Determining the Optimal Structure for Government Debts Ahmad Danu Prasetyo* and Naoyuki Yoshino**
Abstract Recently, there has been an upward tendency for switching external debts to domestic borrowings in many developing countries. While the domestic government bonds market development could reduce the sovereign exposure to currency risk, there are also potential risks faced by the government; namely: higher domestic interest rates, maturity mismatch, and the crowding out effect to private issuers. In this paper we develop a simple general equilibrium model to determine the optimal share for domestic and external government bonds in a sovereign country. We emphasize the important role of demand in forming the optimal structure of government bonds. We found that the bigger the government’s budget deficit, the smaller the proportion of external bonds that must be attained. Nevertheless, the government has to issue the external bonds up to a certain proportion as the supply of bonds goes to infinity. Moreover, the government must adjust the bonds’ supply and its structure simultaneously shall there be any shock to the bonds’ demand. Our empirical evidence in Indonesia shows that during the analysis period, the actual proportion of external government bonds is lower than the optimal proportion. However, the required proportion for domestic bonds is increasing overtime, while the government has been increasing the share of external bonds for the time being. At this rate, the optimal proportion will be surpassed in the near future. JEL Classifications: E60, H63 Keywords: Optimal structure, optimal proportion, domestic government debts, external government debts. * Corresponding Author. Lecturer at School of Business and Management, Bandung Institute of Technology, Indonesia. PhD Candidate at Graduate School of Economics, Keio University, Japan. Email:
[email protected] ** Professor at Graduate School of Economics, Keio University, Japan. Email:
[email protected]
1. Background Deficit in primary balance has become a generic policy for triggering the economy and generating growth. Governments, especially in poor and developing countries, need higher amount of investments to build public facilities and to satisfy their consumptions and expenses compared to the tax revenues that could be attained. Barro (1999) mentioned that the government should run budget deficits at times of temporarily high public outlays. Moreover, the budget deficits should be high at times of temporary economic distress and low (typically negative) in good times. In order to cover the deficit, the government seeks for funding sources other than tax revenues; including financial aids and public debts from domestic and foreign countries. In the past, many poor and developing countries received grants and soft-loans from developed countries and international fund institutions to finance their primary gaps. However, many economists criticize this approach. They argue that these aids are not effective for triggering economic development in poor and developing countries; this is indicated by the poor growth record of the grantee countries (Loser, 2004). On the other hand, there is no such thing as a free lunch; there are economic and political motives behind external aids and debts (Makmun, 2005). Recently, there is a tendency for switching the external debts into domestic debts in many developing countries. On one side, this policy can reduce the government exposure to interest rates and currency risks. In addition, it could also reduce the dependence on external assistance and on external shocks (Arnone and Presbitero, 2008). Nevertheless, there also risks embedded in the domestic debts issuance. Compare to external debts, domestic debts tend to have higher rates and short-maturity1. Higher interest rates imply higher debt services, which aggravate fiscal imbalances and decrease the government's ability to sustain debts. In addition, they eventually lead to a fall in the real demand for government bonds, due to the increase in default risk (Akemann and Kanczuk, 2002). Alternatively, sovereigns that are switching from external to domestic debts could be trading a currency mismatch for a maturity mismatch since few of them are able to issue long-term domestic debts at a reasonable interest rate (Panizza, 2008).
1
However, investors might assume that domestic and external debt rates are indifferent since, as mentioned by Barro (1999), the extra premium required on domestically denominated issues (even if indexed) might justify the extra riskiness of the foreign currency debt.
Muhdi (2007) found that emphasizing on domestic debts as a financing resource had an implication to crowd out private investments. Panizza (2008) explained that this happened because institutional investors and banks were absorbing "too much" government debt. In addition, he also mentioned that there are political reasons that may make domestic debts more difficult to restructure. For some sovereigns, the problem is more fundamental. They are not able to raise the amount needed from domestic sources due to lack of liquidity and saving. Hence, they enter the international capital market since it can provide a large amount of funds without crowding out lending to private sectors or recurring to inflationary finance. However, these countries cannot issue the debts in their own currency in this market, they have to borrow in foreign currency; this is also known as “original sin” (Panizza, 2008; Muhdi, 2007). Debt sustainability has been a central issue in governments’ fiscal policy. Unsustainable debt was one of main causes of why the economic recovery was so slow in Indonesia compared to other countries impacted by the Asian financial crisis in 1998 (Suhud, 2004), and also triggered the sovereign debt crisis in the euro area just recently. Some economists believe that the structure of the government debt (which is associated with its holder) is one of the keys for a sustainable debt. For example, Tokuoka (2010) explained that the large pool of household savings and the stable domestic institutional investor base have contributed to keeping yields steady despite the rapid rise in government debt in Japan. While Wang (2007) believes that the involvement of foreign investors would cause a huge volatility in the market. Because of these pros and contras of the domestic and external debts issuance and the important role of the structure of government debt in order to maintain its sustainability, it is tempting to investigate the optimal share of domestic and external debts in the government debt’s portfolio. Debts are classified into two types, loans and bonds. Loans are non-marketable instruments, in which the lenders are mostly coming from foreign countries and/or international funding organizations. On the contrary, bonds are marketable securities, in which the lenders are coming from private sectors. As their objective is to maximize the profit, the demand for bonds will be determined on the interest rate in the bond market. Hence, the value of bonds is subject to changes in the market. This paper will focus on the later type of debt since it seemed to bear more critical issues than the former. In addition, our terminology of external debts refers to the debt that is denominated in foreign currencies; in this paper we convert all external debts into US dollar denomination.
