Discounting the very distant future

Stefano Giglio, Matteo Maggiori, Johannes Stroebel, 21 June 2014

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Many important policy decisions require a consideration of costs and benefits that arise in the distant future. For example, many of the costs of climate change occur 100 or more years from now, yet actions to reduce greenhouse gas emissions have to be taken today to avert those long-run costs. In recent weeks, the Intergovernmental Panel on Climate Change mitigation report, or UN climate change report, presented and discussed different options for reducing such emissions, but contended that “most mitigation strategies have costs in the present and yield benefits in the future. Policy making involves assessing the values of these benefits and costs and weighing them against each other.”

A crucial step in evaluating distant costs and benefits is the choice of an appropriate discount rate. How much do individuals value cash flows that arise hundreds of years from now and will accrue to future generations? The literature on environmental policy has long focused on the importance of these long-run discount rates in assessing the benefits of policies such as reducing carbon emissions (Weitzman 2001, 2013, Barro 2013, Gollier 2012, Pindyck 2013). For example, Stern (2007) calls for immediate action to reduce future environmental damage based on the assumption of very low discount rates, arguing that while agents discount the future over their lifetimes, they have an ethical impetus to care about future generations. This assumption has been criticised amongst others by Nordhaus (2007), who points out that the private return to capital is 4-6%.

Much of this disagreement about the appropriate long-run discount rate is driven by the fact that little direct empirical evidence exists on how households actually discount payments over very long horizons because of the scarcity of finite, long-maturity assets necessary to estimate households' valuation of very long-run claims.

Estimating valuations of very long-run (but finite) assets

In Giglio, Maggiori and Stroebel (2014), we provide direct estimates of households' discount rates for payments very far in the future, by studying the valuation of very long (but finite) assets. 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 with maturities ranging from 99 to 999 years, while freeholds are perpetual ownership contracts. The price discount for very long-term leaseholds relative to prices for otherwise similar properties that are traded as freeholds is informative about the implied discount rates of agents trading these housing assets. This allows us to gather information on discount rates much beyond the usual horizon of 20-30 years spanned by bond markets.

Our empirical analysis is based on proprietary information on the universe of residential property sales in the UK (2004-2013) and Singapore (1995-2013). These data contain information on transaction prices, leasehold terms, and property characteristics such as location and structural attributes. We estimate long-run discount rates by comparing the prices of leaseholds with different maturities to each other, and to the price of freeholds across otherwise identical properties. We use hedonic regression techniques to control for possible heterogeneity between leasehold and freehold properties; this allows us to identify price discounts associated with differences in lease length.

Figure 1. Estimated leasehold discounts for the UK

Figure 1 presents estimates from the UK of the log difference in prices between leaseholds with varying remaining maturity at the time of sale and otherwise identical freeholds. Leaseholds with 80-99 years remaining are valued about 15% less than otherwise identical freeholds; leaseholds with maturity of 100-124 years are valued 10% less than freeholds. In other words, households attach substantial present value to owning the housing asset in 100 or 125 years. There are no price differences between leaseholds with maturities of more than 700 years and freeholds.

In Giglio, Maggiori and Stroebel (2014), we document how the differences in prices between leaseholds and freeholds can be attributed to their different duration (i.e., the fact that a freehold entitles the owner to ownership of the property after the leasehold expires). We also show that these price differences cannot be explained by dimensions unrelated to contract duration. For example, we can exclude that price differences are driven by unobserved differences in the properties trading as freeholds and leaseholds, since we show that they have the same annual rent. We also show that other possible concerns, such as differences across contracts in the presence of covenants, the liquidity of the assets, financing frictions, or differences in buyer characteristics, cannot explain the observed price discounts.

We use these estimated price discounts to back out the implied discount rate that households use to value cash flows to housing that arise more than 100 years from now. We find the discount rate for very long-run housing cash flows to be about 2.6% per year. Interestingly, we find similar implied discount rates in both the UK and in Singapore – two countries with very different institutional settings.

The estimated discount rate reveals how today’s households value payoffs to future generations, and, as such, has implications for intergenerational fiscal policy and climate change policy. In particular, our estimate of 2.6% provides some empirically-grounded guidance for choosing discount rates to evaluate long-term projects where the benefits arise hundreds of years from now. While the full implications of our findings for climate change policy depend on the precise modelling of the risks inherent to climate change and housing, our result of low long-run discount rates provides early evidence that agents are more willing than previously thought to invest today for the benefit of future generations, particularly if such benefits occur with certainty.

References

Barro, Robert J (2013), “Environmental Protection, Rare Disasters, and Discount Rates.” National Bureau of Economic Research Working Paper 19258.

Giglio, Stefano, Matteo Maggiori, and Johannes Stroebel (2014), “Very Long-Run Discount Rates.” National Bureau of Economic Research Working Paper 20133.

Gollier, Christian (2012), “Evaluation of long-dated investments under uncertain growth trend, volatility and catastrophes.” Toulouse School of Economics (TSE) TSE Working Papers 12-361.

Nordhaus,William D (2007), “A Review of the Stern Review on the Economics of Climate Change”, Journal of Economic Literature, 45(3): 686–702.

Pindyck, Robert (2013), “Climate Change Policy: What Do the Models Tell Us?” Journal of Economic Literature, 51(3): 860–872.

Weitzman, Martin L (2001), “Gamma Discounting”, The American Economic Review, 91(1): 260–271.

Weitzman, Martin L (2013), “Tail-Hedge Discounting and the Social Cost of Carbon”, Journal of Economic Literature, 51(3): 873–882

Topics: Environment, Financial markets
Tags: long-run discount rates

Assistant Professor of Finance at Booth School of Business, University of Chicago
Assistant Professor of Economics at the Department of Economics, Harvard University
Assistant Professor of Finance at the Stern School of Business, New York University

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