Is India’s Public Debt Sustainable?

Abstract

The article assesses the sustainability of public debt in India based on historical time series data on non-monetized liabilities/gross domestic product (GDP), revenue/GDP and expenditure/GDP of the combined central and state governments. The assessment based on unit root analysis of non-monetized liabilities/GDP, and co-integration analysis of expenditure/GDP and revenue/GDP shows the sustainability of public debt, mainly on account of accelerating GDP growth, lower cost of government borrowing, favourable currency composition and longer maturity profile of debt.

JEL Classification: H62, H63, C22, C32, C51

Keywords

Fiscal policy budgetary deficits debt management unit root co-integration

Introduction

A sustained increase in deficits and debt raises question about fiscal sustainability, solvency of government and efficacy of fiscal policy in restoring macroeconomic stability. In the recent past, concern about fiscal sustainability has resurfaced in India due to high levels of debt, persistently high fiscal and revenue deficits, lower gross domestic product (GDP) growth and unprecedented external imbalance. For instance, the Twelfth Finance Commission raised concerns over public debt sustainability in 2004 as debt was rising faster than GDP from 1996 to 2003. Since 2004, the concern modestly eased due to comfortable foreign exchange reserves of around US$300 billion in 2009–2010, and robust economic growth exceeding 7.5 per cent per annum during 2004–2008. The resulting revenue buoyancy helped both the central and state governments to reduce the combined gross fiscal deficits to below 4 per cent of GDP by 2007–2008 (Government of India, 2012). However, the quantum jump in fiscal deficits to over 8 per cent of GDP since 2008–2009 due to the expansionary fiscal policy to protect the economy from the global financial crisis and significant slowdown in GDP growth since 2011–2012 have raised concerns about sovereign rating downgrade and the sustainability of fiscal policy in India. Besides, the current level of debt/GDP (around 70 per cent) in India is far higher than the different Finance Commissions’ long-term target of debt/GDP below 60 per cent mark, and poses significant risk to macro stability. The record current account deficits (CAD) of over 5 per cent of GDP in 2012–2013 seem to have roots in high fiscal deficits since 2008–2009 in India. The major challenge to policymakers at present in India is to revive high GDP growth. However, revival of high growth without macro stability and macro stability with persistently high debt and deficits are incompatible. Thus, sustainability of fiscal policy emerges as a prerequisite for macro stability and robust growth in India. Given the importance of macroeconomic stabilization and the potential destabilizing effects of high public debt and fiscal deficits on the Indian economy, the key objective of this study is empirically verifying whether public debt in India has been sustainable, given the historical time series data on key macro and fiscal variables. However, whether the fiscal policy or public debt has been sustainable and whether it will be in future are two different issues to address.¹ In the present context, the focus is on whether public debt in India has been sustainable or not. It has an important implication in the sense that whether future continuation of the pattern reflected in the historical time series process would be consistent with the requirement of debt sustainability. It also offers to evaluate the success of fiscal consolidation process started since 2004 in the form of the Fiscal Responsibility and Budget Management (FRBM) Act, 2003 for the central government and the Fiscal Responsibility Legalization (FRL) for state governments, to contain and then reverse the trajectory of debt/GDP to keep the concern of India’s fiscal sustainability at bay.

Pioneering research on empirically examining the sustainability of public debt in the global context has been examined by Hamilton and Flavin (1986), Wilcox (1989), Trehan and Walsh (1988), Bohn (1998), Afonso (2005), IMF (2002) and ADB (2010). The empirical techniques used to assess debt or fiscal sustainability are the application of time series unit root test to discounted and undiscounted debt series, co-integration test to revenue and government expenditure series and estimating fiscal or primary balance response function.

In the Indian context, macro stability and debt sustainability became important research aspect since the mid-1970s or early 1980s due to hardening interest rates, expansion of public sector and consequent increase in deficits and debt/GDP (Chelliah, 1996; Khundrakpam, 1998; Rajaraman and Mukhopadhay, 1999; Rangarajan et al., 1989; Seshan, 1987). The above studies called for a comprehensive and deeper analysis on measurement of deficits and debt, due to substantial inter-governmental flow of resources and liabilities between different level of governments and Reserve Bank of India’s (RBI) monetization of deficits.

