The Impact of Atypical Employment on the House Price Volatility

Transcription

1 The Impact of Atypical Employment on the House Price Volatility Jeyakrishna Velauthapillai University of Hagen, Department of Economics, Universitätsstr. 11 (TGZ), Hagen, Germany August 14, 2014 Abstract After the real estate crisis in the last decade, much attention has been paid to the volatility of the price of housing. This article is concerned with the question how the development of the atypical employment influences the volatility of house prices in some industrialized countries. On the basis of a simple extension of the prototype life cycle housing model, we point out that atypical employment has a negative impact on the house price volatility both in the long run and in the short run and that future research should embed atypical employment in their analyses to explain house prices. JEL: R21, R31 Keywords: house price volatility, housing model, atypical employment, labour contracts 1 Introduction In the course of the reforms aimed at making the labour markets more flexible, atypical employment has greatly increased in some OECD countries. This paper touches upon the problem of previous studies, both theoretical and empirical, that have not adequately integrated the characteristics of the labour Tel: address: jeyakrishna.velauthapillai@fernuni-hagen.de 1

2 market into their housing models. In numerous articles, such as, Abelson et al. [2005] and Iossifov et al. [2008], which aim to explain house prices, only the simple superficial employment or unemployment rates are used to characterize the labour market. However, deeper and more comprehensive structural variables like atypical employment 1 are neglected. But one important factor speaks for the integration of those structural variables. There are countries where the superficial variable is insignificant for explaining house prices. Let us take up this aspect in the example of Germany in a purely descriptive way. Figure 1 Figure 1: All time series are indexed to basis year Data Source: Destatis, Datastream. depicts the time series of unemployment, atypical employment, and real house prices for Germany. It is easy to spot the strong negative relation between atypical employment and house prices but the unemployment rate seems to be uncorrelated with the price. A calculation of the simple correlation coefficient corroborates our assertion. 2 Model The following model is a slight variation of the well known intertemporal life cycle model of Poterba [1984]. Let H be the stock of housing, which is fixed in 1 Atypical employment means that the existing employment contract differs from the standard employment relation. Part-time, temporary, marginal, dependent self-employed, and agency work are counted among atypical employment. For a detailed discussion, see Le Blansch et al. [2000], Ogura [2005], Gash [2008], and Allmendinger et al. [2013]. 2

3 the short run. Further the flow supply of housing services HS s is assumed to be proportional to the stock of housing. The desired units of housing services HS d depend on the real rental price R, so the demand function for housing services is HS d = f(r) with f R < 0. So an increase of the real rental price of housing services implies a reduction of the desired quantity of housing. Because the stock of housing is fixed in the short run, the market clearing rental R = R(h(H)) with R H < 0 adjusts to equate the desired quantity of housing services with the existing service flow HS s = h(h). If Q is the real price for one unit of standardized 2 housing. Let ν denote the one period user cost of a unit of housing. Then Q = R(H) + νq (1) describes the housing market equilibrium and the evolution of the real price of a unit of existing housing. Let ν = δ + κ + (1 θ)(i µ) π be the user cost for an owner-occupied structure with δ as the depreciation rate, κ as the maintenance and repair cost, θ as the marginal income tax rate, i as the interest rate both for lending and borrowing, µ as the property tax, and π as the overall inflation. Equation 2 describes the supply function of the industry for the new construction of housing. This accumulation is defined by the gross investment function I = Ψ(Q) with Ψ Q > 0. The net investment function is Ḣ = I δh = Ψ(Q) δh. (2) Figure 2 depicts the resulting saddle point dynamics of a user cost reduction. 3 As a consequence, the Q nullcline shifts to the right and by the assumption of perfect foresight of the agents, the real price jumps to the stable arm of the separatrix (red curve) and gradually seeks the new equilibrium point. This creates an overshooting of the price in the short run. Overshooting is defined as the difference between ˆQ and the new equilibrium price Q new. In the new equilibrium, both the price and the stock of housing are higher than before. 2 It is assumed that there is no qualitative distinction between existing housing and newly built housing. 3 The figure is drawn with the functions Ψ(Q) = Q λ and R(H) = 1. In the baseline model H λ is equal to one, which means that there is no atypical employment. 3

