Материал: Assessment of the situation on the regional housing market in Russia

model of housing prices

function’s assume that there are N (= workforce*employment level) identical individuals (all those who earn income and can spend it on consumption and saving) with homogenous utility function and expectation about future states of the world. Each of them earns a certain amount of money in any form - salary, rent or profit. The representative individual in each period divides the income between current consumption of goods and services including for example such durable goods as household appliances, cars, etc. and savings in the form of either housing consumption or financial assets. So the budget constraint of the representative household can be written as following:

Yit is a total income at t-th period (average monthly value for each year); CGSt is a value of fixed set of goods and services at the t-th; FAit is an amount of individual’s spending at the t-th period of time on financial assets such as stocks, bonds, deposits, etc.; Ht is a quantity of housing consumed at the time t; HPt is a housing prices at the time t.to the fact that accumulation of capital assets is associated with some of rate of return and at the same time real assets such as house or flat depreciate with time, the intertemporal constraint for individual wealth can be formulated as follows:

Wt is accumulated by t-th period amount of individual wealth;  is a real after-tax rate of return on financial assets (FAt);  is a cost of borrowing money for buying real estate - mortgage rate; d is a rate of housing depreciation (for simplicity let’s assume that it constant across all the periods);  - growth rate of real housing prices between (t+1)-th and t-th periods. is assumed to be exogenous in this model framework, because the existence of competitive financial market is suggested. individual gets utility from current consumption of durable and non-durable goods as well as from consumption of housing services. Under housing services the convenience of possession instead of renting real estate will be meant, so this variable is unobservable. Therefore it was assumed that the value of housing services is proportionate to housing stock per person with some coefficient - k. The utility function which is identical for all the individuals is derived from Consumption CAPM model and it is convex function with constant relative risk-aversion, which can be presented in the following way:

rational individual maximizes his utility with respect to current consumption and housing consumption - the variables that he can choose and vary every period. Solving the maximization problem taking into account intertemporal wealth constraint one could obtain the following equality, which reflects the optimal ratio of housing consumption with respect to current consumption:

Calculus appendix.

By dividing first-order conditions to each other and by expressing the variable of interest  with help of other variables, individual demand function will be obtained.order to make this demand function aggregate, let’s sum it up over N consumers and solve it with respect to h, which means finding inverse demand function

(8) (9)

linearization, let’s rewrite the equation in the logarithmic form considering the fact that all values under logarithm are not negative in accordance with their economic sense

should be noted that within the model all the consumers as well as developers for simplicity will be price-takers - none of them as a single agent cannot significantly influence the average price of real estate formed on the market. For future research in this field it can be suggested observing other industrial structures other than perfect competition, because construction and development is an industry with high barriers. That is why regional market most likely takes form of oligopoly with a few big players that can interact with each other in many different ways.for real estate in each particular region is presented majorly by the population of this region. Due to the fact that interregional mobility in Russia is not high (see picture 1 below) - from 1.33% to 2.8% of total population during the period from 2001 to 2013, and 1.63% in average - within the framework of this study interregional demand for real estate will not be considered. Therefore demand in the region is created by inhabitants of the region and cross-regional demand component is omitted out of the model.

due to the fact that competitive construction and development market was assumed, it can also be suggested that cross-regional housing supply is negligible. Competitive market structure implies zero economic profit and low industry entrance barriers, so if there is an excessive profit in some region firms from other regions instantaneously can use this situation for additional financial gains until there is no such gain. Therefore profitseventually become equal among regions again and that is why cross-regional supply can be omitted out of the model as well.

Supply function

homogenous construction and developing firms form the regional housing supply. Each of them decides to built additional housing up to the point where their replacement costs that can be determined as full cost of construction of a new house per one square meter are equal to the expected market price at the period of sale - let it be period t+1. Let’s assume that all the construction costs can be divided into capital expenditures including cost of materials, machinery, construction and installation activities; labor expenditures which can be approximated by average salary and cost of borrowing betweenperiods t and t+1.can be suggested that labor and capital can be considered as substitutes to some extent in the process of real estate building - for example, the company can rent special equipment such as elevators, concrete mixers, etc. to meet their construction deadlines or it can just employ more workers, however both types of these expenditures should be incurred in order to build a house. Therefore the total cost function can be constructed as some sort of Cobb-Douglas function with constant return to scale:

