Managing the UK National Debt 1694-2017

We construct a new monthly dataset for UK government debt over the period 1694 to 2017 based on price and quantity data for each individual bond issued. This enables us to examine long run fiscal sustainability using the theoretically relevant variable of the market value of debt, and investigate the historical importance of debt management. We find the general implications of the tax smoothing literature are replicated in our data, especially around financing wars, although we find major shifts over time in how fiscal sustainability is achieved. Before the 20th century, governments continued to pay bond holders a high rate of return and achieved sustainability through running fiscal surpluses but since then governments have relied on low growth adjusted real interest rates. The optimal debt management literature tends to favour the use of long bonds but we find the government would have been better off over the 20th century issuing short bonds. The contrast with the literature occurs because of an upward sloping yield curve and long bonds rarely providing fiscal insurance. This is particularly true during periods of financial crises when falling interest rates lead to sharp rises in the price of long bonds, making them an expensive form of finance. We examine the robustness of our conclusions to liquidity effects, rollover risks, buyback operations and leverage. In general, these do suggest a greater role for long bonds but do not overturn an issuance strategy based mainly on short term bonds.


Introduction
Managing the national debt is a key economic challenge for any government and requires answering two perennial questions: what is the appropriate level of government debt? and what type of debt should governments issue?
The theory informing the right level of national debt starts from the implication of the government's intertemporal budget constraint that the market value of government debt has to be matched by the net present value of future primary surpluses. If we add the assumptions of distortionary taxes, no default and incomplete markets then the prescription is that the national debt should follow a random walk, as shown by Aiyagari et al (2002). In other words, there is no speci…c right level for the national debt other than limits aimed at ruling out Ponzi schemes. 1 The implication of this was noted already by Adam Smith (1776), "Great Britain seems to support with ease a debt burden which, half a century ago, nobody believed her capable of supporting". 2 In terms of what type of debt governments should issue, a growing consensus has emerged that long bonds provide considerable advantages (Angeletos (2002), Barro (2003), Nosbusch (2008), Lustig, Sleet and Yeltekin (2009)). If the market value of long bonds falls when there are adverse persistent government expenditure shocks then long bonds provide the government with a form of "…scal insurance". The negative covariance between market values and expenditure shocks means, through the intertemporal budget constraint, that taxes have to rise by less than otherwise and hence long bonds are appealing. However, these advantages of long bonds are not uncontested. Buera and Nicolini (2004) and Faraglia el al (2010) show that exploiting the …scal insurance properties of long bonds requires the government to take portfolio positions that are extreme, volatile and potentially unstable, whilst Faraglia et al (2017) show how the advantages of long bonds are much reduced when allowance is made for the reluctance of governments to buyback debt each period.
This paper seeks to provide insight on managing the national debt and answers to the two key questions by utilising new empirical evidence. On the basis of archival research at the Bank of England and the British Library, we construct a new and detailed database showing how the UK national debt has been managed in practice from 1694 to 2017. Key to this dataset is the fact that it is built up from monthly price and quantity data based on each individual bond issued by the government. The breadth and granularity of our data provides two major advantages. The …rst is that it enables us to examine over 323 years the theoretically relevant concept of the market value of government debt rather than the more commonly used amount outstanding. Given our dataset includes upwards of 60 business cycles, 6 major wars and 6 major …nancial crises, it provides a rich understanding of how …scal policy has operated across a range of di¤erent macroeconomic contexts. The second advantage of our dataset is that its gilt-by-gilt foundations allows us to empirically examine the contribution of debt management towards achieving …scal sustainability. By performing historical decompositions and counterfactuals, our dataset enables an assessment of a number of claims made in the optimal tax and debt management literatures and provide insight into observed debt management.
The paper is organised as follows. In Section 2 we outline our dataset and how it is constructed. We 1 See Reinhart and Rogo¤ (2009) for a recent empirically-based analysis documenting apparent debt ceilings 2 The historian Macauley (1899) is even more forthright "At every stage in the growth of debt it has been seriously asserted by wise men that bankruptcy and ruin were at hand. Yet still the debt went on growing, and still bankruptcy and ruin were as remote as ever". provide a detailed narrative of UK public …nances over this period highlighting a number of features about debt structure and management. Key to our analysis is the use of holding period returns to calculate the cost of government funding. Therefore Section 3 derives zero coupon yield curves and calculates the total holding returns for the universe of bonds issued, taking into account both coupon payments and revaluations. Section 4 turns to understanding debt dynamics and the role of macroeconomic variables and debt management in achieving …scal sustainability over the whole sample period, various sub-samples and speci…c episodes such as wars and …nancial crises. In Section 5 we utilise the gilt-by-gilt nature of our dataset and consider alternative debt management policies, performing ex post counterfactuals to assess their performance relative to actual outcomes. Whilst the optimal debt management literature tends to favour the use of long bonds, we …nd in our dataset that relying on short bonds would have led to better out-turns. However, focusing solely on short term bonds raises a number of risks and concerns that tend to occupy actual debt management operations. In Section 6 we extend our analysis to consider whether our …ndings are robust to issues of liquidity and price shifts, rollover risks, leverage and buybacks. We …nd that whilst some of these factors, especially rollover risk, do introduce a greater role for long term bonds, it is still the case that an issuance strategy based on a majority of short term bonds is found ex post to outperform issuance of longer bonds. A …nal section concludes.