The study of Buiter and Patel (1992, 1993, 2006) on debt sustainability and solvency of government in the Indian context incorporated non-monetized liabilities of the central and state governments, long-term loan liabilities of central public sector undertaking (CPSU) excluding nationalized commercial banks and external liabilities net of forex reserves of the RBI. According to them, empirical testing of sustainability of public debt requires that debt/gross national product (GNP) and discounted debt series should not have positive stochastic or deterministic trend. The finding of non-stationarity of both present discounted value (PDV) of debt and debt/GNP based on formal time series unit root testing led to the conclusion that despite fiscal adjustment, the threat of government solvency and consequent fiscal crisis remained a major concern to the policymakers. Their findings also highlighted that maximal use of seignorage would not be enough to close the solvency gap. However, there are limitations of debt sustainability analysis based on solvency criteria that use the discounted debt series. Discounted debt series is highly sensitive to the choice of discount rate, and in India where plethora of interest rates exist; selection of a particular interest rate is problematic. Discounting different components of debt liabilities (e.g., internal debt consisting market debt and loans, treasury bills, small savings, provident funds and external debt with different interest rates and maturity structures) with a particular discount rate is misleading. The requirement of non-positive discounted value of debt at terminal point and generating adequate primary surplus (PS) under the assumption of dynamic efficiency or non-ponzi game condition (NPG) [cost of borrowing (r) strictly not less than growth rate of economy (g), i.e., r $ g] make discounted debt series analysis a weak and not so practical solvency criterion (Buiter and Patel, 1992). Instead, it is better to focus on strong and practical aspects that determine solvency and fiscal stability like unit root analysis of debt/GDP and co-integration analysis of revenue/GDP and expenditure/GDP.

Rajaraman and Mukhopadhay (1999) applied structural time series modelling (STM) to study the sustainability of domestic public debt without incorporating external liabilities and public sector undertakings. Their study constructed the first unbroken series for non-monetized debt of centre and states taken together from 1951 to 1998. Stochastic level and fixed slope with structural break in 1974 were the best fitting model to their data. A secular increase in forecasted debt/GDP as obtained by them reinforced the findings of Buiter and Patel that the debt/GDP path would not stabilize automatically without adequate correction of fiscal imbalance.

Jha and Sharma (2004) applied co-integration technique to the expenditures and revenues of the central government to study the domestic debt sustainability issue in both pre- and post-independence periods. Trend stationarity of both the expenditures and revenues series (i.e., I(0)) with structural breaks led to conclude that the central government domestic had been sustainable.

Ram Mohan et al. (2005) studied whether the central government’s debt had became unsustainable using decomposition analysis, which separates out the effects of GDP growth and the government’s past behaviour on fiscal deficits and debt level. Assuming a nominal GDP growth of 11 per cent and interest payments on government borrowing at 8.25 per cent, they argued that if the present government behaviour were to continue, not only the centre’s debt, but also the combined central and state governments’ debt would stabilize below the level set by the Eleventh Finance Commission at the end of 2009–2010. Rangarajan and Srivastava (2005), in this context, highlighted the adverse effects of high deficits and debt level of both centre and state governments on GDP growth and stressed the need of bringing down the debt/GDP from 80 per cent to a sustainable level of 56 per cent for long-term macro stability.

On the issue of determining the optimal or targeted level of debt/GDP in Indian context, report of the Eleventh Finance Commission (2000), the Twelfth Finance Commission (2004) and the Thirteenth Finance Commission (2009) and the study by Rangarajan and Srivastava (2005) shed light on the aspect of targeted debt/GDP to ensure the long-term prospect of stability and growth. All the studies uniformly targeted a debt/GDP below or close to 60 per cent mark to ensure substantial reduction in debt servicing burden and attainment of deficits targets under the FRBM Act. However, theoretically, it is difficult to determine a particular level of debt/GDP to ensure simultaneous attainment of different fiscal policy objectives such as growth, stabilization, distribution and equity. The optimal debt/GDP for growth maximization might not be the same if the objective is stabilization or equitable distribution. In Indian context, literature mostly targets a specific debt/GDP or deficits/GDP with the broader objective of macro stabilization for sustaining higher growth. Moreover, determination of optimal level of debt/GDP crucially depends on GDP growth rate, interest rates on borrowing and primary or fiscal deficits to GDP ratio. More importantly, the currency composition, maturity structure and ownership structure of debt play crucial role in determining the fiscal health of government, rather than just focusing on the level of deficits or debt/GDP (Roubini and Hemming, 2004).

Rajaraman et al. (2005) studied the debt sustainability of state governments considering the fact that states are highly heterogeneous in respect of several economic parameters such as per capita income, economic size, relative backwardness, fiscal health, etc. The study highlighted by using various indicators of solvency criteria that many states such as West Bengal, Punjab, Bihar, Orissa, UP, MP and Gujarat are dangerously close to the bankruptcy of their exchequer. A recent RBI study (2013a) assessed sub-national debt sustainability based on indicator analysis and panel regression of major states. Indicator analysis showed progress on most of the fiscal and debt sustainability indicators, but non-fulfilment of necessary and sufficient condition of generating PS remained as a concern. The panel regression results concluded that the reduction in sub-national debt/gross state domestic product (GSDP) was due to high nominal GSDP growth, reversal of interest cycle and policy measures such as debt swap scheme (DSS) and debt consolidation and relief facilities (DCRF).

Based on the key objective and review of literature, following are the focus of the present study

The non-monetized liabilities of both the central and state governments along with external liabilities evaluated at historical exchange rates.

