Asian Journal of Economics and Empirical Research Vol. 4, No. 2, 75-90, 2017 ISSN(E) 2409-2622 / ISSN(P)2518-010X DOI: 10.20448/journal.501.2017.42.75.90 75 The Economics of Foreign Aid: Time Series Evidence from a Less Developed Country (LDC) Md Mahadee Hassan1 1Deputy Secretary, Economic Relations Division, Ministry of Finance, and Government of Bangladesh Abstract Empirical literature on aid-growth nexus mostly centered within cross-country framework exploiting typical ordinary least squares (OLS) estimation. As a result, scarcity prevails studies empirically examine country-specific causes of aid-growth nexus exercising distinct methods. This study aims to fill this gap, taking the case of Bangladesh- a leading aid recipient country. Empirical findings based on vector error correction modeling and Granger causality test unearth absence of long-run and short-run causality of aid on GDP growth. Therefore, this study argues that although aid remains a major component of LDCs macroeconomic framework; however, it is yet to emerge as a significant player in their economic growth. Keywords: Aid-growth nexus, Vector error correction modeling, Causality, Bangladesh. Citation | Md Mahadee Hassan (2017). The Economics of Foreign Aid: Time Series Evidence from a Less Developed Country (LDC). Asian Journal of Economics and Empirical Research, 4(2): 75-90. History: Received: 1 October 2017 Revised: 13 October 2017 Accepted: 18 October 2017 Published: 23 October 2017 Licensed: This work is licensed under a Creative Commons Attribution 3.0 License Publisher: Asian Online Journal Publishing Group Funding: This study received no specific financial support. Competing Interests: The authors declare that they have no conflict of interests. Transparency: The authors confirm that the manuscript is an honest, accurate, and transparent account of the study was reported; that no vital features of the study have been omitted; and that any discrepancies from the study as planned have been explained. Ethical: This study follows all ethical practices during writing. Contents 1. Background ....................................................................................................................................................................................... 76 2. Aid-Growth Models, Instrumentation, and Estimation Strategies ....................................................................................... 77 3. Methodologies .................................................................................................................................................................................. 78 4. Estimation Strategies and Empirical Findings .......................................................................................................................... 79 5. Conclusions ....................................................................................................................................................................................... 82 References .............................................................................................................................................................................................. 83 http://creativecommons.org/licenses/by/3.0/ http://creativecommons.org/licenses/by/3.0/ https://orcid.org/orcid-search/quick-search?searchQuery=Md%20Mahadee%20Hassan https://orcid.org/orcid-search/quick-search?searchQuery=Md%20Mahadee%20Hassan Asian Journal of Economics and Empirical Research, 2017, 4(2): 75-90 76 1. Background ‘Foreign aid’ popularly known as official development assistance (ODA) is a saga of over seven decades (Dalgaard et al., 2004). Starting its expedition at the end of World War Two (WW2) and intensifying in 1960s and since then aid-growth nexus has been staying a key area of research interests (Boone, 1996; Alesina and Dollar, 2000; Dalgaard et al., 2004; Doucouliagos and Paldam, 2009). For example, last five decades (1960- 2010) have witnessed a revolution in aid-growth paradigms where record number of cross-country growth regressions proved insufficient justifying aid effectiveness (or ineffectiveness) (Sala-i-Martin, 1997a;1997b; Hansen and Tarp, 2000; Clemens et al., 2004; Hendry and Krolzig, 2004). Major reasons of this aid-growth impasse is because of great controversies in model specification, instrumentation and estimation strategies (Easterly, 2003; Bourguignon and Sundberg, 2007; Rajan and Subramanian, 2008; Deaton, 2010; Galiani et al., 2014). More pertinently, studies before 1990s were unable to draw adequate inferences due to shortage of data, and standard instrumentation and estimation strategies (Easterly, 2003). While, considering donors’ point of views, growth is absent in the core of their major aid agendas. Instead, development assistance largely extended to respond emergency and humanitarian needs, and these sorts of external resources normally originate negative causal link towards growth (Clemens et al., 2004). In addition, aid packages frequently designed to serve other purposes including promoting political systems, supporting democracies, and addressing health and environmental issues. Although, growth is prompted around those kinds of aid but hardly in the long run (Clemens et al., 2004). However, Alesina and Dollar (2000) find nothing significant regarding humanitarian role of aid and argue that it is simply continuing to serve political motives and this notion strongly supported by Rajan and Subramanian (2008) who branded ‘political motives’ as noneconomic reasons. Final category of Clemens et al. (2004)classified foreign aid is exploited for productive purposes and in particular, supporting budget, balance of payments, and invests in infrastructure and other development projects. Research evidence suggests that this type of development assistance maintain robust short run causal link towards economic growth (Clemens et al., 2004). Aid effectiveness literature (AEL)1 has come across a number of phases reaching its extant form (Clemens et al., 2004; Roodman, 2007). Classification of those phases magnificently recorded in a good number of outstanding literature notably in Doucouliagos and Paldam (2009);Roodman (2007);Clemens et al. (2004) and Hansen and Tarp (2000). These exceptional works label the phases as; early, first, second and third generation. Early stage includes studies of 1960s predominantly explain impact of aid on savings and investments rather than examining its effectiveness on growth (Clemens et al., 2004; Roodman, 2007; Doucouliagos and Paldam, 2009). This early phases’ particular academic interest intensified due to the influences of Harood-Domar model, where significance of savings on growth has been strongly argued (Roodman, 2007). Two pioneering early studies are, Rosenstein-Rodan (1961) and Chenery and Strout (1966). Among the authors, Rosenstein-Rodan and Chenery held World Banks’ chief economist position one time each. While, Hansen and Tarp (2000) identify that first generation studies ranging from early 1970s to 1980s also focusing on aid-savings link, and major works include Griffin and Enos (1970); Weisskopf (1972); Papanek (1972); Papanek (1973); Griffin (1978); Gulati (1978) and Mosley (1980). Second generation studies counting from early 1980s to early 1990s explore aid effects on investments and growth, and this generation dominated by a number of works of Mosley (1986;1987) and Mosley et al. (1987). Finally, third generation begins with Boone (1996) and continuing tills the date. Although, AEL has a vibrant legacy; however, this paper centered mainly within third generation works. More importantly, third generation AEL