The Asymmetric E¤ects of Monetary Policy on Housing Across the Level of Development Juan C. Medina, Robert R. Reed, Ejindu S. Ume University of Alabama October 30, 2013

Abstract We study the e¤ects of money growth in a neoclassical growth model with wealth e¤ects. In comparison to existing work, the capital stock is the only component of wealth which contributes to an individual’s utility. Thus, our model should be interpreted as a model of housing production and housing wealth since the capital stock a¤ects utility. Interestingly, multiple steady-states emerge in which the e¤ects of monetary policy vary. In the steady-state with a low housing stock, a higher rate of money growth is associated with a reverse-Tobin e¤ect in which in‡ation further lowers the housing stock. In contrast, in‡ation promotes housing activity in the high housing steady-state. Thus, the model indicates that the e¤ects of monetary policy on housing market activity vary considerably across the stages of economic development.



The objective of this paper is to develop a model to study the e¤ects of persistent monetary policy on housing market activity across countries. A starting point for thinking about the e¤ects of policy across countries is to look at the e¤ects of in‡ation on overall macroeconomic activity. Available evidence indicates that the e¤ects of policy are highly sensitive to the level of economic activity. For example, Ahmed and Rogers (2000) …nd evidence of a long-run Tobin e¤ect on investment in the United States. In a study of fourteen di¤erent industrialized countries, Rapach (2003) observes a positive correlation between in‡ation and output. Unfortunately, policymaking in the developing world is complicated by distortions from low levels of income. Juan C. Medina, Department of Economics, Finance, and Legal Studies, University of Alabama, Tuscaloosa, AL 35487; Email: [email protected]; Phone: (205) 348-7590. Robert R. Reed, Department of Economics, Finance, and Legal Studies, University of Alabama, Tuscaloosa, AL 35487; Email: [email protected]; Phone: (205) 348-8667; Ejindu S. Ume, Department of Economics, Finance, and Legal Studies, University of Alabama, Tuscaloosa, AL 35487; Email: [email protected]; Phone: (806) 577-5415.


In contrast to advanced countries, there is convincing evidence that in‡ation and output are negatively related in developing countries.1 How do the e¤ ects of monetary policy on housing conditions vary across countries? As classic examples, both Summers (1981) and Fama and Schwert (1977) contend that investment in housing is attractive relative to other types of assets in in‡ationary periods in the United States. However, there is limited work on the relationship between in‡ation and the housing stock in the developing world. Consequently, theoretical work can provide important guidance to policymakers seeking to expand access to housing in low income countries. Understanding how housing investment responds to in‡ation across countries requires an understanding of how housing investment depends on the level of income across countries. In a study of nearly 40 countries from 1963-1970, Burns and Grebler (1976) …nd evidence of signi…cant non-linearities from GDP to residential construction. At low levels of income, the share of housing to total income is low but increases as GDP is higher. The share of housing to GDP peaks at moderate levels of income and then declines with income in the richest countries. Fisher and Ja¤e (2003) also …nd that the relationship between GDP per capita and homeownership is non-linear.2 The non-monotonic relationship between GDP and the housing stock observed in the data provides the foundation of our work. In particular, the non-monotonicity leads to important asymmetries in the response of housing to in‡ation across the stages of economic development. Consequently, our work demonstrates that policymakers in the developing world must acknowledge that the e¤ects of monetary policy on housing conditions will not be the same as in advanced countries. Following standard monetary growth models, the transactions role of money is motivated by a standard Stockman (1981) cash-in-advance constraint. As put forward by numerous papers in urban economics, housing wealth is an additional argument along with consumption in individuals’ utility functions.3 From a development perspective, Burns and Grebler provide a wide array of arguments supporting housing for an improvement in the “human condition.” Notably, access to housing promotes health conditions. It also generates stability and is a source of pride for residents. Dietz and Haurin (2003) provide an extensive survey of the consequences of homeownership in developed countries. Interestingly, our framework demonstrates that multiple steady-states exist with di¤erent housing stocks. The high housing steady-state resembles an advanced country with high levels of income while the low housing steady-state is re‡ective of low levels of residential investment in poor countries. Moreover, the e¤ects of in‡ation vary across steady-states. In the poor economy, there is little wealth accumulation. With such a low level of income, the incentives to invest 1 Bae