As the issue of debt sustainability in India became an important research aspect since the mid-1970s, the study period for unit root analysis of debt/GDP is considered from 1974 to 2011. The Exhibit 1 too shows that the debt/GDP has increased very rapidly from 1974 to 2004–2005. Thus, the issue of debt sustainability has its roots since the mid-1970s and justifies the time period considered in present study. As the unit root analysis is highly sensitive to the specification of functional form, trend and detection of structural break, the present study addresses these issues carefully.

However, due to lack of availability of data on the combined central and state governments’ revenue and expenditure with netting-out of inter-governmental flow of resources and liabilities, the study period for co-integration and error correction model (ECM) of revenue/GDP and expenditure/GDP is considered from 1980 to 2011.²

The rest of the article is organized as following. The second section provides a brief description of the evolution of debt/GDP, expenditure/GDP and revenue/GDP over the years. The analytical framework for assessment of debt sustainability is in the third section, while the fourth section provides the empirical framework. The fifth section is devoted to empirical results on structural break, unit root test, co-integration test and ECM. The major conclusions and implications are in the sixth section.

Evolution of Debt/GDP, Revenue/GDP and Expenditure/GDP

The Exhibit 1 clearly indicates four distinct phases in the evolution of Aggregate Public Debt (APD)/ GDP from 1952 to 2011. The period from 1968 to 1974 and 2005 to 2011 showed downward movement while the period from 1952 to 1968 and 1974 to 2004 revealed rapid increase in debt/GDP. The Exhibit 2 shows three components of APD/GDP—the central government’s non-monetized domestic debt (CDD), the state governments’ non-monetized domestic debt (SDD) and outstanding external debt (OED) computed at historically given exchange rates. The movement of these three components shapes the evolution of APD/GDP. The upward movement of APD/GDP during 1952–1968 and 1974–2004 has been largely shaped by the rapid increase in OED/GDP, CDD/GDP and SDD/GDP, respectively. The decline in APD/GDP since 2004 onwards is mainly due to the decline in CDD/GDP and SDD/GDP. The declining trend of OED/GDP since 1992 has continued. The CDD and SDD comprise of the total non-monetized internal government liabilities in India. The important components of CDD are internal debt comprising market loans, bonds and treasury bills and other liabilities that include different types of small savings and provident funds, etc. The important components of SDD are market loans and bonds, small savings, provident funds, insurance and pension funds, loans from banks and other institutions. The movement of the combined central and state governments’ revenue/GDP and expenditure/GDP from 1980 to 2011 as revealed in Exhibit 3 shows the co-movement of the two series. Though the expenditure/GDP had exceeded revenue/GDP, the gap between the two never grew explosively during 1980–2011. Such evolution of expenditure/GDP and revenue/GDP has largely perhaps defined the movement of debt/GDP in India.

Assessment of Debt Sustainability— Analytical Framework

Following Hamilton and Flavin (1986), Wilcox (1989) and Buiter and Patel (1992), the inter-temporal budget constraint of government (IBC) can be developed by assuming the following. Let D_t and D_t₋₁ be the stock of debt at the beginning of period t and t − 1. Y_t, r_t, g_t and P_t are the nominal GDP, nominal interest rate on government borrowing (i.e., bond yield), nominal GDP growth rate and primary deficits, respectively. The IBC is written as D_t(1)r_tD_t₋₁P_t

Exhibit 1.

Source: Author.

Exhibit 2.

Source: Author.

Exhibit 3.

Source: Author.

Expressing Equation (1) by dividing GDP, we have dt(2)r_tg_td_t₋₁p_t

Expressing Equations (1) and (2) with forward-looking recursive substitution for finite and infinite period, we have

D_{t 1}_{j 0}^{N} (Z_{t j}) . D_{t N}_{i 0}^{N} {_{j 0}^{i} (Z_{t j}) P_{t j}}

(3)

D_{t 1}_{j 0}^{} (Z_{t j}) . D_{t N}_{i 0}^{} {_{j 0}^{i} (Z_{t j}) P_{t j}}

(4)

d_{t 1}_{j 1}^{N} (Z_{t j}) . d_{t N}_{i 0}^{N} {(_{j 0}^{i} Z *_{t j}) p_{t j}}

(5)

d_{t 1}_{j 1}^{} (Z_{t j}) . d_{t N}_{i 0}^{} {_{j 0}^{i} (Z *_{t j}) p_{t j}}

(6)

The Z in Equations (3) and (4) is (1 + r) and Z* in Equations (5) and (6) is {(1 + g)/(1 + r)}. D_t_+N and d_t_+N are the stock of debt and debt/GDP at the beginning of t + N period. The debt sustainability requires that PDV of all future PSs should not be less than that of the stock of debt at present. That is, the second term of RHS of both Equations (3) and (4) and Equations (5) and (6) should be at least equal to the LHS of respective equations.

