The ballad of the landlord and the loan – Technical Annex

The Bank Underground blog The ballad of the landlord and the loan includes quantitative estimates of structural tenant demand factors. This technical annex describes the approach adopted for each demand factor.


To calculate the impact of migration and changes student in numbers on PRS demand, we estimate how likely these cohorts are to rent (the propensity to rent), and multiply this by the change in the size of these cohorts over time, making adjustments where necessary to address data limitations.  For other impact of other demographic dynamics, we employ a similar methodology, taking into account changes in the population (excluding students and migrants), changes in household size, and changes in the age profile of the population.

Student population

We estimate the impact of student demand using the following equation:

Annex Equation 1


Annex Equation 2

Students living in university accommodation are classified as residing in the PRS. For simplicity, we assume other students also have a PR of one, although we know this is likely an upper-bound estimate given that some students live at home or own their own place.

We obtained data on student numbers from the Higher Education Statistics Agency and estimated average student household size from the overall population.


To estimate the impact of migration we use data on immigration (adjusting for student immigration to avoid double counting), and emigration (distinguishing between UK born and non-UK born emigrants) from the ONS. Future net migration is projected through keeping the level flat from the last data point in the February 2016 Migration Statistics Quarterly Report. Consistent with data from the Migration Observatory, we assume that the propensity to rent for recent-immigrants is higher than that for the general population.  Due to data limitations, we assume that the propensity to rent for non-student immigrants is equal to that of non-UK born emigrants; that UK-born emigrants have the same propensity to rent as the general population; and that the average household size for both immigrants and emigrants is the same as the general population.

Annex Equation 3


Annex Equation 4

Other demographic dynamics

To estimate the impact of other population dynamics on PRS demand, we estimated how the PRS population would have changed as a result of other demographic changes (population, household size, age), if the share of households living in the PRS in each age cohort remained at 2000-2001 levels.  Pre-2002, the private rental share of total dwellings was broadly stable. The likelihood of an individual in the overall population being in the private rental sector in a given year is specified by:

Annex Equation 5


Annex Equation 6


Annex Equation 7

And the number of households in the private rental sector in a given year is specified by:

Annex Equation 8


Annex Equation 9


Annex Equation 10

These equations give us an accounting identity to estimate the change in demand for private rental sector demand over a given period due to other demographic dynamics.

Annex Equation 11

As noted in the blog, different demographic factors have worked in opposite directions: the effects of a growing population and falling household size have been largely offset by the ageing population (Chart 2). Going forward, if these trends continue, we expect this to effectively reduce the number of people going into the PRS.

Chart 1: Decomposing population dynamic factors

Annex Figure 1

Sources: ONS, English Housing Survey, Migration Observatory, Council of Mortgage Lenders, Department for Communities and Local Government, Higher Education Statistics Agency and Bank calculations.

Social housing provision

The availability of social housing (local authority and housing association properties) to accommodate newly formed households will impact the demand for PRS accommodation. All else equal, we would expect a reduction in social housing to increase the likelihood of new households entering the private rental sector.

To estimate the impact of changes in the provision of social housing on the demand for PRS accommodation, we estimated “latent demand” for social housing associated with new household formation. Our estimate of “latent demand” assumes that the share of newly formed households seeking to live in social housing is equal to the share of households living in social housing in 2001. We then compare this number to the share that actually entered social housing and quantify the wedge between the two.

We also capture those households that actually enter or leave the social rental sector as a result of changes in the stock of social housing. For decreases in the stock we make adjustments for the Right to Buy scheme, where social housing residents purchase their homes.  This is because falls in social housing associated with this scheme will be accounted for through an increase in owner occupation rather than additional PRS demand. However, Right to Buy only offsets decreases in the stock of social housing; it does not increase overall housing capacity and therefore cannot decrease demand for PRS accommodation.

Our estimate of the change in the demand for PRS housing as a result of social housing provision is specified by:

Annex Equation 12


Annex Equation 13

Underwriting standards

To estimate the impact of underwriting standards on demand for the PRS, we needed to estimate the number of prospective first-time-buyers that wanted to secure a mortgage, but were unable to as a result of credit constraints.  In order to do this, we compared the share of households in the 18-35 age cohort securing first-time-buyer mortgages with high LTVs (above 90%) in the pre and post-crisis periods, and multiplied the difference by the number of households in this age cohort over the relevant time period.

Annex Equation 14


Annex Equation 15

We chose to compare the pre-crisis and post-crisis periods for reasons of simplicity and data availability on underwriting standards for first-time buyers.   But it could easily be argued that underwriting standards in the pre-crisis period were too loose.  It proved challenging to establish levels of underwriting standards to use as an “appropriate” benchmark to quantify alternative estimates.  Had we used a tighter benchmark for our calculations, underwriting standards would have made a smaller contribution to PRS demand in the post-crisis period, and potentially a negative contribution than in the pre-crisis period.

Our calculations may also overestimate the impact on PRS demand because they do not take into account how some young adults may live with parents for longer (rather than living in the PRS), or the extent to which first-time buyers in the pre-crisis period had access to larger deposits.

Forward projection

To project this analysis we extrapolate forward trends for immigration, student numbers and household formation, while population projections (both overall and cohort level) are taken from the ONS.  Stock levels for social housing are left flat in our projections, but in practice are likely to change as a result of measures contained in the Government’s Housing and Planning Bill, which was before Parliament at the time of writing.

The largest uncertainty lies around how long, if ever, prospective first-time buyers stuck in the PRS are able to save up for a deposit and eventually do get a mortgage.    If all ‘frustrated’ buyers unable to secure a mortgage since 2008 manage eventually to raise a larger deposit, then some of the additional demand for PRS properties will dissipate as these borrowers make way for new tenants (solid orange bar alone, Chart 3).  We estimated that it might take an additional 10 years relative to the pre-crisis period.  This was calculated using the below specified equation, and assuming  over the next few years, underwriting writing standards loosen slightly, the savings rates falls and house prices grow faster than income before stabilising.

Annex Equation 16

We can use this to work out the number of prospective first-time buyers returning to the market, subsequently reducing the number of households stuck in the PRS because of credit constraints:

Annex Equation 17


Annex Equation 18

But it is not certain that all ‘frustrated’ buyers will secure a mortgage.  If no prospective borrowers from the post-crisis leave the PRS, then all new tenant demand will be additional (both orange bars together). Both are extreme assumptions and the outcome is likely to be somewhere in between, but this allows us to estimate a range for the number of PRS properties needed to satisfy tenant demand going forward.