UK Government Debt 1694-2017
The starting date for UK government debt is widely seen as 1694 when King William III used a syndicate of merchants to sell debt to …nance the Nine Years'War. 3 This syndicate went on to become the Bank of England and so data on the level of UK government debt is available from this date onwards. 4 The government did borrow before 1694 but mainly made use of tallies, e¤ectively bills backed up by speci…c taxes or excise duties falling due over short term horizons. The year 1694 is widely seen as marking the beginning of the institutional framework for government debt which supported the growth of the British economy and ultimately the British empire (Brewer (1989)), although debt issuance in the early years was understandably developmental. 5 Many of the initial loans took an unconventional form by current standards, including annuities and lotteries as parts of their design, but alongside these were a number of perpetual bonds o¤ering di¤erent coupon rates. By 1752 these perpetual bonds were consolidated ("consols") in a smaller number of distinct stocks o¤ering …xed coupon payments and the bond market took a more recognisably modern form. However, it was not until the early 20th century that …nite dated long bonds were issued 6 , marketable debt in the 18th and 19th century consisting entirely of perpetuals/consuls and short term bills. 3 Technically the debt only became UK debt when the United Kingdom was created by the Act of Union in 1707 which joined together the Kingdoms of England and Scotland. 4 http://www.ukpublicspending.co.uk/debt_history. The initial loan from the Bank of England was for £ 1.2million at an 8% interest rate and with a £ 4,000 management fee. It has now been repaid. 5 See Dickson (1967) for a comprehensive history and detailed account of the development of the UK government debt market in the aftermath of the Glorious Revolution of 1688. 6 The …rst …xed term gilt in our sample period (4.5% War Loan 1925-45) was issued November 1914.

Quantities
We use data on the quantity of UK government debt for each gilt 7  . Currently the main forms of outstanding non-marketable debt are a range of retail savings products sold by the National Savings Authority, such as premium bonds (a form of lottery) and investment accounts.
The series for total debt in Figure 1 generally shows the same swings and oscillations as that for marketable debt. In the early years of our sample loans and annuities were the main component of overall debt, but as the market developed during the 18th century the amount of non-marketable debt declined. However, WWI and WWII required a large increase in debt and a substantial amount was in non-marketable form (War Loans) such that by 1947 the debt mix was more 50-50. Subsequent repayment of those loans and some partial default nevertheless rendered most of the government debt again marketable by the end of our sample period.
The overall path of the debt to GDP ratio is well known and re ‡ects the twists and turns of British history. The 1700s sees a series of wars with only brief periods of peace and reductions in debt. Wars became increasingly expensive and led to ever higher levels of debt, peaking with the end of the Napoleonic Wars in 1815 and then beginning a long term decline. Debt then experiences a large increase because of WWI; further increases in the 20s due to weak growth; a further jump because of WWII; a long period of decline after WWII 7 UK government bonds are called "gilts" as originally purchasing the bond meant receiving a gilt edged security as proof of purchase.
until the late 90s (with various cyclical ‡uctuations) and then from the late 90s a ‡attening of the trend and signs of a modest increase before a sharper rise and higher trend in the wake of the 2007/8 Global Financial Crisis. Debt rises sharply after the 2007/8 Financial Crisis, reaching above 100% of GDP but ending the sample slightly below the average for the entire period. 8 The ‡uctuations in Figure 1 re ‡ect only issuance and redemptions over time because the UK government has never formally defaulted on any of its marketable debt. There are though a number of "conversions"in our dataset. UK gilts were redeemable by the government when their value rose above par, so on several occasions the government used this as an opportunity to retire gilts paying a high coupon and reissue gilts paying a lower coupon. This process was called a "conversion" and was often used to reduce the interest payments on debt. Anyone not wishing to switch to the lower coupon bond received payment at par. Reinhart and Rogo¤ (2009) classify one such conversion (the conversion in 1932 of the 1917 War Loan which had been callable since 1929 and was converted from a 5% to a 3.5% stock) as a default but regardless of how we classify this issue our dataset re ‡ects the change -it counts as retirement of an existing bond and the re-issuance of a new one.
The case of non-marketable debt is more complicated, especially regarding US loans. There was an outright default on some WWI loans from the US, connected to Germany's own debt default to the UK, as well as various incidents of suspension of payments and changes to the payment pro…le for the WWII loans. Our focus is however solely on marketable debt so these issues do not impact upon our analysis.
The long sweep of more than 300 years of data in our sample is ideal for considering the long run properties of debt. Whether or not debt possesses a unit root and its persistence relative to other macroeconomic variables has been a mainstay of the tax smoothing literature. Figure 2 plots Cochrane's (1988) measure of persistence for debt, GDP, government expenditure and the primary surplus in our data. This measure is de…ned as (1=k)V ar(y t y t k ) and tends to 0 if a variable is made up of purely stationary components, tends to 1 if it is a unit root, and is greater than 1 if it shows greater than unit root persistence. Figure 2 con…rms the Barro (1979) and Aiyagari et al (2002) …nding that debt shows unit root persistence and the Marcet and Scott (2009) observation that debt shows more persistence than any other variable. This is consistent with the notion of debt playing a bu¤er role in absorbing large temporary expenditure shocks, and implies that bond markets do not provide the insurance that a complete market paradigm would suggest. 9 In other words, over the last 323 years it is debt that has been the main mechanism absorbing …scal shocks.