D_{t 1}_{i 0}^{N} {(_{j 0}^{i} Z_{t j}) P_{t j}}

(7)

D_{t 1}_{i 0}^{} {(_{j 0}^{i} Z_{t j}) P_{t j}}

(8)

d_{t 1}_{i 0}^{N} {(_{j 0}^{i} Z *_{t j}) P_{t j}}

(9)

d_{t 1}_{i 0}^{} {(_{j 0}^{i} Z *_{t j}) P_{t j}}

(10)

The minus sign of primary deficits in Equations (7), (8), (9) and (10) indicates PS. The essential implications are that the first terms of RHS of Equations (3), (4), (5) and (6) are either non-positive or set to zero. This implies that PDV of net debt is zero at terminal point under dynamic efficiency.

_{j 0}^{N} (Z_{t j}) . D_{t N} D_{T} (Say) 0

(11)

_{j 0}^{} (Z_{t j}) . D_{t N} 0

(12)

_{j 0}^{N} (Z *_{t j}) . d_{t N} d_{T} 0

(13)

_{j 0}^{} (Z *_{t j}) . d_{t N} 0

(14)

Equations (11), (12), (13) and (14) depict two different types of terminal conditions. Less than zero refers to super solvency, while equal to zero refers to exact solvency. If the aforementioned conditions are not strictly satisfied by the current and future fiscal policy behaviour, fiscal policy becomes unsustainable under the theoretical setup. However, due to practical difficulty to know the future time path of debt and PS, the researchers apply time series econometric techniques to the historically given time series data on PS (or deficits), public debt or revenue and expenditures for fiscal sustainability analysis (Bohn, 1998; Buiter and Patel, 1992; Hamilton and Flavin, 1986; Wilcox, 1989). As the time series econometric analysis is based on historically given information on relevant variables, it is called backward-looking approach to fiscal or debt sustainability (HM Treasury, 2008). The backward-looking approach implicitly assumes the continuation of historically given trends and patterns of the relevant variables and empirical results in future and accordingly addresses the issue of fiscal sustainability. The forward-looking analysis focuses on the comprehensive projection of future expenditures and revenues of government and their impact on future debt and deficits. It entails wide-ranging indicators such as demographic changes, productivity, GDP growth, interest rates on borrowing and impact of expected programme-specific expenditures for fiscal sustainability analysis.

Empirical Framework

To assess the sustainability of public debt in India, the unit root test of APD/GDP with structural break in 2005, co-integration analysis of expenditure/GDP and revenue/GDP and ECM are used. Before approaching to the unit root test, co-integration and ECM analysis, it is better to specify the empirically estimable equations with theoretically derived and predicted sign conditions of parameters. Details of such exercise are put below.

Unit Root, Co-integration and Error Correction Mechanism

As the Exhibit 1 shows exponential trend of APD/GDP since 1974 with a downward break in trend in 2005, the univariate representation with drift, trend and the dummy for the break in trend can be written as _t(15)a₁a₂ t b_t−1DTn_t

Equation (15) is an AR(1) representation with intercept (a₁), trend components (a₂) and trend dummy (D1 = 1 after 2005, and 0 otherwise), while n_t is the errors which are iid with zero mean and constant variance. Testing unit root in Equation (15) implies testing whether the coefficient of Ln(APD/GDP)_t−1 (i.e., b = 1) is equal to one. That is, null hypothesis: H₀; b = 1, against the alternative hypothesis H₁; b ! 1. If b ! 1, it implies either b > 1 or b < 1. The case b > 1 is ruled out, as it relates to explosive series. Thus, either b < 1 or b = 1 has meaningful implication in unit root analysis (Dickey and Fuller, 1979, 1981). Equations (16) and (17) are the equivalent way of expressing Equation (15).

_t(16)a₁a₂th_t−1DTµt

\begin{matrix} Ln (A P D / G D P)_{t}_{1}_{2} t Ln (A P D / G D P)_{t 1} \\ _{i 1}^{m}_{i} Ln (A P D / G D P)_{t i} D 1 T_{t} . \end{matrix}

(17)

The value of m in Equation (17) is the lag length of the differenced of Ln(APD/GDP) and needs to be determined empirically to take care of auto-correlation problem. Equations (16) and (17) are the Dickey–Fuller (DF) and Augmented Dickey–Fuller (ADF) representation of (15). Testing of b = 1 in (15) is equivalent of testing |h| = 0 in Equation (16) or (17). Thus, the redefined null and alternative hypotheses are expressed as H₀; h = 0, as against H₁; h < 0. Sustainability of debt in the present context requires rejection of null-hypothesis in the presence of downward trend break.

For co-integration test between Expn/GDP and Revn/GDP, one needs to estimate Equation (18).

_t(18)ab_tp_t

In Equation (18), p_t is the error term. According to Jha and Sharma (2004) and Afonso (2005), a meaningful co-integration analysis between Expn/GDP and Revn/GDP for debt sustainability requires estimated β from (18) should be statistically significant and strictly not greater than one. In other words, β should be less than or equal to one. In brief, the sign condition of estimated β # 1.

