Budget Deficits and Inflation: The Case of Sri Lanka

This paper explores the relationship between budget deficits and inflation in Sri Lanka using three approaches: the Granger causality test, Auto Regressive Distributed Lag (ARDL)/Bound test, and ARDL long run cointegration coefficients analysis with time series data for the time period of 1957-2016. Three statistical procedures are also exploited in the study, namely, Toda-Yamamoto (1995) Granger causality test, ARDL/Bound test procedure developed by Pesaran and Shin (1999) and Pesaran et al. (2001), and ARDL Error Correction Model. Moreover, four model specifications are formed that are distinguished by two budget deficit indicators, namely, the budget deficit scaled by narrow money (BDMI), which was developed by Catao and Terones (2003), conventional budget deficit indicator, which is the budget deficit as a per cent of Gross Domestic Product (BDGDP), and two inflation indicators, namely the Consumer Price Index (CPI) and GDP deflator. The findings of the study are statistically significant at acceptable levels (p=10%, p=5%, and p=1%). The results suggest a unidirectional causality coming from the budget deficits to inflation in Sri Lanka and the existence of a long run cointegration with high magnitudes, which interprets that a one percentage point change in natural logarithms of BDM1 and LNBDGDP, will result in a 1.5-2.5 per cent change in inflation in Sri Lanka as measured by natural logarithms of Colombo Consumer Price Index (LNCCPI) and Gross Domestic Product Deflator (LNGDPD). Further the study concludes that the importance of maintaining low budget deficits in view of reaching inflation targeting in Sri Lanka.


Introduction
The relationship between budget deficit and inflation has become one of the key concerns in public economics. As inflation is considered the main culprit that hinders economic development particularly in developing countries, economists are concerned about the determinants of inflation to minimise possible adverse effects in respective economies. The determinants of inflation and their effects, however, may vary among economies owing to country specific economic policies and their priorities. Some economists argue that mismatches of policies and their priorities may also lead to deteriorating economic growth and development objectives of a country. Hence, understanding the interrelationship between policies is very important in formulating and implementing overall economic policies in an economy. This study aims to examine the relationship between monetary policy and fiscal policy in terms of the relationship between the budget deficit and inflation as the main variables concerned.
The relationship between budget deficit and inflation has received extensive attention in the history of economics. As the Keynesian approach explains, public sector variables affect money demand and prices and thereby, aggregate demand. With the concept of Intertemporal Budget Constraints, the monetary-fiscal policy relationship is widely discussed. Moreover, the argument of Unpleasant Monetarist Arithmetic (Tomas J. Sargent and Neil Wallace) suggests that monetary policy may limit its control over price stability under a fiscal dominance regime.
In recent decades, many economists have contributed with different ideas in favor of the role of fiscal policy in an economy. One of the milestones in this regard is the Fiscal Theory of Price Level that emphasises the importance of fiscal factors in price determination.
Traditionally, the budget deficit-inflation relationship is explained through the argument of the inflationary effect of seigniorage i.e. the printing of money by means of financing the budget deficit. Creation of money in such a way is sometimes referred to as inflation tax as it creates an inflationary effect, and is similar to imposing a tax whereas the amount of money created through inflation generates an income to the government as any other government tax. Particularly, in the case of developing countries', economists highlight adverse effects of fiscal policy on the basis of inflationary financing. Such criticism may be backed by undesirable Current AC (Surplus (+) /Deficit (-)) 5.1 1.1 0.4 1.7 -1.9 -3.0 -1.6 Overall Deficit (after Grants) -2.4 -5.8 -6.1 -11.5 -8.4 -8.5 -6.7 Source: Central Bank Annual Reports In the wake of fiscal balances, during the period of 1978-87, overall budget deficits have shown a steady increase to a double-digit (-11.5 per cent) from around -2.5 per cent recorded in the 1950s.
After 1987, the overall budget deficit has declined moderately to around -7 per cent of GDP. With respect to inflation indicators, Consumer Price Index (CPI) and GDP Deflator (GDPD) are widely used. In Sri Lanka, there are three inflation indicators: Colombo Consumer Price Index (CCPI), Wholesale Price Index (WPI) and GDPD as far as historical data is concerned.
As for updating, the base year of CCPI has been changed to 1950=100, 2002=100 and 2006/07=100. Further, as an alternative indicator to CCPI, National Consumer Price Index (NCPI) was introduced recently. Inflation rate measured by CCPI was a double-digit figure for two decades starting from 1978 and it relatively averaged to a higher value of 9.6 per cent and 7.8 per cent respectively during the next consecutive decades. Also, during earlier decades, CCPI inflation recorded a lower rate of about one per cent. Similarly, during the first three decades starting from 1968 GDPD recorded a double digits' inflation rate and during the next consecutive decades there was a slight decline to 9.0 per cent and 7.8 per cent, respectively. In contrast to historical data the budget deficit and inflation rate seem to follow a similar trend; during the period of first four decades starting from the 1950, budget deficit remained between 2.4 and 11.5 per cent while inflation rate remained between the range of 0.6-12.6 per cent.
During the last three decades starting from 1988, the budget deficit changed from 8.4 to 6.7 per cent while CCPI inflation rate has changed from 12.8 to 7.8 per cent. 6 With respect to the patterns of other variables in this study, average historical data categorised by decades is shown in Table 2. Accordingly, in the 1950s, growth of narrow money supply (M1) stood at 2.5 per cent and then, it almost doubled decade by decade, to 12 per cent during the 1968-77 period. Over the period except the last decade, broad money supply (M2) followed a similar pattern of change. A higher volatility of annual growth rates has shown, however, in the growth rates of M1 in comparison to M2.
Regarding the change in the exchange rate of Sri Lankan Rupee (LKR) as against the United States dollars (USD) also amounted to 14.3 per cent during 1978-87 periods, doubling the growth rates in the previous decade. However, it has gradually decreased thereafter.
Conversely, GDP growth rate stood at 3.4-3.8 per cent over three decades starting from 1951, and it increased to 4.8-6.0 per cent thereafter. The highest growth rate was recorded during the last decade. In addition, the growth of foreign reserves shows noticeable high volatility during the period concerned. In summary, the comparison of data suggests that many of the variables such as M1, M2 and exchange rate, importantly, seem to be following the similar pattern of changing; the variables have gradually increased until the period of 1978-87 and slightly fallen thereafter.

