Doing Housing Trajectories – “the science of confusing stocks with flows” (after Kalecki)
No this isnt an attempt to an award for the most planoraky title of a post under the new #planorak hashtag 2012, but advice on how to mathematically correctly treat the issue.
There are two ways to cover this in planning; under this category or indeed under any sub category of supply.
- Firstly in terms of calculating any estimate of housing requirements for local plans;
- Secondly in terms of ‘completions’ – dwellings ticked off the 5 year supply.
Now clearly these two lists should be compatible over a plan period. If they are calculated in a consistent manner then over a plan phase you will have, if enough houses are completed etc., meet ‘objectively assessed needs’ as the NPPF says (many times), if they dont you have miscounted somewhere. The biggest risk is having a 5 year supply running out in less than 5 years not because of strong markets, solely or at all, but because of bad maths.
Greg Clark said in the commons that filling of long term vacancies would count towards housing supply in the NPPF publication debate. This is the same as in the London Plan and many of us urged this position. Its not in the NPPF however but it seems we are allowed it as a new government accounting rule.
However you need consistent accounting. Consistent accounting needs proper treatment of stocks and flows. Now please no eyes glazing over because understanding stock flow consistency (or SFC as it is known) is key to understanding policy effectiveness not just over empty homes but also over brownfield first, windfall, garden grabbing, loss of employment sites, phasing greenfield releases etc. etc. – I can’t stress enough its importance. Its an idea from engineering and systems dynamics and is causing something of a revolution in economics at the moment (even Nobel Paul Krugman has made a fool of himself but demonstrating his ignorance of it in the last week – dozens of blog posts telling him he is wrong – and even I have been mentioned honorably in dispatches!!!). The fact that those who understood it were the only ones who predicted the 2007/8 global financial crisis gives you a clue as to why you should know about it.
Whenever there is a dynamic relationship, a number that counts something that changes over time. That change is either a change to a stock or change to a flow. So for example or bank account is a stock, you measure it with a time free dimension, money. However your income and your expenditure are flows, you can’t measure it in a time dimensionless way, rather you have to measure them in units of £/days (it doesn’t matter what length of time you use as the denominator as long as you are consistent). If the rate of flow in is greater than the rate of flow out you are making wonga.
I hope you can see the relationship to planning because what you do when you have a local plan sum of allocations is setting of a ‘stock’ designed to deplete over the plan period, with flows to another stock – housing completions. All of the time however another stock – objectively assessed need (for now not the future) is having flows in and out of its own, people added to need is the flow in, people occupying housing completions are flows out. Indeed it is a very good idea to colour code and map out from your trajectory spreadsheet whether you assume a cell is a stock or a flow. If you are assuming flow in and stock out etc. then you will get what is known as ‘stock flow inconsistency’ this will mean your projections will be wrong.
Back to empty homes. Occupied homes are a stock, Long terms vacant homes (those empty for over 6 months) are another stock. When homes become vacant they add to the flow of ‘homes which have become vacant’ most of these will quickly become occupied because they are what are known as frictional vacancies – houses which have been built but not yet occupied, where people have moved but not yet sold their house etc. Now you have to account for this level of frictional vacancies when you convert from a household projection number to a plan housing requirement. So for example is at at one time 2% of all houses are frictionally vacant you have to multiple household growth by a factor of 1.02. There are several such adjustments you need to make and another one concerns long term vacancies. If a house becomes long term vacant it is no longer part of the ‘flow’ of short term frictional vacancies.
Now this is where it gets interesting for if you treat occupancy of long term vacancies as completions and treat on the needs side the calculation of the inclusion of vacant homes differently you are immediately in the realm of stock flow inconsistency. If you want to start ticking off occupancy of long terms vacant homes on the supply side, you need to add in a term on the plan/needs side of the equation. You might not be able to solely rely on a plan number – you might have to add in an adjustment for your projection of how many homes (net) you expect to become long term vacant over the 5 year period. If you do better than the ‘policy free’ assumption you are genuinely meeting housing need, if you arn’t then its getting worse. The 5 year supply is based on this ‘policy off’ baseline assumption, without planning if we do nothing then housing needs will have increased by this number in 5 years time, if our projections and modelling were correct.
So you dont only have to count the flows out of the stock of long term vacant you also need to count the flow in, properties which become long term vacant.
Lets give an example lets say in any one year you have 50 units becoming long term vacant and 40 units refurbished from long term vacant to the active housing stock you have actually gone backwards by 10 units not forward by 40.
Similarly on the policy side you need to be SFC. If you are modelling changes to a stock which is used to adjust, up or down, another stock then you always must base your model on the delta of that stock, its Net Change, rather than the absolute number. So for example if you assume over 10 years you will have net 200 properties falling long term vacant you need to add 200 units to your plan number, then you can treat every house brought back to use as a net completion. If you dont do this however you should only count ex-empties once you have passed the net 200 figure, only then will you be in positive range.
You also need to be consistent on the policy side of the equation to avoid double counting. For example if you model the net change in long term empties you should only include a frictional adjustment factor based on the total number of the proportion of units which are short term vacant not long term vacant, if you dont you are double counting empties as a stock and a flow.
Now of course data on units falling vacant and the period of vacancy are hard to come buy, council tax records however will get you a long way. If you can’t or wont do this you should be counting empties of the completions side at all however, you will be counting the positives without counting the negatives and your final number will be wrong. So put simply unless you can accurately model this (which isnt that difficult) simply ignore empties.
Modelling empties is easy if the rate of change in empties is constant. Then its easy, just key stage 4 arithmetic. If however you assume that rate of change will be change over time then sorry – calculus – second order partial differential equations aaaaaarrrrghhhhh!! maths above A level grade and not even taught to most economics PHD students (which is of course one reason why the treasury taliban are so frequently wrong). Don’t worry however are there are computer programmes out there can can do the maths for you, you just have to wire up the stocks with links and tell it the rate of flow and starting stock conditions.
You bet though that once you understand these principles you aint ever going to make mistakes in your housing trajectory again.
Now if someone wants to send me some real world numbers I can do one of the animations like that above – sorry by the hour im afraid – now if that doesn’t impress the assistant director or a planning inspector nothing will.
Ps. Why arent planning schools teaching this as a core competency?
Stock and flow
Bezemer – Are Stock Flow Consistent Models the Next Paradigm? – http://winton.ashmus.ox.ac.uk/PastSeminars/Trinity%202011/bezemer.pdf