Co-integration test used to detect long-term relationship between two variables does not rule out the possibility of short-term error or disequilibrium (Engel and Granger, 1987). Therefore, p_t, in Equation (18) is an equilibrium error. Thus, the findings of co-integrating relation between expenditure/GDP and revenue/GDP should have ECM representation and needs estimation of Equation (19).

(19)

In Equation (19), D denotes the first difference operator; Є_t denotes random errors, which are iid, and ${\overset{}{}}_{t 1}$ denotes one period estimated lagged value of errors from Equation (18). The W in Equation (19) is the speed of adjustment parameter and decides how quickly the equilibrium is restored. Thus, statistical significance of Ψ denotes a meaningful ECM representation. The null hypothesis of ECM representation of Equation (19) is H₀; W = 0, against H₁; W ! 0.

Technique of Estimation

To test whether Ln(APD/GDP) is stationary or not, we follow a couple of steps. First, visual inspection from Exhibit 1 reveals that there is downward structural change in trend in 2005. The econometric test for structural change as revealed in Table 2, too supports it. Thus, without incorporating break, direct application of unit root test would be misleading. Second, it is to check the correlogram statistics. As structural change exists, the correlogram diagram and statistics would be inappropriate and hence not reported. Third, de-trend the Ln(APD/GDP) series by estimating Equation (20) and then check the stationarity of estimated de-trended residuals by applying DF or ADF test.

_t(20)a₁a₂ t DTn_t

Let us denote the residuals after de-trending as Ln $(\overset{}{A P D / G D P})_{t}$ and test for stationary by estimating Equation (21) or (22).

L n (\overset{}{A P D / G D P}) a_{1} L n (\overset{}{A P D / G D P})_{t 1} e_{t} .

L n (\overset{}{A P D / G D P})

(21)

a_{1} L n (\overset{}{A P D / G D P})_{t . 1}_{i 1}^{m}_{i} Ln (\overset{}{A P D / G D P})_{t i} e_{t} .

(22)

Equations (21) and (22) are the DF and ADF representations, respectively. The modified null hypothesis following Perron (1989) is H₀; a₁ = 1, as against H₁; a₁ ! 1. Rejection of the null would confirm the stationarity of the estimated de-trended residuals from Equation (20). To test the existence of long-run equilibrium relationship between government expenditure/GDP (Expn/GDP) and revenue/GDP (Revn/GDP), it is important to check whether they are individually I(0), that is, stationary or not. If they are individually I(0) series, then public debt is strongly sustainable. If both the series are I(1), for testing co-integration, the Engel–Granger (EG) test of (18) is followed. The EG methodology is to estimate the β from Equation (18), check whether it is statistically significant and is less than or equal to one, that is, β # 1. Then, it is to collect estimated residuals errors to test whether they are serially co-related or not. After co-integration, following Engel and Granger (1987), estimating Equation (19) would ensure ECM representation between Expn/GDP and Revn/GDP. Table 1 summarizes the description, measurement and data sources of different fiscal and macro variables used in the study.

Data and Variables Description

Table 1.

Measurement and Data Sources of Variables

Variable	Description	Data Source(s)
CDD	Central governments’ internal liabilities, which exclude securities issued to international financial institutions and all monetized components. Internal liabilities consist of internal debt and other liabilities. CDD excludes liabilities on account of Market Stabilization Scheme (MSS) from 2004 to 2005 onwards.	Rajaraman and Mukhopadhay (1999) and various issues of Indian Public Finance Statistics, from 1980 to 2013, Government of India.
SDD	Aggregate non-monetized liabilities of states—loans and advances from centre to state governments.	Rajaraman and Mukhopadhay (1999), RBI (2013b) and various issues of Indian Public Finance Statistics, from 1980 to 2013, Government of India.
OED	Outstanding external public debt evaluated at historical exchange rates prevailing at the end of each financial year.	Various issues of Indian Public Finance Statistics from 1980 to 2013, Government of India
APD/GDP	(CDD + SDD + OED)/market value of GDP at current prices. Nominal GDP has been used as denominator to arrive at the debt ratios, as the debt stocks are nominal in nature.	RBI (2013b).
Expenditure/GDP	Combined expenditures of centre and states after adjusted for loans and advances from centre to state governments.	Various issues of Indian Public Finance Statistics, from 1980 to 2013, Government of India.
Revenue/ GDP	Combined revenue receipts of centre and states after correcting inter-governmental transfer.
GDP	Gross domestic product at current market prices with base year 2004–2005.	RBI (2013b).

Source: Author.

Results

Test for Structural Change in APD/GDP

The exponential increase in APD/GDP since 1974 warrants the incorporation of exponential trend to have a better fit of the data. The descriptive statistics of Table A1 in Appendix show that APD/GDP expressed in exponential trend produces better fit than linear trend due to a substantial decline in standard deviation and Jarque–Bera (JB) statistic to indicate normality in the distribution of Ln(APD/GDP). The negative and statistical significance of trend dummy (D1) confirms the that Ln(APD/GDP) has indeed entered into the new regime after 2005. Table 2 reports the results of trend break test of Equation (15).

