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Inflation effects on capital accumulation in a model with residential and non-residential assets

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Published/Copyright: May 16, 2014
The B.E. Journal of Macroeconomics
From the journal The B.E. Journal of Macroeconomics Volume 14 Issue 1

Abstract

We study aggregate effects on capital accumulation of changes in the permanent rate of inflation in a model that incorporates both residential and non-residential capital. The framework is a dynamic general equilibrium life-cycle economy populated by heterogeneous individuals with respect to age, income and homeownership status. Inflation raises the non-residential capital income tax burden, affects the user cost of housing capital and raises the opportunity cost of holding money. A numerical analysis is provided based on parameter values from the US economy. We find that housing capital and inflation exhibit a positive correlation while inflation reduces savings in business capital. It is shown that this outcome arises from the interaction of inflation with individual tenure decisions and a number of characteristics and tax provisions available in the housing market.

Keywords: housing capital; long run inflation; tenure choice
JEL classification:: E22; E31; H21
Corresponding author: Katerina Koka, Department of Economics, Brock University, 500 Glenridge Ave., St. Catharines, ON, Canada L2S 3A1, e-mail:

Acknowledgments

I would like to thank Brian Ferguson, Stephen Kosempel, Jim MacGee, Gregory Smith, Kathleen Rybczynski and participants in the Canadian Economic Association, Eastern Economic Association and Spring Meeting of Young Economists conferences for their valuable comments and suggestions. I have also greatly appreciated comments from the editor of this journal and two anonymous referees.

Appendix

Alternative specification

An alternative specification for the problem of the financial firm is to assume that real estate in the current period can only generate housing services in the next period. This is the specification in Gervais (2002).

In this case the price of housing services relative to the price of non-durable goods is given by:

(25)vt=it+δh (25)

Table 6 shows outcomes obtained by applying this condition. The results are robust to this specification and all the main relationships discussed in the paper remain the same.

Table 6

Benchmark economy-alternative specification for the financial firm.

K/YH/YM/YH.rateHo/(A+Ho)W/YvH/(C+vH)
Model infl. 1%1.75400.99130.174960.720.29082.89270.1038
Model infl. 3%1.72571.10190.157571.400.34492.97230.1370
Model infl. 6%1.65381.11870.124776.250.36942.92690.1707

Solution algorithm

The equilibrium of the model economy is found in the following way:

  • Step 1: Guess the aggregate capital stock that is used in production. Given a constant efficient labor supply and a Cobb-Douglas production function, factor prices can be computed. Using the Fisher equation, the real rate of return to business capital and the long run inflation rate we can find the nominal interest rate. From the problem of the financial intermediary, the price of housing services is also determined.

  • Step 2: We iterate on the value function to solve the individual problem. The state variable in the model is the wealth of the individual household. We construct a finite state space: Γ=[ϖmin, ϖmax] containing all points that an individual may choose in each period for her next period savings. The size of the grid is large enough to not be binding for choices of the household. We tabulate the value function over grid points starting from the last period of life and iterating backwards. For every j and a combination of (ϖj, ϖj+1)∈Γ, we solve the intra-temporal problem in order to find the level of consumption, housing services and the portfolio allocation of assets. When choosing housing, agents make a tenure choice and decide whether to own or to rent housing services.

  • Step 3: Choose ϖj+1 given ϖj which maximizes:

    G(ϖj, ϖj+1)+βψjVt+1(ϖj+1). We use two neighboring points on the wealth grid to bracket the maximum of the value function. Then a Golden Section Search is applied to locate the maximum of the Bellman equation. Linear interpolations are performed to obtain values of the value function off the grid points.

  • Step 4: From optimal choices of households, we compute the aggregate capital stock used in production. If the new level of capital matches our guess, then an equilibrium is found, otherwise update the guess until convergence.

