A housing absorption rate formula—first cut

Housing supply is one of the most misunderstood processes in economics. The reason for this is that the core standard theory of economics is a static one-period model of production with a fixed capital endowment. They confuse the optimal density of dwellings, given the fixed capital of one unit of land, with the optimal rate of supply of new dwellings per period of time.

To be clear, the decision to supply existing housing to the rental market at any point in time is short-run production decision given a fixed stock of homes. That is why most homes that exist are not vacant. The marginal cost of renting (compared to keeping vacant) for a dwelling owner is typically far below the marginal revenue.

Building new homes is instead a capital allocation decision. Land and cash assets must be given up to build new homes. These assets earn a return over time and can be used in future periods instead of the current period. Building too many homes today depresses prices and rents, thereby reducing the return to both existing homes and homes you can build in the future.

So how is the optimal rate of new housing determined?

It is clearly not determined by the optimal density, as static models assume. Take a look at the figure below showing a housing subdivision in a street. The static theory says that if you approve a subdivision of five housing lots, you increase the rate of supply per period by five dwellings. They all sell in period one.

In reality, these dwellings do not sell all in period one (i.e. all in one day). They are drip-fed to the market over time, with one possible series of sales shown in the figure below. When I looked at the land banks of Australia’s top eight listed housing developers, the average age of their housing subdivisions and apartment blocks since their first sale, was ten years. The oldest was 25 years! They were still selling housing subdivisions approved in the last millennium. 

This slow rate is optimal because housing developers are rational. Selling faster reduces both the value of the rest of their subdivision and the growth rate of the prices they receive over time. They are giving up future returns if they flood the market today.

What do those future costs look like?

In the figure below we can see the effect of new dwellings sales on market prices and growth. The top line is the counterfactual price path if no new dwellings were supplied. Each additional dwelling when it is sold goes to the highest bidding buyer at that point in time, taking them out of the market and reducing the price to the second bid. This gap between the highest bid and next bid is labelled as alpha, and represents the “thickness” of the market in terms of how many people have bids clustered at the top of the curve. If you rank bidders from highest to lowest and get prices of 1.0, then 0.9, then 0.8, then alpha is -0.1 (the slope of this bid curve when buyers are ranked). If the market is “thicker” the bids might be 1.0, 0.95, 0.9, meaning alpha is -0.05.

Each sale at any point in time takes out a buyer and reduces the maximum price. Meanwhile, the other bids grow over time (or not) depending on macro and market factors. The next sale has the same effect, wiping off the next highest bidder and reducing the price, and so on.

So each sale has a pure price effect in terms of alpha. We can add these up on the above figure, and with a rate of sales of three per period, the price effect—the difference between the end of period price on the counterfactual end of period price is three times alpha.

This is standard economic theory, whereby increasing supply per period has a price effect. No surprise there.

But notice something else. The result of this pure price effect is that the price path is flattened compared to the counterfactual. Not only are end of period prices lower, but seen as a path, prices are growing more slowly.

The faster the rate of sales today, the lower future prices tomorrow. In essence, the pure price effect can be reinterpreted as a reduction in the growth rate of prices over time rather than a static price effect.

We can see this in the figure below where we reduce the rate of sales from three per period. Notice that the first lot is sold at a higher price because it is sold later, as is the next lot, with the third lot still to be sold at the end of the chart at an even higher price.

Somewhere between selling zero new dwellings, and selling enough to ensure that prices never rise above costs, is an optimal rate—an absorption rate that maximises returns to landowners from converting their sites to cash by selling lots to residents.

How should we think about what is optimal? Sticking with the basics, we can choose a rate of supply maximises the expected present value of the flow of lots into cash.

It is tricky to think of supply as a rate. But a simple logic can be used here to understand what is optimal. You want to at a rate that maximises the revenue this period and the value of the flow of revenue from all future periods, based on expectations and discounting. At this optimal point there is no gain from increasing the rate, since increase the rate comes at a cost of future price growth (and vice-versa).

The immediate revenue from the rate of sales is simply the price times the rate of sales. We can ignore the price effect in this because we capture it in the growth term which affects the value of future revenues (you can imagine supply as a sequence of sales, with any individual sale not having a price effect as it is the price setter at the margin at that point, but it reduces the price of the next sale in the sequence).