We develop a simple general equilibrium model to determine the optimal share for domestic and external government bonds in a sovereign country. We emphasize the important role of demand in forming the optimal structure of government bonds. We found that the bigger the government’s budget deficit, the smaller the proportion of external bonds that must be attained. Nevertheless, the government has to issue the external bonds up to a certain proportion as the supply of bonds goes to infinity. In addition, the government must adjust the bonds’ supply and its structure simultaneously should there be any shock to the bonds’ demand. Moreover, we also do back-testing by using the empirical data in Indonesia. The result shows that during the analysis period, the actual proportion of external government bonds is lower than the optimal proportion. However, the required proportion for domestic bonds is increasing over time. The rest of this paper is structured as follows: in the next section, we review the existing literature about domestic and external government debts’ sustainability, and also the government debt management in Indonesia. The development of the model will be discussed in the third section. Section 4 will discuss about the empirical evidence in Indonesia. Lastly, the concluding remarks will appear in section 5 2. Literature review 2.1. Domestic Government Debt Sustainability The study of government fiscal sustainability, especially concerning the sustainability of debt, has flourished in the past decade. The IMF (2006) defined debt sustainability as “a situation in which a borrower is expected to be able to continue servicing its debts without an unrealistically large correction to the balance of income and expenditure”. However, there is no exact parameter to measure a sustainable debt. Some economists just set a threshold that serves as a warning indicator, while other economists set a dynamic parameter that depends on the economic situation at the moment. Maybe the most famous debt threshold is stated in the Maastricht Treaty by the European Council. This treaty is arranged to establish the criteria for European Union member states to enter the third stage of European Economic and Monetary Union (EMU) and adopt the euro as their currency. One of the criteria in the treaty is to maintain the ratio of gross government-debt-to-GDP not exceeding 60% at the end of the preceding fiscal year. Even if the target cannot be achieved due to the specific conditions, the ratio must have sufficiently diminished and must be approaching the reference value at a satisfactory pace. Another threshold is stated by Aiyagar and McGrattan (1997). Using the U.S. economics data, they reach a conclusion that the optimal debt ratio is 2/3 of the country’s GDP.
On the dynamic parameter study, Makmun (2005) argued that when a sovereign is obliged to pay annual payment, the total output produced in the country plus the capital inflows (including net use of foreign exchange reserve) must exceed the domestic consumption plus the interest of current investments. Ferrucci and Penalver (2003) develop a probabilistic method in forecasting the debt’s sustainability. They found that with strictly positive probability, debts will be unsustainable when the variance of expected debt-to-GDP ratio is infinite. Thus, a finite variance of expected debt-to-GDP ratio is a prerequisite in order to sustain the government debt. Other economists set the parameterization of debt’s sustainability depending on the Debt-to-GDP ratio. The current debt would be considered as sustainable when its present value of the debt-to-GDP ratio converges into zero; this parameterization is also known as the inter-temporal budget constraint (Akyuz, 2007). Inter-temporal budget constraint is often formulated with respect to conditions for solvency which requires that the present discounted value of future primary budget balances should at least equal to the value of outstanding debt. This constraint implies that a sovereign that is able to run a larger primary surplus can have a higher initial stock of debt while maintaining long-term sustainability. Alternatively, a country that is growing fast can run a lower primary surplus for a given stock of debt and interest rate. Another implication is the public sector cannot be a debtor, and the private sector cannot be a creditor, in present-value terms; any debt incurred should eventually be fully payable. This would require the government to constantly increase taxes and reduce spending on goods and services. In addition, the theoretical concept of sustainability based on solvency is problematic because it does not impose specific constraints on debts and deficits at any point in time. Since current deficits are collateralized by surpluses in some distant future, any level of debts and deficits could be compatible with the present-value budget constraint. On the other hand, both the underlying economic conditions as reflected by the growth adjusted interest rate and the fiscal policy stance are variable over time and highly uncertain (Akyuz, 2007). Another approach is static budget constraint; that is when the public sector is able to finance its current expenditures with its revenues and new borrowing, and meet or rollover its maturing liabilities; that is, if it is not liquidity constrained (Akyuz, 2007). As mentioned, this parameter would depend on the demand side of the market. This approach, to our knowledge, is less explored in debt sustainability studies. In practice, a holistic assessment is needed so the government could flexibly apply the best strategy in issuing its debts. Waluyanto (2009; in Abimanyu et al., 2009) mentioned that the traditional paradigm to see public debts as a residual had caused an upward revision without accommodating the demand of
