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4 EMPIRICAL RESULTS

Section 3 examined the theoretical premise for the Scottish Model of Housing Supply and Affordability and provided a conceptual discussion on module design. The purpose of this section is to provide empirical detail on the operational modules. The discussion in this section covers data sources and variable definitions as well as a review of the empirical performance of each of the five econometric modules.

4.1 Household formation ( HF)

The household formation module estimates individuals' probabilities of forming independent households. Forming an independent household means that a person or his/her partner rents or owns an accommodation. The probabilities are then used to project the number of households in the next thirty years based on official population projections. The HF module describes linkages between births / deaths, population and household formation. International migration, and that from elsewhere within the UK, also feeds into population change. Meanwhile, the predicted number of households feeds into the determination of owner occupied housing demand.

The model is based on Andrew and Meen (2003). The driving forces of forming a household are a selection of demographic variables ( e.g. gender, age, marital status, dependent children) and economic factors ( e.g. income and housing cost). As the HF module contains variables derived from the HSG module ( e.g. housing cost) and the labour market module (income), the predictions of the HF module change over time in the affordability simulation model.

The data are drawn from the British Household Panel Study ( BHPS) 1999-2005, because there was a boost in the sample size in Scotland in 1999. The panel data provide detailed information on individuals before and after their formation of households, which allows us to examine the determinants of transitions in and out of different states. Individuals are included in the analysis if they lived in Scotland and were between 16 and 39 years old in 1999. The model focuses on young people because they are supposed to experience more demographic and economic changes. Altogether there are 766 people in a balanced panel, 333 males and 433 females. In 1999, 612 people (79.9%) formed independent households. In 2005, 692 people (90.3%) lived independently.

A dynamic random effects probit model was employed. The model includes a lagged dependent variable as an explanatory variable to capture state dependence, i.e. those who formed independent households in the past are more likely to live independently in the future. Random effects were used to deal with the unobserved individual characteristics (heterogeneity). The presence of a lagged dependent variable is likely to lead to bias in conventional panel regression models; the error variance and the effects of explanatory variables tend to be underestimated and the lagged effect is likely to be highly overestimated (Chay and Hyslop 2000). This is due to the initial conditions problem, which occurs when a longitudinal binary process has a first order Markov property and contains unobserved heterogeneity. It means that individuals are part of the way through the process under study when the sample period begins, and the first observation (initial conditions) for each individual is affected by the same process as in other periods. Therefore, the initial observations of the binary dependent variable should be treated as endogenous due to its correlation with the individual-specific error term.

Heckman (1981) provides an effective method to deal with initial conditions problems, which was used in this analysis. The method suggests estimating the distribution of the initial conditions (t=1) by a different process but makes the estimation correlated with the main process (t=2,…,T). Thus, the estimators approximate the joint probability of the dependent variable in all sequences.

4.1.1 Results

The dependent variable takes the value of 1 when an individual forms a household and 0 otherwise. The independent variables include: lagged dependent variable, male, age bands, child present, partner present, acquire a spouse across two consecutive years, divorced/separated, real income at t-1, and mortgage costs (= mortgage interest rate*regional real house price).

Table 7 displays the coefficients of the main probit model (t=2,…,T), which are used for household projections in this study.

Table 7 The coefficients of the household formation model

Notes:

The omitted dummy variable categories are 'not forming an independent household at t-1', female, age between 16 and 19 years, no child, no partner, single across two consecutive years.
Standard errors in parentheses
* significant at 10%; ** significant at 5%; *** significant at 1%.

The table shows significant state dependence; people who formed households at period (t-1) are 6.9 times (=exp(1.9293582)) more likely to stay in separate households at period (t), compared with those who did not live independently at period (t-1), other things being equal. Most of the other variables in the model have the expected effects. For example, the probability of forming an independent household increases with age; people with partners or dependent children have a higher propensity to form households than those without families. Females are 1.7 times (=1/exp(-0.5325730)) more likely to stay in independent households than males. One explanation is that females marry at a younger age (Andrew and Meen, 2003). Higher income significantly increases the probability of living independently.

Consistent with most of the literature ( e.g. Asberg, 1999; Andrew and Meen, 2003), demographic variables have stronger effects on household formation than economic factors.

4.1.2 Projections of household numbers

Household projection begins with official population projections provided by the GROS. In each housing market region, population is disaggregated into 112 individual types, taking into account gender (2 types), age groups (7 types), martial status (2 types), having dependent children (2 types) and forming an independent household at t-1 (2 types).