The value of the flow of future sales is the capitalised value of the end of period price, which is now lower because the rate of current sales has lower the growth rate.

As a mathematical approximation, we have the following equation to maximise (where I use f() to as a shorthand way to say this is some function of this term, but I’m not going to specify that function).

The maximisation happens when the marginal benefits from higher rates of supply today (the derivative of current revenue with respect to the rate of sales) equals the marginal cost in terms of lower value of future revenues (the derivative of the present value of future revenue).[1]

The rate of sales that maximises this value is

What is the intuition here behind the direction of the relationship between each market parameter and the rate of sales?

First, if the growth rate is higher, you need to increase the rate of sales in the next period to capture more of that value of that growth, which, because we are dealing with an instantaneous rate of sales, means increasing sales this period into the next period.

Second, a higher interest rate increases the rate of sales. This is because the future cost of lowering price growth by increasing sales is worth less today with a higher interest rate. A low interest rate means that the price effect on the future is more valuable today.

Third, the alpha term is negatively related to the optimal rate of sales. This makes sense. The thinner the market (the higher the alpha) the fewer sales can be made with the same price effect.

Notice how different this “optimal rate” thinking is to the usual economic analysis housing supply. This equation does not care how big your subdivision is—approving a larger subdivision won’t force anyone to sell or develop more quickly.

There is a lot more to this story. We actually don’t yet have an answer for how fast our five lot subdivision above should sell to be optimal. We know that if price growth and interest rates are low that they will sell lower than otherwise. We know if the market is thin they will sell slower than otherwise (say if they are in a small town compared to a large city).

I am working on a neat way to show the present-future trade-off, but it is not that simple. This might explain why theories of optimal rates of housing supply don’t really exist yet. There is a lot more to this mathematical story and if there are economic theorists out there who would like to help me ensure that my next “absorption rate formula” is consistent, please get in touch. 

_____________________
Fn. [1] I have taken a bit of liberty here to simplify the equation. Strictly speaking, the problem is a recursive one, in which the value of future revenue itself depends on future values. Also, strictly speaking, you could capitalise future incomes by the interest rate minus the expected growth rate, but this has problems. And, there are issues about the representative agent owning all the land, and whether you should account for the value of current housing or the value of the options for development in the price effect. The above equation is the simplest version that captures the direction of all effects and is the clearest way to show the future cost of faster supply.

Economic tide reveals naked policies

Superannuation

It seems that when people want to withdraw their money from super, the money is not there, and it requires asset selling that reduces asset prices across the board. This same effect happens ALL THE TIME. That is why a scheme that requires nearly 10% of wages to be spent on asset purchases is a bad idea, as it boosts asset prices. When the super system needs to pay out more than it gets in, asset prices are squeezed, and the value of what we thought we had saved begins to fall.

If only someone had warned about this.

Valuing life and the cost of lockdowns

Every policy involves trade-offs that can not only be measured in the monetary value of resources, but in blood. It is very standard to think of gains from health policy in terms of Quality-Adjusted Life Years (QALYs) as a metric of performance. Every public policy—from road rules to medical funding, to retirement, to workplace safety, to minimum standards—has an implicit trade-off of resources for lives.

Yet everyone has lost their shit about coronavirus as if lives lost this way are worth orders of magnitude more than lives lost any other way. In two to three weeks time the reality will set in that there are real costs of locking down society that can be measured both in value of resources wasted and in blood. All perspective has been lost at present.

Money was never an issue

Perhaps the greatest change from the crisis is that money was never a constraint. Politicians spend on things they like and don't spend on things they don't like. The budget was always an excuse.

I have often told policy advocates to stop arguing to politicians how cheap their solutions are to homelessness, or environmental losses, and other issues. They should instead argue how large of an investment is required to fix them! At the moment we are in a political vortex of one-upping each other in the ‘tough on the virus’ stakes, and this is coming with ever bigger cash splash promises.

But this is actually how things work all the time. Useless “ego-infrastructure” projects that give politicians a plaque and a ribbon-cutting photo-op are the norm. Big spending decisions are driven by political egos, not logical resources trade-offs. 

Housing was always a macro issue

I have heard for years from experts in my field of housing economics that zoning was constraining supply and rezoning would see a construction boom like never before. In fact, according to their numbers, we could double, or triple, the rate of construction by changing just a few words in a few town plans to allow higher densities.