the market. As a result, the government acts as an opportunistic issuer – applying the front loading strategy to get more available funds. This make the investor seem less confidence in the government, even though a clear calendar-of-issuance of public debts has been announced. 2.2. External Government Debt Sustainability The formal definition of external government debt sustainability is “the ability of a country to meet the current and future external obligations without running into arrears, recourse to debt-rescheduling and eventually a drastic balance-of-payments adjustment” (Akyuz, 2007). Like in the domestic debt sustainability, there is no exact parameterization on how to measure the external debt sustainability. For example, the IMF (2002) considers an external debt ratio of 40% as a useful benchmark, however many economists relate external debt sustainability with a level of trade surplus. The amount of trade surplus desired is not directly linked to policy, but influenced by a host of variables operating on imports and exports, particularly the exchange rate and the rate of growth (Akyuz, 2007). Fisher in 1933 propounded a paradox regarding external debt sustainability: the heavily indebted countries are trapped in a net transfer problem – that is when debt services are higher than new debts while at the same time are experiencing depreciation in unit value and terms of trade of their export commodities. The unit value and terms of trade of export commodities can be depreciated as the foreign reserves are exhausted due to high debt services (Suhud, 2004). In fact, increasing external debts itself will potentially depreciate the local currency, thus the total redemption will increase (Muhdi, 2007). Another characteristic of external debts is they are subject to the shock of external events. An external event will result in an increase in borrowing costs and a capital outflow (Loser, 2004). Creditors are less willing to roll over loans when there is an expectation that the debtor will be unable to repay in the future (Ferrucci and Penalver, 2003). In the extreme cases, debt overhang is followed by massive capital flight as investors’ confidence is eroded (Muhdi, 2007). However, sudden stops in lending or rolling over debt do not always signal solvency problems. Investor behavior and risk appetites tend to vary over time without any significant change in the economic fundamental. Furthermore, a country’s history of default and the nature of its government and institution also play a significant role in influencing the investor’s confidence (Akyuz, 2007). Despite these drawbacks, the preference for the domestic debt issuance is not always superior to the external debt issuance. As shown by Arnone and Presbitero (2008), the ex-post evaluation of the sustainability condition of 14 heavily indebted poor countries shows that the inclusion of domestic debts
makes the evolution of debts not always sustainable as the results that are obtained by looking exclusively at the external public debts. 2.3. Government Debt Management in Indonesia Indonesia was one of the countries most severely impacted by the financial crisis in mid-1997 in South East Asia. One of the factors that made it hard to struggle out from the crisis was the increase of accumulative government debts (Suhud, 2004). These government debts especially took the form of external debts, which is denominated in foreign currency. As the IDR was depreciated drastically against the USD, the debt services had multiplied over a short period. The Indonesian government took several actions in response, including seeking soft loans from bilateral and international institutions, rescheduling the existing debts, privatizing its assets, and issuing domestic government bonds in order to bail out the collapsed banking system. During 1998-2000, the Indonesian government had issued a total of IDR 643.8 Trillion of domestic government bonds. By the end of year 2000, the bond holders (which are the national banks that bailed out by the government) started to trade these bonds to other investors, which initiated the development of domestic government bonds market. In 2002, the Indonesian government issued the Government’s Bond Act No. 24/2002, which contains the government’s objective of bonds management and other general concerns related to government bond issuance.
It was then elaborated more specifically in the Financial Minister Decree about the
Government’s Debt Management Strategy No.447/KMK.06/2005, which stated: “In more specifics, the objectives of debt management are (1) To finance the gap in primary balance and to maintain fiscal sustainability which is in line with the macroeconomic condition, and within the lowest cost, (2) To increase the prudence in debt management in order to minimize the risks embedded, (3) To be persistent with all of the scheduled plans and estimated costs”. Those objectives are then translated into several actions, i.e. (1) Maintaining the debt issuance below 1% of GDP, (2) Prioritizing the issuance of domestic debts and maintaining the external bond in a balanced proportion in order to reduce the crowding out effect in the local market, (3) Issuing bonds with longer maturities and continuously rearranging the maturity profile through buyback and debt-switch in order to mitigate the refinancing risk. Furthermore, it also established a debt management office under the ministry of finance to monitor the debts development and to implement strategies for sustaining debts. Thus, the government has started to manage its debts more professionally.
