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The Debt Equation Explained

1. Examine the factors that determine the dynamics of the debt-to–GDP ratio.

2. Define the deficit bias and provide three reasons for its existence.

Debt to GDP ratio is defined as the ratio of the countries national debt to its Gross Domestic Product (GDP). Debt is what a country owes and GDP is the total production of the country. By comparing both the ratio indicates the country’s ability to pay back its debt. Often expressed as a percentage, the ratio can be interpreted as the number of years needed to pay back debt if GDP is dedicated entirely on debt repayment. There has been no ideal level of debt-to-GDP ratio determined for a country, whereas there has been a focus on the certain debt levels. A country is referred to be stable if its debt payments are done without refinancing or harming the economic growth. A high Debt-to-GDP ratio may make more difficulty in paying its debts. If a county fails to pay its debt, it would default and would also create a panic in the national and international market. The higher the debt-to-GDP ratio, the higher the risk of fulfilling the payment and thus the higher default risk. (Julio, 2010)

The factors which contribute to the determining of the dynamics of the government Debt-to-GDP ratio are Primary budget balance as a percentage of the country’s GDP, GDP growth and the difference between the real interest rate. The debt path is determined by the overall fiscal balances; interest bills and primary balances. Debt in terms of equations can be explained as :

                  Bt = (1+r) Bt-1 + Gt - Tt                                                                                       …[E1]

This equation explains the debt which is, debt at the end of the year t is equal to (1+r) times debt at the end of the year t-1, plus the Primary deficit which is the difference between total deficits and interest payments. The factors that determine the dynamics are primary deficits (or surpluses) and the real rate of interests. The change in any would change the percentage of debt to GDP. Thus there can be two cases realized:

1. The normal case: when the growth rate of GDP is smaller than the real interest rates. Here, E1 is a straight line with slope greater than 1. If the initial debt is positive then the government needs primary surplus to stabilize the debt ratio. The real rate of interest is the rate at which the government accumulates debt because of the debt inherited from the past in terms of interest. If new debt is recalled to pay such interests rather than by primary surpluses, the debt to GDP ratio will continue to grow at a rate equal to rate of interest. Real GDP, however, grows at a rate g- less than r- therefore the debt ratio increases over time. This happens even when the government maintains a primary budget balance or runs primary deficits.

2. The exotic case: when the growth rate exceeds the real interest. E1 is then described by a straight line with lower slope than 1 (1+ r – g < 1). The debt to equity ratio with time converges to steady rate value indicated as b-. The debt ratio converges to zero as the primary budget is balanced and the debt ratio exceeds.

Normal Case: When GDP Growth is Smaller than Real Interest Rates

The dynamics of debt to GDP ratio can be explained through these two graphical diagrams:

1. If g < r, and if country has past deficits or runs primary deficits (Gt - Tt > 0), then the debt ratio increases going further away from equilibrium.

2. If g > r and the government runs primary surpluses (Gt - Tt < 0), then the debt ratio always converges to its equilibrium level.

There has been a increase in debt of the government of many countries past few decades. The major causes of debt accumulation can be seen as the governments cut in taxation. But debt also has its determinants from the GDP growth rate and the inflation levels of the country. Countries reach debt tolerance limits as sharp increase in price levels and interest rates devalue the growth and in turn the money supply in the market. As for inflation levels, an obvious connection comes from the fact that high inflation can reduce the real cost of servicing the debt. Also, understanding how the debt builds up is also important. Natural disasters, wars and peace time also help in the debt accumulation for the path to recovery to happen. For developed economies the relation of inflation and growth does not much matter to the debt amount while for emerging economies they have a direct relation and affects the debt accumulation. Also emerging economies depend upon developed economies for borrowings which ads up to the debt amount. The aftermath of the financial crisis of 2007-2009 also showed that debt accumulation in the countries was majorly because of the dependant on short term borrowings to fund the past growing debts. (Reihart, 2010)