But I have yet to hear rezoning proposed as the solution to the inevitable construction crash. Why not? Could it be that the argument was always bullshit and that housing supply is (you will never guess) constrained not by regulations, but by demand from new buyers? When buyers leave, construction falls.

This is not some radical “crisis-only” situation. This is always the case.

A "Central Housing Bank" proposal for a crisis and beyond

Cameron Murray
Henry Halloran Trust, The University of Sydney
20 March 2020

Download proposal as a PDF

• We propose that State governments (or Federal) create a “Central Housing Bank” (CHB) that stabilises the housing construction sector by swapping assets, in this case, cash, for new dwellings. Just as the Central Bank swaps cash for other financial assets to solve liquidity problems in financial markets, the CHB would do the same for one of the nation’s largest economic sectors. 

• As a national program, a dwelling target for the first year could be 30,000 dwellings across the 20 largest towns and cities in the country (around 0.5% of the number of dwellings in these towns). This is roughly 15% of the new dwelling completions in 2019, a significant demand buffer for the housing construction industry, supporting an estimated 150,000 highly productive jobs. 

• In balance sheet terms, these actions are costless for any government that undertakes them, as they receive a dwelling of equal (or perhaps higher) value to the cash they give up. Margins on housing development are typically above 25%, so this would be an opportunity for a public agency to engage in discounted counter-cyclical asset purchases to support jobs in the construction sector. 

• The CHB can then use those acquired dwellings in a number of ways to support policy objectives, such as 

1. renting in the private market to help stabilise rents, 
2. using them for public housing at discounted rents, 
3. selling to social housing providers at discounted prices, 
4. or selling to the private market in future periods when prices are rising to dampen the housing cycle. 

• Housing construction investment is a volatile, but productive, part of the economy, currently accounting for around 5% of GDP and 7% of Australia’s workforce (including housing construction and ancillary industries).

• Ensuring continuity and utilisation of productive organisations, such as builders, manufacturers of construction materials, and the design and management professions, can help ensure productive capacity is maintained during the crisis, and in the post-crisis period.

• The basic implementation of a CHB would be as follows:

1. Employ a small group of senior construction and project management experts to manage the CHB, ideally from the non-housing construction sector, such as mining and oil (to avoid conflicts of interest). 
2. This CHB team would request tenders from private housing developers or landowners to supply new apartments at an agreed price. The objective is to utilise the pipeline of already approved housing developments to speed up the process. In Sydney alone, there are an estimated 20,000 approved yet not-yet-commenced dwellings. Nationally, the top eight housing developers have a landbank of over 200,000 apartments and houses. There is a massive pipeline of sites that the private sector has queued up for housing that they will be looking to sell to reduce exposure to falling land prices. 
3. They could also shop for development sites as a market participant. 
4. The CHB management team would be incentivised to meet dwelling supply targets both in terms of the quantity delivered, and the location-adjusted average price paid. Independent assessment by State Valuers, in conjunction with State or Federal Treasury, can determine the value for money and hence the performance bonuses of the management team. 
5. Rough annual new dwelling purchase targets for the CHB could be set as a schedule across major towns and cities in proportion to their population, for example, 0.2% of the population in every town or city above 100,000 residents (of which there are 20 towns and cities nationally). Expansion to smaller towns can be conditional upon the success in the first three years of the CHB. This would be roughly 30,000 dwellings in the first year. 

• There are enormous macroeconomic stabilisation benefits of this system. The accumulated stock of rental housing owned by the CHB can be used to dampen housing price upswings by introducing a selling rule. For example, if dwelling prices begin to rise above a set rate, of say 5% per year, this would trigger sales of the stock of dwellings held in that region to private sector buyers at the rate necessary to keep growth below the target rate (again, like Central bank intervention to stabilise interest rates), absorbing speculative demand and stabilising housing prices.
• This system is not dissimilar to housing systems in Singapore, and public housing systems in Europe, and previous housing systems in Australia and North America.

Economic crisis? How about ‘equity mate’?

During 2009 farmers were paid $61million per month in drought assistance as part of Exceptional Circumstances Subsidies. But the public got nothing for it.

I have often said that public subsidies, even in a crisis, should always come with obligations. The simplest of all is to make the subsidy an asset swap rather than a gift—provide the cash, but take an equity stake in exchange, diluting ownership. This 'equity mate' public policy can help ensure the continuity of productive capacity during crisis periods.