 is a region-specific proportion coefficient which reflects the extent of total cost inflation if capital and labor prices go up;  is average capital expenditures in i-th region at t-th period;  is average labor expenditures in i-th region at t-th period; α and (1-α) are total cost elasticities of capital costs and labor costs respectively;  is a financial cost for t-th period which is equal among all the regions because there exist the unified national financial capital market. companies in each region (denoted by index i) form their expectation about the future period t+1 based on the all information available to them at the period t - where  is an information set of t-th period. Current housing prices and cost of funding will be considered as exogenous for companies, because of competitive market structure. Expectations of construction firms are based on the current market situation, but also they can consider region-specific factors such as general growth of GRP, mortgage subsidy program, etc. and time-specific effect related to nation-wide economic cycles. So expected prices will be defined in the following way:

 is a regional-specific growth factor calculated as a function of Gross Regional Product (GRP) growth rate;  is time-specific growth factor;  and  are associated coefficients. GRP is considered as an exogenous variable within this model - despite the fact that construction and development companies participate in GRP formation, their influence is negligible within the whole regional economy. to the fact that secondary real estate market is observed in this study, the main indicator of supply is real estate stock which is available at a certain moment in time, which can be calculated as follows:

- real estate stock, available by the end of period t;     SoDt - size of dwelling for period t;UHt - value of uninhabitable real estate for period t. change of housing supply in t-th period can be defined as a difference between size of dwelling and the disposal of uninhabitable housing in the i-th region at t-th period. Therefore the growth rate of housing supply at t can be calculated as:

Where  is a rate of housing supply growth between period t and t+1 in i-th region;  is a size of dwelling that had been started at t-th period and was offered for sale at t+1 at i-th region;  is a size of uninhabitable residential real estate which was removed from housing market;  is a housing stock available at the market at t-1 period.supply can be determined as a function of expected real estate prices relative to full replacement cost of construction according to Q-theory formulated by J. Tobin. In the context of real estate market this theory implies that construction firms make their investment decision to build a house based on benefit-cost analysis: they build additional housing is expected prices are higher than current total costs. Therefore housing supply equation will be determined as follows:

taking a logarithm of both right-hand and left-hand sides for linearization and by substitution of  and  with correspondinglogarithmic expressions, the following log-linear supply function:

 is price elasticity of supply parameter;  is a coefficient which reflects the influence of region-specific factor;  is a coefficient which reflects the influence of time-specific factor; is an overall error term.appendix:’s create a logarithmic form of expected housing prices and total costs equations:

form of housing supply equation is:  . By substitution of two former expressions into supply function, the following log-linear form of housing supply will be obtained:

final form of housing supply equation can be obtained by grouping items on the basis of their compliance - mathematical and economic.

formulation

theoretical framework that was formulated above is based on the plain idea of equilibrium between supply and demand(see figure 3), which are formed in turn under the influence of outlined characteristics of the whole Russian economy, regional specific features and personal characteristics of individual households.