Table 2.

Test for Structural Change

Regression equation: Ln(APD/GDP)_t = a₁ + a₂T + D1T + f_t, where D1 = 1 after 2005 and 0 otherwise
Dependent variable Ln(APD/GDP). Time period: 1974 to 2011. N = 38
Variable	Coefficient	t-Statistic	Probability	R² = 0.939Adj R² = 0.936F = 272.6Probability of F = 0.000
Constant	3.22	100.8	0.0000
Trend	0.034	19.4	0.0000
Trend dummy	−0.0051	−3.51	0.0013

Source: Author’s compilation from the estimates of (15).

Table 3.

Unit Root Test in Presence of Structural Change

Dependent variable: Ln $(\overset{}{A P D / G D P})$
Variables	$L n (\overset{}{A P D / G D P})_{t 1}$	$L n (\overset{}{A P D / G D P})_{t 1}$	$L n (\overset{}{A P D / G D P})_{t 2}$	$L n (\overset{}{A P D / G D P})_{t 3}$
Value	0.54	0.42	0.26	0.37
‘t’ value	−3.5*	3.41*	−2.52*	2.11*
	SBC = −2.98	AIC = −3.16	R² = 0.73	Adj. R² = 0.7

Source: Author’s compilation from the estimated regression Equation (22).

Notes: The ‘t’ value of a₁ is calculated based on the null hypothesis that H₀; a₁ = 1, while the null hypothesis for rest of the coefficients is equal to zero. ^*Denotes that the rejection of null hypothesis at 5 per cent significance level.

Testing Stationarity of Ln(APD/GDP) Using Unit Root Test

Table 3 reports the estimated results of Equation (22) for unit root test with a structural break in 2005. The ‘t’ value of Ln $(\overset{}{A P D / G D P})_{t 1}$ indicates that the null hypothesis of unit root, H₀; a₁ = 1 is rejected at 5 per cent level of significance. This implies that the null hypothesis of non-stationarity of Ln(APD/GDP) during the period of 1974–2011 with trend break in 2005 is rejected. Based on Schwartz Bayesian Criterion (SBC) and Schwartz Bayesian Criterion (AIC) criteria, the value of lag length has been determined to take care of auto-correlation problem and specification issue. The minimum value of AIC (−3.16) and SBC (−2.98) when DLn $(\overset{}{A P D / G D P})_{t 1}$ , DLn $(\overset{}{A P D / G D P})_{t 2}$ and DLn $(\overset{}{A P D / G D P})_{t 3}$ are added ensures that the model specification is correct. The high value of both the R² and adjusted R² depicts the goodness of fit of the model.

Co-integration and ECM Representation between Expn/GDP and Revn/GDP

The result of test of stationarity of Expn/GDP and Revn/GDP at level reported in Table 4 shows that both Expn/GDP and Revn/GDP are non-stationary, that is, I(1) series. The test statistics of ADF, PP (Phillips and Perron, 1988) and KPSS (Kwiatkowski et al., 1992) test fail to reject the null hypothesis of non-stationarity of Expn/GDP and Revn/GDP at level. However, both Expn/GDP and Revn/GDP become stationary, that is, I(0) after the first difference as ADF and PP test statistics reject the null hypothesis of non-stationarity. Thus, both Expn/GDP and Revn/GDP being I(1) are ideal for co-integration analysis.

The estimated co-integrating regression of Equation (18) is given below.

(\overset{}{E x p n / G D P})_{t}

(23)

‘ τ ’ values (3.56**) (8.27*).

Adj. R² = 0.69, DW = 0.65. ** and * indicate significance at 5 per cent and 1 per cent level.

Table 4.

Unit Root Test of Expn/GDP and Revn/GDP

Intercept and Trend				Intercept and Trend
Variables	ADF Test	PP Test	KPSS Test	Variables	ADF Test	PP Test
Expn/GDP	−2.038$	−2.12$	0.072@	DExpn/GDP	−5.92***	−5.91***
Revn/GDP	−2.62$	−2.15$	0.098@	DRevn/GDP	−3.8**	−3.47*

Source: Author’s compilation from the unit root test of expenditure/GDP and revenue/GDP.

Notes: $ = null hypothesis of unit root not rejected at 1 per cent significance level. @ = null hypothesis of trend stationarity is not rejected at 1 per cent significance level. ***, ** and * = null hypothesis of unit root rejected at 1, 5 and 10 per cent level significance.

The estimated value of β being less than one, following Afonso (2005), suggests that both Expn/GDP and Revn/GDP have meaningful co-integration for inter-temporal debt sustainability. Result of unit root test on estimated residuals from Equation (23) confirms that estimated residuals from the co-integrating regression of Expn/GDP on Revn/GDP of Equation (18) are I(0). Equation (24) represents unit root result of estimated errors from Equation (23).