Instruments
Whilst the debt management literature tends to focus on the relative merits of short versus long run bonds, hardly any attention is given to the actual number of bonds a government issues, something our dataset enables us to document. Figure 3 Figure   3(c) shows that the average size of each distinct gilt (as a percentage of GDP) has shown a near continuous decline over our sample period, except at the end where it slightly increases. 12 The increase in the number of gilts issued is not then simply a result of ‡uctuations in the level of debt, but a change in behaviour by government debt managers. 13 1 0 A gilt is distinguished by its date of original issuance, its original maturity and its stated coupon rate, e.g., if a twenty year gilt were issued in 1953 and a ten year gilt in 1963 then in 1963 these would count as two distinct gilts, despite them both having ten years remaining to maturity. In some instances the government would "top up" previous issues of gilts and we do not count these top ups as distinct. 1  issuance of undated bonds at the time, but found no investor support. 1 2 This is due to the retirement of Consols, which were the oldest vintage of government bonds and were relatively small in size compared to modern day issuance. The retirement of Consols also explains why the number of bonds retired shows a sharp rise towards the end of Figure 2b. 1 3 There are numerous potential explanations for this, e.g., exploiting the whole of the yield curve in order to improve debt  Figure 4 shows the maturity structure of government debt and its evolution over the period. The main trend has been a move away from a total reliance on consols to a mix of consols and long gilts, and then an increasing use of short and medium term gilts. However, by the end of the sample there is still a strong preference for longer gilts, with 60% of bonds outstanding of maturity greater than 8 years. In July 2017 the weighted average time to maturity of UK government debt was 15.4 years -more than 10 years higher than the US and the only OECD government with an average debt maturity greater than 10 years. management, concerns about concentrating debt issuance at certain maturities because of rollover risk, the fear of prices being adversely a¤ected by large issues, or a desire to create a market in risk free securities at a range of di¤erent maturities.  shown by the presence of downward diagonals, government tends not to buyback debt until it matures at its redemption date. 14 ;15 Closer inspection shows that only 8 of the 537 gilts issued over this time period were redeemed before their maturity date. In other words, once issued, governments tend not to repurchase gilts until at or close to their redemption date. The other feature of Figure 5, related to Figure 3a, is how the government has increasingly …lled the maturity spectrum over time by seeking to …ll "holes", preferring to issues gilts at each maturity.

Prices
We have so far examined the volume of bonds outstanding but key to the intertemporal budget constraint is the link between the market value of government debt and the net present value of future primary surpluses.
Constructing market prices for our debt series is therefore crucial for our analysis.
The market prices of individual gilts for 1694-1887 are taken from the Global Financial Data database, which draws on the database of Neal (1990)  onwards. We combine our price data for each gilt with the amounts outstanding to derive the series for the market value of government debt shown in Figure 6.
For most of our sample period the market value has been less than the par value. In the 18th century bond prices would fall during a war, given uncertainty as to who would win, and then rise after the war ended.
Then for the next two hundred years the market and par values remain very similar until the second half of 1 6 It is important to price di¤erent gilts separately, especially in the run up to the Goschen's Conversion of 1888. Our approach ensures that the market value of government debt is calculated appropriately even if some individual gilts are redeemed or converted early. We therefore avoid two of the pitfalls in estimating consol yields identi…ed by Klovland (1994).
twentieth century. The high in ‡ation period of mid 1960s to late 1970s sees the market value of debt go below its outstanding value whereas the low interest rate period of the last 20 years sees market value rise relative to outstanding values. It is striking that the market value of debt at the end of the sample stands at its highest ratio to par value since our sample begins.

Yield Curves
A focus of this paper is the cost of debt management and so we need to calculate the one period holding returns investors receive on each gilt, which in turn requires dealing with the fact that in practice gilts pay a semi-annual coupon. As a result the total nominal return on gilts is comprised of a nominal coupon payment plus a nominal revaluation term that captures any capital gains or losses made.
The availability of our gilt-by-gilt data means we can calculate these revaluation e¤ects. However, our approach is also problematic as each gilt has a di¤erent maturity and may also o¤er a di¤erent coupon.