Central banks provide liquidity via asset swaps to financial institutions in exceptional times. 'Equity mate' is just a way to provide cash via asset swaps to the companies that do the actual production in the economy. 

But in practice, this is not easy.

In a crisis, the value of equity falls. By taking a new equity stake when the value is low, you are providing much less cash per share while diluting an already lower equity value.

How this could work in practice is to have a “standing facility” whereby a rule about the value of equity the Treasury or Central Bank would pay is set in advance, and businesses can choose to use it up to a maximum share, of say 10% of the business value. As an example the rule could be:

For listed companies, equity comes at a price of the lower of—

1. The middle of the price range of the two prior years, or
2. The middle of the price range of the prior year, or
3. The current price plus 15%.

For unlisted businesses, equity comes at a price of—

1. The average of the marked-to-market balance sheet from the two prior years.

These rules would have to be broadly considered, but you get the idea. When equity values are rising, the price paid would be too low compared to the option of expanding cash for investment by issuing equity to private investors. Only during downturns would this kick in, when sudden declines in economic activity spook the market as a whole. Having this option in place might also dampen selling during a crisis, just like the government guarantee on bank deposits deters bank runs. 

This ‘equity mate’ injection of funds is a way to provide liquidity insurance to our productive enterprises without massively changing their incentives. A problem with drought assistance, for example, is that the expectation of future subsidies gets capitalised into the value of farmland. The insurance is free, and the incentives to invest in a way to mitigate loses from predictable rain variation are reduced. 

Buying up the nation's companies in a downturn is also just a smart investment. Buy low, sell high, make money. In the 2008-09 financial crisis, the Reserve Bank of Australia used counter-cyclical investment in currency to stabilise the dollar. It bought a lot of AUD using its USD reserves when the AUD fell to below USD0.60. In the following years, the AUD increase to above USD1, making a large profit for the Bank, which is an income for the public sector. Like this example, counter-cyclical purchases of a small public stake in a wide range of companies will provide future public revenues. 

What are your thoughts?

The easiest retirement system - Retiree Tokens

People are often confused about retirement income systems. Understandably so. Most economists, and organisations such as the IMF, OECD, national treasuries, and think-tanks, have promoted a view that countries that rely more heavily on taxation and transfers to facilitate retirement incomes (pay-as-you-go systems) are at an economic disadvantage compared to countries with “pre-funded” systems. The aggregate value of assets held in pension funds is believed to measure a country’s capacity to support a retirement income system. More funds, more capacity.

But this is wrong, and it is easy to demonstrate why.

All retirement income systems merely allocate goods and services to the retired at the time they are needed. They only differ in terms of the accounting system used to implement them. Some use public finance and cash transfers, while others, such as superannuation, require compulsory asset transfers.

But the problem of allocating goods and services to the retired does not necessarily need any accounting system at all. Just make a law that requires all retailers to supply their products to people over retirement age for free. Voilà. Retiree incomes, in terms of the goods and services they consume, are automatically and immediately guaranteed.

When a retiree fills their car with fuel, there is no charge. When they shop at the supermarket, again, there is no charge. When a customer reachers their magical retirement age birthday, their electricity and gas bills go to zero. New clothes? Free for the elderly.

This system redirects real resources to the retired. The cost is borne by the non-retired in the form of higher prices and hence lower real incomes. All retirement income systems do this — the non-retired have less ability to consume goods and services, the retired have more.

But, this "no accounting" retirement could be easily gamed. Retirees could begin to sell their free goods in secondary markets, on-selling to non-retirees to profit for themselves.

To fix this problem you could introduce a Retiree Token system. Each retired person gets a limited number of Retiree Tokens that they use at retailers to exchange for the free goods they are entitled to. This Retiree Token system would limit the ability for retirees to on-sell in secondary markets the goods and services provided to them for free. Hypothetically, you could provide each retiree with, say, 24,000 Retiree Tokens each year that they can swap at a 1:1 exchange rate to the dollar for the free goods and services that businesses are legally obliged to provide.

As you can see, a retirement income system can be achieved without any accounting system. It might be operationally problematic, and could be improved by using Retiree Tokens to limit the free goods and services that the retired are entitled to.