{\overset{}{}}_{t} 0.401 {\overset{}{}}_{t 1} .

(24)

‘ τ ’ values (−3.13*); R² = 0.24; and * indicates significance at 1 per cent level.

The estimated ECM representation of Expn/GDP and Revn/GDP is given below.

(\overset{}{E x p n / G D P})_{t}

{\overset{}{}}_{t 1}

(25)

‘ τ ’ values (0.92) (3.57*) (2.18*)

R² = 0.33; Adj. R² = 0.28; and *indicates statistically significance at 5 per cent level.

Statistically significant and expected negative sign of ECM term $({\overset{}{}}_{t 1})$ ensures the stability of the model and suggests that Expn/GDP adjusts by 0.28 in the next period to a unit change in Revn/GDP. The positive and statistically significant coefficient of D(Revn/GDP)_t suggests that short-run change in Revn/GDP has a positive impact on Expn/GDP by 0.59. That is, in the short run, if Revn/GDP increases by one unit, the Expn/GDP increases by 0.587 units. Thus, one can interpret the value of 0.587 of D(Revn/GDP)_t and 0.991 of Revn/GDP as the short-term and long-term impact of Revn/GDP on Expn/GDP, respectively.

Major Conclusions

The major conclusions of the present study are following.

First, assessment based on unit root analysis of non-monetized liabilities/GDP, and co-integrating analysis of expenditure/GDP and revenue/GDP and consequent ECM shows that public debt in India has been sustainable during the study period. The conclusion of the present study based on empirical results differs from the existing studies by Buiter and Patel (1992, 1993). Statistical test suggests that the underlying time series of debt/GDP is stationary as opposed to the findings of non-stationarity (i.e., unit root) by Buiter and Patel. The finding of trend stationarity with downward break since 2005 of debt/GDP signifies the sustainability of underlying fiscal policy. The meaningful co-integration between expenditure/GDP and revenue/GDP and subsequent ECM with expected sign and statistical significance of co-integrating and adjustment parameters too confirm that public debt in India has been sustainable. The diagnostic checks suggest that the specification of the model under unit root test, co-integration test and ECM representation are consistent for model stability.

Second, the present study also provides a different explanation to the findings of public sector insolvency as obtained by Buiter and Patel (1992). Quadratic trend specification of their net total public debt (NTD)/GNP series and statistically significant positive deterministic trend support their conclusion of government insolvency rather than the finding of stochastic trend based on linear specification as reported by them.

However, the findings do not suggest that debt/GDP would come down automatically from its current level any time soon to the optimal level of below 60 per cent as set by different Finance Commissions (FCs) without implementation of suggested fiscal corrections measures by them. However, although the current debt/GDP ratios are higher than the FC’s target, public debt in India is sustainable mainly because of high GDP growth, lower cost of government borrowing, favourable currency composition and longer maturity profile of debt.

One major limitation of the study is its focus on backward-looking analysis that implicitly assumes the continuation of historically reflected trends and pattern in future to assess a country’s debt sustainability. Forward-looking fiscal projection or budget-forecasting exercise that requires full macro-econometric model would have been better from policy implication perspective and remains as an important aspect of future research.

Footnotes

Appendix

Estimated quadratic polynomial regression (A1.1) D(NTD/GNP)_t = 37.27 - 3.11 T + 0.207 T² - 0.78 (NTD/GNP)_t−1.

‘t’ value (3.93*) (−3.89*) (4.37*) (−3.98*). Adj. R² = 0.72.

All coefficients are significant at 5 per cent level and reject the null hypothesis of non-stationarity with quadratic trend. For tabulated critical value of quadratic trend specification to unit root test, see MacKinnon (2010, p. 15). Thus, Buiter and Patel’s (1992) finding of non-stationarity of NTD/GNP to establish unsustainable public debt is refined by the findings of trend stationarity rather than unit root.

Acknowledgements

The present article is based on the ongoing PhD at the ‘Institute for Social and Economic Change (ISEC)’, under the supervision of Professor M.R. Narayana on the ICSSR institutional doctoral fellowship scheme. An earlier draft was presented at the ‘Annual Conference on Papers in Public Economics (PIPE)’, in the honour of Dr Raja. J. Chelliah, conducted by the National Institute of Public Finance and Policy (NIPFP), New Delhi, during 7-8 November 2012. Grateful thanks are due to Dr Urjit R. Patel, Dr M. Devendra Babu and Ms B.P. Vani for valuable comments and suggestions on earlier version of the article. In addition, I sincerely acknowledge the anonymous referee whose comments and suggestions have been instrumental in revising this article. However, the usual disclaimer applies.

Notes

References

ADB. (2010). Fiscal sustainability in developing Asia. Asian Development Bank (ADB) Economics Working Paper Series No. 205, Asian Development Bank, Manila.