Fig. 3. Graphic representation of the theoretical modelinfluence of the national economy as a whole is represented by borrowing and lending terms: loan rate for construction and developing companies which is suggested equal to the rate of return at which households invest their funds and mortgage rate for households. Despite the fact that mortgage rate varies over the regions it is based on the Russian key rate which defines the cost of the money in the economy and on observed and expected inflation rate. That is why mortgage rate can be considered more as a factor reflecting the situation in the whole economy rather than in the separate regions. coefficient  included into the demand function reflects the relative expensiveness of investing in the housing (which presented by cost of borrowing (mt) and depreciation rate that assumed to be constant over time and regions) instead of placing saved funds in financial instruments that brings some rate of return - rt. So the higher costs of buying of an additional real estate the lower demand should be which eventually would depress housing prices. : The higher relative costs of buying real estatecompared to an alternative rate of return the lower housing prices arethe influence of business cycle and the overall trend in the economy is accounted in the supply function through time-specific effect. The presence of this effect implies a positive trend in housing construction, which could include technology improvement over time which allows building real estate faster and/or cheaper, the increase of labor productivity or the fact that over time population becomes richer due to for instance trade unions activities and increase of minimal wages. All these factors can facilitate the increase of constructors’ profit margins and push prices higher relative to the cost of construction dynamics. So the positive influence of time factor which is included into the expected price formation process goes without saying. regional-specific factors of demand there are working force of the region, employment level and housing stock of the region. Due to the fact that housing stock is naturally higher for regions with higher population, it was scaled by employed population of the region (those who create efficient demand). So real estate stock per capita is included in the demand function. The law of demand connects the price of real estate and the amount of the occupied housing: the higher the price is, the lower the amount of housing is purchased. regional-specific growth factor calculated as (1+ GRP growth rate) in the supply function as a part of anticipations of construction companies about future prices. The dynamic of production which accurately reflects the situation in the economy appeared to be highly significant in the majority research papers such as (Grimes and Aitken, 2004), (Kishor and Marfatia, 2016), (Berger et al, 2015) and some others. So the assumption about fact that economic agents base their expectations on the past was validated. However these models were tested on quarterly data so it could be concluded that this result was proved only for short-term periods. Besides the significance was shown mainly for developed countries and on country-wide data, the importance of cross-regional differences has not been yet tested for developing countries. Therefore the following hypothesis can be suggested. : Gross Regional Product plays significant role in the formation of price expectations on housing market in Russian regionstotal cost function of construction companies is based on the distribution of expenses between human and capital resources. So theoretically this function should be individual for each company. Howeverdue to the existence of the assumption about competitive industrial structure all the companies are price-takers on the labor market and market of construction materials, machinery, financial resources, etc. And considering regional economy level this assumption seems to be reasonable because if there was higher than average salary in the construction industry there would be an inflow of workers on that market and wages would converge to the average level. Therefore the average regional value of such variable as labor cost and capital cost were used. Anyway themore expensive resources to the company relative to the anticipated housing prices are the less incentive to build additional living spaces constructors and developers have.: The inflation of total cost which is not supported with corresponding increase of housing prices holds back construction activityof unavailability of information about cost structure of each builder in each region such cost equation coefficients as the elasticity of substitution (alpha) and proportion coefficient (gamma) are unobservable and therefore impossible for separate estimation. They are assumed as constant and would be incorporated into estimated empirical parameters of the linear supply function.individual features that participate in the demand formation there is a share of current consumption of perishable and non-housing durable goods in the households disposable income (not only wage, but rent, profit from entrepreneurship or any other type of income). Housing consumption and consumption of goods and services are connected through the income constraint which means that the household have to distribute its income between these positions -if it spends more on current consumption it has less to invest in housing. At the same time the law of demand implies inverse relationship between the amount of housing purchased and the price of housing. Therefore the lower demand for real estate is the higher the prices are. That is why theoretical model formulated beforehand suggests that housing prices and consumption of goods and services are connected directly to each other. the fact that all the unobservable variables in the demand equation such as the risk-aversion and coefficient of housing services are theoretically individual to each household there is no ability to measure them separately for every individual and therefore test hypotheses about their influence. That is why these coefficients considered as constant in the equation and therefore will be incorporated into the estimated parameters of the empirical model.order to test whether developed theoretical model describes the real situation on the regional housing market in Russia the appropriate data should be collected from reliable sources of information. The process of data collection and discussion of data features are presented in the following sections.

Data collection and processing methodology

order to determine a type of relationship between the set of independent variables and housing prices and obtain marginal effects, the empirical model need to be estimated. Due to the fact that housing prices varied a lot during the period after the collapse of the Soviet Union to our days as well as the majority of predictors, time variance also should be considered. Therefore panel data analysis should be implemented.housing prices in Russian regions are modeled with help of yearly data which covers the period between 1996 and 2012, so data need no seasonal correction.Due to the fact that mortgage became mass financial product only in 2005-2006 in Russia, statistics on mortgage conditions (i.e. mortgage interest rates) is available only for the period from 2006 to 2012.is also worth mentioning that during the period in study there were a different number of regions in Russia - some of the regions were included into the others: some, vice versa, were separated. Those regions that stopped their independent existence between 1996 and 2012 were included as separate object of observation if all the variables were available for at least 5 years. Otherwise the values of each variable for the region were from the beginning added to the values of the region which turned out to be its absorber. Those regions that were separated during the period in study were included whatever the time they appeared (anyway the minimal length of time series for such regions was 5 years). As a result 85 regions were observed during 17 years, so the total number of observation is 1445. demand side and supply side indicators can be collected from official free sources such as Federal and Regional Statistics Services and The Central Bank of Russian Federation.Regional-level data is availableonly in “Russian regions Handbook” which is published by Russian Federal Statistic Service on a yearly basis.

The Bank of Russia provides analysts with regional-level information on mortgage rates, but regional differences of loan rates are unobservable.Cross-regional difference of borrowing rates is negligible for a couple of reasons. First of all, large constructors and developers are borrowing money not only in one particular region - they can optimize their choice and find cheaper funds, which makes space arbitrage impossible. Besides, if somewhere loan rates were higher in comparison with other regions, banks would have been started allocating more resources and issuing more loans there. At the same time banking can be considered as competitive industry - they “sell” undifferentiated product (money), so in order to “sell” more they compete on price (loan rate), and as a result interest rates become more or less equal to each other. (Wagner 2008)

2.of information about factors studied in the research

the indicators have numerical values; however they are measured with help of different units. The Table 3 reflects each variable name in the research and their units of measurement.

3.names and units of measurement