enter in a new order with the emergence of ‘conditional growth studies’ in early 2000s (Easterly, 2003). Burnside and David (2000) led this uprising and more significantly, majority of third generation AEL organized in such a fashion keeping (Burnside and David, 2000) ‘influential’ conclusions that ‘aid works better in good policy environments’, in the middle (Easterly et al., 2003). On the other hand, most of the AEL based on cross-country empirics exploiting typical OLS estimation (Hansen and Tarp, 2001; Doucouliagos and Paldam, 2009). In addition, more difficulties would appear when OLS estimations deliver ‘spurious’ outcomes (Wassell and Saunders, 2005). For this reason, scholars and practitioners express their reservations capitalizing conventional OLS estimations in policy implications due to ‘unclear and ambiguous results’ (Bourguignon and Sundberg, 2007). Accordingly, major objectives set for this study consist of estimating development assistances’ impact on growth within country-specific framework through applying a logical instrumentation approach. Moreover, we want to employ rational estimation strategies which have the mechanisms of amending typical OLS estimation errors. In doing so, we adopt popular econometric methodologies of augmented Dickey-Fuller (ADF) test, Johansen test of cointegration, vector error correction modeling (VECM), and Granger causality test. Selecting the case, we consider size of the economy, stability in growth, population, and volume of development assistance. We take Bangladesh, an economy of $227 billion2 identified as one of the new growth-engines of Asia3 experienced an average GDP growth over 6 per cent (6.22%)4 for the last ten years (2007-2016), and forecasts show that she will grow at the rate of 7 per cent (7%)5 in the next six years (2017-2022) also (International Monetary Fund (IMF), 2017). More importantly, Bangladesh is a major aid-recipient country who consistently manages sizable amount of development assistance measuring nearly 2 per cent (1.5%) of GDP6 during the period of 2005 to 2014 (World Bank, 2017). Remainder of the article is structured as follows: section 2 reviews major aid effectiveness literature focusing on models, instrumentation and estimation strategies adopted there. Section 3 deals with this works’ modeling and instrumentation strategies. Section 4 runs an exclusive analysis on estimation strategies, and present and discuss empirical findings. Finally, section 5 summarizes the findings and makes concluding remarks. 1We take the term AEL from Doucouliagos and Paldam (2009). 2According to IMF World Economic Outlook 2017, volume of Bangladesh’s GDP in 2016 stands at $227 billion 3In his inaugural speech at the Asian Development Bank (ADB) 50thBoard of Governors annual meeting on 6 May 2017 at Yokohama, Japan, President Takehiko Nakao outlines six member countries as the new growth-engines of Asia. Among the six countries Bangladesh is one of them. Other five countries are: India, Indonesia, Myanmar, the Philippines and Vietnam (source: http://www.thedailystar.net/frontpage/asias-new-growth-engines-1401721) 4 Authors’ calculation based on IMF World Economic Outlook 2017 5Authors’ calculation based on IMF World Economic Outlook April 2017 6 Authors’ calculation based on World Bank World Development Indicators 2017 Asian Journal of Economics and Empirical Research, 2017, 4(2): 75-90 77 2. Aid-Growth Models, Instrumentation, and Estimation Strategies After surveying vast pile of AEL we find that numerous arguments derived in the formulation of aid-growth strategies. Majority of those debates are well documented in two classic studies of Deaton (2010) and Doucouliagos and Paldam (2009)who systematically scrutinize the methods applied in key aid-growth studies. Ultimately, a consensus emerged from this couple of documents along with other relevant literature that test of aid effectiveness on economic growth has been a regular practice of typical OLS estimation within cross-country framework using standard growth regressions (Hansen and Tarp, 2000; Hendry and Krolzig, 2004; Doucouliagos and Paldam, 2009; Deaton, 2010). As a result, organizing our review initially we focus on highly exploited typical Barro (1991) cross- country growth regression commonly outlined in the form of: γ = α + β1 .x1 + β2 .x2 + ……….. + βn .xn+ ε (1) In this model γ represents the vector of rates of economic growth, αis the constant, and x1,...,xn are vectors of explanatory variables usually have different numbers and forms depend on the characteristics of particular research work and author (Doppelhofer et al., 2000). While, in classical aid-growth strategy, growth means real GDP growth, universally expressed in terms of GDP per capita (Doucouliagos and Paldam, 2009). Examining contemporary aid-growth strategies we want to concentrate on legendary work of Deaton (2010). Deaton (2010) aid-growth strategy structured in the form of following expression: ΔInYct+1 = β0+ β1InYct+ β2 + β3Hct+ β4Zct+ θAct+ μct (2) Where Y is the per capita GDP, I represent investments, H is an indicator of measuring human capital, A is the ratio denoting share of aid to GDP, and Z remains for other control variables. In addition, subscripts c stands for country and t for time. Deaton (2010) acknowledges that this approach basically an extension of Solow growth model except the inclusion of A, and Z variables. Deaton (2010) is extremely critical regarding instrumentation strategies but praises (Boone, 1996) who pioneers employment of standard set of instruments in growth regressions. Estimating country-specific effects (Boone, 1996) uses several dummies and incorporates log of population size. Defending the significance of population size, Deaton (2010) argues that aid is extended primarily on the country basis, instead of considering size of the population. Hence, populous countries per capita aid receipt is lower than those of less-populated countries, and it bears great significance since, performance of aid frequently evaluated on the basis of per capita GDP. Therefore, influenced by Boone (1996) next generation influential aid- growth studies7 widely capitalize both of GDP per capita and population size or one of these variables in their growth regressions (Deaton, 2010). However, Deaton (2010) is not convinced with the quality of instruments overcoming ‘exogeneity’ and ‘heterogeneity’ problems, and identifies inadequacy of standard theories validating the competency of instruments. Accordingly, Deaton (2010) conclude that with the current set of instruments it is quite challenging reaching to a robust conclusion on aid-growth nexus. Deaton (2010) raises all important concern that typical aid-growth estimation strategy considers whole volume of aid is duly invested. However, this is quite unrealistic, therefore, for better inferences, at first, it is required to identify the status of tangible investments and then to conclude on effectiveness. Another constraints noted, is the use of instrumental variables as Deaton (2010) shows great reservation in this regard; since, major AEL are in great jeopardy justifying the adoption of instrumental variable methods. Deaton (2010) warns that econometric estimation strategies changed drastically and centered merely within the statistical program evaluation packages rather than to focus on models originated from theories. Therefore, incorporation of instrumental variables in the estimation strategy creates severe disputes and which is leading to quasi-randomization (Deaton, 2010). Similarly, mishandling of instruments explode confusions and challenge the potentials of econometric analysis responding all