Debt simulation models

not available/marketable at all.¹⁵ In less developed markets it may be necessary to issue short-term debt indexed to foreign currency to attract investors and borrow at reasonable rates.

Secondly, it is not a straightforward exercise to assess the future correlation between the budget balance and debt-service cost of different financial instruments. The correlation structure based on historical observations may be unstable, and it is uncertain whether it will prevail in the future. In addition, domestic interest rates may to some extent be detached from the domestic business cycle – and thus the government-budget balance – in an increasingly integrated world.

characteristics. If the objectives are not fulfilled, the strategy may be adjusted, and the model is run again. Thus, the models can provide a basis for making informed decisions about the choice of government debt policy strategies.

Annex 3.A contains a more detailed description of the general structure of government debt simulation models.

Different types of models

Some countries use so-called scenario models, which only consider a limited number of scenarios. As only a limited number of scenarios are generated, it is not possible to achieve a direct quantification of the risk by relating potential outcomes to their likelihood. However, new models are under development in many countries. More advanced models use stochastic simulation. By simulating a large number of scenarios, it is possible to form a distribution of future costs of government debt. Based on the cost distribution, expected costs and risks can be determined.

A widely used approach is to conduct stochastic simulation of interest rates for different deterministic scenarios of the primary budget balance. By running the model for different scenarios of government budget balances, the sensitivity and robustness of the results to changes in the government’s budget balance can be assessed.

Another class of models is based on models of the economy. In this type of models, the budget balance and interest rates are modelled jointly within a macroeconomic model framework that links relevant financial and macroeconomic variables such as interest rates and GDP. The reason for taking this approach is to take consistently into account the relationship between the primary budget balance and debt-service cost.¹⁶

There are two main ways to construct a model for the development in financial and macroeconomic variables. The first alternative is based on a statistical analysis of relationship between macroeconomic and financial variables on the basis of a correlation matrix. The second alternative is to use structural equations for the relationships between different variables. In the former case, one merely determines the average correlations between different variables. In the latter case, one detemines a behavioural link between economic and financial variables. For example, an equation could describe the link between economic growth and the yield curve, while another could specify the link between the budget balance and economic growth. The structural relationship between the yield curve and the budget balance would then be derived on the basis of these two structural equations. (This is the basic idea underlying the simulation model used by the Swedish Debt Office.) Macroeconomic models can be used to relate debt-service costs to the government’s primary budget situation so as to assess the budget smoothing

effects of the debt strategy. In practice, budget smoothing effects are examined by simulating debt-service costs-to-GDP. GDP can be interpreted as a measure of the government’s budget situation, since the budget normally co-varies with GDP via both taxes and expenditures. A smooth cost-to-GDP ratio indicates that the debt portfolio reduces the risks to the budget by typically having low costs when GDP is low and government finances are strained.

Time horizon for the simulation and initial portfolio

Government debt management is a long-term business. Theoretically, there are arguments for considering a very long time horizon in the simulations assuming that the government is rolling over its debt forever. A common choice, however, is to work with a ten-year horizon and to aggregate debt-service costs on an annual basis. The annual frequency corresponds to the fact that the government produces annual budgets, and that the government budget is a key concern in government debt management.

Debt managers consider both short-term and long-term simulation results in order to get a better insight into the debt portfolio and associated costs over different time periods. Often the political focus will be on the following year’s budget, while also considering that interest costs and the simulation results are more reliable for a short simulation horizon than for a long horizon. However, the debt management horizon is long-term (several years) and long-term simulations also allow for a consistency check of the different strategies.

The difference in simulation horizon may also reflect different objectives for the simulation. In simulations over a relative short horizon the focus may be on estimation of the cost and risk of the actual portfolio. In simulations over a long horizon, say 30 years, the focus may be on the examination of the long-term characteristics of “steady state” portfolios.

The choice of simulation horizon is related to the question of the initial debt composition in the simulation. In case the focus is on estimating cost and risk of the actual portfolio over both long and short time horizons, it is appropriate to start with an initial debt composition corresponding exactly to the actual debt.¹⁷

If, on the other hand, the focus is on the long-term characteristics of various portfolio structures, the simulations may start with a “steady state”

portfolio (that is in accordance with the duration and allocation targets of the strategy) as the cost and risk differences between strategies are due to different debt structures rather than transition of the initial portfolio to the

“steady state”.¹⁸

Implications of assumptions and complexity of simulation model It is important to consider carefully the degree of detail needed in the simulation model. First, the more complex the simulation model, the more resource intensive the development of the model. One should always ask oneself whether more complexity improves the reliability of the results and serves the purposes of the model. Second, there is a trade-off between complexity and transparency of results. The more complex the model, the harder it is to track and interpret the results.

A general lesson from building simulation models is to start out simple and gradually expand the model. A first step is to develop a model for financing requirements and government debt portfolio based on deterministic scenarios for interest rates and government-budget balance. When this is achieved, more sophisticated features such as interest-rate and government-budget-balance could be considered next.

Another general modelling point is that the output results are not better than the model’s underlying assumptions and input. In order to get a tractable model, it is necessary to base the model on a number of simplifying assumptions. The output results obtained are sensitive to these assumptions and also to the model’s estimated parameters. It is therefore important to examine and describe the underlying assumptions and their influence on the results.

A footnote in the IMF/WB Guidelines for Public Debt Management¹⁹ states that: “Complex simulations models should be used with caution. Data constrains may significantly impair the usefulness of the models, and the results obtained may be strongly model-dependent and sensitive to the parameters used. For example, some parameters may behave differently in extreme situations or be influenced by policy responses.” These considerations explain why stress tests are useful.

As noted above, macroeconomic models have the advantage that they model the relationship between interest rates, economic growth and budget balance in a consistent way. This relationship is at the heart of ALM management used for government debt. On the other hand, structural macroeconomic models may impose too rigid and stylised relations between macroeconomic and financial variables. For instance, often a demand-driven macro model is used and it is important to note that this demand feature has an important impact on the output results. In a demand-driven economy, with a strong positive link between GDP and inflation, portfolios with large shares of inflation-linked debt will appear as a low-risk financing strategy when costs are measured relative to GDP. In contrast, in a supply-driven model this would not be true.

One way of dealing with this problem is to use stress tests by applying different sets of parameters to the stochastic equations. The model is then run again and the impact on the results can be studied. The probability of experiencing such a shock can then be altered and the resilience of certain issuance rules to supply-side events can be estimated.

In practice there are relatively few examples of the use of macroeconomic models by debt managers. The key reason is that it is a very demanding and complex task to develop the tools needed formally to carry out this analysis. It may therefore be difficult to reach meaningful operational conclusions. But even if the link between the budget balance and interest rates is not explicitly modelled, it may still be used; for example, via an ad hoc analysis outside the model and via stress tests.

Internal or external development of simulation models

Thus far, most countries have developed their models internally. This has certain advantages. It ensures transparency and internal understanding of the functioning of the model. Building a simulation model is also a learning process providing insight into the debt management problem. It gives more flexibility than when existing models from, for example, investment banks are used. Finally, as it is a demanding and stimulating task, it is likely to attract and retain skilled people.

On the other hand, internal development is resource-intensive. Moreover outside peers, primarily the Ministry of Finance, may view the model less credible if it is completely an internal creation.

A possible intermediate solution is to develop the model in-house, while making use of an external peer group. The peer group could consist of investment bank specialists, but even more valuable is to discuss the development results with colleagues in other countries who have done similar work. Over the past few years, many countries have posted descriptions of their work on web sites.