In recent years, residential real estate prices have received enormous attention from policymakers, the media, and academic researchers. Much of this interest was motivated by sizeable swings in house prices in many countries, particularly in the US and the UK. The top panel of Figure 1 plots real house prices in the UK, showing a strong increase in prices from the late 1990s to 2007, a pronounced reversal during the financial crisis 2007-2009, and a renewed boom after that. The media often describe these periods of strongly increasing prices as exhibiting the features of a housing bubble (e.g., Businessweek 2014). A sizable academic literature, recently reviewed by Glaeser and Nathanson (2014), has also speculated about the presence of bubbles in housing markets over this period.

**Figure 1**. UK house prices (top), average discount of 999-year Leaseholds relative to Freeholds (bottom).

Market efficiency, and in particular the existence of bubbles, is one of the fundamental debates in finance, and has received renewed attention in the discussions surrounding last year’s Nobel Prize (Fama 2013, Shiller 2013). The workhorse model of bubbles is based on a failure of the so-called ‘no-bubble condition’ that requires the present value of a payment occurring infinitely far in the future to be zero. We call this financial claim the ‘bubble asset’. A positive price for this asset implies a bubble because it attaches present value to a claim that postpones any payment indefinitely. The asset can have positive value because each person buys the bubble asset with the expectation of reselling it to someone at a higher price. This expectation of ever increasing prices can continue forever because the bubble has infinite maturity. While this is not the only model of bubbles, it is a prominent model in both macroeconomics and finance.

The natural test for this type of bubble is to verify whether assets that only pay off infinitely many years from now do, in fact, have zero or positive present value. This direct test, however, has been impossible to conduct because we normally do not observe traded claims to payments that only occur at (even approximately) infinite maturity. We generally either observe prices of claims to cash flows at all horizons between now and infinity (e.g., equities), or prices of claims to cash flows for finite, but relatively short, horizons (e.g., bonds).

# The joint hypothesis problem and a solution

Due to the challenges with measuring the price of extremely long-run financial assets, the academic literature has resorted to indirect, model-dependent tests of bubbles, thus incurring the joint hypothesis problem: Every test of a bubble is a joint test of the presence of the bubble in the data and the validity of the model applied by the econometrician.

In Giglio, Maggiori, and Stroebel (2014), we provide direct tests for the presence of infinitely-lived bubbles. We exploit a unique feature of residential housing markets in the UK and Singapore, where property ownership takes the form of either very long-term leaseholds or freeholds. Leaseholds are temporary, pre-paid, and tradable ownership contracts, often with initial maturities of 999 years, while freeholds are perpetual ownership contracts. The price difference between leaseholds with extremely long maturities and freeholds for otherwise identical properties captures the present value of rental income starting at leasehold expiry, and thus provides an estimate of the price of the bubble asset.

In particular, the leaseholder owns the property for 999 years. The freeholder owns the property not only for the first 999 years, but also for all periods after that date. Therefore, the difference in the price of the freehold and the leasehold reveals the value today of owning the property 999 years from now. Ownership of a house 999 years from now is essentially a claim to the bubble asset. It entitles the owner to a single payment (the value of the house) in 999 years. This is so far in the future that it should have no value today, even if discounted at extremely low rates (say 1% per year).

Our empirical analysis is based on proprietary information on the universe of property sales in the UK and Singapore between 1995 and 2013. These data contain information on transaction prices, leasehold terms, and property characteristics such as location and structural attributes. We estimate the bubble component by comparing the prices of leaseholds with maturities between 700 years and 1,000 years to the prices of freeholds across otherwise identical houses. We use hedonic regression techniques to control for possible heterogeneity between leasehold and freehold houses.

We find that extremely long leaseholds are valued identically to otherwise similar freeholds. Our results, therefore, show no evidence for infinitely-lived bubbles in these markets. We find this to be true even in geographic regions where people argued that housing bubbles were likely to be present (e.g., Prime Central London). The bottom panel of Figure 1 plots the percentage price discount of 999-year leaseholds relative to identical freeholds, year by year. The candlesticks show, for each year, the point estimate (the wide bars), and the two standard deviation confidence interval (narrow bars). The no-bubble condition held remarkably well – the price discount is small and not statistically different from zero – in every year since 1995. In particular, we find no evidence of infinitely-lived bubbles even during the house price boom that culminated in 2007.

It is important to emphasise that our empirical set-up is, if anything, biased toward finding a bubble. The obvious concern, in fact, is that very long maturity leasehold contracts might be *less* valuable than freehold contracts for reasons unconnected to their finite maturity, for example due to the possibility of a ‘full ownership premium’ based on psychological preferences. We also note that our article tests infinitely-lived bubbles and remains silent on bubbles that can occur in finite horizon.

# Concluding remarks

We conclude that, while much of the policy and media debate around house prices in Singapore and the UK evolves around the existence of bubbles, our results show that no infinitely-lived bubble was actually present.

# References

Businessweek (2014), “A Feeding Frenzy for London Homes Triggers Talk of a Bubble”.

Fama, Eugene F. (2013), “Two Pillars of Asset Pricing”, Nobel Prize Committee.

Giglio, Stefano, Matteo Maggiori, and Johannes Stroebel (2014), “No-Bubble Condition: Model-Free Tests in Housing Markets”, NBER Working Paper 20154.

Glaeser, Edward L, and Charles G Nathanson (2014), “Real Estate Bubbles.” Unpublished Manuscript Harvard and Northwestern Universities.

Shiller, Robert J. (2013), “Speculative Asset Prices”, Nobel Prize Committee.