Domestic bonds recently have become the main source to cover the primary deficit. From table 1, it can be seen that, except in 2008, the additional amount of domestic bonds are higher compared to the additional amount of external debts. In 2008, the government borrowed a significant amount of external debt as a preventive action for facing the impact of the sub-prime mortgage crisis. Table 1 Statistics of Indonesian government debts
(In Trillion IDR) 2007
2008
2009
2010
2011
Primary Balance Surplus/Deficit
-4.12
-88.62
-133.75
-124.66
Domestic Debt Sources Net flows Stock of Domestic NonTradable Debt (Domestic Loans)
46.73
52.45
66.29
90.24
0.17
0.81
836.31
902.43
992.03
-98.54
20.07
37.04
611.2
612.45
615.83
143.15
161.97
195.63
Stock of Domestic Tradable Debt (Domestic Bonds)
737.13
783.86
External Debt Sources Net flows 200.6 Stock of External Non-Tradable 586.36 730.25 Debt (External Loans) Stock of External Tradable 65.93 122.64 Debt (External Bonds) Source: Debt Management Office, Indonesian Ministry of Finance
In order to expand the investor base, the Indonesian government has been issuing USD denominated external bonds (also known as Yankees Bonds) since 2004. It then continues to issue JPY denominated bonds (also known as Samurai Bonds) starting 2009. Most of the external bonds issuances are done in the foreign country’s jurisdiction; namely in the U.S. and Japan. However, recently, the government has also issued foreign denominated bonds locally in order to absorb the excess liquidity of foreign currencies within the country. Table 2 the development of Indonesian external government bonds
2007 USD (million)
2008
2009
2010
2011
7,000 11,200 14,850 16,850 20,350
JPY (million)
35,000 95,000 95,000
Currency IDR/USD 9,419 10,950
9,400
8,991
9,068
Currency IDR/JPY
101.7
110.3
116.8
Source: Debt Management Office, Indonesian Ministry of Finance
3. Development of the Model 3.1. The demand for domestic government bonds In 1988, Bernanke and Blinder proposed the extended IS-LM curve by including bank loans in the asset market. They believe that bank loans have an important role in the monetary transmission mechanism as banks serve as financial intermediaries for households and firms. Changes in the loan market and money market would affect the demand for government bonds due to the restriction of financial wealth. Bernanke called this model the CC-LM model, also known as IS-MP-BL model. This model works in a closed economy, and there is no credit rationing assumed. In this paper, we bring the model into an open environment. We assume that the demand for domestic government bonds comes from domestic private sectors. We ignore the foreign investor ownership of domestic government bonds. There are two private sectors involved in the market, banks, and households and firms. Banks’ assets consist of reserves (R), loans ( ), and government bonds ( (
); on the liabilities side there are deposits
) and the bank’s net worth ( ̅ ), which is assumed to be zero for simplicity. Banks’ reserves consist of
required reserves (
), whose amount would change as the deposit changes, and excess reserve (ER).
Thus, the consolidated budget constraint of banks at any particular time would become: (Banks’ budget constraint)
(1a)
Table 3 Banks’ consolidated balance sheet
Assets : reserves : loans : government bonds
Liabilities : deposits ̅ : banks’ net worth (assumed to be zero)
Rearranging equation (1a) we could obtain the equation for disposable deposits. (
)
(1b)
The fraction of excess return to disposable deposits ( ) is a function of interest rate of government bonds ( ) since the banks would put it in a risk-free rate asset. While the fraction of loans to disposable deposits ( ) is a function of loan rate ( ) and interest rate ( ). ( )( (
)(
) )
(Excess reserves)
(2)
(Loans Supply)
(3)
Substituting equation (2) and (3) into equation (1b), we can obtain a bank’s demand for domestic government bonds. (
)
(Banks’ demand for domestic ( )
(
(
))(
(4)
government bonds)
)
The actual reserve-deposit ratio can be expressed as the summation of required reserves rate and the fraction of excess return to disposable deposits multiplied by disposable rate (
). This is also equal
to the inverse of the money multiplier ( ( )). ( )(
)
(Reserve to deposit ratio)
(5)
( )
Since the model ignores domestic currency, the money supply available for households and firms equals to the supply for deposits. Therefore, ( )
(Money Supply)
(6)
As no cash is available, the households’ and firms’ assets are dispersed into deposits ( government bonds (
) while they are having bank loans (
) and
) as liabilities. The difference between
assets and liabilities is the net worth (W) of the households and firms. Thus, the households’ and firms’ budget constraint would be as expressed in equation (7) (Households’
and
firms’
(7)
budget constraint) Table 4 Households’ and firms’ balance sheet
Assets : deposits : government bonds
Liabilities : loans : financial wealth (net worth)
Fields and Hart (2011) noted that the money demand function from the basic LM curve failed to capture the independent effect of rise in government spending on the interest rate. They suggest including the
financial wealth variable into the function of money demand to overcome this problem. The demand for loans is simply a function of loan interest rate, government bonds’ rate and income. ( (
) )
(Money Demand)
(8)
(Loan Demand)
(9)
In addition, financial wealth is accumulation of saving, where saving is equal to disposable income deducted by consumption.