important empirical enquiries (Deaton, 2010). Let we concentrate on another exceptional survey of Doucouliagos and Paldam (2009) whose epic analysis on 97 econometric studies covering a period of four decades (mid-1960s to mid-2000s) summarizes overall standard aid-growth estimation strategy in the following form: git = α + μhit + γjx’jit +uit (3) Explaining Equation-3, git is the real growth rate expressed in GDP per capita, hit is the percentage aid to GDP/GNI, xjit is the vector of j control variable, and uit is the residuals, μ and γ are the two commonly estimated coefficients. More importantly, Doucouliagos and Paldam (2009) organize existing aid-growth models into three ‘family’ groups specified as ‘accumulation’, ‘growth direct’, and ‘conditional’. Among those paradigms, ‘accumulation’ strategies frequently hypothesize that rise of domestic savings and balance of payment; particularly, ‘accumulation’ factors are vital for growth. The next family ‘growth direct’ is the overall model stated in equation- 3, and more explicitly, while estimating ‘accumulation’ impact; growth of domestic savings (sit) and investments (iit) are measured instead of real GDP growth (git). Accordingly, this couple of ‘accumulation’ strategies frequently estimated in the form of following two equations: sit= α + μhit+ γjx’jit+ μit (4) iit= α + μhit+ γjx’jit+ μit (5) Apart from above aid-growth paradigms, emergence of ‘good policy’ studies led by Burnside and David (2000) surge most sensational arguments in aid effectiveness literature (Easterly, 2003; Clemens et al., 2004; Roodman, 2007). Undoubtedly, this development drives entire aid-growth debate into a new height, and Doucouliagos and Paldam (2009) place ‘good policy’ studies into the family of ‘conditional growth model’, and branded this group of scholars as ‘World Bank group’ since they are sponsored or somehow affiliated with aid industry8 World Bank. In ‘good policy’ paradigm it is strongly argued that aid is effective simply in good policy environments. Burnside and David (2000) ‘good policy’ strategy structured splendidly in Roodman (2007) in the following way: 7Deaton (2010). list of next generation studies includes Burnside and David (2000). Hansen and Tarp (2000;2001). Guillaumont and Chauvet (2001). Lensink and White (2001). Clemens, Radelet and Bhavnani (2004). Dalgaard, Hansen and Tarp (2004). Easterly, Levine and Roodman (2004). Roodman (2007). and Rajan and Subramanian (2008). 8Doucouliagos and Paldam (2009).Use the term ‘aid industry’ while branding influential aid organizations the World Bank, and Danish International Development Agency (DANIDA). Asian Journal of Economics and Empirical Research, 2017, 4(2): 75-90 78 ΔY= αA+ βA× P + γP + xδ + ε (6) Where Y is the per capita GDP, aid is represented by A, policy is denoted by P, x is a vector of controls, and ε is the error term. Similarly, Doucouliagos and Paldam (2009) prescribed ‘good policy’ models’ unique feature is that it employs a right hand side ‘good policy’ variable z, and which is the good policy index of particular country comprising weighted sum of budget surplus, inflation rate, and trade openness. In addition, two more coefficients δ and ω are also estimated. Consequently, Doucouliagos and Paldam (2009) outline ‘good policy’ model estimation strategy in the following manner: git = α + μhit + δzit+ ωhitzit + γjitx’jit + uit (7) Regarding origins, Burnside and David (2000) approach based on neoclassical growth model, and their ever dominant theory suggests that aid works positively on growth until recipient country’s GDP growth stays below the zenith of her transitional growth rate. According to Burnside and David (2000) negative impact of aid caused due to the presence of distortionary economic policies. Therefore, Burnside and David (2000) advocate for policy development achieving enhanced aid effectiveness, but they are not certain that inclusion of policy instruments will act properly because other factors can make whole spectrum complicated. However, Burnside and David (2000) two universal hypotheses are: aid and ‘good policy’ combination is most effective, and effects of ‘good policy’ triggered by foreign aid. While, corresponding ‘good policy’ study of Collier and Dollar (2002) analyze real aid allocation scenarios through developing a poverty-efficient aid allocation framework using World Bank ratings of aid recipient countries national policies on aid utilization plans. For example, a country with severe poverty but has good policies is fit to be in the priority of poverty-efficient aid allocation framework. Their findings suggest that existing aid allocation mechanisms is not poverty-efficient although, aid works magnificently bringing out millions of people from absolute poverty. Dollar and Kraay (2002) add a couple conditions to Burnside and David (2000) original variables precisely, stability in inflation and small government size. Overall, Dollar and Kraay (2002) conclude that governance, good trade policies, robust financial systems have little systematic effects on growth. Another branch of ‘conditional growth’ studies pioneered by Dalgaard et al. (2004); Dalgaard and Hansen (2001); Hansen and Tarp (2001) and Hansen and Tarp (2000) employ different types of policy instruments in estimation strategies. For example, Dalgaard et al. (2004) claim that ‘climate-related circumstances’ are the vital factors prompting degree of growth. However, Dalgaard et al. (2004) remain in suspicion concerning the competence of policies in aid effectiveness. Their concluding remarks indicate that size and structural characteristics of aid inflow and policies ‘may’ influence aid effectiveness. Similar inferences also outlined in Hansen and Tarp (2001) as they suggest that aid has ‘likelihood’ influences on growth but not conditional on ‘good policies’. More significantly, ‘estimated’ aid effectiveness highly depends on the set of exploited instruments. For instance, positive impact of aid is absent when ‘investment’ and ‘human capital’ is controlled. Overall, Hansen and Tarp (2001) suggest that extensive theoretical works on aid effectiveness require before capitalizing existing literature in policy formulations. Correspondingly, Hansen and Tarp (2000) widespread survey on three decades cross-country literature comprehensively examine aid-growth, aid-savings, and aid-investment relationships. After careful scrutiny, Hansen and Tarp (2000) confirm that Burnside and David (2000) ‘good policy’ model considerably discarded in existing empirical cross-country literature. Moreover, Hansen and Tarp (2000) explore that aid effectiveness is not conditional on good policies; instead, it also works significantly in such environments where good policies are absent. Dalgaard, Hansen, Tarp and fellow scholars’ association with Danish International Development Agency (DANIDA) highlighted remarkably in Doucouliagos and Paldam (2009). Keeping consistency with the ‘World Bank group’ they are identified as ‘DANIDA group’, and their model labeled as ‘Medicine Model’ exploits an ‘aid squared’ term in the right hand side and more notably, aid is treated as a condition in the estimation strategies. Since, aid itself is a condition; therefore, Doucouliagos and Paldam (2009) empirically define ‘Medicine Model’ in the following way by reducing Equation 7: git = α + μhit + ωh2 it+ γjitx’jit + uit (8) 3. Methodologies 3.1. Model Specification and Instrumentation Strategy The origin of our aid-growth model is derived from production functions. In addition, setting the instrumentation strategies we are inspired by a number of works of Ackerberg et al. (2015); Yeoh and Stansel (2013); Bloom