and Ratti (2000) conclude that output is negatively related to money growth in Argentina and Brazil. Other contributions study the impact of in‡ation on output growth – Fischer (1993) and Barro (1995) …nd that in‡ation is negatively related to growth. 2 Malpezzi and Mayo (1987a, 1987b) study the determinants of housing demand in developing countries using household data. 3 Wheaton (1982) and Arnott et al. (1999) are prominent examples.


in housing are low. Consequently, the higher levels of in‡ation result in less residential capital formation. By comparison, in the high housing steady-state, housing provides high levels of consumption value and income. As a result, the e¤ects of monetary policy on housing are consistent with available evidence in the United States showing that in‡ation promotes residential investment activity. The closest paper to our work is Gong and Zou (2001) who incorporate the “wealth-is-status” model of Cole, Mailath, and Postlewaite (1992) into a Stockman (1981) monetary growth model.4 If the cash-in-advance constraint applies to both consumption and investment in their framework, the e¤ects of in‡ation are ambiguous. However, in contrast to our work, they do not make any claims about existence of multiple steady-states in their model. Moreover, both forms of wealth (real money balances and the capital stock) are arguments in the utility function in their model. In contrast, we argue that the capital stock is probably the only component of wealth that is costlessly observable in society. And, we believe this mostly applies to housing in terms of a status symbol. Finally, we contend that the e¤ects of monetary policy on housing in our framework are consistent with observations on in‡ation and economic activity across countries.5 The paper is organized as follows. In Section 2, we describe the model. We show that multiple steady-state equilibria exist in which the e¤ects of policy on housing vary. We o¤er concluding comments in Section 3.


The Model

The representative agent solves the following problem of choosing a mix of consumption c(t), and housing accumulation h(t) over time t:








h(t)1 1

c(t)1 1

+ (1


h(t) + v(t)



subject to: _ m(t) _ + h(t) = Ah


and is limited by the following cash-in-advance constraint: _ [c(t) + h(t)]



where is the discount factor, the coe¢ cient of relative risk aversion, and is the fraction of utility derived from the consumption good. Aside from 4 Wang and Yip (1992) study the e¤ects of monetary policy on capital accumulation in a monetary growth model with endogenous labor supply. 5 For additional discussion, see Ghossoub and Reed (2010, 2013).


housing capital, real cash balances m(t) comprise the other asset in the economy. The monetary authority injects a lump sum transfer of money at time t, v(t). There exists a housing technology Ah for which 0 < < 1 and A describes its productivity parameter. The depreciation rate is and represents the in‡ation rate. The cash-in-advance constraint (1) applies to both consumption and investment where denotes the fraction of expenditures in the economy requiring cash-…nancing. We apply Pontryagin’s Maximum Principle to solve the agent’s problem. Letting z(t) = m(t), _ the corresponding current-valued Hamiltonian is:

H [c(t); h(t);

1 (t);

1 (t)z(t)

+ (t) [m(t) 3

2 (t);

3 (t)]

2 (t)

Ah(t) (c(t) + z(t))] :

c(t)1 + (1 1 c(t) h(t) + v(t)


h(t)1 + 1 m(t) z(t) +


The optimal choices of control variables are given by: @H( ) = c(t) @c(t) @H( ) = @z(t)

2 (t)

1 (t)

2 (t)

3 (t)

3 (t)





The Euler equation for the housing stock is: _1 (t) =

1 (t)

2 (t)[A








By comparison, the Euler for money balances can be expressed as: _2 (t) =

2 (t)


3 (t)

2 (t)]