(
)
) )
((
(Financial Wealth)
(10)
(Saving)
(11)
Substituting equation (8) to (11) into equation (7), we can obtain households’ and firms’ demand for the domestic government bonds. (Households’ and firms’ ( (
) )
) )
(( (
)
(12)
demand for the domestic government bonds)
According to Walras’ Law, we could define the domestic demand for government bonds as the summation of banks’ and other private sectors’ demand for government bonds when the money market and the loan market are at equilibrium. The total demand for domestic government bonds is given in equation (15.b) ( )
(
)
(Equilibrium in money
(13)
market) (
)(
)
(
)
(Equilibrium in loan market)
(14) (15.a)
( )(
)
(Total demand for domestic government bonds)
(15.b)
3.2. Foreign demand for government external bonds The government’s external bonds are issued in foreign currency denomination, and thus so is the interest payment. Even though there is no restriction for domestic investors to invest in the government external bonds, we assume that the demand for external bonds fully come from foreign investors due to the fact that domestic investors would be exposed to currency risk when they invest in the government’s external bonds. In addition, the interest return of external bonds is far less than the interest return for domestic bonds. This would discourage the domestic investors from investing in the government’s external bonds. The foreign demand for government external bonds is a function of risk premium (RP), change of income in home country (
), and change of income in foreign country (
difference between the external bonds rate (
). Risk premium is defined as the
) and the interest parity, which is affected by the current
exchange rate ( ) and expected exchange rate ( (
)). The expected exchange rate is assumed as a
function of current exchange rate, domestic inflation rate ( ), and foreign inflation rate (
). Moreover,
the domestic income would rely on the government bonds’ interest rate, loans rate, and government spending in each country. Note that all other variables affecting the demand of external government bonds are exogenous, except (
and (Foreign investors’ demand
)
(16)
for external government bonds) ( ( ( (
)
)
)
)
(Interest rate parity)
(17)
(Domestic income)
(18)
(Expected exchange rate)
(19)
3.3. Government supply for domestic and external bonds One of the main considerations for the government in determining the amount of government debt is the budget constraint of its primary balance. Here we assume that all debts take the form of marketable bonds. The government revenues comes from tax (
) and raising new bonds (
). On the other side,
the government has to spend its expenditure (G) and to pay the interest payment of previous bonds. In this paper, we assume that the government only issues fix-rated-short-term-bonds for both domestic
and external bonds. It means that the interest rate to be paid at the end of the observed period is determined at the beginning of the period. The portion for domestic government bonds is denoted by . Thus, (
) denotes the portion for government’s external bonds. The government’s budget
constraint is expressed as below. (
[
)
]̅
(20)
The new stock of bonds is the accumulation of outstanding stock of bonds and newly issued bonds. By this definition, we could rearrange equation (20) into equation (22). ̅
(21) (
)
(Government’s budget (
( [
) ̅
)̅
]
(22)
constraint)
In order to attain the optimal share of domestic bonds and external bonds, the government has to take the dynamic condition of both markets into consideration. Thus, the government would take the equilibrium in both markets as a constraint in achieving its objective. Equilibrium in the domestic bond market would be achieved when the domestic partial supply of government bonds is equal to the sum of banks’ and other private sectors’ demand of government bonds. Likewise, the external bonds market is at equilibrium when the external partial supply of government bonds is equal to the demand of external bonds. ( )(
)
(Equilibrium
in
domestic
(23)
government bond market) (
)
(
)
(Equilibrium
in
external
(24)
government bond market)
Many economists assume that the government bonds would be perfectly rolled over into the next period (Ferrucci and Penalver, 2003; Penalver and Thwaites, 2006). However, this assumption is not applicable in reality. Ceteris paribus, the stock of debt would naturally increase as the debt services are integrated in the new debts issuance. These accumulative debts would raise a general concern towards the debt sustainability in the long run. For developing countries, such as Indonesia, debt services are the ultimate source of the foreign reserves’ outflows. The Indonesian government spending is less likely to
act as a stimulus for the economic growth due to the debt-service-to-revenue ratio being very high (Makmun, 2005; Suhud, 2004). Thus, the government objective function is not only to minimize the interest payment, but also to minimize the new borrowings. (
)
̅
(
(
) )
̅
)
(Government objective
(25)
function) (
(
)
(
)
Subject to equation (22), (23), and (24) The terms
(
)
is the discount factor that brings the interest payment to its present value. The
expected interest rate is a function of current interest rate and inflation rate. (
)
(26)
Solving the first order condition for
,
and
, we could obtain the optimal supply for
government bonds as formulated in equation (26). (Optimal supply for (
Government bonds)
) ))
(
(
(27)
Where (
(
(
) )( (
)
(
))
) (
(
)
)(
(( (
)(
(
))
(28.a)
)
(28.b)
) ( )
)
(28.c)
The optimal share of domestic government bonds can be obtained by rearranging equation (27) as follows:
(Optimal share for domestic (
(
(
) ))
government bonds)
(29.a)
( (
)
(
(
(
(Optimal share for external
) ))
government bonds) ) ))
(
(
(29.b)
3.4. Analysis and Policy Implication From equation (27), it is known that we could get an exact
value when
reaches 0 or 1. That is:
(
)
(30.a)
(
)
(30.b) (
(
))
However, this relationship does not apply inversely. When will converge to a certain value as
goes to zero,
will goes to infinity. While
goes to infinity.