So if retirement income systems do not need money at all, where does that leave the idea of “pre-funding” a system? After all, there is no way to use financial markets to create more Retiree Tokens, just as there is no way for airlines to uses financial markets to “pre-fund” their frequent flyer token system.

The answer is simply that it is not possible to “pre-fund” a retirement income system. In terms of goods and services consumed by the retired, all systems possible systems are pay-as-you-go. There should be no confusion about this.

The puzzle of high home prices and vacant homes

One pattern that stands out in the property market is that although homes prices are at all-time highs, so too is the proportion of vacant dwellings. This is a puzzle. How can it be the case that when housing is in high demand it is also rational to keep more housing vacant?

Australian data shows that the number of residential dwellings has grown faster than the number of households for the past decade, indicating a substantial rise in the proportion of empty homes. This phenomenon has been a broad one, experienced in cities such as Sydney, Vancouver, and Toronto. Here are some of my previous thoughts on the topic.

The resolution to this puzzle is as follows. Housing is an asset, and in asset markets there is a trade-off between liquidity and returns. A vacant home is a more liquid asset than an occupied home. Timing a sale is easier, the sale is faster, and it is likely to result in a higher price when vacant. When capital gains are a large proportion of the total return, and capturing this return requires timing the market because of price variability, the value to liquidity from vacancy can be high.

In short, when yields are low and prices high and variable, the benefits to vacancy are high.

Here’s an example. In Scenarios A and B the total asset return to housing is 10%. But in Scenario A the price is high and yields are low. Here, leaving the property vacant forgoes only a quarter of the total return from the asset. If prices are variable in this Scenario, then timing a sale becomes an important factor for earning the capital gains. Hence, the liquidity from vacancy has a large benefit.

	Return	Cap. gains	Rent
Scenario A	10%	7.5%	2.5%
Scenario B	10%	2.5%	7.5%

In Scenario B the price is low, as the rental yield is 7.5% of the price. Capital gains are also low at 2.5%. In this low price, low capital gain, scenario, keeping the property vacant requires giving up three-quarters of the total return. The benefits from doing so are limited since capital gains are low, and hence less variable.

So there is an economic logic behind the puzzle of high prices and high vacancy, and it stems from the fact that housing is an asset as well as a consumption good. But there is also a criminal logic. Much of the vacant housing in Australia (and probably Canada and a few other locations) is due to money laundering. There are no checks on the source of finance for home purchases and no checks on who the ultimate beneficiaries are in the ownership structure. You can buy a home in a trust or company name, and the identity of the trustees and the company owners need not be disclosed. If you then also do not earn rental income, the corporate structure is protected from scrutiny by tax authorities. Housing is a great way to hide ill-gotten gains.

The criminal logic and economic logic are closely aligned. When most of the return to housing comes from capital gains it makes housing a more attractive place to hide money as three-quarters of the total return can still be had. But when most of the return comes from rent it is much less attractive — and it may require corporate disclosure due to local incomes warranting taxation.

Finally, some new data
On another note, new data from the Australian Bureau of Statistics came out recently, filling one of the holes in the housing data landscape — the share of lending to investors that is directed towards purchasing or building new homes.

This data helps to answer questions about the economic value of new credit in the economy, the real economic effects of monetary policy, and more. In standard economic thinking, low interest rates make borrowing to invest in new buildings and equipment more viable. Because standard economic models do not include secondary markets, the effect on the trade of existing assets is mostly ignored. Yet we can see that the majority of home purchases are simply trades of existing housing, and hence are a key mechanism through which low interest rates mostly cause higher prices without having much effect on new construction.

As you can see in those few months of investor data,  investor lending is not substantially more biased toward new housing than lending for owner-occupiers. For investors, 24% of loans have been for new housing in the past few months, just as 24% of loans to owner-occupiers have been.

The main difference seems to be that the typical existing home bought by owner-occupiers is more expensive than the typical new home, whereas for investors the mean value of lending to both is the same. 

Rent control is totally normal price-cap regulation

Bernie Sanders has smashed the Overton window. Rent control is going global.

Unfortunately, this means that the economics 101 brigade has come out in force to smugly Vox-splain their incorrect model of rent control and housing market dynamics.