The government budget constraint
The dynamics of the ratio of marketable debt to GDP are governed by an accounting identity closely related to the standard government budget constraint for cash ‡ows and the outstanding value of government debt.
De…ningB t and B t as the total real market value of nominal and indexed debt in period t, the ratio of marketable debt to GDP develops according to: wherer j t 1;t and r j t 1;t are the nominal holding returns on the real values of nominal and indexed gilts of maturity j andB j t 1 and B j t 1 denote the real value of nominal and indexed bonds of maturity j in period 1 8 As in Figure 11 of Hall and Sargent (2011), the one year revaluation term is highly volatile (showing swings between +40% and -20% GDP around the Napolean Wars). The …ve year moving average follows the same general trends but helps isolate the economic magnitudes more easily. 1 9 We are restricted to 1730 due to the nonavailability of consol prices and GDP data prior to that date. t 1. In ‡ation t 1;t is measured by the growth in the GDP de ‡ator between periods t 1 and t, and g t 1;t denotes the growth in real GDP between periods t 1 and t. The term N F R t is the net funding requirement, the quantity of marketable debt the government issues in the period to …nance its primary de…cit in period t.
In the case where no nonmarketable debt is used N F R t is the primary de…cit.
In other words, debt increases because of the upward pressure of nominal return paid to bond holders, is reduced by in ‡ation and GDP growth (which a¤ect the growth adjusted real interest rate) and is pushed upwards by the current primary de…cit. Year war is noticeable -bond holders receive a high return which pushes debt higher, the government runs a small average surplus to try and restrain debt, and there is a small favourable revaluation e¤ect on bond prices. The long and relatively peaceful period between 1816 and 1913 sees debt fall by more than 100% GDP.

Decomposition
Bond holders again receive a good return (an average real return of 3.8%, the highest across all subsamples but equal to that in the …nal period) but the debt is reduced by a substantial contribution from primary surpluses. The period 1946 to 1970 sees a major fall in government debt of over 100% of GDP. For this period the government on average runs a small surplus but the major channel for debt reduction is poor real returns for investors (-1.9%). Low growth adjusted real interest rates (-4.7%) help reduce the debt to GDP ratio despite relatively small surpluses. Between 1971 and 1997 debt increases but by a relatively modest 15% of GDP due to poor rates of return and weaker …scal policy. The …nal period (including New Labour, Bank of England independence and the …nancial crisis) shows a large increase in debt. The contribution of nominal returns is high and this is also a period of large primary de…cits. In ‡ation and GDP growth exert small downward e¤ects but these are more than o¤set by the larger primary de…cits and higher nominal returns. While this period is generally one of low interest rates, the returns to bond holders through capital gains are substantial, especially in the period after the …nancial crisis. Figure 11 presents a graphical summary of this decomposition for each subsample and shows changes in behaviour clearly. Up until the 20th century primary surpluses and GDP growth were used to try and achieve debt sustainability in the face of strong upward pressure on debt from nominal returns. In the twentieth century the upward pressure from nominal returns was less and, especially after WWII, in ‡ation played an important role. Before the 20th century bond holders received a good rate of return and debt was reduced by primary surpluses. As noted by Crafts (2016), the pressure for social expenditure was less and governments found it easier to produce …scal surpluses before the extensions to the electoral franchise that occurred in the 1920s. In the 20th century however debt sustainability was achieved more by poor returns to bond holders than through …scal surpluses.

Contribution of maturity structure
Our gilt-by-gilt dataset enables us to look at the contribution of the maturity structure in supporting …scal sustainability. As argued by Angeletos (2002), if the price of long bonds co-moves negatively with the government's net funding requirement then issuing long bonds provides the government with partial insurance against net funding requirement shocks.   The correlations between the primary de…cit and revaluations of the consol strengthen if we consider correlations at leads and lags, which suggests that a simple bivariate vector autoregression analysis may be useful. Figure 13(b) presents the resulting impulse response function, showing how the consol is revalued after a one percentage point shock to the primary de…cit as a percentage of GDP. Identi…cation is achieved by assuming that shocks to the price of consols have no contemporaneous e¤ects on the primary de…cit, the lag length of the vector autoregression is 4 and 95% con…dence intervals are shown. It is di¢ cult to identify shocks by contemporaneous zero restrictions with annual data, so our results should be treated with caution but the tentative conclusion from Figure 13(b) is that long bonds are unlikely to provide the government with signi…cant …scal insurance. Bond prices move in the right direction after a primary de…cit shock, but the movement is transitory and only borderline signi…cant.

Wars
Our long data sample enables us to examine how several di¤erent wars were …nanced. A cursory glance at British history over this period reveals a near never-ending list of con ‡icts (in only 52 years from 1700 to 2017 is the UK not involved in some form of military con ‡ict). However, examination of the government expenditure series suggests the following as substantial con ‡icts in terms of their …nancing needs:  Table 3 shows the decomposition of debt dynamics for these periods and compares it to periods of peace.
All these wars lead to a broadly similar increase in debt of around 30% of GDP during the time of con ‡ict, although in many cases debt continues to increase after the con ‡ict has ceased. Comparing times of war and times of peace, the obvious di¤erences are i) during war the country runs de…cits and in peace surpluses ii) during wars in ‡ation plays twice as large a role in containing debt iii) on average bond prices provide some …scal insurance by falling during war and rising in peace iv) the contribution of GDP growth to lowering the debt to GDP ratio is about twice as important during wars v) long bonds are responsible for all of the …scal insurance e¤ect but their most important role is as a conduit for the in ‡ation e¤ect which is around four times larger than the revaluation e¤ect. The nominal return on government bonds decreases in periods of war (3.7% compared to 4.7% during peace), as does the real return (0.7% compared to 3.1%), due to a rise in in ‡ation (3.0% compared to 1.6%).
Whilst there is considerable similarity across the di¤erent wars there are also inevitable di¤erences. The role of in ‡ation in …nancing wars has become more signi…cant over time and the revaluation/…scal insurance e¤ect is particularly unstable across di¤erent time periods. In general, wars are …nanced by de…cits that are subsequently o¤set by surpluses in peacetime when long bond holders in particular experience a low real return due to higher in ‡ation.