(31.a) (
) ))
(
(
(31.b) (
) ))
(
(
(
(
(
) ))
The value of the optimal proportion of domestic and external government bonds would vary depending on changes in government bonds’ supply, domestic interest rate, external bond interest rate, and exchange rate. Ceteris paribus, the change in optimal proportion of domestic and external bonds with respect to the changes in
, ,
, and
is given in equation (32), (33), (34) and (35) respectively. (32)
(
(
(
) ))
(33) (
[
)(
(
(
(
)
(
(
))
(
(
(
) ))
(
(
) )(
)
) ))
(
)(
(
(
(
) ))
(
(
(
]
(34)
)
) )) (35)
(
)( (
) ))
(
(
)
) ))
(
(
(
Furthermore, rearranging equation (29.a), it can be concluded that there is an interrelationship between interest rates in the external government bond market and in the domestic government bond market through a structural change mechanism. This interrelationship is explained in equation (36).
( ( [
)( (
(
) ( (
)(
(36)
)
))
( (
)
)
(
( (
( ) ( ) ( ))
) )) ] )
From equation (33) and (34), the measurement of changes in expressed as below:
with respect to changes in
is
(
[
)(
(
(
(
(
(
(
)
(
(
))
(
(
)(
(37)
) ))
) )(
)
]
(
) ))
)
Given equation (17), the risk premium calculation can be approached by formula as below:
( ( [
)( (
(
) ( (
)(
(38)
)
))
( (
)
)
(
( (
( ) ( ) ( ))
) )) ]
( (
)
)
)
From equation (38) above we can conclude that the risk premium is a function of ,
,
, and
.
Graphically, the interrelationship of variables in domestic and external bonds market is depicted in figure 1. Suppose that there is an appreciation shock in the interest rate. Then the demand for external bonds will be decreased; the demand curve will be shifted to the left. As a consequence, the external interest rate will increase. If the government wants to keep the external interest rate remaining at the initial level while keeping the same amount of deficit, then the proportion of external bonds must be reduced, thus increasing the proportion of domestic bonds. This will further increase the interest rate in the domestic government bonds market.
Domestic Government Bond Market
External Government Bond Market rf
(1-β1) BG
BF1 e
BF0 e
β0 BG
r
rf1
r1
rf0
r0
β1 BG
BD
(1-β0) BG (1-β) BG
β BG
Figure 1 The interrelationship between variables when the government changes only the bond’s structure
Since the trade-off between the interest rates involves change in the market structure, thus changing the proportion of domestic and external bonds alone in order to sustaining steady interest rates in both markets is not the right policy to be taken. The government has to make adjustments in their deficit policy while changing the bonds’ proportion simultaneously. The mechanism is depicted in figure 2. Suppose there is a shock in the external bonds supply that increase rate is depreciated from
to
to
(in this case the exchange
). First the government must reduce the bonds proportion from
; this will reduce the interest rate of the external bonds market to the domestic bonds market will increase to
to
. However, the interest rate in
as the domestic proportion increases. Reducing
into
will decrease the external interest rate further to its initial level while reducing the domestic interest rate at the same time. Note that, in the domestic bonds market, the distance between between
and
and
is equal to the distance
. Thus, changes in the stock of government bonds multiplied by new
proportion of domestic bonds is equal to the changes in the proportion of domestic bonds multiplied by the current stock of bonds. (39.a) (39.b)
Domestic Government Bond Market
External Government Bond Market rf
BF1 e1
BF0 e0
rf1 rf2
r
β0 BG=β1 BG1
β1 BG
BD
r1 rf0
r0=r2
(1-β1) BG1
(1-β0) BG (1-β1) BG (1-β) BG
β BG
Figure 2 The interrelationship between variables when the government changes the bond’s structure and the outstanding amount
Likewise, the distance from
to
is equal to the distance between
and
. Assuming the demand
for domestic and external government bonds is linear, the relationship of changes in optimal stock of domestic bonds and changes in the domestic interest rates is determined by the slope of the demand of domestic bonds. Mathematically, this relationship is described in equation (40). (40)
Thus the optimal change in domestic bonds proportion is expressed as: (41)
Similarly, in the external bonds market, this relationship also applies. The slope of demand for external bonds will determine the impact of changes of the interest rates towards the optimal stock of external bonds.