et al. (2012); Lee et al. (2005) and Aschauer (1989) who capitalize production technology while investigating economic growth and productivity. More importantly, production function’s universal recognition as a fundamental theory of economics and its long history of being capitalized for more than two centuries (Ackerberg et al., 2015) propel us to exploit one of its advanced form- the Cobb-Douglas production function. Moreover, Cobb-Douglas functions’ intensity in illustrating ‘real-world production processes’ makes it a better technology and a credible strategy in econometric estimation process (Besanko and Braeutigam, 2011). Besides, wide ranges of literature suggest that Cobb-Douglas production function is a substantial instrument for linear estimation of various productivity activities (Lee et al., 2005). General framework of Cobb-Douglas production function structured in Besanko and Braeutigam (2011) in the following form: Q= ALαKβ (9) In this framework Q stands for quantity of output derived from L units of labor and K units of capital, and A, α, and β are positive constants. While, Cobb-Douglas production function’s convenience as an augmented neoclassical model encouraged many scholars modifying its original framework. For example, while estimating public expenditures (G) productivity on the economy (Aschauer, 1989) exploits Cobb-Douglas method in the form of: Yt = At *f (Nt, Kt,Gt) (10) Aschauer (1989) add an extra right hand side variable, public expenditure (G) with employment of labor (N), and stock of nonresidential capital (K). Similarly, examine the role of IT on firms’ productivity (Bloom et al., 2012) extend original model by employing two more right hand side variables, materials (m) and IT capital (c) in addition to labor (l) and capital (k). Therefore, remodeled Cobb-Douglas production function organized in Bloom et al. (2012) in the way of: Asian Journal of Economics and Empirical Research, 2017, 4(2): 75-90 79 qit= ait+ ait Mmit+ ait L lit+ ait Kkit + ait Ccit (11) Alongside, investigating ICT’s impact on the economy (Lee et al., 2005) expand Cobb-Douglas model in the form of: Y= AICTβ1 Kβ2 Lβ3 (12) In their approach (Lee et al., 2005) incorporated ICT as a new instrument with existing labor (L) and capital (K). Where A is a constant represents other elements of production, β1, β2, and β3 are the elasticities of production resources. We follow both Bloom et al. (2012); Lee et al. (2005) and Aschauer (1989)approaches studying the role of foreign aid (ODA)9 in economic growth. Therefore, we rewrite Cobb-Douglas production function in the below form: Y= AODAβ1 K β2Lβ3 (13) Where ODA is the net disbursement flows of official development assistance measured as the percentage of GNI, K is the gross capital formation in terms of percentage of GDP. Due to the inadequacies of labor statistics we proxy labor (L) with population growth (POPLG)10. Because, growth of population stimulates productivity in a couple of ways; through supplying additional labor force and create extra demand in the economy (Oxley and Greasley, 1998). Therefore, we argue that economic growth of Bangladesh is the function of foreign aid (ODA), gross capital formation (CAPITAL), and population growth (POPLG). Accordingly, we organize of our aid-growth strategy in the subsequent way: Y= AODAβ1 CAPITALβ3POPLGβ3 (14) Finally, for estimation conveniences we capitalize classical (Barro, 1991) cross-country growth regression and structure the above function in the following form: Y= α + β1ODA+ β2CAPITAL+β3POPLG + ε (15) 3.2. The data We use annual time series data of World Bank’s World Development Indicator (WDI). The data has a span of 42 years ranging from 1973 to 2014, and comprises 4 series including per capita GDP (current prices and in US$), net ODA received as percentage of gross national income (GNI), gross capital formation as percentage of GDP, and population growth. We rely on this single source because no other institutional sources have comprehensive time series data on Bangladesh for longer period than World Bank has. In addition, we consider that other source resources may not act properly with World Bank data because of different methodologies applied in data collection and processing and which eventually lead to inconsistencies in estimation and analysis11. 4. Estimation Strategies and Empirical Findings Setting the estimation strategies we carefully consider following two factors: at first, inability of typical OLS estimation extending standard inferences for policy implications (Deaton, 2010) and the recent surge of time series application (for example, (Nowak-Lehmann et al., 2012; Juselius et al., 2014; Lof et al., 2015; Juselius et al., 2017)) in growth studies. Both reasons prompted us exploiting time series instruments in our empirical strategies. In addition, time series applications’ universal acceptance as a superior technology of handling stationary data, motivated us in a great deal (Phillips and Perron, 1988). Generally, time series data are nonstationary in nature and models with nonstationary variables and their statistical significance vastly a debated issue (Wassell and Saunders, 2005). Since, regressions between two or more nonstationary series often produce spurious outcomes; notably, in the form of high coefficient of determination (R2), and significant t-statistics even in the absence of sensible correlation (Granger and Newbold, 1974; Phillips and Perron, 1988; Wassell and Saunders, 2005). For this reason, regressions output derived from nonstationary series frequently disqualify for rational policy implications (Wassell and Saunders, 2005).To address this problem, time series techniques initially examine (unit root test) quality (stationarity) of data before using it in empirical investigations. 4.1. Testing Stationery: The Unit Root Test Unit root testis predominantly exploited to identify the stationarity (whether a variable is stationary or nonstationary) of a series (Gujarati, 2004). Major features of stationarity is that when mean and autocovariances of a series does not depend on time then the series is stationary; and in contrast, a series which mean and autocovariances depend on time labeled as nonstationary (Gujarati, 2004). A typical nonstationary series is the random walk can be expressed in the following form: Yt= ρYt-1 + ut (16) In this model ut is a white noise error term. The variance of series Y is changing over time since it depends on the condition of t. While random walk is a difference stationary series and the first difference of Y is stationary and can be written in the form of: ΔYt = δYt-1 + ut (17) Estimating above equation we take null hypothesis δ= 0, If ρ=1 then δ= 0 meaning that series under consideration has a unit root, and the series is not stationary. The notion is that a difference stationary series is integrated and symbolized as I(d), and d denotes order of integration, the number of unit roots a series contained or the number of difference operations required to make a series stationary. For example, a series has one unit root signified as I(1) series, and a stationary series free of unit root symbolized as I(0) series. In analytical environments several types of unit root test practiced. Among those tests, we utlize a popularly accepted method of an advance option of Dickey-Fuller (DF) test- universally known as augmented Dickey-Fuller (ADF) test (Ng and Perron, 1995).Generally, DF test conducted in three distinct forms considering diverse possibilities, and the options are: random walk process has no drift, random walk process may have drift, and random walk process may have both deterministic and stochastic