Afonso

(2005). Fiscal sustainability: The unpleasant European case. FinanzArchiv/Public Finance Analysis, 61(1), 19–44.

Bohn

(1998). The behaviour of US public debt and deficits. The Quarterly Journal of Economics, 113(3), 949–963.

Buiter

W. H.

Patel

U. R.

(1992). Debt, deficits and inflation: An application to the public finances of India. Journal of Public Economics, 47(2), 171–205.

Buiter

W. H.

Patel

U. R.

(1993). Indian public finance in the 1900s: Challenges and prospects. Centre Discussion Paper No. 706, Economic Growth Centre, Yale University.

Buiter

W. H.

Patel

U. R.

(2006). Excessive budget deficits, a government-abused financial system, and fiscal rules. India Policy Forum, 2(1), 1–54.

Chelliah

R. J.

(1996). Growth of Indian public debt: Dimensions of the problem and its remedies. In Chelliah

R. J.

(Ed.), Towards sustainable growth: Essays in fiscal and financial sector reforms in India, (pp. 98–137). New Delhi: Oxford University Press.

Dickey

D. A.

Fuller

W. A.

(1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74(366), 427–431.

Dickey

D. A.

Fuller

W. A.

(1981). Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica, 49(4), 1057–1072.

10.

Engel

R. E.

Granger

C. W. J.

(1987). Cointegration and error correction: Representation, estimation and testing. Econometrica, 55(2), 251–276.

11.

Government of India. Indian public finance statistics, various issues from 1980 to 2013. Ministry of Finance, Department of Economic Affairs. New Delhi.

12.

Government of India. Indian public finance statistics (2000). Report of the Eleventh Finance Commission. New Delhi: Finance Commission.

13.

Government of India. Indian public finance statistics (2004). Report of the Twelfth Finance Commission. New Delhi: Finance Commission.

14.

Government of India. Indian public finance statistics (2010). Report of the Thirteenth Finance Commission. New Delhi: Finance Commission.

15.

Hamilton

J. D.

Flavin

M. A.

(1986). On limitations of government borrowing: A framework for empirical testing. American Economic Review, 76(4), 808–819.

16.

HM Treasury. (2008). Long-term public finance report: An analysis of fiscal sustainability. United Kingdom (UK): HM Treasury.

17.

IMF. (2002). Assessing sustainability. Prepared by Policy Development and Review Department. International Monetary Fund, Washington, DC.

18.

Jha

Sharma

(2004). Structural break and unit roots: A further test of the sustainability of the Indian fiscal deficits. Public Finance Review, 32(2), 220–231.

19.

Khundrakpam

J. K.

(1998). Sustainability of central Government debt. RBI Occasional Paper, 19(1), 61–87.

20.

Kwiatkowski

Phillips

Schmidt

Shin

(1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54(1–3), 159–178.

21.

MacKinnon

J. G.

(2010). Critical values for co-integration tests. Queen’s Economic Department Working Paper No. 1227. Queen’s University.

22.

Perron

(1989). The great crash, the oil price shock, and the unit root hypothesis. Econometrica, 57(6), 1361–1401.

23.

Phillips

P. C. B.

Perron

(1988). Testing for a unit root in time series regression. Biometrica, 75(2), 335–346.

24.

Rajaraman

Bhide

Pattainaik

R. K.

(2005). A study of debt sustainability at state level in India. Reserve Bank of India.

25.

Rajaraman

Mukhopadhay

(1999). Sustainability of domestic public debt in India. NIPFP Report No. 97.

26.

Ram Mohan

T. T.

Dholakia

R. H.

Karan

(2005). Is India’s central debt sustainable? Revisiting an old debate. Economic and Political Weekly, 40(10), 951–959.

27.

Rangarajan

Basu

Jadav

(1989). Dynamics of interaction between government deficits and domestic debt in India. RBI Occasional Paper, 10(3), 163–220.

28.

Rangarajan

Srivastava

D. K.

(2005). Fiscal deficits and government debt: Implications for growth and stabilization. Economic and Political Weekly, 40(27), 2919–2934.

29.

RBI. (2013a). Sub-national debt sustainability: An assessment of the state governments. State Finance: A Study of Budgets of 2012–13, RBI, Mumbai.

30.

RBI. (2013b). RBI handbook of statistics on the Indian economy 2012–13. RBI, Mumbai.

31.

Roubini

Hemming

(2004, 16–17 January). A balance sheet crisis in India? Paper presented at the IMF/NIPFP Conference on Fiscal Policy in India, New Delhi.

32.

Seshan

(1987). The burden of domestic public debt in India. RBI Occasional Paper, 8(1), 45–77.

33.

Trehan

Walsh

(1988). Common trends, the government budget constraint and revenue smoothing. Journal of Economic Dynamics and Control, 12(2–3), 425–444.

34.

Wilcox

D. W.

(1989). The sustainability of government deficits: Implications for the present value borrowing constraint. Journal of Money, Credit and Banking, 21(3), 291–306.