The Onion’s Vox parody is so spot on I can’t stop laughing pic.twitter.com/Q9oQKFr46P

— 𝐂𝐚𝐫𝐥𝐨𝐬 (@ChuckEChaves) September 15, 2019

Regulating housing rents makes economic sense because homes are attached to land monopolies. Monopolies are inefficient, and regulations can improve outcomes. The two classic regulations are 1) a tax on monopoly super-profits, which is common for mineral and energy resources, and 2) a price cap, which is usually applied to network infrastructure, like rail, electricity, and water. If price caps sound to you a bit like rent control, then you would be spot on. They are rent control.

Rent control is not weird or unusual for regulating monopolies. The weird thing is that land is no longer considered a form of monopoly.

Let me explain how these two classic regulations would work in housing markets to socialise monopoly profits from housing locations.

A super-profits tax would work like this. When a new home is constructed, the owner would be able to seek the market rent. That first year’s market rent would become the regulated price that would attach to that home in a rental database. The home would still be allocated in the rental market using open market prices. But any gap between the market price and the regulated price would be 100% taxed. This is shown in the figure below.

If the market price fell below the regulated price for some reason, that loss would accumulate as a credit against future tax obligations when the market price increased again.

With a super-profits tax system housing resources, including new construction, are always allocated by market prices.

Since the financial crisis, rents have increased by roughly 25% in the United States. A quick guess-timate suggests that around a trillion dollars of rents are paid in the US each year. Had such a tax been implemented ten years ago it would now raise about $250 billion a year with no efficiency loss. In Australia, total housing rents have increased from around $30 billion to $45 billion in that period, meaning a housing super-profits tax would now raise around $10 billion per year (after adjusting for the increased housing stock).

The second way to regulate the land monopoly in the housing market is with price caps (rent controls). Here, the sitting tenant is protected from price increases that are not the result of additional housing investment or renovation but arise due to the favourable location-monopoly of the owner.

As before, market prices match tenants to housing and provide incentives for new construction. However, a sitting tenant is protected from price increases that arise from the location-monopoly. This only works if their tenure is secure, and they cannot be evicted as a way to change the rental price back to the market price.

The image below shows how the gap between market price and rent-controlled prices is a transfer to sitting tenants. If market prices fall below the regulated price, the tenant can have the option to renegotiate or move to pay the lower market price. Again letting markets decide resource allocations. It is only in periods of rapid price growth that sitting tenants are protected.

On balance, this type of regulation transfers some monopoly super-profits to tenants in the short-term but gives them back to owners as tenants relocate and homes are again allocated by market prices.

Either system of regulations will socialise some of the monopoly rents in housing markets. In fact, it is widely acknowledged that a reduction in volatility of returns can accelerate new housing investment. Recent studies also show that owners of older housing choose to accelerate redevelopment into more dense housing if their rents are regulated.

Both regulations are common in other monopolistic sectors of the economy. The main issue is that these regulations will transfer billions of dollars of value away from landlords, and landlords won’t like it. And the economic 101 brigade will always find a way to argue that policies to help the poor are bad for them.

Housing subsidy and UBI confusion

When the Australia government introduced a cash grant for first home buyers, the aggregate effect was to increase home prices by roughly the amount of the grant, quickly negating its effect on affordability.

This observation has led many people to mistakenly believe that giving cash grants in any form will pass through one-to-one into higher home prices (or rents). In discussions of all types of welfare—from UBI, to traditional welfare payments—this error comes up.

The error comes about because people fail to see that when given a choice, people spread their extra buying power across all the different types of goods they consume. An income subsidy is not the same as a subsidy for a particular type of expenditure.

Economists have been studying the way spending patterns vary with income for over 150 years. Ernst Engel noticed in 1857 that as incomes rise, households spend a lower proportion of their income on necessities like food. This observation became known as Engel’s Law, and the income-spending relationships for different goods became known as Engel Curves.

Housing, like food, is a necessity. As such, the share of income spent on housing usually falls as incomes grow. The Australian data shows that even for private renters—where one would expect competition from higher-income renters to bid up housing rents—the share of income spent on rent falls from nearly 50% of gross income for the lowest income quintile households to just 13% for the highest-income households.

This data might seem to imply that it is possible for up to 50% of a cash welfare payment to “pass through” to landlords for low-income households. But remember, this is not the marginal amount that would come out of extra income. Because the share of spending on housing falls as income rises, the spending on housing out of the extra income must be far lower than the average. In fact, across income quintiles in Australia, the marginal additional spending on housing per dollar of additional income sits tightly in the 5-7c range. It may be possible that long-run adjustments mean that more than this marginal amount is spent on housing out of extra income, but it will always be less than the average amount.