trends (Gujarati, 2004). While, conducting a DF test, hypothesis is that error term ut 9We proxy foreign aid as the net disbursement flows of official development assistance (ODA) 10 Details of the variable descriptions stated in appendix C 11According to World Bank (2017). Bangladesh’s per capita GDP (current prices) in 2014 is US $1,086.80. On the contrary, IMF World Economic Outlook April 2017 shows that Bangladesh’s per capita GDP (current prices) in 2014 is US $ 1,162.74. αi m i=1 Asian Journal of Economics and Empirical Research, 2017, 4(2): 75-90 80 remains uncorrelated (Gujarati, 2004). However, difficulties surfaced when ut is correlated. To resolve this, Dickey and Fuller (1979) developed a modified version by ‘augmenting’all three types of DF test equations and adding a lagged value of dependable variable ΔYt. However, in this paper we estimate the regressions based on the following two ADF test equations12 (Gujarati, 2004): ΔYt = β1 + δYt-1+ ΔYt-i + εt (18) ΔYt= β1 + β2t + δYt-1 + ΔYt-i + εt (19) Table-1. Augmented Dickey-Fuller (ADF) test output (5% level of significance) Variable ADF test statistic (t-statistic) Test critical values (t-statistic) Prob. Constant Constant, trend Constant Constant, trend Constant Constant, trend Level GDP -2.935001 -3.523623 3.553140 1.660312 1.0000 1.0000 ODA -2.936942 -3.540328 -0.479362 -2.056948 0.8848 0.5514 CAPITAL -2.936942 -3.526609 -1.581257 -3.330771 0.4827 0.0759 POPLG -2.938987 -3.529758 0.392503 -2.200237 0.9801 0.4762 First difference D(GDP) -2.936942 -3.526609 -4.222689 -5.446197 0.0019 0.0003 D(ODA) -2.936942 -3.526609 -9.563917 -9.593832 0.0000 0.0000 D(CAPITAL) -2.936942 -3.526609 -5.269162 -5.291244 0.0001 0.0005 D(POPLG) -2.938987 -3.529758 -9.291159 -8.351394 0.0000 0.0000 The ADF test statistic displayed in Table 1, indicate that all four variables are integrated in order of 1 meaning that all four variables are I(1)series. Since, the variables are I(1), therefore, we need to identify the number of cointegrating vectors in the subsequent analytical process (Oxley and Greasley, 1998); (Masih and Masih, 1997). However, conducting remaining tests, we need to determine optimal lag length, at first. 4.2. Selection of Optimal Lag Order Determining optimal lag length we follow Toda and Yamamoto (1995) approach. In doing so, we capitalize usual methods and conduct an unrestricted VAR estimate involving data in levels with automatic 2 lag order. The lag order selection output exhibited in Table 2, and five lag selection criterions (LR, FPE, AIC, SC, HQ) suggest that optimal lag length is 3. For cross checking, we attempt another unrestricted VAR estimation with 4 lag order. Nevertheless, this calculation also recommends same lag length, 3. Since, all the series are integrated in order of I(1), therefore, following T-Y approach we decide optimal lag order is 4 (3+1) by adding an extra lag. Consequently, we use 4 lag orders in all the remaining estimations. Table-2. VAR lag order selection output Lag LogL LR FPE AIC SC HQ 0 -375.7156 NA 5617.1111 19.98503 20.15741 20.04636 1 -177.8088 343.7328 0.392830 10.41099 11.27288 10.71764 2 -139.9454 57.79162 0.128150 9.260282 10.81168 9.812257 3 -98.49156 54.54447* 0.036300* 7.920608* 10.16152* 8.717906* 4 -82.76160 17.38575 0.043093 7.934821 10.86524 8.977441 Source: Authors’ calculation * indicates lag order selected by the criterion LR: sequential modified LR test statistic (each test at 5% level) FPE: Final prediction error AIC: Akaike information criterion SC: Schwarz information criterion HQ: Hannan-Quinn information criterion 4.3. Testing Cointegration Using Johansen’s Methodology Analysis of this chapter involves testing cointegration. To move forward, we conduct Johansen (1991;1995) multivariate system of cointegration test to ascertain cointegration relations among the variables. Engle and Granger (1987) are the pioneer of cointegration methodology (Ahmed and Kenji, 2017). However, emergence of Johansen (1991;1995) and Johansen and Juselius (1990) methodologies and their procedural supremacy due to system-based evaluation technologies of cointegration vectors has gained sensible edge over Engle and Granger (1987) theory (Ahmed and Kenji, 2017).While, in a multivariate time series approach with maximum likelihood procedures; Johansen’s methodolgy considered as an advanced option (Masih and Masih, 1997). Typically, Johansen methodology is suitable in such an environment where all the variables integrated in order of I(1) (Österholm and Hjalmarsson, 2007). Since, all variables of our model qualify to this criteria therefore, it would be an appropriate practice to apply Johansen’s method. Moreover, within a vector error correction (VEC), framework Johansen’s methodology extensively utilized to develop substantial strategies identifying cointegrating relations between the variables (Oxley and Greasley, 1998; Ghosh, 2002). Accordingly, determining cointegration vectors we estimate following equation with order of p: yt = μ + A1yt-1 +.........+ Apyt-p + Bxt + ϵt (20) 12Equation 16 estimates regression with intercept, while in Equation 17 regressions’ estimated with trend and intercept αi m i=1 Asian Journal of Economics and Empirical Research, 2017, 4(2): 75-90 81 In this framework yt is a vector of nonstationary I(1) variables, xt is a vector of deterministic variables and ϵt is a vector of innovations. We can rewrite the equation in the following form also: Table-3. Johansen cointegration test output (lags interval in first differences: 1 to 4) Hypothesized No. of CE(s) Test statistic 0.05 critical value Prob.** Trace Max-Eigen Trace Max-Eigen Trace Max-Eigen Trend assumption: Linear deterministic trend None 119.5347* 61.00638* 47.85613 27.58434 0.0000 0.0000 At most 1 58.52829* 38.02562* 29.79707 21.13162 0.0000 0.0001 At most 2 20.50268* 16.66634* 15.49471 14.26460 0.0081 0.0205 At most 3 3.836339 3.836339 3.841466 3.841466 0.0501 0.0501 Trend assumption: Linear deterministic trend (restricted) None 160.7710* 62.71900* 63.87610 32.11832 0.0000 0.0000 At most 1 98.05200* 48.77429* 42.91525 25.82321 0.0000 0.0000 At most 2 49.27772* 32.61259* 25.87211 19.38704 0.0000 0.0004 At most 3 16.66513* 16.66513* 12.51798 12.51798 0.0096 0.0096 Source: Authors’ calculation a. Trace and max-eigen value test indicates 3 cointegrating equations at 0.05 levels under the linear deterministic trend b. Trace and max-eigen value test indicates 4 cointegrating equations at 0.05 levels under the linear deterministic trend (restricted) *Denotes rejection of hypothesis at 0.05 level **MacKinnon et al. (1999) p-values To identify cointegration relationships firstly, we capitalize estimation within linear deterministic trend with 4 lag order to conclude on null hypotheses of 0, 1 and 2cointegration vectors. The output sited in Table 3 indicates that both Trace (119.5347; 58.52829; 20.50268), and Max-Eigen value (61.00638; 38.02562; 16.66634) statistic are significant at 0.05 critical level, and which confirms existence of 3 cointegrating vectors. Similarly, testing null hypotheses of 0, 1, 2 and 3 cointegrating vectors, output of another estimation with 4 lag order and within linear deterministic trend (restricted) find that Trace (160.7710; 98.05200; 49.27772; 16.66513), and Max-Eigen value (62.71900; 48.77429; 32.61259; 16.66513) statistic also remain significant at 0.05 critical level confirming 4 cointegratiing vectors. Thus, existence of multiple cointegrating vectors has been proved through this test. 4.4. Vector Error Correction Estimate In the preceding two tests we examine quality of data. The initial one, ADF test determines that order of integration of all series stand