Many of the costs associated with climate change occur hundreds of years into the future, yet actions to mitigate those long-run costs have to be taken today, as evidenced only recently at the United Nations conference on climate change in Paris.

In evaluating the trade-off between immediate costs and potentially uncertain long-run benefits, even small changes in discount rates can dramatically alter policy conclusions. As an example, assume that an investment to reduce carbon emissions costs $3 billion, and is expected to avoid environmental damages worth $100 billion in 100 years. At a discount rate of 3%, the present value of those damages is $5.2 billion and the project seems appealing. At an only slightly higher discount rate of 5%, the present value of the investment drops by an order of magnitude to $760 million, and the project no longer appears attractive.

With little direct empirical evidence on the way households discount payments over very long horizons, academics and policymakers have mostly resorted to theoretical arguments or have tried to infer discount rates from realised returns of traded assets such as private capital, equity, bonds, and real estate. Not only has this approach produced widely varying discount rate suggestions, ranging from close to 1% (Stern 2006) all the way up to almost 5% (e.g. Gollier 2013, Nordhaus 2013), it also tends to ignore important considerations regarding the maturity and risk properties of such investments.

To develop this point, we may think of any asset as a portfolio of claims to single payments at specific horizons. For example, consider an investment that pays off some cash flows for the next ten years. It can be thought of as a portfolio of claims to ten single yearly cash flows. Asset pricing theory teaches us that the rate at which each of these expected payments should be discounted depends on the situation in which the payment is realised – payments that materialise primarily when investors are doing relatively well anyway are less desirable and hence more risky. They should therefore be discounted at a higher rate. Since such risks may vary by horizon, each of the single payments of the portfolio might have a different per-period discount rate. The average rate of return to an asset only captures the value-weighted average discount rate applied to all its payments. Therefore, it is not necessarily informative for discounting the payments of climate change investments, which tend to occur at much longer horizons and might have substantially different risk profiles.

## Estimating a term structure of discount rates

In recent work, we provide estimates of the term structure of discount rates for an important asset class – real estate – over a horizon of hundreds of years (Giglio *et al *2015a). We start by estimating the average return to real estate, which we find to be above 6%. In combination with recent estimates from Giglio *et al *(2015b), who find discount rates for real estate payments 100 or more years into the future to be around 2.6%, this implies a downward-sloping term structure of discount rates for real estate.

To estimate the average return to real estate for the US (1953-2012), the UK (1985-2012), and Singapore (1989-2012), we employ two complementary approaches. The balance sheet approach is based on information from the three countries’ national accounts. It combines the total value of residential real estate and housing with the total value of real estate and housing services consumed by households (the ‘dividend’ from the real estate and housing stock). After controlling for the growth of the real estate and housing stock over time, we obtain a return series for a representative property. The price-rent approach constructs a time series of returns by combining a house price and a rental price index with a price-rent estimate for a baseline year. After adjusting both results for inflation and subtracting maintenance costs, depreciation, and any tax-related decreases in returns, we obtain real expected returns for real estate that are above 6% for the countries we consider.

These return estimates are above the risk-free rate and imply a positive real estate risk premium. Consistent with the notion of real estate as a risky asset, Panel A of Figure 1 shows the average reaction of real house prices to financial crises. Financial crisis dates for 20 countries over the period 1870-2013 are based on Schularick and Taylor (2012), Reinhart and Rogoff (2009) and Bordo *et al.* (2001). The onset of a crisis is normalised as time zero and the house price level is normalised to one at the beginning of the crisis. On average, house prices rise in the three years leading up to a crisis, peak just before the onset of the crisis, and fall by up to 7% in the following three years. Similarly, Panel B of Figure 1 shows the average behaviour of house prices during rare disasters as identified by Barro (2006) and Barro and Ursua (2008). Consumption reaches its trough (normalised as time zero) after declining for three years. House prices fall along with consumption over these first three years, but fail to recover along with consumption over the following three years. We also demonstrate that real house prices are positively correlated with consumption growth in general. Both of these patterns contribute to the riskiness of real estate as an asset.