The story is rather different, however, if welfare payments are tied to a particular type of spending. This even more important in the case of housing, where the total stock changes extremely slowly and where landowners have monopolistic incentives to prefer price gains over investing in additional supply.

An example is if everyone received a fixed $1000 per month that could only be spent on housing. Because this money cannot be spread across the consumption basket, people would soon learn that they are best off using it to bid up the rent to access their preferred housing location. The macroeconomic reality is that this additional buying power will chase roughly the same number of dwellings, increasing their price.

The difference between a “general income subsidy” and a “housing expenditure subsidy” can be shown using Engel curves. The chart below shows three Engel curves for a household, with the orange representing housing. Blue represents other normal goods, where expenditure rises with income, but a bit faster than for necessities (as per Engel’s Law). The green curve is an inferior good. Household spend less on these goods after their income reaches a certain level.

A “general income subsidy” shifts the household up to a higher income level, and they spend more on all the types of goods in their consumption basket. The effect on housing expenditure is relatively small, as expected by our previous 5-7% assessment of marginal housing expenditure.

The next chart shows the effect of a “housing expenditure subsidy”. The total income of the household is unchanged. They are only able to direct the subsidy towards their housing expenditure. Here, the effect will be to boost buyer competition for scarce housing locations and increase home rents (or prices). This was the case with the first home buyers grant.

Though it is tempting to see them as quite similar, subsidising household incomes and subsidising a particular type of expenditure have rather different economic effects. 

Microeconomic success, macroeconomic failure

When I teach macroeconomics, I use a dog and bone analogy to demonstrate that the macro-economy is not equivalent to just “adding up” the micro.

Let’s see the analogy in action.

In the dog and bone economy, ten dogs repeatedly try to find nine bones buried in the yard. Each round, at least one dog misses out. We think that this outcome is undesirable— we can’t have an economy with over 10% dog “bone poverty” and perpetual “dog unemployment”!

Some astute dog economists notice that dogs that miss out on a bone are usually a little slower, or have some other traits that make them relatively poor performers. They reason that there is a “skills mismatch” that, if corrected, could solve the macro-economic problems in the dog economy.

These economists go the extra mile and conduct some randomised controlled trials on interventions that seem promising.

1. Give the dogs that miss out a head start
2. Provide the dogs that miss out advice about where to find the bones
3. Train the dogs that miss out to sniff out bones better

After trialling each of these interventions, the results come in. They are astounding!

In each policy experiment, dogs that missed out on finding a bone 75% of the time in the control group only missed out 5% of the time in the treatment group.

The researchers responded to media enquiries about their results. “This is the largest effect I’ve ever seen in a social science intervention,” they said.

If it can be replicated at scale, the experimenters may have hit on a powerful new tool for dismantling bone poverty in the dog economy. Policymakers are now looking to invest in expanding these programs in dog parks across the country.

I don’t know about you, but it always helps me to understand what is really going on when we talk in the abstract. In the dog economy, it is clear that regardless of the microeconomic success of these interventions, there is still going to be “dog poverty” and “dog unemployment” because of the macroeconomic conditions. There are always nine bones and ten dogs. At least one dog still misses out and experiences “dog poverty”.

Helping someone jump the queue for access to scarce resources is obviously going to help that individual. But it can’t help everyone in the queue.

And yet, these microeconomic “queue-jumping” policies are politically attractive. Job training is widely thought to be an important tool for solving unemployment. But if the unemployed are competing over scarce jobs, then job training can only change the preferred ordering of candidates.

A recently popular policy in this vein has been “intensive housing counselling”. This involves lobbying landlords on behalf of housing voucher tenants and advising these tenants to move to “high opportunity areas”. Not surprisingly, these tenants took up the professional advice and assistance given to them.

As one tenant noted, after deciding where they would like to move, the housing counsellors “pretty much took care of the rest. I gave them my information, they gave my information to the leasing office, they applied for me, and they helped with the first month’s rent and the renter’s insurance for a year.”

Making renting and finding a home easier is great. I’m not going to argue against that.