at I(1) confirming the existence of unit roots and more specifically, data will be stationary at first differences. However, major concern is that data in levels suffer significant damage of information linked to their co-movement while making it stationary through first differencing operations (Wahab and Applanaidu, 2015). Subsequent investigation, Johansen maximum likelihood (ML) test of cointegration locates multiple cointegrating vectors and which indicates presence of long-run equilibrium relationship among the variables. Considering such an environment, Engle and Granger (1987) suggest that a vector error correction modeling (VECM) is the appropriate approach instead of a typical VAR estimation to explain the relationships. Therefore, we capitalize (Engle and Granger, 1987) vector error correction framework in the following form to identify causal relationships: ΔGDPt = α+ Σβ1ΔGDPt-n+ Σβ2ΔODAt-n+ Σβ3ΔCAPITALt-n+ Σβ4ΔPOPLGt-n+ λECTt-n+ εt (22) Where α is the constant, λ stands for coefficient of error correction term, ECTt-n is the error correction term and εt is the white noise error term. In addition, n is the optimal lag length and β1, β2, β3 and β4 are the coefficients which explain short-run Granger causality of explanatory variables on dependent variable. While coefficient of ECT exploited to determine the long-run equilibrium relationships, and for Granger causality it must be negative and significant (Ahmed and Kenji, 2017). Table-4. Vector error correction estimates output Variable Coefficient t-statistic Prob. Model A: Dependent variable ΔGDP ECT -0.018332 -1.654018 0.1146 C 32.67681 1.834772 0.0822 Δ GDPt-1 0.192055 0.743635 0.4662 Δ GDPt-2 -0.132601 -0.603823 0.5531 Δ GDPt-3 0.326056 1.735313 0.0989 Δ GDPt-4 -0.021262 -0.103901 0.9183 Δ ODAt-1 0.944205 0.114328 0.9102 Δ ODAt-2 2.950476 0.259035 0.7984 Δ ODAt-3 4.675114 0.469008 0.6444 Δ ODAt-4 0.230430 0.032125 0.9747 Δ CAPITALt-1 -8.834268 -0.827020 0.4185 Δ CAPITALt-2 -7.986122 -0.876074 0.3019 Δ CAPITALt-3 2.340438 0.306893 0.7623 Δ CAPITALt-4 0.218031 0.032159 0.9747 Δ POPLGt-1 574.9397 1.388137 0.1812 Δ POPLGt-2 -917.3912 -1.020177 0.3205 Δ POPLGt-3 682.4348 0.777814 0.4463 Δ POPLGt-4 -136.3971 -0.337605 0.7394 Asian Journal of Economics and Empirical Research, 2017, 4(2): 75-90 82 There are 4 models emerged from the vector error correction estimates (details in appendix, E-2). Out of 4 models we are basically focus on a solo model which is taking GDP as the dependent variable. For analytical convenience, we define this model as model-A. Similarly, we define rest of the three models as model-B (dependent variable Δ ODA) model-C (dependent variable ΔCAPITAL), and model-D (dependent variable Δ POPLG). All coefficients of vector error correction estimates (displayed in Table 4) of model-A found insignificant at 5% and 10% significance level stating the nonexistence of short-run or long-run causality among the explanatory variables and GDP growth (ΔGDP). Since, major purpose of this study is to explain aid-growth nexus therefore; we check four aid coefficients through conducting Wald Test (taking null hypothesis ΔODAt-1 = ΔODAt-2= ΔODAt-3= ΔODAt-4= 0). Results displayed in Table 5, and it indicates the absence of short-run causality of aid on GDP growth. Table-5. Output of Wald Test Null Hypothesis: ΔODAt-1 = ΔODAt-2 = ΔODAt-3 = ΔODAt-4 = 0 Test Statistic Value df Probability F-statistic 0.113678 (4,19) 0.9761 Chi-square 0.454714 4 0.9778 On the contrary, error correction term (ECT), which is used to examine long-run causality estimated at: coefficient, -0.018332 and probability (prob.) 0.1146 respectively. The ECT also confirms the nonexistence of long- run equilibrium relationships among the dependent and explanatory variables. 4.5. Vector Error Correction Granger Causality/Block Exogeneity Wald Tests Identifying causal relationship we conduct another test- Granger causality/block exogeneity Wald tests using vector error correction framework. The output (details in appendix, F) in Table 6 demonstrates the absence of Granger causality while taking ΔGDP as the dependent variable. In contrast, when ΔODA, ΔCAPITAL, and ΔPOPLG are considered dependent variable we can reject null hypothesis of no causality at 5% significance level and that confirms the presence of Granger causality. Therefore, this estimation endorses our analytical approach since, it is consistent with one of the important features of the significance of VEC models that cointegrated variables must have causality ‘at least one direction either unidirectional or bidirectional’ (Granger, 1986; Granger, 1988; Masih and Masih, 1997). Table-6. Vector error correction Granger Causality/Block Exogeneity Wald Tests output Model Dependent variable Independent variable Chi-sq df Prob. A ΔGDP ΔODA ΔCAPITAL ΔPOPLG 10.42330 12 0.5789 B ΔODA ΔGDP ΔCAPITAL ΔPOPLG 22.25028 12 0.0348 C ΔCAPITAL ΔGDP ΔODA ΔPOPLG 31.27932 12 0.0018 D ΔPOPLG ΔGDP ΔODA ΔCAPITAL 27.84601 12 0.0058 4.6. Residual Diagnostic Tests of VECM We examine model-A’s significance through conducting several residual diagnostic tests (details in appendix, G) and output exhibited in Table 7. At first, we conduct Breusch-Godfrey serial correlation LM test to check serial correlation. Estimated F-statistic and corresponding probability (prob.) reveals that model-A is free of autocorrelation problem. While, three types of heteroskedasticity tests including Breusch-Pagan-Godfrey, Harvey, and ARCH carried out to identify the heteroskedasticity of time series regression of model-A. All three estimated F-statistic and corresponding probabilities suggest that null hypothesis of no heteroskedasticity is not in a position for rejection. Finally, we conduct histogram normality test of Jarque-Bera to check data distribution status. The Jarque-Bera statistic and corresponding probability (prob.) suggests that data are normally distributed. Therefore, all the residual diagnostic tests confirm the significance of model-A. In addition, model-A’s statistical significance also established in other ways particularly, with a good R2 of 0.692773 and a significant prob. (F-statistic) of 0.027249 (appendix, E-2). Table-7. Summary of residual diagnostic tests Breusch-Godfrey Serial Correlation LM Test* Heteroskedasticity Test Histogram- Normality Test Breusch-Pagan- Godfrey Harvey ARCH** F- statistic Prob. (4, 15) F-statistc Prob. F (20, 16) F-statistc Prob. F (20, 16) F- statistc Prob. F (20, 16) Jarque- Bera Probabilit y Model: Dependent variable ΔGDP 0.926414 0.4746 1.047583 0.4686 1.661351 0.1532 0.843695 0.5094 0.846931 0.654774 Source: Authors’ calculation * Lag to include 4 **Number of lag 4 5. Conclusions We endeavor to answer few crucial issues raised at the prevailing aid-growth literature including model specification, instrumentation, and estimation strategies. Firstly, we address the issue of model specification proposing an aid-growth approach exploiting both neoclassical cross-country growth model (Barro, 1991) and Cobb-Douglas production technology. In relation to instrumentation strategies, we intensely survey ‘conditional growth studies’ where it is argued that aid effectiveness depends on good macroeconomic, trade, political, and environmental policies. However, we simply rely on conventional macroeconomic statistic instead of incorporating policy variables; since, highly rated (Rajan and Subramanian, 2008) remain unsuccessful finding any significance of development assistances while incorporating policy variables with conventional macroeconomic variables following Asian Journal of Economics and Empirical Research, 2017, 4(2): 75-90 83 four major ‘conditional aid-growth studies’13. We