Financial Crises
The  Table 4 shows the debt dynamics for …nancial crisis periods (where we include three years after the …nancial crisis) and contrasts them with periods of non-crises. Comparing averages we see i) crisis years witness an increase in government debt whereas non-crisis years witness small declines in debt ii) on average …nancial crises see …scal policy reducing the value of debt not increasing it (the 2007-9 period being the major exception) i.e. historically the government has tightened …scal policy during …nancial crises to improve the …scal position iii) nominal holding returns tend to boost government debt more in crises than otherwise with most of that contribution coming from an unfavourable revaluation of long bonds iv) low in ‡ation during …nancial crises tends to lead to a higher debt to GDP ratio.
The most striking di¤erence between …nancial crises and other periods is the ex post real return on nominal debt. During periods of …nancial crises the return is 4.9% compared with 0.2% otherwise. This is only partly due to a fall in in ‡ation (-0.5% compared to 0.2%), with the rest being due to upwards revaluation in bond prices. Financial crises tend to be followed by low interest rates and bond price increases. Note that the most recent 2007-9 …nancial crisis saw a real return of 4.7%, slightly above the average across the sample. This upward shift in bond prices is important as it means that long bonds provide the opposite of …scal insurance during a …nancial crisis. One striking manifestation of this is the fact that, at the end of our sample period after the 2007-9 …nancial crisis, the market value of government debt is at its highest premium relative to its face value for the whole 323 years of our sample.  In performing these counterfactuals we follow Hall and Sargent (2010) in making a strong exogeneity assumption that yields do not vary with the volume and maturity structure of government debt, i.e., that the yield curve is una¤ected by debt issuance. There are two reasons why varying the debt structure would in practice in ‡uence yields. The …rst is at the heart of macroeconomic analyses of debt management, e.g., Aiyagari et al. (2002), Angeletos (2002), Buera and Nicolini (2004). In these models di¤erent issuance policies lead to di¤erent market values of debt, and so di¤erent processes for tax rates and outcomes for consumption and rates of return. The second channel is based on market microstructure. Debt management o¢ ces are very concerned that if they try and sell too much of any particular maturity they will face liquidity e¤ects which adversely a¤ect the price at which they can sell (see Guibaud, Nosbusch and Vayanos (2013)). The magnitude of these e¤ects di¤ers across di¤erent maturities and is not linear (see Lou, Yan and Zhang (2013), Breedon and Turner (2016) and Song and Zhu (2016)), implying that changing the composition of debt issuance will a¤ect yields.
Ignoring these two channels is clearly a limitation of our ex post counterfactuals. However, it is worth noting that studies using structural models tend to …nd that variations in the maturity structure usually have very  Table 1 showed how the total market value of UK national debt evolved over our sample period under observed debt management. In this section we consider how that evolution would have di¤ered if the government had followed alternative debt management policies. We build multiple counterfactual scenarios that are di¤erentiated by the maturity of debt the government issues. The simplest counterfactuals assume the government concentrates all its issuance in zero coupon nominal bonds of a speci…c maturity, i.e., the government only ever issues bonds of 3, 5 or 10 year maturity. Subsequent counterfactuals permit a wider range of maturity options as well as issuing a mix of bonds of di¤erent maturities.