The problem in step 2 can be summarized as follows: At the end of life, J, individuals know that they are not surviving in the next period and thus set ϖJ+1=0. Given this end period value and ϖJ∈Γ, intra-temporal outcomes can be computed for each value of ϖJ to obtain a vector of last period’s value VJ. In period J–1, the individuals use combinations of ϖj, ϖj+1∈Γ to find within period outcomes. Given G(ϖJ–1, ϖJ) we choose the optimal amount of savings ϖJ to be transferred over to the next period and compute VJ–1. We continue this way until the entire distribution is computed.

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Published Online: 2014-5-16
Published in Print: 2014-1-1

©2014 by De Gruyter

Articles in the same Issue

  1. Frontmatter
  2. Advances
  3. Optimal portfolios with wealth-varying risk aversion in the neoclassical growth model
  4. Inventories and the stockout constraint in general equilibrium
  5. Optimal second best taxation of addictive goods in dynamic general equilibrium: a revenue raising perspective
  6. Inflation effects on capital accumulation in a model with residential and non-residential assets
  7. Optimal capital-income taxation in a model with credit frictions
  8. Contributions
  9. Interest rate fluctuations and equilibrium in the housing market
  10. News shocks and learning-by-doing
  11. Capacity utilization and the effects of energy price increases in Japan
  12. Small-scale New Keynesian model features that can reproduce lead, lag and persistence patterns
  13. Optimal policy and Taylor rule cross-checking under parameter uncertainty
  14. The impact of American and British involvement in Afghanistan and Iraq on health spending, military spending and economic growth
  15. Why does natural resource abundance not always lead to better outcomes? Limited financial development versus political impatience
  16. The skill bias of technological change and the evolution of the skill premium in the US since 1970
  17. Aggregate impacts of recent US natural gas trends
  18. Organizational learning and optimal fiscal and monetary policy
  19. Industrial specialization, financial integration and international consumption risk sharing
  20. Leverage, investment, and optimal monetary policy
  21. Public debt in an OLG model with imperfect competition: long-run effects of austerity programs and changes in the growth rate
  22. Temporal aggregation and estimated monetary policy rules
  23. International transmission of productivity shocks with nonzero net foreign debt
  24. Did the euro change the effect of fundamentals on growth and uncertainty?
  25. Topics
  26. Real factor prices and factor-augmenting technical change
  27. Monetary policy and TIPS yields before the crisis
https://doi.org/10.1515/bejm-2013-0149
Keywords for this article
housing capital; long run inflation; tenure choice

Articles in the same Issue

  1. Frontmatter
  2. Advances
  3. Optimal portfolios with wealth-varying risk aversion in the neoclassical growth model
  4. Inventories and the stockout constraint in general equilibrium
  5. Optimal second best taxation of addictive goods in dynamic general equilibrium: a revenue raising perspective
  6. Inflation effects on capital accumulation in a model with residential and non-residential assets
  7. Optimal capital-income taxation in a model with credit frictions
  8. Contributions
  9. Interest rate fluctuations and equilibrium in the housing market
  10. News shocks and learning-by-doing
  11. Capacity utilization and the effects of energy price increases in Japan
  12. Small-scale New Keynesian model features that can reproduce lead, lag and persistence patterns
  13. Optimal policy and Taylor rule cross-checking under parameter uncertainty
  14. The impact of American and British involvement in Afghanistan and Iraq on health spending, military spending and economic growth
  15. Why does natural resource abundance not always lead to better outcomes? Limited financial development versus political impatience
  16. The skill bias of technological change and the evolution of the skill premium in the US since 1970
  17. Aggregate impacts of recent US natural gas trends
  18. Organizational learning and optimal fiscal and monetary policy
  19. Industrial specialization, financial integration and international consumption risk sharing
  20. Leverage, investment, and optimal monetary policy
  21. Public debt in an OLG model with imperfect competition: long-run effects of austerity programs and changes in the growth rate
  22. Temporal aggregation and estimated monetary policy rules
  23. International transmission of productivity shocks with nonzero net foreign debt
  24. Did the euro change the effect of fundamentals on growth and uncertainty?
  25. Topics
  26. Real factor prices and factor-augmenting technical change
  27. Monetary policy and TIPS yields before the crisis
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