Theoretical overview of monetary policy and fiscal policy
There are some different views in economics on the interrelation of fiscal policy and monetary policy in an economy 2 . Establishing one of the milestones in economic history, the Keynesian 2 In this study, fiscal policy and monetary policy are considered in the scope of only the budget deficit and inflation relationship.
and the primary surplus is given = (ℒ − ).
Where −1 −1 is interest payments on government debt holdings in previous period, is government constant expenditure, denotes government borrowings from the household sector in current period and − −1 indicates the change in money supply between two periods. Thus, primary surplus denotes the difference between lump-sum taxes and fixed expenditure.
Alternatively, IBC can be demonstrated as in Eq.
(2) in real terms. 5 Where 1 is real interest rate, and are primary surplus and debt respectively, and present value of present and future government tax collection ( , ).
In other words, the given endowed government bonds are assumed to be in real terms and financed through taxes and seigniorage. In the scope of IBC, as against the outstanding debt stock, the government needs to maintain a surplus, by changing expenditure or revenue.
Contrary to the theoretical views in the previous section, some economists argue that such an impact of seigniorage on inflation as explained in the monetarist arithmetic cannot be applicable for some counties, particularly developed countries (King 1995, Woodfold, 1996. Similarly, if fiscal policy influences price level through money supply, it is again supportive to the monetarist's argument that inflation is determined by monetary factors rather than fiscal factors (Carlstrom and Fuerst 2000). Among these arguments, the Fiscal Theory of Price Level (FTPL) explains the alternative approach of the behavior of monetary policy and fiscal policy in determining and controlling price. Introducing FTPL, Leeper (1991), Woodford (1998), Sims (1997) and Cochrane (2005) discuss that inflation would be determined by policy coordination, led by merely fiscal policy rather than monetary policy. As given in the following formula, FTPL describes that any change in real primary surpluses and discount rate is absorbed by a change in price level, owing to constant real debt stock with the assumption that IBC is satisfied. Therefore, the opponents argue price determination is directly linked with fiscal policy matters.
Explaining further with several theoretical aspects of FTPL, firstly, assuming that government's bond holdings and money supply in IBC are given in nominal terms, FTPL suggests that the value of the initial amount of assets and change in such assets will be determined through price changes over time. IBC, therefore, indicates the real value of government bond holdings and money supply with respect to time. Supposing that monetary policy and fiscal policy are independent and similarly, even these policies do not consider the status of IBC, and the price level should change to satisfy IBC, in response to the nominal change of the variables in IBC.

