Housing investment and house prices.

• Author: Jacobsen, Dag Henning

In this article, we analyse developments in housing investment and the interaction between demand and supply in the housing market. The analysis indicates that the pronounced increase in housing investment since 2004 is related to low interest rates and high house prices. In the past 3 1/2 years, house prices have increased by close to 50 per cent. The sharp rise in housing demand has pushed up house prices, since supply is determined by the existing housing stock in the short term. Capacity constraints in the building sector are preventing a rapid adjustment of the total housing supply to increased demand. When the housing stock over time adapts to demand, this will in isolation push down house prices. House prices may therefore have become higher in the short term than they will be in the somewhat longer term. However, a model-based analysis illustrates that there may be a soft landing for house price inflation despite monetary policy tightening and an increased supply of dwellings.

1 Introduction

A substantial portion of household demand comprises housing purchases, renovation and rehabilitation. Since 1978, fixed housing investment has averaged about one third of total fixed investment and 5 per cent of gross mainland GDP (see Chart 1).

Fluctuations in housing investment influence cyclical developments in the Norwegian economy. At the same time, developments in the housing market may affect financial stability. About three quarters of Norwegian households own their own dwelling. Housing wealth accounts for close to 60 per cent of households' total wealth, and a substantial portion of banks' lending to households is secured on dwellings. Housing investment may also influence total gross household debt, as household borrowing normally increases with sales of new dwellings. (2) A higher level of housing investment than that necessary to maintain the housing stock results in an increase in housing capital. Over time, an increase in housing stock will in isolation push house prices down. If house prices decline, collateral values may fall below the value of many of the associated housing loans. This increases the risk of loan losses for banks. A fall in house prices will also reduce household wealth and the possibility of raising a mortgage-secured loan. This may dampen private consumption and the general level of economic activity.

Since housing investment has a bearing on business cycles, banks' collateral and household debt, we aim to identify the most important macroeconomic forces driving investment in dwellings. We also seek to elucidate how rapidly and strongly housing investment reacts to changes in the explanatory factors. In addition, we analyse the interaction between demand and supply in the housing market.

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The next section considers which macroeconomic factors may influence housing investment. Section 3 presents the empirical model and Section 4 analyses the interaction between housing investment and house prices.

2 Which factors influence housing investment?

This section discusses possible explanatory factors behind housing investment based on economic theory. It forms the basis for the empirical analysis in the next section.

Analyses of the housing market often employ models in which house prices are determined by demand for housing services and the supply of housing capital, while housing investment is determined by investment profitability. (3) Investment profitability depends positively on house prices. Higher house prices result in higher housing investment and thereby higher housing capital. An increase in housing capital contributes in turn to curbing the rise in house prices. Norges Bank has previously estimated house price models using demand factors and housing stock as explanatory variables. (4) An empirical model for housing investment, simulated in conjunction with a house price model, can be used for a more long-term analysis of the housing market. The focus in this section is on developments in the supply of housing capital.

Property developers' housing capital investment

The presentation below broadly follows Obstfeld and Rogoff (1996) and Hubbard (1998). The point of departure is the investment decision of a typical enterprise that earns income from selling completed housing capital. This means that income is earned by selling new dwellings and services such as rehabilitation and renovation. (5) In order to accumulate housing capital, the enterprise has to invest. The enterprise chooses the investment level that maximises its value. The real value of the enterprise at a time t, [V.sub.t], is given by the value of the sum of the current and discounted future profit:

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

The present value of future profit is calculated by means of a discount factor which depends on the real interest rate, R. The discount factor is shown in the first set of brackets in equation (1), and the real interest rate is here assumed to be constant. The first expression in the square brackets, the function [PI]([K.sub.S]), expresses the real income the enterprise earns in each period through selling housing capital, [K.sub.S]. The enterprise's costs are expressed in the next two expressions in the square brackets. The first expression represents the direct costs, where C is the real factor price of housing investment, [J.sub.S]. C is an index composed of prices for factor inputs such as materials, labour, land etc. Simplifying, in this section we assume below that the real factor price, C, is equal to 1. In addition to the direct costs, the enterprise incurs extra costs associated with changes in its capital assets, expressed as C x [PHI] x [([J.sub.S] - [delta][K.sub.S]).sup.2]/2[K.sub.S], where [PHI] is a constant and positive parameter. If, for example, the enterprise wishes to increase the scope of building projects in a given period, there are extra costs associated with the procuring of factor inputs. The extra costs reflect the fact that it is more expensive for the enterprise to invest a large amount in a single period than to distribute its investment over several periods. The larger the enterprise--in terms of the size of its fixed capital--the lower the extra costs.

The condition under equation (1) describes the relationship between capital and gross investment, and [delta] is the depreciation rate. If investment is higher than what is required to maintain the existing capital, net investment is positive and the capital stock will increase.

The investment decision

The enterprise maximises its value, shown through equation (1), with respect to investment and desired future capital stock. See annex for a mathematical derivation. The first order condition describing the enterprise's investment decision is given by:

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

The investment decision depends negatively on the size of the parameter [PHI], which is part of the expression of extra costs, and positively on the depreciation rate [delta]. The investment decision also depends positively on the present value of the future return on housing investment, [Q.sub.S]. The variable [Q.sub.S] can be expressed as follows:

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

The first element in the square bracket denotes the rise in income following a marginal increase in the housing stock. The second element, which also contributes positively to return, shows that increased investment today reduces future extra costs. The present value of the sum of the two elements is Q, which expresses the market value of one extra unit of capital relative to investment costs. (6) Equation (2) shows that net investment is positive if the value of a marginal increase in capital is greater than the investment costs (Q > 1).

In the derivation above, the variable [Q.sub.S] contains all information relevant to the investment decision. However, this variable cannot be observed empirically. An alternative is therefore to use an average Q, expressed as the ratio of average house prices to costs of increasing the housing capital. This average Q will not necessarily capture all information relevant to the investment decision. (7) The real interest rate is a particularly important variable for estimating the profitability of investments. Since we only observe average Q, we investigate whether the real interest rate is a determinant of housing investment as well as the ratio of house prices to construction and land costs. (8) The real interest rate measures both the real interest expenses associated with loan-financing building projects and the real return lost by financing the construction of dwellings with equity.

Different information for property developers and lenders

A number of studies have pointed out that the costs of financing investment projects may be lower if the enterprise uses its own capital rather than loans. (9) This is because lenders do not have full information regarding the risk associated with the investment. They may therefore require a risk premium for loans that are not secured on the enterprise's assets. (10) The risk premium will in general increase with the size of the unsecured loan and push financing costs up and investment down. Enterprises that increase their earnings can finance a larger share of their investment with equity. An improved capacity for internal funding may therefore lead to increased investment. In the empirical analysis in the next section we investigate whether retained earnings by property developers is an important explanatory factor for housing investment.

Land prices

Available land is a necessary factor input for house building. Land prices are therefore a factor price for property developers who sell new dwellings. There are no time series for representative trends in average land prices in Norway. One alternative is to use one or more other variables that can capture changes in land...