It is experienced that higher the public debt, higher the primary surplus to keep the debt levels from growing any further. But with the primary surpluses comes the taxes which if increased can create havoc in the economy. The degree to which high public debt can be danger to the economy can be explained with the help of the E1, the debt-GDP ratio:

Let’s say, a country having a high debt ratio of 100%. Suppose real rate of interest is 3% and GDP growth rate is 2%. Then first term on the right hand side is (3%-2%) X 100% = 1% of GDP. Now this can fluctuate as per the situation of the country. For example, Government generates a primary surplus of 1% then the right hand side will be equal to 1% + (-1%) = 0 , or because of any scandal or disinvestment in the country the central banker raises the interest rates from 3% to 7% then again the right side changes. To maintain this primary surpluses needs to be raised and to increase them will increase the tax rate. Alternatively the government may not be able to increase the primary surpluses then again the debt will rise and financial markets may fall which will bring in negative sentiments to the investors and further no investments would be attracted. The end lesson to this will be that the countries facing high debt should reduce it as soon as they can.

Exotic Case: When GDP Growth Exceeds Real Interest Rates

2) Policy: the rapid increase in government debt in most OECD economies in the 1990s lead economists to argue that fiscal policy was subject to a deficit bias and that discretionary policy had to be abandoned in favour of fiscal rules. However, the recent explosion in government debt suggests that the rules approach was not sufficient for stable public finances and the need to search for new ways of ensuring fiscal discipline. An idea that has received widespread attention is the establishment of independent fiscal institutions.

What is Deficit bias?

The Organization for Economic Cooperation and Development Nations was founded in 1961 for the development of world trade and push towards the economic growth of the member nations. It is a forum of countries coming together for democracy and market economy and sharing policies, problems and coordinating for a better world economy. Since the 1990’s there has been a rapid increase in government debts in most of its members and to overcome the same fiscal policies were subjected to the deficit bias and all the rules were made in favor of the same. Fiscal policy is a government tool for planning its expenditure on taxes and revenues through borrowings. The deficit bias comes in this planning stage itself. It can be defined as a situation “when the structure of a government’s budget is such that its promised disbursements exceed the structures of its receipts”. The reasons for deficit bias can be explained as below:

  • Insufficient collection of taxes- this is a very common problem for many countries. Due to the dynamic income distribution and generation of income in the economy, the tax slabs vary and collection is also distributed.
  • The collection of taxes is also dynamic making only few people of the population to pay the taxes. Also countries have very high marginal rates of taxes. People either work less and pay more or they work where tax evasions are possible.
  • Obligations towards the welfare and upliftment of the society and equality in distribution of the wealth. The people expect social and security benefits from the government which in return are expensive and obliging them requires a huge sum of money to be invested which can be either through government reserves or majorly through borrowings thus creating deficits further.

Discuss how fiscal councils can contribute to fiscal discipline by reducing the problem of deficit bias.

Fiscal policy is a mainstream tool used by the government officials for the planning and estimating the expenditure and revenues of the government. These policies are used by all the countries to stabilise the government action and forecasting future requirements. Fiscal councils can be said to be “independent bodies set up by a government to evaluate fiscal policy” (Wren-Lewis, 2011). Fiscal discipline can be defined as the government’s capacity to keep the smooth flow of financial operations and long term fiscal development. After the financial crisis of 2008 many countries formed its fiscal councils one such being the Swedish forum for crisis preparedness.

There has been a rapid increase in the deficit bias in countries and major reasons cited were as these countries did not follow the fiscal discipline and after a while there were no contingencies in the improve the situations. These fiscal problems have led to the establishment of fiscal institutions. These have also been approved by world development institutions like the IMF, World Bank, OECD etc. The recent interest in these establishments was widely supported by academic proposals. The common objective of these councils is to adapt the systemised working of the central banking to the fiscal sphere. The working of these fiscal councils are to be determined as whether they should do forecasting or evaluating the governments forecasts or they should give normative recommendations.