Research methodology
Different statistical methods were used in empirical studies to assess the relationship between budget deficit and inflation where each has its own advantages and disadvantages. In recent studies, the budget deficit-inflation relationship has been examined in different approaches namely causality analysis, linear regressions, cointegration analysis, other non-linear analysis, etc. Among them, the Granger causality test provides a statistical hypothesis in deciding whether one time series granger causes another. In other words, this approach exposes dependent-independent relationships among variables. The cointegration approach considers the predictability of two or more-time series. Thus, the time series are said to be cointegrated, if such series are non-stationary at levels, but stationary at the first differences. In other words, cointegration describes a long run relationship of time series. In the error correction approach, error correction models estimate the short-term and long-term effects of one time series to another provided that those time series are cointegrated. In other words, the speed of adjustment of a dependent variable to equilibrium is declared in response to a change in other variables. Some researchers, however, use a variety of statistical methods and tests with the mix of above alternative approaches. In terms of methods and tests, methods such as the Ordinary Least Square (OLS) model, Vector Auto Regressive (VAR) models and Vector Error Correction (VEC) models are also commonly used with the appropriate statistical tests.
Researchers further consider a variety of variables that are appropriate for the model specifications that represent all four sectors in the economy: fiscal sector, monetary sector, external sector, and real sector.
In this study, three approaches are used to explore the relationship between budget deficit and inflation, in terms of adopting the best suited methods for the investigation: Granger causality test method, which has been developed by Toda-Yamamoto (1995); Bound test procedure with Auto Regressive Distributed Lag (ARDL) approach, which has been developed by Pesaran and Shin (1999) and Pesaran et al. (2001); ARDL error correction model specifications, which is used to capture long-run relation with short term dynamics.

The model specification
In the model specification, budget deficit is considered as the independent variable in two different ways which include budget deficit scaled by GDP and budget deficit scaled by narrow money (BDM1). Accordingly, BDM1 considers the impact of change in money supply even with the constant budget deficit, in measuring the inflationary effects. Other explanatory variables, along with the two indicators of inflation, are also considered in this study, with respect to four separate multivariate models.
This study follows the model specification designed by Catao and Terrones (2003). The basic formulation in modeling BDM1 is based on the general equilibrium model developed by Liungqvist and Sargent (2000), which explains the relationship among money supply, inflation, and government sector variables. The variables are incorporated by means of the government budget constraint that explains fiscal-monetary relation in explaining inflation with a theoretical approach. In this specification, several assumptions are made: the representative household maximises its utility; the economy is a small open economy; money in the economy is as explained in the shopping time model. The shopping time model also entails several assumptions: constant amount of income per period (y), that is divided into private consumption (ct) and government consumption (gt); one unit of time, that is divided into leisure (lt) and shopping (st). The subsequent equations are demonstrated as follows: Given + ≤ and + = 1 Where t ≥ 0 and y > 0, Where, Hc, Hcc, Hm/p,m/p ≥ 0 and Hc,m/p ≤ 0, which denote that shopping time is a function of consumption and money holdings; the shopping time is negatively linked to real money balances of the household ( +1 ) owing to transaction cost and m and p denote money supply and inflation respectively. According to the money demand function of the shopping time model, the return on risk-free bonds is higher than money holding with transaction costs.
With the description of the shopping time model, equations related to the household sector and government sector are presented to signify the equilibrium positions in each sector.
In Eq. (6), the components are defined: nominal money balances with household is +1 during the period between time t and t+1; denotes lump sum tax; is the real value of one-period risk-free bond; is the price level and denotes the real gross rate of return.
Therefore, the necessary condition of above maximisation problem is: Eq. (7) can be rewritten as in Eq. (8), that is equivalent to the Fisher equation: Where and imply the real interest rate and inflation rate, respectively. In addition, shows the inverse relation of inflation rate on real gross return on money holdings during the time t and t+1 and 1 + = indicates the gross nominal interest rate.
Accordingly, the relevant Lagrangian equation with respect to Eq. (4), (5) and (6) is: Related first order conditions are derived with respect to , , +1 , +1 as given in following equations: In addition, the following expression for λ is obtained using Eq. (8) and Eq. (9).
Similarly, by substituting Eq. (14) to Eq. (12), the real interest rate is expressed: Furthermore, Eq. (12) and Eq. (13) are rearranged to obtain Eq. (16) which equates cost and benefits of holding a marginal unit of real money. In other words, there may be a loss, because of money holdings instead of investing in interest bearing bonds whereas the consumer may be benefited by having money in hand, owing to reduce shopping time. Accordingly, Eq. (16) is derived: To derive money demand function in this model, Eq. (17) forms as follows, using Eq. (11), Eq. (14) and Eq. (16) and equating u c (t) and u ℓ (t) at ℓ = 1 − ( , +1 ). ( Finally, the money demand function is defined in the first part of Eq. (18): Similarly, the first part of the equation is equal to the latter parts with respect to the expressions given in Eq. (7) and Eq. (8); the third part of the Eq. (18) demonstrates that is positively related to money demand while negatively related to the interest rate 1+ as derived in Eq.
(8). Furthermore, according to the explanation of Catao and Terrones (2003), since the model assumes interest rate parity of ( ⋆ = ), the last part of the Eq. (18) shows that is positively related to money demand and is negatively related to international interest rate ⋆ and domestic inflation rate = +1 . With the completion of household sector equilibrium, the government sector is to be explained.
The government budget constraint as explained in the chapter on theoretical literature is: Where denotes the government borrowing from the private sector in terms of units of goods in time t and denotes money stock. Further, 0 and 0 are assumed to be given in the model. Finally, the long run equilibrium is formed to obtain an estimated form of this study, incorporating equations related to the household sector and government sector.