4 Q. H=0 Q Q*. new Q=0 new Q*. Q=0 H* H* H new Figure 2: Phase plane of a user cost reduction of 5% to 4%. Based on Poterba [1984]. 3 Extension Atypical employment as the new element is now going to be integrated in Equation 1 in the user cost formula. We assume that an increase in atypical employment leads to insecure living and working conditions. This insecurity is to be found as a risk premium in the user cost formula, which is integrated into the model in the style of Himmelberg et al. [2005] with the difference that our premium reflects the labour market variable. It follows that νnew = δ + κ + (1 θ)(i µ) π + ξ.4 Let λ be the ratio of the amount of standard working contracts to overall employment, and 1 λ be the ratio of atypical employment to overall employment, with λ (0, 1]. Then ξ = β(1 λ) is the premium of atypical employment with the coefficient β. On the construction side, atypical employment and thus the flexibilisation of the working contracts, leads to a reduction of construction costs and the construction industry can react faster to demand shocks and house price changes.5 Therefore we assume that changes in prices have a bigger impact on the investment function than in the base model, if atypical employment is higher (see ECB [2003]). Unfortunately, the exact specification is extremely difficult and varies between different studies. We will try to assume economically plausible coefficients and functions. We have to bear in mind that other functions also lead to the same dynamics 4ξ is a risk premium, which express the increased risk of owning towards renting. price elasticity of the supply of new housing becomes higher. 5 The 4

5 in this model. 6 The new system of equations is of the following form Q = 1 H + [ν + ξ]q (3) Ḣ = Q λ δh. (4) Once more, the resulting autonomous system of first order nonlinear differential equations can be analysed in a phase plane. The integration of the new element does not alter the existence, uniqueness, or stability conditions of the system, but only the dynamics is affected. 7 Now, as in the base model, we can examine the impact of the same user cost reduction, for example caused by a property tax reduction, on the house prices. Here, we do this for different environments of λ and therefore we want to analyse how atypical employment affects the short run overshooting and the long run price adjustment. Figure 4 illustrates the Figure 3: Long run adjustment of prices caused by a user cost reduction (ν=0.05 to ν = 0.04) subject to 1 λ. outcomes of the numerical simulation. The ordinate represents the change 8 of the equilibrium house prices caused by a 1% reduction in the user cost ν. It is clearly visible that atypical employment has a negative effect on the long run equilibrium price adjustment, and therefore on the long run volatility caused by a user cost reduction. Figure 5 captures the behaviour of the above mentioned overshooting of the price and therefore the short run volatility. The figure picks 6 Specifications: δ = 0.025; ν = 0.05; Ψ(Q) = Q λ ; R(H) = 1 H ; β = See the mathematical appendix. 8 The difference between the new and the old equilibrium price. 5

6 Figure 4: Short run overshooting of the price caused by a user cost reduction (ν=0.05 to ν = 0.04) subject to 1 λ. up the negative effect of atypical employment on the short run overshooting of house prices caused by a user cost reduction. Therefore we conclude that both the long run and the short run volatility decrease with increasing atypical employment. The explanation for this can be found in the flexibilisation of the labour market and the consequential reduction in rigidity. Therefore the price elasticity of the supply of new housing becomes higher and the housing market becomes more efficient. 4 Conclusion The major finding of this article is that a higher level of atypical employment in an economy reduces the volatility of house prices both in the short and in the long run. This can be explained by the flexibilisation of the labour market, so it will be more efficient and lead to a higher price elasticity of the supply of new housing. 9 An important implication of this paper is that if atypical employment increases in the future to a significant portion of the working contracts in an economy, this could have a dampening effect on the volatility of future house prices. 9 The relation between the price elasticity of the supply of new housing and the volatility of house prices is empirically validated (see ECB [2003]). 6