There is no further disaggregation of the economic factors, as these factors do not have strong effects on household formation rates. Some variables in the HF model are dropped when disaggregating populations, e.g. acquiring a new spouse across two consecutive years. This is because individual types would increase greatly with more variables. Also, the dropped variables are thought to be less important in affecting household projections.

The proportions of people with different age/gender/marital status/dependent children in different housing market regions are derived from the 2001 census. People living in the communal accommodations are excluded. The shares of people who are in independent households at period (t-1) are derived from the BHPS, as the census did not trace individuals in the previous year. The shares at the national level in BHPS are used, because of the small sample size in each individual type at the sub-Scotland level.

For each individual type, the probability of forming a household is calculated from the HF module. Using the normal distribution, these scores are converted into probabilities of household formation. The probabilities in subsequent years might be different, because income and housing costs, estimated from labour market and housing market modules respectively, vary with years.

Table 8 shows an example of the probabilities of forming independent households in the Aberdeen housing market region. For instance, a single female aged 20-24 without dependent children has a 20.1% probability of forming an independent household, if she lived with her parents or relatives in the previous year. The probability rises to 86.2% if she lived independently in the previous year.

Table 8 Probabilities of household formation in Aberdeen

The last step of the household formation module is to multiply the probabilities and the number of individuals falling into each category, in order to obtain the total number of households.

4.2 Inter sub-regional household migration ( MIG)

The migration module is designed to predict household outward migration at sub-regional level. The number of migrant households then feeds into the housing market module influencing housing demand in a particular region. A relatively simple panel econometric specification is used and this is estimated using a 1997-2006 sample period owing to unavailability of reliable household migration data prior to this. The household migration data are based on amalgamation of Health Board figures to sub-regional level using NHSCR data, i.e. movements in patient registrations.

The dependent variable in the model is OUTHH, total outward migration expressed as a proportion of total households in the sub-region. Building on previous migration studies, the specification includes a number of spatial interaction variables, measuring housing and labour market conditions in the contiguous sub-regions. This specification permits a significant degree of spatial interaction. For example, it might be expected that outward migration from a particular sub-region depends partly on employment prospects and the price of housing in neighbouring destinations over and above the internal sub-regional labour and housing market conditions. A formal definition of the variables included in the model is as follows:

As the variable definitions suggest, household migration is thus determined through an interaction of recent house price growth in neighbouring sub-regions, changes in the ratio of employment in the financial services sector, household incomes, sub-regional shares of working population and the relative cost of housing (user cost of capital). A more detailed description of the latter is set out in the next section (housing market module), but this is essentially a composite variable measuring the effects of mortgage interest rates, depreciation and taxation on property and households' expectations of future price growth. The model is estimated as a panel with an SUR (seemingly unrelated regression) estimation method. The estimation results are shown in table 9.

Table 9 Migration panel estimation results

The seven coefficients are correctly signed and the model results make intuitive sense. For example, sub-regions and/or time periods in which neighbouring
sub-regions have higher levels of house price growth experience higher levels of

household outward migration. This is consistent with many previous migration studies that suggest households "chase" house price growth, i.e. tend to migrate from lower to higher house price growth areas. Equally, the model results show that outward migration tends to be higher when neighbouring sub-regions have higher household incomes, a greater share of Scotland's working population or a positive shift in weighting of employment towards the financial services sector.

The user cost of capital is the only statistically significant internal variable in the specification ( i.e. a measurement of conditions in the sub-region rather than in neighbouring areas). This variable is positively signed suggesting that outward migration increases in periods of higher interest rates or when households in a particular sub-region expect relatively low future house price growth in that sub-region.

The explanatory power of the model is high, as shown by the model diagnostics in table 9. The coefficients are estimated with White's standard errors and the weighted statistics shown do not suggest serial correlation.

4.3 The housing market ( HSG)

The housing market module takes the form of a series of models designed to explain and predict rates of house price growth. The dependent variable is the difference (between t and t-1) in natural logarithm of real, mix adjusted house prices. Equations are estimated for Scotland, and for the eight sub-regions. A seemingly unrelated regression ( SUR) approach is adopted to allow coefficient flexibility between the defined sub-regions and to take account of correlation in residuals between the spatial areas.