But what puzzles me is this. Like the nine dogs and ten bones, not everyone in a “low opportunity area” can move to a “high opportunity area”. And in fact, as people start to move out of these “low opportunity areas” those areas will have even fewer economic opportunities for residents that ultimately move into them! The policy can’t “add up” to the macro, despite its success at the micro-level.

So what sort of policies do work at a macro level?

In the dog economy, the thing that works is to compress the “bone distribution”—take the nine bones, cut off one-tenth of each bone, and let the ten dogs access 9/10ths of a bone each. Alternatively, have a handler keep some bones in reserve to share amongst the dogs that miss out. Macroeconomic success requires a mechanism that changes the nature of the game itself, rather than the individual behaviour within it.

Two problems with opportunity cost

If there is one idea that defines economics, it is opportunity cost. Unfortunately, muddled thinking about this idea means that across the economics discipline it is applied rather inconsistently. Economists often use the word to mean whatever they want it to mean. 

In its most basic form, opportunity cost just means your next best alternative use of resources. What opportunity did you forgo to undertake this action instead of an alternative? But it gets much more difficult to translate this idea consistently into more detailed economic theories.

I want to highlight two big inconsistencies with the use of opportunity cost in economics. To do that I want to start with a question that triggered a mini-controversy in the discipline a few years back when it was revealed that economists did worse than chance in answering a multiple-choice textbook question about opportunity cost.

The question was:

You won a free ticket to see an Eric Clapton concert (which has no resale value). Bob Dylan is performing on the same night and is your next‐best alternative activity. Tickets to see Dylan cost $40. On any given day, you would be willing to pay up to $50 to see Dylan. There are no other costs of seeing either performer.
What is the opportunity cost of seeing Eric Clapton? A. 0, B. 10, C. 40, D. 50.

According to the textbooks, the answer is B.

There are two mistakes here.

Comparison with different costs

First, the two given alternatives have different resource costs. If you see Dylan you have $40 less to spend. Therefore, a clean comparison of opportunity costs requires us to compare these alternatives

A. See Clapton for free.
B. See Dylan that night and have $40 less to spend.

If we don’t account for the full costs of each alternative, we end up with ridiculous scenarios, like comparing the profit from investing $1m with the profit from investing $1k. It makes no sense when we abstract into raw financial terms, and it makes no sense here either.

Strictly speaking, the correct answer is $10 minus the net benefit from my next best use of $40. But then again, maybe I don't know what opportunity cost is either!

Alternative options are not discrete

Another problem with opportunity cost is that, in reality, there is a continuum of alternatives to any action. The next best option to Alternative A is usually doing Alternative A but cutting some corners slightly. In this case, if seeing the Clapton concert is Alternative A, then seeing Clapton and going to the bathroom when your favourite song is played might be a “next best” alternative.

We could, if we want, break out any of the discrete alternative actions into an infinite array of alternatives. Each of those could be broken out again until we have a continuum.

If we zoom in on this continuum, then the opportunity cost is always equal to best Alternative, and even the opportunity cost of the best Alternative is itself.

This point is important. If, for example, we think that supply curves include opportunity costs of resources, then economic profits are always zero or below by definition.

In a topic I study, property markets, this is also important. Many people think that the second-best alternative use of land sets the price. For example, in regard to the price of land for housing:

…in the absence of any restrictions on supply, the price of raw land on the fringes should be tied reasonably closely to its value in alternative uses, such as agriculture.

Why is agriculture the next best alternative to housing? Surely there are multiple residential subdivision options that are alternatives, and some will be better than others.

Property valuers (appraisers) are clear that the value of property rights comes from its highest and best use, but for some reason many economists think they know better. Valuers test out the various legal options for land use to determine which one provides the highest value to land, and it is this use that determines its value.

The opportunity cost logic, in this case, becomes more absurd when we think about the case where there are three possible legal uses of land—say agriculture, industrial, and residential (in order of value). If the second-best alternative sets the price, then you can make the land cheaper by regulating against the second-best use of industrial development, making agricultural use the second-best alternative and decreasing land prices for housing.

And I haven't even considered the case when there is only one allowable use of land. Doesn't this make the second-best use to do nothing, therefore bringing the land price to zero?

Like many seemingly insightful economic ideas opportunity cost is less powerful than it appears and often confuses more than it clarifies. 

NOTE: Here are some recent articles that follow up on the original survey question that show just how varied the interpretations of opportunity cost can be.