7 A Mathematical Appendix ( ) ( ) H Let u = and f( u) δh + Q λ = Q 1 H + ν be the dynamic system. Then newq d dt u = f( u). (5) From f( u*) = 0 it follows that u* is the stationary point and vice versa. Then the nullclines are By equating (A2) and (A3) we get Q Q=0 = 1 ν new H (6) Q Ḣ=0 = δhλ. (7) 1 H = ± ν new λδ (8) The negative solution can be omitted because a negative stock of housing is economically senseless. Q = δλ ν new (9) This means that the existence and uniqueness conditions are not affected by the values of the parameters. For positive values of the parameters, there exists one and only one solution of the system. Therefore, the qualitative outcome of the model does not depend on the exact specification of the parameters. In the case of the gross investment function Ψ(Q) and the market clearing rental R(H), the strict monotonicity and the continuous differentiability of the functions in the first quadrant guarantee the existence of a unique solution. Now we have to determine the stability of the system. Because of its nonlinearity, we will first linearise the system and look at the local stability within a small neighbourhood of a stationary point. Let u = u + ɛ with ɛ << 1 be a small perturbation. Then the Taylor expansion is f( u) = f( u ) }{{} 0 + f }{{} u J f u= u ɛ + 2 f u 2 u= u 1 2 ɛ (10) 7

8 Then f( u + ɛ) J f ɛ with J f as the Jacobian matrix of the system. d dt ( u + ɛ) = d dt ɛ J f ɛ (11) By applying the Hartman Grobman Theorem 10, because our fixed point is hyperbolic, the eigenvalues µ i and the eigenvectors x i with i = (1, 2) can be calculated by The characteristic polynomial χ J f ( µ) evolves as J f x = µ x. (12) det( µi 2 J f ) = χ J f ( µ) = µ 2 + µ(δ ν) δν! = 0 (13) ( ) 1 with Jf = δ λ. A straightforward calculation shows that there are two νδλ ν distinct and real eigenvalues with different signs. Therefore our fixed point is a saddle point. References [1] Abelson, P., Joyeux, R., Milunovich, G., and Chung, D. [2005]: Explaining House Prices in Australia: In: The Economic Record, Vol. 81, pp [2] Allmendinger, J., Hipp, L., and Stuth, S. [2013]: Atypical Employment in Europe WZB Discussion Paper P , Berlin [3] ECB [2003]: Structural Factors in the EU Housing Markets. European Central Bank, Frankfurt/Main [4] Gash, V. [2008]: Bridge or Trap? Temporary Workers Transitions to Unemployment and to the Standard Employment Contract. In: European Sociological Review, Vol. 24, pp [5] Himmelberg, C., Mayer, C., and Sinai, T. [2005]: Assessing High House Prices: Bubbles, Fundamentals and Misperceptions. In: Journal of Economic Perspectives, Vol. 19, No. 4, pp See Teschl [2012] for a detailed proof of the theorem. 8

9 [6] Iossifov, P., Cihak, M., and Shanghavi, A. [2008]: Interest Rate Elasticity of Residential Housing Prices. IMF Working Paper WP/08/247, International Monetary Fund, Washington, D.C. [7] Le Blansch, K., Muller, G., and Wijntuin, P. [2000]: Atypical Work in the EU. Social Affairs Series Soci 106 EN, European Parliament, Luxembourg [8] Ogura, K. [2005]: International Comparison of Atypical Employment: Differing Concepts and Realities in Industrialized Countries. In: Japan Labor Review, Vol. 2, pp [9] Poterba, J.M. [1984]: Tax Subsidies to Owner-Occupied Housing: An Asset-Market Approach. In: The Quarterly Journal of Economics, Vol. 99, No. 4, pp [10] Teschl, G. [2012]: Ordinary Differential Equations and Dynamical Systems. American Mathematical Society, Providence, RI 9