Alternative Fiscal Histories
When we change the maturity of debt we change the cash ‡ow of government …nancing, as this depends on both the current primary de…cit and the value of bonds maturing each period. The …rst step in our counterfactual is therefore to isolate the historical component of the primary de…cit that was …nanced by the issuance of marketable bonds ? (N F R t ) and then construct alternative …nancing histories by using this and recalculating the redemption pro…le of debt in light of the di¤erent issuance policy. We do this in the following manner. At the beginning of our sample period all the national debt was in the form of consols so there are no initial coupon or redemption payments on previously issued …xed term nominal debt. The government hence issues N jt = ? N F R t =P j t zero coupon bonds of maturity j for the …rst time at time t, where P j t is the price of a zero coupon bond of maturity j at time t. Issuing these bonds changes future redemptions, in particular the government will have to fund ? N F R t+j + N jt in j years'time, which will require issuing ( bonds. Moving forward recursively we can then construct counterfactual series for issuance, redemptions and the market value of debt, under the exogeneity assumption that yields are una¤ected by issuance. Table 5 presents results for the alternative debt management scenarios and shows that the level of debt in 2016 would have been lower by 28.1% of GDP (a debt to GDP ratio of 53.8% rather than 81.9%) had the government only issued 3 year bonds between 1914-2016. The corresponding debt to GDP ratio if the government only issued 5 year bonds in this period would have been 65.9%, and for 10 year bonds 92.5%. As the yield curve usually slopes upwards, issuance policies that concentrate on long maturities lead to higher one period holding returns and hence higher levels of debt than policies based on short maturities. Table 5 reports results from di¤erent sub-periods and Figure 14 shows graphically for every combination of dates in our sample the periods over which 3, 5 or 10 year issuance would have performed best. In Table 5, only for 1946-1970 do our alternative debt issuance policies produce worse end-of-period outcomes than the actual UK debt management policy. This is also the period where long bonds perform best as it conforms closest to the general insight of the optimal …scal policy/debt management literature. Post war there is an increase in government expenditure, the price of long bonds falls more than the price of short bonds, so an issuance strategy based on long bonds helps insure the government against greater increases in taxation. However, in the vast majority of subperiods this does not hold. Particularly striking is the most recent subperiod 1997-2016, which suggests that the UK policy of focusing on issuing long maturity bonds led to a substantial increase in the market value of debt. Long-term interest rates fell after the …nancial crisis, triggering unfavourable revaluation e¤ects and high one period holding returns on long bonds. This would have been avoided had the government issued shorter maturity bonds.
Part of the reason why the policy of always issuing 3 year bonds performs so well is that the yield curve usually slopes upwards, in which case short maturity bonds have a lower yield. However, the superior performance when issuing 3 year bonds is due to more than just cheapness of the yield.    O¢ ce. One such concern is around liquidity and the worry that concentrating issuance in large volumes will drive prices against the government. Another concern is rollover risk, whereby if borrowing is concentrated in single maturities then large de…cits create a lumpy redemption pro…le. This leads to worries that the government either will not be able to sell enough bonds to …nance its activities or will …nd itself issuing large amounts of bonds at a time when interest rates are very high. Issuing across a range of maturities helps to lessen both these liquidity concerns and rollover risk. In addition to these practical debt management concerns, the theoretical optimal debt management literature emphasises that the government may need to leverage its position in order to get maximal bene…ts from long bonds and fully exploit movements in the yield curve. This literature also normally assumes that each period the government buys back the entire stock of bonds (not just those which are maturing) and then reissues, in doing so maximises the bene…ts of long bonds. As we have so far excluded leverage as a debt management option and assumed no buyback, our …ndings favouring short bonds may therefore be misleading. In this section we examine the robustness of our counterfactuals to these features.

Liquidity E¤ects
In this section we calculate how large adverse liquidity e¤ects would need to be to o¤set the gains displayed in our counterfactual policies. The value of nominal debt to GDP in the data for 2016 is 81.9% whereas in the counterfactual when the government only issues 3 year bonds it is 53.8%. How much would the yield curve need to move in order to nullify this implied gain of 28.1% of GDP?
The yield to maturity ytm j t of a j period bond in period t satis…es where P j t is the current market of a nominal bond of face value £ 100 that matures in j periods. The counterfactuals performed previously assume the government always received P j t for each £ 100 it promised to pay in j periods, irrespective of the volume of debt it issued. We now allow for issuance to a¤ect the cost of borrowing through a premium x on the yield -the larger x the greater the impact of issuance on borrowing costs. In this case the government receives onlyP j t for each £ 100 it promises to pay in j periods, wherẽ " 100 SinceP j t < P j t the government needs to issue more debt to ful…l a given net funding requirement. Over the period 1914-2016 the average one period holding return on 3 year bonds is 5.3% so a liquidity premium of 85 basis points is substantial. However so too is the increase in issuance required by our policy of focusing just on three year bonds. For the same period the average annual issuance of debt with maturity of 3 1 years (to allow for debt that was not issued with a maturity of exactly 3 years) amounted to 0.8% of GDP whereas in our counterfactual with only 3 year bonds being issued the level of average annual issuance rises to 15.2% of GDP. Therefore in order for three year bonds to outperform actual UK policy for the period we require that the elasticity of the yield curve with respect to issuance is less than Q=Q ytm= ytm = ((15:2 0:8))=0:8 530=85 = 108. In practical terms, this means a doubling of issuance should lead to an increase in yields of no more than 530=108 = 4:9 basis points. Breedon and Turner (2016) evaluate the costs of the UK government both buying and issuing large quantities of government bonds. They report in their Table A2.1 that a doubling in the value of issuance moves yields by a maximum of 3:300 log(2) = 2:3 basis points, depending on the precise speci…cation estimated. This is lower than the critical value calculated above suggesting that the 3 year bond counterfactual will continue to generate gains even allowing for liquidity e¤ects.

