral differential equation arising in economics," CORE Discussion Papers RP 2449, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Boucekkine, R. & Fabbri, G. & Gozzi, F., 2014. "Egalitarianism under population change: Age structure does matter," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 86-100.
    10. Raouf Boucekkine & Giorgio Fabbri & Fausto Gozzi, 2012. "Egalitarism under Population Change: The Role of Growth and Lifetime Span," Working Papers halshs-00793188, HAL.
    11. Boucekkine, R. & Fabbri, G. & Gozzi, F., 2010. "Maintenance and investment: Complements or substitutes? A reappraisal," Journal of Economic Dynamics and Control, Elsevier, pages 2420-2439.
    12. Augeraud-Véron, Emmanuelle & Leandri, Marc, 2014. "Optimal pollution control with distributed delays," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 24-32.
    13. Giorgio Fabbri, 2015. "Ecological barriers and convergence: a note on geometry in spatial growth models," Working Papers hal-01159253, HAL.
    14. Fabbri, Giorgio, 2016. "Geographical structure and convergence: A note on geometry in spatial growth models," Journal of Economic Theory, Elsevier, pages 114-136.
    15. Raouf Boucekkine & Giorgio Fabbri & Patrick-Antoine Pintus, 2011. "On the optimal control of a linear neutral differential equation arising in economics," Working Papers halshs-00576770, HAL.
    16. Deli, Yota D., 2016. "Endogenous capital depreciation and technology shocks," Journal of International Money and Finance, Elsevier, vol. 69(C), pages 318-338.
    17. Giorgio Fabbri, 2014. "Ecological Barriers and Convergence: A Note on Geometry in Spatial Growth Models," Documents de recherche 14-05, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
    18. Mauro Bambi & Cristina Di Girolami & Salvatore Federico & Fausto Gozzi, 2014. "On the Consequences of Generically Distributed Investments on Flexible Projects in an Endogenous Growth Model," Discussion Papers 14/15, Department of Economics, University of York.
    19. repec:hal:journl:halshs-00786419 is not listed on IDEAS
    20. Raouf Boucekkine & Giorgio Fabbri & Fausto Gozzi, 2010. "Life span and the problem of optimal population size," Working Papers halshs-00536073, HAL.
    21. Alice Albonico & Sarantis Kalyvitis & Evi Pappa, 2011. "Real Business Cycles with Capital Maintenance," Quaderni di Dipartimento 147, University of Pavia, Department of Economics and Quantitative Methods.

    More about this item

    Keywords

    Maintenance; investment; optimal control; dynamic program- ming; infinite dimensional problem;

    JEL classification:

    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

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