|
(
| (
Since
)
( )
(42)
)
(
)
, the optimal change in stock of government bonds is then expressed as (43)
4. Empirical Analysis 4.1. The data In order to comprehend what equation (32) to (35) imply, we simulate the behavior of the optimal share of domestic and external government bonds with respect to changes in the supply of government bonds, domestic interest rate, external interest rate and also exchange rate. We use Indonesian government bonds’ market and macroeconomic data to get a more perceptive analysis. We gather the annual data of domestic government bonds, external government bonds, total government bonds, domestic bonds interest rate, external bonds interest rate, GDP, and USD exchange rate. The required reserve rate is regulated at 8% from the deposit amount, while the tax rate is assumed to be fixed at 10%. The statistical summary of the data is shown in table 5. Table 5 Statistical summary of the data
Units BD
Year Range
Min
Max
Mean
Std Deviation
(Trillion IDR)
2002-2011
648.75
992.03
756.06
120.37
F
(Million USD)
2004-2011
1,000.00
20,350.00
10,031.25
6881.649
G
B
(Trillion IDR)
2002-2011
648.75
1,187.66
834.32
191.33
r
%
2002-2011
3.64%
40.34%
17.14%
12.39%
r
%
2004-2011
1.74%
4.60%
3.13%
0.97%
Y
(Trillion IDR)
2002-2011
1,479.25
5,620.48
3,176.97
1,467.64
B
f
e USD/IDR 2002-2011 7.64E-05 0.00016 0.00011 Source: World Bank and Debt Management Office, Indonesian Ministry of Finance We regress the GDP with the domestic interest rate and inflation rate to get the
2.49E-05
slope. It yields a
2
negative slope and statistically significant at α=1%. The model is fit with R =0.99. The result is shown in table 6. We gather a monthly monetary rate (Bank of Indonesia rate) and a daily data of USD/IDR
exchange rate to manage a smoother expectation of
and
. The result yields in table 7 and 8
respectively. Table 6 Regression result of income and domestic interest rate
Dependent Variable : Y
Coefficient
Std. Error
Constant Y(-1) r i
1.55E+14 1.143033 -1.20E+15 9.15E+14
5.99E+13 0.012558 3.35E+14 2.06E+14
R-squared
0.998397
t-Statistic
Prob.
2.580011 0.0179 91.02045 0 -3.5804 0.0019 4.443617 0.0002
Table 7 Autoregression result of domestic interest rate
Dependent Variable: r
Coefficient
Std. Error
t-Statistic
Prob.
Constant r(-1) i
0.006037 0.84169 0.087315
0.001523 0.026306 0.012385
3.964791 31.99582 7.050037
0.0002 0 0
R-squared
0.984721 Table 8 Autoregression result for exchange rate
Dependent Variable: e Coefficient Constant e(-1) g i g_f(-2)
2.10E-05 0.815985 1.59E-06 -3.86E-05 0.000171
R-squared
0.891848
Std. Error 6.08E-06 0.055628 6.07E-07 1.61E-05 6.55E-05
t-Statistic
Prob.
3.456047 0.0012 14.66849 0 2.622589 0.012 -2.394661 0.0211 2.612621 0.0123
It is hard to obtain the slope of both demand for domestic government bonds and external bonds by simply using the bonds market’s data. The stock of Indonesian government bond has been growing higher over the analysis period, whereas the interest rates have decreased along with the improvement of macroeconomic condition. By simply regressing the yearly data, we will get negative demand slopes for both types of bonds, which is definitely untrue. To overcome this problem, we obtain some micro data from the bonds auctions. We use the data from the auction of a domestic bond with serial number FR0059 and an external bond with serial number RI0422 that is denominated in USD as a proxy for both types of bonds. For simplicity, we assume that the slopes would be linear and be fixed over the periods;
the changes of any parameter other than interest rate will only shift the demand curve, not affecting the slope. The summary of the data can be seen in table 9. Table 9 Summary of domestic and external bonds proxies
Bidding Amount Highest Yield Lowest Yield Weighted Average Yield Coupon Auctioned Amount Maturity Date Settlement Date
FR0059 IDR 4.98 trillion 7.41% 6.94%
RI0422 USD 6.32 billion
7.17%
3.85%
7.00% IDR 3.65 trillion 15-May-27 15-Sep-11
3.75% USD 2 billion 25-Apr-22 25-Apr-12
Source: Debt Management Office, Indonesian Ministry of Finance Using these data, we can obtain the value of the slopes of the demand for domestic government bonds with respect to changes in domestic interest rate, and also for the demand for external bonds with respect to changes in external interest rate. The value of the slopes is calculated in equation (44) and (45) respectively.
(44)
(45)
The slope of demand for external government bonds with respect to changes in domestic interest rate is measured by multiplying equation (46). The value of
with
⁄
. This multiplication yields a quadratic function as shown in
is given in equation (47.a).