Since a long time fiscal rules have been violated by the governments and thus the councils have come up with fiscal disciplines. There are several ways in which the fiscal councils can deal with the deficit bias by contributing to fiscal disciplines, few are:

  • Informational problems- there have been many instances when there has been wrong inflow of information among the people in the country resulting into a fall in the severe indicators of economic growth. For example, over optimism among the people either by any leader or any people can create deficit bias because revenues can be below expectations over expectations may lead to regrets in future. To make such information flows correct and clear, councils need to step in and play a better role for the profitability of such information.
  • Impatience- this can also create deficit bias among the people. An example would be when a government is discounting at a higher rate than the electorate it is giving a deficit bias as this would lead to the loss of individual politicians in elections. Here the election commission may not be able to cater to the flaw effectively as the magnitude of the election may be very large, thus fiscal councils could provide an alternative political pressure and manage the situation.
  • Common-pool theory- a government’s duty is to provide welfare to the people and thus they come up with ideas to benefit them. But sometimes there stays a flaw in this process. Ministers may formulate overflowing budgets and thus fail to provide optimum results out of it. This theory provides a relationship between the departments of government and the deficit bias created. Here the recommendations of the fiscal councils may empower the financial ministers and help in the optimum utilisation of the money of the people.
  • Time inconsistency and inflation bias- the deficit bias is also related to the inflation bias. The fiscal policies are used to stabilise the economy by raising the output and inflation in the short run. Sometimes this leads to deficit bias with the inflation bias. The changes in the institutions that reduce the inflation bias through the monetary policy might encourage the inflation through fiscal policies with an associated deficit bias. Thus the fiscal councils can act as a guard for changes in such rules and advise on the long term benefits of the economy.
  • Exploiting future generations- there has been experiences when the government has failed to succeed in the security and development of the future generations of the country. The exploitation of the next generations can be directly by cutting taxes immediately and be paid by the future generation later or indirectly by adding government debts and capital. Here the fiscal councils may be represented by the future generations themselves. But again, these young councils should also have the fiscal powers and decision making strengths.(Wren-Lewis, 2011)

Discuss why there exists the potential for the UK government to exert some indirect influence on the OBR’s forecasts and to undermine its independence.

Office for budget responsibility is a fiscal forum established for the fiscal cooperation and management of the UK government. As discussed it is difficult for a government to establish a fiscal council as it would provide hindrances in its activities. Thus it has been noted that governments exert influences on the councils in there country. The UK government too tries to influence the forecasts of OBR’s.  This is because of the issue that independence simply moves time inconsistency problem to another level. The councils advises may bring in hindrances and problems in the government activities.  Sometimes fiscal councils are created by opposition parties for the critique to the government. Conflicts between the government and the fiscal councils are not inevitable. The fiscal council has the power to validate optimal departure from simple rules. Thus the UK government has been creating unduly interferences in its fiscal council. (McCullum, 1994)

Independence of the fiscal councils have always been undermined. Though there is a consensus of academic professionals on the need for the independence of these councils. This independence can be achieved through the following ways-

  • Budgetary independence.
  • Recruitment process to be completely professional and no political preferences accepted.
  • Restriction on the electoral’s freedom to fire then members of the councils.
  • Reduction in the periods of undertaking the charge in the office.
  • Strict prohibitions on the interference of the government advise on the functioning of the body.

calmfors. (2003). Fiscal policy to stabilize the domestic economy in EMU. In calmfors, Fiscal policy to stabilize the domestic economy in EMU (p. 49). CESifo Economic Studies.

Julio, E. (2010). A Practical Guide to Public Debt Dynamics. Retrieved january 24, 2015, from

McCullum. (1994). Two fallacies concerning central banks independence. American Economic review.

Reihart, M. (2010). Growth in the time of debt. In M. Reihart. American Economic Review.

Wren-Lewis, L. C. (2011). What should fiscal councils do. In L. C. Wren-Lewis, What should fiscal councils do (pp. 649-695).

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