Imposing steady-state on the system yields consumption as a function of the housing stock:

c(h) =



A h (1 1+( + )





Equation (6) is the analogue to the standard modi…ed golden rule equation in our model. Further, the budget constraint each period must be balanced: c(h) = Ah


(7) 4

In terms of describing steady-state activity, we begin by discussing the interpretation behind (6). As mentioned, this equation would be the standard modi…ed golden rule modi…ed by the constraint that a fraction of transactions must be …nanced with cash. That is, in a standard cash-in-advance model we would have: A h




+ + ( + )

However, in our framework, the optimal level of housing accumulation is based upon the fact that housing directly provides utility to individuals because of the services housing provides. That is, (6) indicates that the optimal amount of consumption expenditure involves a tradeo¤-between the marginal utility of consumption and the marginal utility from housing wealth.

Lemma 1. (Consumption-Housing Allocation) The consumption-housing allocation of (6) may be written as follows: ca (h) =

( )








( ) + )h

( )

A h


[1 + ( + ) ] and c(h)


i1 ca (h).

Corollary 1. Assume that + = 1: Also, let As a result, ca (h) 0 and is expressed as: ca (h) =

( )



( ) + )h

A ]

= 1=(2n) for n 2 N+ .


(8) 1

The locus from (8) behaves as follows. Let ha = h

(>)ha ,

c0a (h)

A ( )+

: For any


The behavior of equation (8) is the centerpiece of our framework and is consistent with the observations of Burns and Grebler who …nd that there is a non-monotonic reationship between income and residential sector activity. At low levels of income, higher levels of income are associated with lower con1

A sumption as individuals begin to favor housing more. At ha = ; ( )+ the share of residential investment peaks. Beyond ha , residential activity and consumption expenditures move together. The second steady-state equilibrium condition is pretty standard in neoclassical growth models:

cb (h(t)) = Ah(t)


(9) 5


Steady-State Equilibrium Activity

Using the geometric properties of the two consumption equations (8) and (9), we arrive to the following Proposition: Proposition 1. (Existence of Multiple Steady-States) Assume that + = 1: Also, let = 1=(2n) for n 2 N+ . Under these conditions, there are two steady-state equilibria. The graphical description of steady-states is provided in Figure 1. In the low housing steady-state, there is little wealth accumulation as a large amount of income is instead used to …nance consumption expenditures. By comparison, in the high housing steady-state, there is a lot of housing wealth which provides large amounts of service ‡ows to residents. We turn to the e¤ects of monetary policy across countries. The e¤ects of monetary policy on activity revolve around the behavior of (8): Lemma 2. (The E¤ects of Monetary Policy on the Consumption-Housing Choice). Assume the conditions in Proposition 1 hold. Then, dca =d < 0 for ^ and dc=d > 0 for h ^ < h < h . In addition, dca =d h



The objective of this paper is to provide insights into the e¤ects of in‡ation on housing market activity across countries. A key hypothesis in our work is that there are signi…cant non-linearities in the relationship between residential investment and GDP. Interestingly, we demonstrate that the presence of a nonlinearity generates multiple steady-states in a standard monetary growth model in which the capital stock also enters as an argument into the utility function. Moreover, we …nd that the e¤ects of in‡ation on housing market activity vary in systematic ways across steady-states. In the housing market with low amounts of housing accumulation, monetary policy generates a reverse-Tobin e¤ect in which housing market activity is lower in response to in‡ation. However, housing accumulaton increases in the high capital steady-state. In this manner, our results are consistent with a number of studies that …nd that the e¤ects of in‡ation depend on the level of economic activity across countries.