In order to take advantage of lead-lag relationships between the price changes of the sub-regions, some of the equations include lagged price growth of other sub-regions. In other cases, lead-lag relationships could not be established, or were found to be statistically insignificant.

The equation specifications include macro level and sub-regional level variables. At sub-regional level, lagged growth in mean household incomes is included. This variable is determined endogenously in the simulation model overall (being predicted by the labour market module), but is taken as exogenous in the housing market module. The ratio of households to dwellings at sub-regional level is included as one of two key long-run drivers of house price growth. The second key driver is the ratio of real house prices to twice real household incomes. The definition of this variable is similar to that used in the English model. Experimentation with this ratio (prices to either 1.5 or 2.5 household incomes) confirmed, with reference to empirical performance, that "price to twice incomes" variable is also an important and appropriate driver of house price growth in the Scottish content. Both of these long-run drivers ( HHDW and PD2Y) are entered as lagged variables to permit price adjustment through an error correction process.

Macro variables include lagged growth in stock market returns, inflation acceleration (defined as growth in inflation), and consumer price inflation. The user cost of capital is included as an explanatory variable. This is a combination of macro and sub-regional variables, being defined from a combination of mortgage interest rates, expected future growth in house prices (proxied by past rates of growth), property taxation levels and a home ownership risk premium.

A formal definition of the variables included in the specifications is given below:

Table 10 Summary of housing market module coefficients

Table 10 sets out a summary of the coefficients. The ratio of sub-regional house prices to twice household incomes is significant in all equations with a coefficient ranging from -0.088 (Edinburgh) to -0.314 (Aberdeen). In two sub-regions (Borders/Dumfries & Galloway and Highlands/Moray/Islands) the variable definition is sub-regional house prices to twice Edinburgh city region household incomes. This specification is empirically superior. Indeed, the ratio of sub-regional prices to twice incomes is not otherwise significant in either case, leading to generally poor empirical performance and an unreliable predictive model.

The ratio of households to dwellings is significant in all of the equations, with coefficients ranging from around 0.21 (Edinburgh) to approximately 0.50 (Borders/Dumfries & Galloway). These results are also in keeping with prior expectations, i.e. in the long-run the rate of house price appreciation is correlated with the ratio of households to dwelling stock.

Growth in household income is significant and positive in two sub-regional equations, although the appropriate lag structure varies between areas. The elasticities are in the range 0.31 (Edinburgh) and 0.47 (Highland/Moray/Islands). Growth in stock market returns is significant only in the Edinburgh city region and is negatively signed. This is at odds with the England model (in which this variable is positive and explained as a wealth effect). However, the negative coefficient in the Edinburgh sub-regional model could be interpreted as disincentive for households to speculatively invest in the housing market during times of strong stock market performance.

Coefficients on the remaining macro variables are also in keeping with expectations. Consumer price inflation appears to encourage house price growth, but the magnitude of the effect is small. Inflation acceleration, defined as a proxy for uncertainty or instability in the Meen et al study, is significant in six sub-regional equations and has a negative coefficient, as expected. This suggests that when inflation is rising rapidly, there is a negative effect on house price growth.

The user cost of capital, which is a composite variable as discussed earlier, is significant in all of the sub-regional equations, although slightly different specifications are used in some of the sub-regions. In the Edinburgh equation, the value of expected future price growth is derived from price appreciation in time periods t-2 and t-3. In all other sub-regional equations, this element of the user cost variable is derived from the overall Scotland rate of price appreciation in time period t-1 and t-2 using an adaptive expectations formulation (weighting 75% on t-1 and 25% on t-2). The appropriate lag on the user cost variable also differs between sub-regions. As noted, the variable is significant and negatively signed in all equations. This suggests that price growth falls in response to a rise in interest rates, and rises in response to a rise in expected future price growth.

Significant lead-lag relationships were found in a number of the sub-regions. For example, the Edinburgh city region leads the Ayrshire sub-region while Aberdeen city region leads the Edinburgh city region. These terms help to enhance the explanatory and predictive power of the model while strengthening spatial interactions.

Table 11 sets out the model fit statistics and some diagnostic information. The adjusted R squares range from 0.608 (Borders/Dumfries & Galloway) to 0.902 (Highlands/Moray/Islands), which is an acceptable level of fit for a model estimated in differences. The Durbin-Watson statistics do not indicate the likely presence of autocorrelation.