18
In forming the long run equilibrium, the additional assumptions with respect to prices and taxes are given; demand for money equals the supply of money ( = ); bond holding is ( = ) at the point that household maximises its utility and entity holds that = + .
Therefore, economy-wide budget constraint is, Furthermore, in the long run stationary equilibrium, the following conditions are assumed: As shown in Eq.21, the stationary equilibrium is obtained using Eq. (15) and Eq. (18).
In order to form the estimated formula, Eq. (21) Hence, the estimated form, = − is derived considering the approximation: Having defined BDM1, the ARDL model specification is formed along with the other variables.

ARDL model
The synthesis of budget deficit and inflation is formed according to the procedure proposed by Pesaran and Shin (1999) and Pesaran et al. (2001), in terms of cointegration and error correction models in this study, which provides an appropriate framework to find the long run relationship with short-run dynamics. One advantage of the ARDL methodology is that it avoids the prerequisite of the existence of the same order of integration in time series data as other methodologies. In addition, the ARDL model/Bound testing methodology estimates and interprets a simple model with a single equation form. Furthermore, the different lag levels may be included into the model, with respect to dependent and independent variables.
Before proceeding to the cointegration process with the ARDL model equations, it will be necessary to describe properties of ARDL.
Where y is the dependent variable; α 0 is the constant term and 1 is the coefficient of linear trend, is the coefficient of lag variables of dependent variables used as repressors; β is the coefficient of other explanatory variables; εt is the random disturbance term.
Secondly, in the long run ARDL model, the long run coefficients are presented in Eq.24.
Accordingly, ARDL cointegrating regression relationship EC and the bound test null hypothesis form is derived considering the differences of Eq.23 and substituting Eq.24: Conversely, if the calculated F-statistics fall above the upper bound, the upper bound assumption is accepted, with the meaning that there is a long run relationship between dependent and independent variables. If the computed value falls between the lower and upper bounds, however, the result tends to be inconclusive.
It is also worth to note that the ARDL model assumes no serial correlation issue in the system owing to the fact that the formation includes lag variables of dependent variables as regressors.
Serial autocorrelation is known as the situation where the residuals of a series that is known as the unexplained part of a regression, are correlated with its own lag values. Simply, ε of the above model is said to be serially correlated, if ε is correlated with ε −1 , ε −2 and so on.
If the model is suffered from a serial correlation issue, however, the coefficient of the regression is considered to be biased and respective standard errors may be incorrect. Thus, it is important to identify the serial correlation issue of a certain model before proceeding with the model.