(46)
√ Where
(47.a)
(
[
)
(47.b)
(
(
(
(
( (
(
[
)
(
(47.c) (
))
(
(
)
(
(
))
) (
(
)
))
)( (
(
)
(
)
)
)
))
(
(
)
(
(
))
)
(
(
(
(
(
) ))
(
(
)
)] (47.d)
(
)) (
)
(
))
(
(
(
)
(
(
( ))
) ))
)
) ]
4.2. The simulation As predicted in equation (32), the plotting diagram of in figure 3, the beta will go to infinity as
and
is forming a quadratic function. As seen
goes to zero. Nevertheless, since
is ranged from 0 to 1,
we can put limitations to get insight from the analysis. This paper concerns only when the government is running a cumulative deficit policy, thus the government budget surplus (that is the negative side in the diagram) can be neglected. It can be seen that the government is allowed to fund the deficit entirely from external bonds as long as the total stock of bonds are below
⁄ . Beyond this point, it is
suggested for the government to issue domestic bonds. Even though the optimal proportion for external bonds is decreasing as the stock of bonds increases, somehow it is suggested for the government to involve external funds in their portfolio. The value of the optimal share for external bonds when unlimited equals ⁄(
(
(
).
))
is
350% 300% 250% 200% 150% β
100% 50% 0%
-1E+15
-50% 0
1E+15
-100% -150%
BG
Figure 3 The relationship between supply of bonds and the optimal proportion of domestic bonds
From figure 4 and figure 5, it can be seen that there are negative correlations of the optimal proportion of domestic bonds and domestic and external interest rate respectively. By comparing figure 4 and figure 5, it can be seen that there is a positive correlation between domestic and external interest rate. This correlation is consistent with the interest parity that is showed in equation (17) and the interrelationship between interest rates that is shown in equation (37). 82% 80%
β
78% 76% 74% 72% 70% 0
0.2
0.4
0.6
0.8
1
r
Figure 4 The relationship between the optimal proportion of domestic bonds and domestic interest rate
82% 81% 80%
β
79% 78% 77% 76% 75% 74% 0
0.2
0.4
0.6
0.8
1
rf
Figure 5 the relationship between the optimal proportion of domestic bonds and external interest rate
As seen in figure 6, the value of beta is converged as the exchange rate increases. The value of beta when the exchange rate goes to infinity is expressed as below: (
(
)
(
(
(
))
) (
(
(
(47)
))
))
100% 90% 80% 70% β
60% 50% 40% 30% 20% 10% 0% 0
0.00005
0.0001
0.00015
0.0002
0.00025
0.0003
(USD/IDR)
Figure 6 The relationship between the optimal proportion of domestic bonds and exchange rate
1
Government bonds' supply
0.95
0.9
0.85
0.8
0.75
0.7
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
opt beta 0.75895 0.78151 0.77738 0.75401 0.75104 0.77888 0.77861 0.75941 0.79031 0.80766 beta
1
1
0.98597 0.95036 0.93321 0.9179 0.86471 0.85385 0.84783 0.83528
Figure 7 The simulation result for comparison between optimal and actual share for domestic government bonds
We also performed back testing to see whether the Indonesian government has implemented the optimal proportion for their bonds’ portfolio. As seen in figure 7, during the analysis period, the actual proportion of external bonds is lower than the optimal proportion. However, the required proportion for domestic bonds is increasing overtime. For the time being, the government has been increasing the share of external bonds. At this rate, the optimal proportion will be surpassed in the near future.
5. Conclusion This paper is purposed to determine the optimal proportion for domestic and external government debts. We develop a simple general equilibrium model emphasizing the important role of demand in forming the optimal structure of government bonds. We employ Bernanke’s CC-LM model in determining the demand of domestic government bonds, while assuming the demand for external government bonds is a function of risk premium, change of income in home country, and change of income in foreign country. On the supply side, we set the government objective as minimizing the interest payments and also the newly issued bonds
We found that there is an inversed-quadratic interrelationship between the supply of government bonds and the optimal proportion of domestic government bonds. As the supply of bonds goes to infinity, the optimal proportion of domestic government bonds will converge to a certain value. This implies that it would not be optimal for the government to rely only on the domestic debts to finance their deficit. The government still needs to issue the external bonds up to a certain proportion. Another main finding in the paper is, due to interrelationship between domestic and external interest rate, any change in the domestic bonds market will affect the external bonds market. Thus, changing the proportion of domestic and external bonds alone in order to sustain steady interest rates in both markets is not the right policy to be taken. The government has to make adjustments in their deficit policy while changing the bonds’ proportion simultaneously. Our empirical study through the Indonesian bonds market data suggests that the actual proportion of external government bonds is lower than the optimal proportion. However, the required proportion for domestic bonds is increasing overtime while the government has been increasing the share of external bonds for the time being. At this rate, the optimal proportion will be surpassed in the near future.
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