Table 11 Model fit and diagnostics

Aberdeen and Aberdeenshire

Ayrshire

Borders, Dumfries and Galloway

Dundee and Tayside

Edinburgh city region

Glasgow city region

Highlands, Moray and Islands

Stirling and central Scotland

4.4 The labour market ( LM)

The ultimate aim of the labour market module is to estimate average income per household. The variable of income is important because it influences aggregate housing demand, which drives tenure choices and partly determines affordability.

An aggregate model is derived based on the earlier work of Brown et al (2003). The structure of this aggregate model is based on the assumption that the working population in a housing market area can be disaggregated into one of four alternative labour states - full time employment, part time employment, unemployed and economically inactive - and that the total earnings of individuals within an area ( l) (EARNINGS _l) can be estimated by calculating the average earnings of workers in each labour market state and the probability of the working population ( TPOP_l) in each location ( l) being in each labour market state.

This gives the following aggregate model which approximates total income for each house market area as:

Where,

TPOP_lt Total population in the lth sub-region and tth time period

Mean earnings for full-time employees in the lth sub-region, tth time period

FT_lt Number of full-time employees in the lth sub-region, tth time period

Mean earnings for part-time employees in the lth sub-region, tth time period

PT_lt Number of part-time employees in the lth sub-region, tth time period

Mean earnings (transfer payments) for unemployed in the lth sub-region, tth time period

UE_lt Number of unemployed in the lth sub-region, tth time period

Mean earnings (transfer payments) for economically inactive people in the lth sub-region, tth time period

EI_lt Number of economically inactive in the lth sub-region, tth time period

The above model required input estimates for , which relate to the estimated average earnings of individuals in each labour market state in each housing market. Due to the lack of data available on the proportion of the working population on various benefits and the specific nature of benefits and other earnings collected by individuals, the earnings of economically inactive individuals of working age is assumed to be equal to 0 whereas the standard job seekers allowance for individuals over 21 is assumed for .

The Quarterly Labour Force Surveys 1993-2007, reweighed in 2007, were used to estimate the probability of individuals being in each labour market state, and to calculate historic full time and part time wages. The following sections discuss the models for labour market status and wages separately.

4.4.1 Estimating percentage of population in each labour market state

A multinomial logit model was used to estimate the probability of the labour market status of individual types in each sub-region. The dependent variable comprises four categories: full-time employment, part-time employment, unemployment and economically inactive. Independent variables include qualifications, health, demographical controls and labour market status in the previous year. A list of all variables and their definitions is provided in table 12.

Table 12 Labour market module data sources and variable definitions

The parameters of the multinomial logit model were estimated using a maximum likelihood method of estimation with the economically inactive probability representing the default cases. This means that the parameter coefficients give the odds ratio ( i.e. the probability of an employed or unemployed individual occurring relative to the probability of being economically inactive). The probabilities in each labour market status for different types of individuals can be calculated.

As the sample sizes of different types of individuals contained in the Quarterly Labour Force Survey was small in the more rural housing market areas we were prevented from making useful estimates of the average wages related to each type of individual. Therefore, the decision was made to differentiate only between individuals with and without degrees and estimate average probabilities across these two types of individuals in each housing market area. These probabilities were then used to estimate the proportion of the working population within each labour market state. The results of the multinomial logit models in Scotland are shown in table 13, with the sub-national model results shown in appendix B.

Table 13 Scotland level MNL model

Note: Equation includes year and region dummies.

4.4.2 Estimating wage models

Historic and for Scotland, and each housing market area, were calculated using gross weekly earnings recorded in the Quarterly Labour Force Survey. These average real earnings figures were then modelled using unemployment rates and a range of supply and demand variables. An attempt was made to model full- and part-time wages as a Fixed Effects panel model but the variations in the dynamics of the labour markets within each housing market implied that this was an inappropriate modelling technique. Therefore, the Scottish full-time and part-time earnings and the ratio of full- and part-time earnings within each area to the national average were modelled as separate equations using Ordinary Least Squares ( OLS), making allowances for autoregressive and moving average residuals. These separate equations were modelled as a system model but the magnitude of common variables also proved to be too diverse to be modelled as a common variable across the system.

Total income (INCOME _lt) within each housing market area and at the national level was estimated as:

The long run total earnings to income ratio was generated using data on UK total earnings and total income produced and published by Oxford Economics, and assumed to hold constant into the future.

Table 14 lists variables with their formal definitions. The results of the Scotland level wage model are reported in tables 15 and 16, with the sub-national models reported in full in appendix C.