Toda-Yamamoto granger causality procedure
The Granger causality between the dependent variable and independent variables is very important in modeling ARDL single equation formation that finds the causality between two or more series of stationary data that are cointegrated. As an example, with two time series data 'x' and 'y', x is said to Granger-cause y if y can be explained/forecasted more strongly after taking x and y together, rather than taking only y. In testing Granger causality, a null hypothesis is tested against an alternative hypothesis at the appropriate significance level, based on the model specification as demonstrated below, assuming the VAR model.
Where and symbolise coefficients for the variables x and y. Regarding Eq.26, the relevant null hypothesis is set to be: H0: 1 = 2 = ⋯ = = 0 that implies that x does not Granger cause y, as against H1 that assumes, H0 is not true. Similarly, the set of hypotheses is also formed with respect to Eq. 27, : 1 = 2 = ⋯ … … … = = 0 , that assumes y does not Granger cause x. Accordingly, the existence of Granger causality is concluded by rejecting H0 with a suitable confidence level.
Engle and Granger (1987), however, point out that if the data is stationary at the different orders, even though they are cointegrated, the testing procedure explained above may be erroneous. The Engle-Granger causality test, therefore, may not provide a strong decision rule for the data in the current study. Therefore, the Granger causality procedure developed by Toda and Yamamoto (1995) is used in this study, as that is the most appropriate testing procedure for the data in the study that are integrated in different order. Toda and Yamamoto (1995) provide very comprehensive information about the procedure with the abstract of their paper as given in the following quotation: The Toda and Yamamoto procedure, thus, provide the testing method, which is free from the problems of the order of integration or cointegration.
The testing process has several steps. The first step includes determining the maximum order of

Empirical analysis
This study examines the relationship between budget deficit and inflation in Sri Lanka in terms of causality, long run cointegration and magnitude of long run coefficients using time series data from the period 1957-2016. As explained previously, the variables and models are appropriately applied with statistical tests, 6 to assess this relationship. In summarising the variables in the study, firstly, two measures of budget deficit are used: budget deficit scaled narrow money supply (BD/M1), budget deficit scaled by Gross Domestic Product (BDGDP).

Secondly, two alternative indicators of inflation are also considered in this study: Colombo
Consumer Price Index (CCPI) and GDP deflator. Additionally, the study considers several explanatory variables in the selected models: the exchange rate of Sri Lankan Rupees vs. US$ (US$), Broad money supply (M2), GDP growth, three months Treasury Bill Yield (TBR). The data in this study are taken from the latest Annual Reports of the Central Bank of Sri Lanka.
Graphical representation reveals the hypothesis of this study demonstrating a long run trend with random cycles. LNBDM1 shows an upward trend with a curvature. In addition, the variables namely, LNFR, LNUSD and LNM2 and LNTBR demonstrate an upward trend. In common, the variables appear to be a mix of stationary and non-stationary.

The analysis of unit root
Although testing for the unit root is not a necessary condition or pre-test requirement in the ARDL system, owing to the ability to deal with variables in the different order of integration, it is advisable to test for the presence of unit root to clarify that the data series are not I (2). This is because the system of ARDL tends to be erroneous, when dealing with integrated stochastic trends of I (2) variables. Thus, with understanding of the nature and the behavior, the variables are tested for prevalence of unit root. To test for the unit root, Augmented Dikey-Fuller (ADF) test has been applied in this study with Akaike Information Criteria (AIC).
Accordingly, t-statistics of the ADF test statistics are compared with the test critical values at different significance levels. Consequently, the null hypothesis of non-stationarity is rejected considering related probabilities to determine order of integration. The t-statistics and related probabilities demonstrate the variables are integrated at different levels: integrated at levels I (0) or integrated at the first difference I (1).
The results show that the stationarity of variables is varied owing to the presence of different probabilities with different options. The statistical tests, however, reveal that none of the variables are I (2). This data series, thus, are well fitted for the ARDL model specification, which are designed particularly for the data in this nature.

Estimated models
There are four functional forms modeled in this study: VAR models in the Toda-Yamamoto Ganger causality analysis and the ARDL model specifications in cointegration analysis. Thus, the functional forms are designed based on the nature of the variables and the order of integration. Accordingly, this study considers four separate models, which are divided into two, depending on separate alternative indicators for inflation: CCPI and GDPD.