Re…nancing Risk
The current objective of the UK Debt Management O¢ ce is to "minimise, over the long term, the costs of meeting the government's …nancing needs, taking into account risk..."Issuing short bonds requires constantly rolling over large volumes of debt each period, exposing the debt management o¢ ce to both interest rate risk (de…ned by the Debt Management O¢ ce as "interest rate exposure arising when new debt is issued") and re…nancing risk ("interest rate exposure arising when debt is rolled over, with an increase in re…nancing risk if redemptions are concentrated in particular years"). This section extends our counterfactuals to take these risks into account.
We quantify the risks and vulnerabilities in our counterfactuals by recognising that there are likely to be implementation lags in policy. If the government has to commit to a …xed volume of bond issuance at least one period in advance then they will face interest rate risk (the market price may fall short of what is expected) and re…nancing risk (di¤erent maturity pro…les will lead to di¤erent gross funding requirements). Inspired by the …nance literature on Value at Risk, our preferred risk measure is the prospective shortfall in bond issuance receipts that the government su¤ers when bond price movements are in their 5th most unfavourable percentile.
For example, a 1.5% level for the 5% Value of Risk measure means there is a 5% probability that a government deciding issuance in advance will face a shortfall in receipts of at least 1.5% of GDP. Two countervailing forces will be at work when comparing the Value at Risk across di¤erent maturities. Firstly, long bonds will typically be bad for Value at Risk because they concentrate issuance at the long end of the yield curve where prices are volatile. Secondly, long bond policies tend to be good for Value at Risk as they reduce gross issuance and debt rollover each period.  To the right of the bottom of the U-shape, increasing the maturity of issuance allows the government to roll over a smaller proportion of debt each period, but issuing longer bonds is expensive and risky in itself so the government ends up with both a higher debt stock and a greater absolute need to roll over debt each period. Figure 16b shows the average Value at Risk and average debt outcomes for counterfactuals in which the government can issue …xed proportions of two zero coupon nominal bonds of di¤erent maturity each period.
We are interested in the most e¢ cient maturity structures that minimise the Value at Risk for a given debt level, so Figure 17 plots the convex hulls of Figure 16 alongside the convex hull associated with an issuance policy based around three distinct bonds. It is noticeable that the latter provides relatively small gains so we focus below on the two bond case. 2 2 The pattern is robust to assuming an implementation lag of more than one period in the Value at Risk calculation. Longer implementation lags lead to higher Values at Risk but still produce a U-shape.
Average debt-GDP 25 Figure 18 as e¢ ciency frontiers then the performance of the actual issuance strategy over the period 1914-2016 has been sub-optimal. By switching to a di¤erent issuance strategy, the government could have reduced its Value at Risk exposure without compromising on its average debt to GDP performance. Alternatively, the government could have lowered the average debt to GDP level without taking on additional Value at Risk.
These gains are based on assuming no liquidity e¤ects and that the only risk facing debt managers are ‡uctuations in bond prices. Figure 18 shows how the distance from the data to the frontier for the one maturity strategy reduces as we allow for larger liquidity e¤ects on price from issuance. We …nd that a 30 basis points premium on the yield to maturity is now su¢ cient to place the actual data on the frontier when we model liquidity e¤ects as in Section 6.1.
Average debt-GDP 25 Figure 18: Lower bounds on average VaR for given average debt to GDP ratios and liquidity e¤ects To consider the impact of other risks take the case of a buyers strike, e.g., where not all bonds can be sold. In Figure 17 the distance between the data and the 9 year counterfactual is a Value at Risk of 1:62% 1:37% = 0:25% of GDP. Consider the arbitrary risk of a buyers strike in which market participants were only prepared to purchase 90% of the bonds the government issued. The average annual issuance of 9 year bonds under our counterfactual is 4.9% of GDP so if the probability of the new strategy inducing a 10% buyers strike were 5% then we would need to add 0.49% of GDP to our Value at Risk measure. So long as the probability of a buyers strike is less than 5% 0:25=0:49 = 2:4% then there would be no rise in total Value at Risk. In other words, as long as implementation fails less than once in 40 years then the additional risk is tolerable and does not substantially a¤ect our conclusion.

Leverage
The superior outcome of our counterfactual 3 year funding strategy raises the issue of whether even better performance were possible if the government took a leveraged position. Alternatively, leveraging could undermine the superior performance of borrowing using short maturities. As emphasised by Buera and Nicolini (2004) the usual optimal debt management literature recommendation of issuing long bonds involves highly leveraged positions in order to magnify the limited shifts in the yield curve that occur in practice.
To investigate the e¤ects of leverage we return to the counterfactuals in which the government issues two bonds of di¤erent maturities (but in …xed proportions). We model leverage strategies by allowing the government to issue a negative quantity of one of the bonds, i.e. the proportions of each bond are z and 1 + z respectively, where z > 0. The results are shown in Figure 19, which reproduces the red e¢ ciency frontier from Figure 17 as the baseline case with no over-issuance or leverage.  Over-issuance facilitates two types of outcome that were previously unattainable. In the south east of Figure 19 the government can lower its Value at Risk exposure without increasing the average debt to GDP ratio. These outcomes are achieved by the government over-issuing long bonds, although the bene…ts here are somewhat illusory since all these new outcomes are dominated by ones attainable without leverage. Of greater interest are the new possibilities in the north west of Figure 19, which arise when the government over-issues short debt. By adopting this strategy the government is able to reduce average debt to GDP levels below anything possible with non-leveraged strategies. Because short rates are less than long rates the government can reduce debt by overborrowing short and investing in other assets. The drawback is that these new outcomes are all associated with very high Value at Risk, as over-issuance exposes the government to risk on both its borrowing and on its savings. Therefore at least within this Value at Risk framework using leverage neither changes our conclusions about the attractiveness of long bonds nor suggests an alternative best practice debt portfolio from our counterfactual analysis. Obviously leverage involves the government taking even larger positions than in our standard counterfactuals. If liquidity e¤ects and transaction costs are important then this makes using leverage even less attractive.