**Figure 1**. House price riskiness

For an estimate of the long-run discount rate hundreds of years into the future, we rely on recent work by Giglio *et al *(2015a). In the UK and Singapore, residential properties trade either as freeholds, which are permanent ownership contracts, or as leaseholds, which are pre-paid and tradable ownership contracts with finite maturities between 99 years and 999 years. By comparing the relative prices of leasehold and freehold contracts for otherwise identical properties, they estimate the present value of owning a freehold after the expiration of the leasehold contract. Figure 2 reports the estimates from the authors for the UK between 2004 and 2013. It shows that price discounts of leaseholds are strongly associated with maturity. In particular, leaseholds with remaining maturities between 100 and 124 years trade at a discount of 11% as compared to infinite-maturity freeholds. Put differently, at least 11% of the value of a freehold is due to payments accruing more than 100 years into the future. After ruling out alternative explanations, the authors conclude that this implies a discount rate of 2.6% for payments more than 100 years into the future. In combination with an average rate of return of more than 6%, this implies a downward-sloping term structure of discount rates for real estate.

This result indicates that for a major asset class, i.e. real estate, the term structure of discount rates is very different across maturities, highlighting the importance of using horizon-specific discount rates when thinking about discounting the distant future.

**Figure 2**. Estimated leasehold discounts for the UK

## The discount rate for long-run climate hedging investments is below 2.6%

Our empirical evidence shows that real estate is a risky asset. Its returns are positively correlated with consumption growth and it performs particularly poorly in times of disaster. Therefore, appropriate discount rates for each of its payments have to be *above* the risk-free rate at all horizons. For any long-run investment in climate change abatement that acts as a hedge against climate disasters on the other hand, discount rates have to be *below* the risk-free rate, and hence below the long-run discount rate of 2.6% that we estimated for risky real estate. This is a simple yet informative result.

Indeed, climate change abatement investments are often considered as hedges in the literature (Barro 2013, Lemoine 2015, Wagner and Weitzman 2015, Weitzman 2012). Our estimate also provides a tight bound that is only consistent with the lowest of the three certainty-equivalent constant discount rates of 2.5%, 3%, and 5% per year suggested by the interagency group tasked with valuing reductions in carbon dioxide by the US government (Greenstone *et al *2013). Finally, this upper bound is also lower than numerous estimates in the existing academic literature on climate change abatement that are as high as almost 5% (Nordhaus 2013, Gollier 2013). It is more consistent with a discount rate of 1.4% suggested by Stern (2006), or long-run discount rates close to the risk-free rate (Weitzman 2012).

## References

Barro, R J (2013) “Environmental protection, rare disasters, and discount rates”, NBER Working Paper 19258.

Barro, R J and J F Ursua (2008) “Macroeconomic crises since 1870”, *Brookings Papers on Economic Activity*, 39(1): 255–350.

Bordo, M, B Eichengreen, D Klingebiel and M S Martinez-Peria (2001) “Is the crisis problem growing more severe?”, *Economic Policy*, 16(32): 51–82.

Giglio, S, M Maggiori and J Stroebel (2015a) “Very long-run discount rates”, *The Quarterly Journal of Economics*, 130(1): 1–53.

Giglio, S, M Maggiori, J Stroebel and A Weber (2015b) “Climate change and long-run discount rates: Evidence from real estate”, NBER Working Paper 21767.

Gollier, C (2013) “Evaluation of long-dated investments under uncertain growth trend, volatility and catastrophes”, Toulouse School of Economics TSE Working Papers 12-361.

Greenstone, M, E Kopits and A Wolverton (2013) “Developing a social cost of carbon for US regulatory analysis: A methodology and interpretation”, *Review of Environmental Economics and Policy*, 7(1): 23–46.

Lemoine, D (2015) “The climate risk premium”, Available at SSRN 2560031.

Nordhaus, W D (2013) *The climate casino: Risk, uncertainty, and economics for a warming world*, Yale University Press.

Reinhart, C M and K S Rogoff (2009) *This time is different: Eight centuries of financial folly*, Princeton University Press.

Schularick, M and A M Taylor (2012) “Credit booms gone bust: Monetary policy, leverage cycles, and financial crises”, *American Economic Review*, 102(2): 1029–1061.

Stern, N (2006) *Stern Review on the Economics of Climate Change*, London, UK: Her Majesty’s Treasury.

Wagner, G and M L Weitzman (2015) *Climate shock: The economic consequences of a hotter planet*, Princeton, NJ, Princeton University Press.

Weitzman, M L (2012) “Rare disasters, tail-hedged investments, and risk-adjusted discount rates”, NBER Working Paper 18496.