Causality analysis
In performing the causality test, this study examines the nature of the causal relationship between budget deficit and inflation. In other words, the causality test is carried out to determine the relationship, which was established in the hypothesis of this study; the causality may come from budget deficit to inflation. As mentioned in the methodology, this study applies the Toda-Yamamoto procedure to test Granger causality followed by the pre-tests for serial independence and stability. In line with pre-testing steps, maximum lag length (dmax) is determined based on the Akaike Information Criteria (AIC) and maximum order of integration (k) is concluded in line with the unit root analysis. Subsequently, this study has applied the VAR residual serial correlation LM test with the null hypothesis of no serial correlation at the lag order, of which acceptance is based on higher chi-square probabilities.
In addition, the pre-testing procedure has observed the AR root graph to ensure the stability of the VAR model, which must proceed with the Wald test at the next step.
Regarding all the models, the maximum order of integration (k) equals one that indicates all the variables are I (0) or I (1). Also, the maximum lag length (dmax) selected on the basis of AIC is higher than the value of k. With the acceptance of the null hypothesis at 5 per cent significance levels, the result of the serial correlation LM test concludes the serial independence of all four models. Further the result of the stability test also conclude that the selected VAR models are dynamically stable.
With the success of pre-tests as described above, the selected VAR models have been rematerialised imposing (k+dmax )th lags as exogenous variables. Subsequently, with the result of the Granger causality/Block Exogeneity test, Granger causality has been determined by rejecting the null hypothesis of no dependent-independent relation between the selected two variables with lower probabilities. Using the same logic, higher probabilities conclude acceptance of null hypothesis.
The results, as shown in Table 3, indicate that all four models reject the null hypothesis at the one per cent significance level, confirming causality coming from budget deficit to inflation.
Similarly, all four models reject the opposite causality by accepting relevant null hypotheses.
This concludes that a unidirectional relationship exists between representative variables namely BDM1 and BDGDP (indicative variables of the budget deficit) and CCPI and GDPD (two indicators of inflation) at acceptable significance levels: model 1 at 10 per cent, model 2 at 5 per cent, model 3 and model 4 at one per cent. On the other hand, all null hypotheses of no opposite direction cannot be rejected with a very high significance level. In other words, the unidirectional relationship of the deficit-inflation relationship has been revealed with the evidence given in Table 3 below. Importantly, irrespective of the difference in the indicators of both budget deficit and inflation, the results are confirmed with strong statistical evidence.
This study, thus, concludes strong statistical evidence for the existence of unidirectional causality, coming from budget deficit to inflation in Sri Lanka.
In completion of testing procedure for Granger causality, cointegration testing process can be proceeded to explore budget deficit-inflation interaction. Regarding the cointegration analysis, the ARDL model specification designs a single equation system where the dependentindependent causality is considered to be very important.
In addition, the results provide strong evidence to proceed with the estimated models for further investigation of possible long-run cointegration.

ARDL regression and bound test procedure
To assess the cointegration between budget deficit and inflation, the ARDL model specifications associated with ARDL/Bound test procedure need to be formed. To form the relevant ARDL model specifications, this study follows the similar model formulation that tested for Granger causality in the previous section. The illustrative long run ARDL model formulation is as follows:- + ω 0 CCPI −1 + ω 1 BDM1 −1 + ω 2 M2 −1 + ω 3 US$ −1 + ω 4 TBR −1 + ω 5 RGDP −1 + ε The graphical representation suggests a mix of possible stationarity and non-stationarity time The results obtained from the bound test presented in Table 4 that shows the related Fstatistics of all four models exceed upper bounds, at acceptable significance level, revealing statistical evidence to accept the cointegration relationship as formed in the models.
Accordingly, F stat of Model 1 exceeds bound at a 10% significance level and Model 2 passes the test with a 2.5% significance level. Model 3 and 4, however, exceed the upper bound at 1% significance level. The results reveal the long-run relationship between the budget deficit and inflation in Sri Lanka. In other words, the overall findings of cointegration confirm further that the existence of cointegration in both the deficit indicators (BDM1 and BDGDP) irrespective of the scales and the results are commonly applied to the two different inflation measures (CCPI and GDPD) as well. Thus, these results are in line with the results obtained in causality tests.