Table 14 Wage model variable definitions

Table 15 Scotland level wage model estimation results

Table 16 Scotland level part-time wage model estimation results

4.5 Tenure choice ( TC)

The tenure choice module examines the determinants of owning a property. The model interacts with the household formation model to sort households into tenure categories and hence refine the numbers of owner-occupied households in each period.

The driving forces of the module are identified as user cost of owning a property, household income, wealth/savings, and household characteristics ( e.g. age and gender, marital status of household head, and presence of children).

The user cost of ownership is calculated as a rate of interest, depreciation, property taxes, and expected real capital gains for owners, with the rent for tenants in comparison. The variable reflects the relative cost of owning versus renting. It is expected that higher user cost reduces the likelihood of owning a property.

Permanent household income is used rather than current income, because the variable of current income is likely to result in downward bias to the income elasticity estimates (Ermisch et al., 1996). Permanent income is constructed from a hedonic regression on current income, and characteristics of household heads such as age, educational qualifications and labour market status. The fitted value relates to lifetime earnings as a measure of permanent income (a consistent estimator). The residual is transitory income, which may reflect unmeasured luck or efforts.

The model drew data from the Scottish Household Surveys 1999/2000, 2001-02, 2003-04, and 2005-06. The dependent variable takes the value of 1 when an individual owns a property and 0 otherwise. The independent variables are coded as shown in table 17.

Table 17 Tenure choice variable coding

A two-step modelling technique was used to estimate the coefficients. The first step is a hedonic regression for permanent household income.

1 ^st step:

Ln(household income) = f (household head's age, gender, marital status, dependent children, education, labour market status, whether spouse in paid employment)

The second step is a binary probit model for tenure choice, with a predicted value from the first-stage regression to replace an endogenous variable (permanent household income).

2 ^nd step:

Ownership versus renting = f (permanent income, interaction of UCC and permanent income, household head's age, gender, marital status, dependent children, whether in permanent jobs, saving bands, region and year dummies)

The results of the tenure choice model for Scotland are displayed in table 18.

Table 18 The coefficients of the binary probit model

Notes:
Equation also includes year and region dummies.
The omitted dummy variable categories are age between 16 and 19 years, male, no partner, no child, no permanent job, no savings, year of 2000, and Aberdeen.

Consistent with the literature, economic variables ( e.g. household income and UCC) are significantly related to the decision-making of owner occupation. Higher income increases the probability of owning a property, while the interaction term of UCC and income is negative. Most of the other variables are significant and have expected signs. For example, the probability of ownership increases with age; people living with partners are more likely to own a property. Permanent jobs and savings increase the likelihood of ownership, partly because of the improved accessibility to mortgages.

4.6 The simulation model

As discussed briefly earlier in the report, the Scottish Model of Housing Supply and Affordability is a simulation model. The five econometric modules are essentially building blocks. When the modules are used for the purpose of prediction, and are allowed to interact, a simulation model is formed. This simulation model can then be used to assess the affordability outcomes (over a forward period to 2041) resulting from macro economic and supply scenarios.

The simulation model, and the simulation results themselves, are discussed in detail in a separate report. However, it is worth noting that the model is integrated in a Microsoft Excel workbook, an approach that simultaneously allows the storage of key input datasets with econometric module results. It also allows user controlled inputs and changes to important policy variables, such as net additions to the housing stock

The key alterable sub-regional parameter is the net rate of net additions to the housing stock. A control is also provided to allow the user to enter these assumptions in two different forms - the annual rate of housing stock increase, or the absolute annual increase to the housing stock. Macro, or Scotland level, variables include RPI and CPI inflation, annual stock returns (log difference of FTSE-100 index), growth in Scotland-level gross value added ( GVA), property tax (affecting the user cost of capital), the proportion of adults with a university degree and the nominal mortgage rate.

GROS population projections are a very important component of the simulation model. Population projections in the forward simulation period are effectively converted to predicted numbers of households in the 8 sub-national areas. These predictions are made by the household formation module. The " GROS assumptions" control in the simulation model allows the user to switch between a standard set of population projections, and an alternative set based on a different set of assumptions. The alternative set builds in higher estimates based mainly on higher assumed rates of international inward migration. When selecting between these two sets of GROS population projections, the household formation module updates the number of households in the 8 sub-national areas over the simulation period. This then alters a range of outcomes of the simulation model including household migration between sub-national areas, house prices and household incomes.

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