References Ahmed, S. and J.H. Rogers, 2000. In‡ation and the Great Ratios: Long Term Evidence From the U.S. Journal of Monetary Economics 45, 3-35. Arnott, R., R. Braid, R. Davidson, and D. Pines, 1999. A General Equilibrium Model of Housing Quality and Quantity. Regional Science and Urban Economics 29, 283-316. Bae, S.K. and R.A. Ratti, 2000. Long-run Neutrality, High In‡ation, and Bank Insolvencies in Argentina and Brazil. Journal of Monetary Economics 46, 581-604. Barro, R.J., 1995. In‡ation and Economic Growth. Bank of England Quarterly Bulletin, 166-76. Burns, L.S. and L. Grebler, 1976. Resource Allocation to Housing Investment: A Comparative International Study. Economic Development and Cultural Change 25, 95-121. Cole, H. G. Mailath, and A. Postlewaite. Social Norms, Saving Behavior and Growth. Journal of Political Economy 100, 1092-1125. Dietz, R.D. and D.R. Haurin, 2003. The Social and Private Micro-Level Consequences of Homeownership. Journal of Urban Economics 54, 410-450. Fama, E. and Schwert, G., 1977. Asset returns and in‡ation. Journal of Financial Economics 5, 115–146. Fischer, S., 1993. The Role of Macroeconomic Factors in Growth. Journal of Monetary Economics 32, 485-512. Fisher, L.S. and A.J. Ja¤e, 2003. Determinants of International Home Ownership Rates. Housing Finance International 18, 34-42. Ghossoub, E. and R. Reed, 2010. Liquidity Risk, Economic Development, and the E¤ects of Monetary Policy. European Economic Review 54, 252-68. _____ and _____, 2012. The E¤ects of Monetary Policy at Di¤erent Stages of Economic Development. Economics Letters 117, 138-141. Gong, L. and H. Zou, 2001. Money, Social Status, and Capital Accumulation in a Cash-in-Advance Model. Journal of Money, Credit and Banking 33, 284293. Malpezzi, S. and S.K. Mayo, 1987a. User Cost and Housing Tenure in Developing Countries. Journal of Development Economics 25, 197-220. _____ and _____, 1987b. The Demand for Housing in Developing Countries: Empirical Estimates from Household Data. Economic Development and Cultural Change 35, 687-721. Rapach, D.E. 2003. International Evidence on the Long-Run Impact of In‡ation. Journal of Money, Credit and Banking 35, 23-48. Schneider, F. and D. H. Enste 2000. Shadow Economies: Size, Causes, and Consequences. Journal of Economic Literature 38, 77-114. 8

Summers, L. 1981. In‡ation, the Stock Market, and Owner-Occupied Housing. AEA Papers and Proceedings 71, 429-434. Stockman, A.C., 1981. Anticipated In‡ation and the Capital Stock in a Cash-In-Advance Economy. Journal of Monetary Economics 8, 387-393. Tobin, J. 1965. Money and Economic Growth. Econometrica 33, 671–84. Wang, P. and C. Yip, 1992. Alternative Approaches to Money and Growth. Journal of Money, Credit, and Banking 24, 553-562. Wheaton, W.C., 1982. Urban Spatial Development with Durable but Replaceable Capital. Journal of Urban Economics 12, 53-67.


Appendix. Proof of Proposition 1. It is easily shown that cb (0) < ca (0): In addition, ca (ha ) < cb (ha ). Thus, there is one steady-state on the interval [0,ha ]: Further, there is an h0 (ha ; 1) where cb (h0 ) = 0: However, ca (h0 ) > 0. Consequently, there is a second steady-state on the interval (ha ; 1): Proof of Proposition 2. By taking the …rst order conditions of consumption with respect to the in‡ation rate we have: 1


dca = d

( ) + ]h ( )

( h


A ) ( )2

We also have: dha = d


A (


( )+ )


Let 0 > and note that (1 )= ^ < h < h , where dc=d > 0 for h b ^= h

< 0: ^ and is odd. Then, dca =d < 0 for h < h

A [ ( )+ ] : 2 [ ( ) ]+ [ ( )+ ]

Similary, dca =d

0 when h

hb .


Figure 1: Existence of Multiple Steady-States


Figure 2: The E¤ects of Monetary Policy


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