ARDL regression and long run analysis
In obtaining long-run coefficients of the ARDL model, which was suggested by the bound test procedure, this study applies error correction versions of the ARDL model. Accordingly, similar model specifications of ARDL/Bound test procedure are rearranged to the ARDL cointegration and long run form in E-views to obtain relevant coefficients. With the successive application of the tests, the results are demonstrated in Table 5

Conclusion
The purpose of this study is to examine the relationship between the budget deficit and inflation in Sri Lanka. Accordingly, the relationship is assessed using three alternative statistical approaches: the Toda-Yamamoto Granger causality procedure, which examines the causal relationship between the variables; the ARDL/Bound test cointegration approach, which investigates the long-run relationship with short-term dynamics; the ARDL error correction form, which examines the cointegration term and long-term coefficients. Using these statistical approaches, this study models budget deficit in two different scaling. Firstly, budget deficit is scaled by narrow money (BDM1), based on the theoretical approach of Intertemporal Budget Constraint (IBC) and secondly, budget deficit is scaled by GDP used as a conventional indicator. Moreover, separate inflation indicators (CCPI and GDPD) are also used in this study, in order to capture different aspects of inflation within the scope of the two inflation measures.
With respect to the estimated models, four separate model specifications are designed to estimate the aforementioned relations, which are categorised according to the separate indicators for budget deficits and inflation. Additionally, several explanatory variables are also included in all the models, representing macroeconomic sectors directly associated with budget deficit and inflation. As discussed previously in this study, background information and empirical research designs are considered in forming the above models. Furthermore, empirical analysis of the current study works out with time series annual data during the period of 1957-2016.
Turning to the findings, this study concludes firstly, unidirectional Granger causality with respect to all the estimated models. In other words, the results reveal that the budget deficits Granger caused inflation, but not vice versa in Sri Lanka. This causal relationship was commonly evidence in all four models irrespective of the difference in the indicators used in the models. Furthermore, the conclusion of the Granger causality tests proves a strong statistical significance of acceptable level.
Secondly, in line with the result of Granger causality tests, this study reveals a long run cointegration relationship between budget deficit and inflation in Sri Lanka. Moreover, the results of the cointegration tests also prove that the cointegration results are seemingly common to all the estimated models. In addition, the cointegration test results are proved with acceptable statistical evidence of significance levels (p=0.10, p=0.5, and p=0.01).
Thirdly, this study concludes the positive long-run correlation with considerable magnitudes between budget deficit and inflation in Sri Lanka. The long-run cointegration coefficients of estimated models are less than one with negative sign and are significant at one per cent level.
The magnitudes of long-run cointegration terms in all the four models are between -0.6 and -0.8 per cent, commonly indicating 60 per cent to 80 per cent of disequilibrium between principal variables would be corrected within a one-year period; the speed of adjustments was comparably high. Regarding the magnitudes of long run cointegration coefficients, the long run coefficients of the ARDL error correction models reveal that one per cent change in budget deficits as measured by LNBDM1 and LNBDGDP will result in a 1.5-2.5 per cent change in inflation as measured by LNCCPI and LNGDPD in Sri Lanka at acceptable significance levels (10%, 5%, and 1%). Moreover, four separate models formed in this study conclude nearly similar results suggesting strong evidence of the positive relationship between variables interested in this study.
The results of all three approaches: Granger causality test results, ARDL/Bound test results and the ARDL long run coefficients collectively confirm the hypothesis in this study that the existence of considerable magnitude of the positive relationship between the budget deficit and inflation in Sri Lanka are proved with strong statistical evidence.
Referring to the theoretical literature, Unpleasant Monetarist Arithmetic (Sargent and Wallace, 1981) that is considered as one of the milestones in uncovering the budget deficit-inflation nexus, emphasises the importance of fiscal policy in price determination, particularly under fiscal dominance. In recent economic history, theoretical arguments have emerged in favor of a considerable role of fiscal policy in determining price level, with approaches such as fiscal theory of price level. The findings of the current study are supported by these theoretical explanations.
According to the findings of the empirical studies, some researchers conclude the strong positive relationship between budget deficit and inflation, particularly, in developing countries.  Abu and Karim (2015) which did not include Sri Lanka in the sample of the study; findings of country-specific studies, such as the studies of Solomon and Wet (2004), Helmy (2008), Ndanshanu (2012), and Ekanayake (2012), which was conducted using similar country data. Similarly, Devapriya and Ichihashi (2012) also found a similar positive long-run relationship with bi-directional causality using country data for Sri Lanka.

Policy recommendations
The findings of this study entail several important implications for policy makers and future researchers. Firstly, the findings explore fiscal policy influence into the inflation in Sri Lanka.