Buyback
We have so far followed observed practice and assumed that once the government issues a bond it does not repurchase it before maturity. As shown in Faraglia et al (2017), under incomplete markets the assumption as to whether the government does or does not buy back its own debt before maturity matters as it a¤ects the timing of cash ‡ows, reduces the e¤ectiveness of long bonds in providing …scal insurance and creates a "lumpiness" in the repayments pro…le. We therefore introduce the possibility of government buybacks one year after issuance to see if this lessens the desirability of using short bonds.  Table 6: Decomposition of growth in market value of …xed-term nominal debt to GDP with buyback Buyback strategies also introduce two further disadvantages from a debt management considerationincreasing roll over risk and potential liquidity e¤ects. Buyback strategies clearly increase substantially the amount of debt that needs to be purchased each period and so if we maintain the assumption of Section 5.3 that the government determines its issuance one period ahead then Value at Risk will increase under buyback.
This is clear in Figure 20, which plots average debt to GDP and average Value at Risk to GDP with and without buyback. The increased Value at Risk that buyback introduces is substantial. Note further that in this subsection we abstract from transaction costs and liquidity e¤ects. Clearly introducing these in the case of buyback will reduce further the performance of this strategy.
Av erage debt-GDP Overall we …nd that allowing for debt management concerns, especially those around rollover risk and liquidity e¤ects, suggests a greater but still minority role for longer maturity bonds. However it remains the case that based on our 100 years of data the best ex post performing debt management strategy involves the majority issuance of short term debt. The upward sloping yield curve makes short debt cheap and this …rst order e¤ect continues to dominate even when we consider a greater range of risks and factors.

Conclusion
We have used a new dataset covering 323 years of UK government debt to shed light on issues of optimal …scal policy and debt management. In particular our use of individual bond data on quantity and price enables us to consider long run …scal sustainability using the theoretically correct measure of the market value of government debt and to perform counterfactuals to investigate whether alternative debt management policies would have provided better outcomes.
Using the market value of debt con…rms previous …ndings that debt in general follows the principles of tax smoothing, especially in response to wars, with debt acting as a bu¤er and showing the longest lasting swings amongst macroeconomic variables in response to …scal shocks. There are however clear di¤erences over time, with the twentieth century moving away from primary surpluses combined with high returns to bond holders as a means of stabilising debt. Instead, …scal sustainability was achieved by greater use of in ‡ation and low growth adjusted real interest rates. In general we …nd that shifts in bond prices/changes in yields have contributed little to …scal sustainability and that long bonds rarely o¤er much in the way of …scal insurance and even when they do it is of limited quantity. Long bonds are particularly expensive during …nancial crises as falls in interest rates lead to large capital gains for long bonds and high returns to investors, and so high funding costs for governments. This has been strikingly apparent in the most recent …nancial crisis with the market value of debt ending our sample at its highest premium relative to face value for the whole 323 years.
Because the yield curve is normally upwards sloping and because long bonds o¤er little in the way of …scal insurance, our counterfactual analysis suggests that over the 20th century the UK government would have been better o¤ issuing just three year bonds. Had they done so, debt in 2016 would have been lower by around 28% of GDP. The …rst order e¤ect of lower yields dominates any second order considerations regarding the volatility and covariance of long bond prices. This is a function both of the size of the term premium but also the limited and intermittent ability of long bonds to provide …scal insurance outside of certain sub-periods.
To reduce the outperformance of short bonds in our 100 year counterfactuals requires either increasing their yields or introducing additional risks. If liquidity e¤ects are an important feature of government bond markets then this has the potential to make a focus on issuing just short bonds expensive. However these liquidity e¤ects themselves need to be large and are less a disadvantage of short bonds per se but of any issuance strategy based around only a few maturities. Focusing on rollover risk does suggest reducing the role of short bonds but even in this case short bonds should form a majority of the portfolio. We …nd little role for debt managers using leverage or buyback -in both cases rollover risk is increased by an order of magnitude and if transaction costs are important then these will be costly to implement. More importantly we …nd that neither strategy enables the government to achieve a better debt-risk trade o¤ then more simple policies.
These …ndings question the empirical relevance of the optimal debt management literature's preference for long bonds and also comes to critical conclusions on the UK's practice in supporting the longest average maturity government debt portfolio in the world. At the heart of these …ndings is a term premia that gives a strong preference to short term debt and covariance properties of long run debt that provide only a limited insurance role in an issuance strategy. Any explanation of why the government issues so many bonds of so many di¤erent maturities and why the average maturity is so great will have to focus not on stochastic features of the yield curve but on the nature of bond market microstructure and bond market speci…c risks which are as yet ill-de…ned in the literature.