consider this will act to get back the aid-growth debate on the right track. In the next, we address the concerns of Deaton (2010) and Rajan and Subramanian (2008) regarding the inability of typical cross-country OLS estimations to get rid of the ‘spurious regressions’ problem due to the existence of noise in the data. We adopt country-specific approach by taking the case of a leading aid-recipient country. Our estimation strategies equipped with error correction techniques which are able keeping the outcomes free of ‘spurious regressions’ problem. Capitalizing vector error correction modeling and Granger causality test within the vector error correction framework, we do not find any short-run or long-run causality of development assistance on real GDP growth. Therefore, our findings strongly support (Rajan and Subramanian, 2008) and reject the conclusions of so-called ‘conditional growth studies’. We consider this study has great policy implications since; core development planning of LDCs still depends on the size of ODA. Given this context, country’s like Bangladesh who aspires rapid economic development need to redefine major growth strategies and to revisit existing approaches regarding ODA financed development programs. References Ackerberg, D.A., K. Caves and G. Frazer, 2015. Identification properties of recent production function estimators. Econometrica, 83(6): 2411-2451. View at Google Scholar | View at Publisher Ahmed, K.Y. and Y. Kenji, 2017. Source of economic growth in Ethiopia: An application of vector error correction model. Australian Academy of Business and Economics Review, 2(4): 285-292. View at Google Scholar Alesina, A. and D. Dollar, 2000. Who gives foreign aid to whom and why? Journal of Economic Growth, 5(1): 33-63. View at Google Scholar Aschauer, D.A., 1989. Is public expenditure productive? Journal of Monetary Economics, 23(2): 177-200. View at Google Scholar Barro, R.J., 1991. Economic growth in a cross section of countries. Quarterly Journal of Economics, 106(2): 407-443. View at Google Scholar | View at Publisher Besanko, D.A. and R.R. Braeutigam, 2011. Macroeconomics. 4th Edn., Hoboken, NJ 07030-5774, USA: John Wiley & Sons Inc. 111 River Street. Bloom, N., R. Sadun and J. Van Reenen, 2012. Americans do IT better: US multinationals and the productivity miracle. American Economic Review, 102(1): 167-201. View at Google Scholar | View at Publisher Boone, P., 1996. Politics and the effectiveness of foreign aid. European Economic Review, 40(2): 289-329. View at Google Scholar Bourguignon, F. and M. Sundberg, 2007. Aid effectiveness: Opening the black box. American Economic Review, 97(2): 316-321. View at Google Scholar | View at Publisher Burnside, A.C. and D.D. David, 2000. Aid, policies, and growth. American Economic Review, 90(4): 847–868. View at Google Scholar Chenery, H.B., 1966. Foreign assistance and economic development. In capital movements and economic development. UK: Palgrave Macmillan. pp: 268-292. Clemens, M.A., S. Radelet and R.R. Bhavnani, 2004. Counting chickens when they hatch: The short term effect of aid on growth. Retrieved from http://econwpa.repec.org/eps/if/papers/0407/0407010.pdf. Collier, P. and D. Dollar, 2002. Aid allocation and poverty reduction. European Economic Review, 46(8): 1475-1500. View at Google Scholar | View at Publisher Dalgaard, C.J. and H. Hansen, 2001. On aid, growth and good policies. Journal of Development Studies, 37(6): 17-41. View at Google Scholar | View at Publisher Dalgaard, C.J., H. Hansen and F. Tarp, 2004. On the empirics of foreign aid and growth. Economic Journal, 114(496): F191-F216. View at Google Scholar | View at Publisher Deaton, A., 2010. Instruments, randomization, and learning about development. Journal of Economic Literature, 48(2): 424-455. View at Google Scholar | View at Publisher Dickey, D.A. and W.A. Fuller, 1979. Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74(366a): 427-431. View at Google Scholar | View at Publisher Dollar, D. and A. Kraay, 2002. Growth is good for the poor. Journal of Economic Growth, 7(3): 195-225. View at Google Scholar Doppelhofer, G., R.I. Miller and X. Sala-i-Martin, 2000. Determinants of long-term growth: A Bayesian averaging of classical estimates (BACE) approach (No. w7750), National Bureau of Economic Research. Doucouliagos, H. and M. Paldam, 2009. The aid effectiveness literature: The sad results of 40 years of research. Journal of Economic Surveys, 23(3): 433-461. View at Google Scholar | View at Publisher Easterly, W., 2003. Can foreign aid buy growth? Journal of Economic Perspectives, 17(3): 23-48. View at Google Scholar | View at Publisher Easterly, W., R. Levine and D. Roodman, 2003. New data, new doubts: A comment on burnside and Dollar's" aid, policies, and growth" (2000) (No. w9846). National Bureau of Economic Research. Retrieved from http://faculty.haas.berkeley.edu/ross_levine/papers/Forth_Comment_New%20Data%20New%20Doubt.pdf. Easterly, W., R. Levine and D. Roodman, 2004. Aid, policies, and growth: Comment. American Economic Review, 94(3): 774–780. View at Google Scholar Engle, R.F. and C.W. Granger, 1987. Co-integration and error correction: Representation, estimation, and testing. Econometrica: Journal of the Econometric Society, 55(2): 251-276. View at Google Scholar | View at Publisher Galiani, S., S. Knack, L.C. Xu and B. Zou, 2014. The effect of aid on growth: Evidence from a quasi-experiment. Journal of Economic Growth, 22(1): 1-33. Ghosh, S., 2002. Electricity consumption and economic growth in India. Energy Policy, 30(2): 125-129. View at Google Scholar | View at Publisher Granger, C.W., 1986. Developments in the study of cointegrated economic variables. Oxford Bulletin of Economics and Statistics, 48(3): 213-228. View at Google Scholar | View at Publisher Granger, C.W., 1988. Some recent development in a concept of causality. Journal of Econometrics, 39(1-2): 199-211. View at Google Scholar | View at Publisher Granger, C.W. and P. Newbold, 1974. Spurious regressions in econometrics. Journal of Econometrics, 2(2): 111-120. View at Google Scholar | View at Publisher Griffin, K., 1978. Foreign capital, domestic savings and economic development. In International Inequality and National Poverty. UK: Palgrave Macmillan. pp: 57-80. Griffin, K.B. and J.L. Enos, 1970. Foreign assistance: Objectives and consequences. Economic Development and Cultural Change, 18(3): 313- 327. View at Google Scholar | View at Publisher Guillaumont, P. and L. Chauvet, 2001. Aid and performance: A reassessment. Journal of Development Studies, 37(6): 66-92. View at Google Scholar | View at Publisher Gujarati, D., 2004. Basic econometrics. United States Military Academy, West Point. Gulati, U.C., 1978. Effect of capital imports on savings and growth in less developed countries. Economic Inquiry, 16(4): 563-569. View at Google Scholar | View at Publisher Hansen, H. and F. Tarp, 2000. Aid effectiveness disputed. Foreign Aid and Development: Lessons Learnt and Directions for the Future: 103- 128. View at Google Scholar Hansen, H. and F. Tarp, 2001. Aid and growth regressions. Journal of Development Economics, 64(2): 547-570. View at Google Scholar | View at Publisher Hendry, D.F. and H.M. Krolzig, 2004. We ran one regression. Oxford Bulletin of Economics and Statistics, 66(5): 799-810. View at Google Scholar | View at Publisher International Monetary Fund (IMF), 2017. World economic outlook database April 2017. [Accessed 2017 May 30]. Johansen, S., 1991. Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica: Journal of the Econometric Society, 59(6): 1551-1580. View at Google Scholar | View at Publisher 13The studies are: Burnside and David (2000). Hansen and Tarp (2001). Collier and Dollar (2002). and Dalgaard, Hansen and Tarp (2004). https://scholar.google.com/scholar?hl=en&q=Identification%20properties%20of%20recent%20production%20function%20estimators http://dx.doi.org/10.3982/ecta13408 https://scholar.google.com/scholar?hl=en&q=Source%20of%20economic%20growth%20in%20Ethiopia:%20An%20application%20of%20vector%20error%20correction%20model https://scholar.google.com/scholar?hl=en&q=Who%20gives%20foreign%20aid%20to%20whom%20and%20why? https://scholar.google.com/scholar?hl=en&q=Is%20public%20expenditure%20productive? https://scholar.google.com/scholar?hl=en&q=Economic%20growth%20in%20a%20cross%20section%20of%20countries http://dx.doi.org/10.2307/2937943 http://dx.doi.org/10.2307/2937943 https://scholar.google.com/scholar?hl=en&q=Americans%20do%20IT%20better:%20US%20multinationals%20and%20the%20productivity%20miracle http://dx.doi.org/10.1257/aer.102.1.167 https://scholar.google.com/scholar?hl=en&q=Politics%20and%20the%20effectiveness%20of%20foreign%20aid https://scholar.google.com/scholar?hl=en&q=Aid%20effectiveness:%20Opening%20the%20black%20box https://scholar.google.com/scholar?hl=en&q=Aid%20effectiveness:%20Opening%20the%20black%20box http://dx.doi.org/10.1257/aer.97.2.316 https://scholar.google.com/scholar?hl=en&q=Aid,%20policies,%20and%20growth http://econwpa.repec.org/eps/if/papers/0407/0407010.pdf https://scholar.google.com/scholar?hl=en&q=Aid%20allocation%20and%20poverty%20reduction http://dx.doi.org/10.1016/s0014-2921(01)00187-8 http://dx.doi.org/10.1016/s0014-2921(01)00187-8 https://scholar.google.com/scholar?hl=en&q=On%20aid,%20growth%20and%20good%20policies http://dx.doi.org/10.1080/713601081 http://dx.doi.org/10.1080/713601081 https://scholar.google.com/scholar?hl=en&q=On%20the%20empirics%20of%20foreign%20aid%20and%20growth https://scholar.google.com/scholar?hl=en&q=On%20the%20empirics%20of%20foreign%20aid%20and%20growth http://dx.doi.org/10.1111/j.1468-0297.2004.00219.x https://scholar.google.com/scholar?hl=en&q=Instruments,%20randomization,%20and%20learning%20about%20development https://scholar.google.com/scholar?hl=en&q=Instruments,%20randomization,%20and%20learning%20about%20development http://dx.doi.org/10.1257/jel.48.2.424 https://scholar.google.com/scholar?hl=en&q=Distribution%20of%20the%20estimators%20for%20autoregressive%20time%20series%20with%20a%20unit%20root http://dx.doi.org/10.2307/2286348 https://scholar.google.com/scholar?hl=en&q=Growth%20is%20good%20for%20the%20poor https://scholar.google.com/scholar?hl=en&q=The%20aid%20effectiveness%20literature:%20The%20sad%20results%20of%2040%20years%20of%20research http://dx.doi.org/10.1111/j.1467-6419.2008.00568.x https://scholar.google.com/scholar?hl=en&q=Can%20foreign%20aid%20buy%20growth? http://dx.doi.org/10.1257/089533003769204344 http://faculty.haas.berkeley.edu/ross_levine/papers/Forth_Comment_New%20Data%20New%20Doubt.pdf https://scholar.google.com/scholar?hl=en&q=Aid,%20policies,%20and%20growth:%20Comment https://scholar.google.com/scholar?hl=en&q=Aid,%20policies,%20and%20growth:%20Comment https://scholar.google.com/scholar?hl=en&q=Co-integration%20and%20error%20correction:%20Representation,%20estimation,%20and%20testing http://dx.doi.org/10.2307/1913236 https://scholar.google.com/scholar?hl=en&q=Electricity%20consumption%20and%20economic%20growth%20in%20India http://dx.doi.org/10.1016/s0301-4215(01)00078-7 https://scholar.google.com/scholar?hl=en&q=Developments%20in%20the%20study%20of%20cointegrated%20economic%20variables http://dx.doi.org/10.1111/j.1468-0084.1986.mp48003002.x https://scholar.google.com/scholar?hl=en&q=Some%20recent%20development%20in%20a%20concept%20of%20causality http://dx.doi.org/10.1016/0304-4076(88)90045-0 http://dx.doi.org/10.1016/0304-4076(88)90045-0 https://scholar.google.com/scholar?hl=en&q=Spurious%20regressions%20in%20econometrics http://dx.doi.org/10.1016/0304-4076(74)90034-7 http://dx.doi.org/10.1016/0304-4076(74)90034-7 https://scholar.google.com/scholar?hl=en&q=Foreign%20assistance:%20Objectives%20and%20consequences http://dx.doi.org/10.1086/450435 https://scholar.google.com/scholar?hl=en&q=Aid%20and%20performance:%20A%20reassessment https://scholar.google.com/scholar?hl=en&q=Aid%20and%20performance:%20A%20reassessment http://dx.doi.org/10.1080/713601083 https://scholar.google.com/scholar?hl=en&q=Effect%20of%20capital%20imports%20on%20savings%20and%20growth%20in%20less%20developed%20countries https://scholar.google.com/scholar?hl=en&q=Effect%20of%20capital%20imports%20on%20savings%20and%20growth%20in%20less%20developed%20countries http://dx.doi.org/10.1111/j.1465-7295.1978.tb00526.x https://scholar.google.com/scholar?hl=en&q=Aid%20effectiveness%20disputed https://scholar.google.com/scholar?hl=en&q=Aid%20and%20growth%20regressions http://dx.doi.org/10.1016/s0304-3878(00)00150-4 http://dx.doi.org/10.1016/s0304-3878(00)00150-4 https://scholar.google.com/scholar?hl=en&q=We%20ran%20one%20regression https://scholar.google.com/scholar?hl=en&q=We%20ran%20one%20regression http://dx.doi.org/10.1111/j.1468-0084.2004.102_1.x https://scholar.google.com/scholar?hl=en&q=Estimation%20and%20hypothesis%20testing%20of%20cointegration%20vectors%20in%20Gaussian%20vector%20autoregressive%20models http://dx.doi.org/10.2307/2938278 Asian Journal of Economics and Empirical Research, 2017, 4(2): 75-90 84 Johansen, S., 1995. Likelihood-based inference in cointegrated vector autoregressive models. Oxford University Press on Demand. Retrieved from http://econpapers.repec.org/bookchap/oxpobooks/9780198774501.htm. Johansen, S. and K. Juselius, 1990. Maximum likelihood estimation and inference on cointegration—with applications to the demand for money. Oxford Bulletin of Economics and Statistics, 52(2): 169-210. View at Google Scholar | View at Publisher Juselius, K., N.F. Møller and F. Tarp, 2014. The long-run impact of foreign aid in 36 African countries: Insights from multivariate time series analysis. Oxford Bulletin of Economics and Statistics, 76(2): 153-184. View at Google Scholar | View at Publisher Juselius, K., A. Reshid and F. Tarp, 2017. The real exchange rate, foreign aid and macroeconomic transmission mechanisms in Tanzania and Ghana. Journal of Development Studies: 1-29. View at Google Scholar Lee, S.Y.T., R. Gholami and T.Y. Tong, 2005. Time series analysis in the assessment of ICT impact at the aggregate level–lessons and implications for the new economy. Information & Management, 42(7): 1009-1022. View at Google Scholar | View at Publisher Lensink, R. and H. White, 2001. Are there negative returns to aid? Journal of Development Studies, 37(6): 42-65. View at Google Scholar Lof, M., T.J. Mekasha and F. Tarp, 2015. Aid and income: Another time-series perspective. World Development, 69: 19-30. View at Google Scholar | View at Publisher MacKinnon, J.G., A.A. Haug and L. Michelis, 1999. Numerical distribution functions of likelihood ratio tests for cointegration. Journal of Applied Econometrics, 14(5): 563-577. View at Google Scholar | View at Publisher Masih, A.M. and R. Masih, 1997. On the temporal causal relationship between energy consumption, real income, and prices: Some new evidence from Asian-energy dependent NICs based on a multivariate cointegration/vector error-correction approach. Journal of Policy Modeling, 19(4): 417-440. View at Google Scholar | View at Publisher Mosley, P., 1980. Aid, savings and growth revisited. Oxford Bulletin of Economics and Statistics, 42(2): 79-95. View at Google Scholar | View at Publisher Mosley, P., 1986. Aid-effectiveness: The micro-macro paradox. Ids Bulletin, 17(2): 22-27. View at Google Scholar | View at Publisher Mosley, P., 1987. Foreign aid, its defense and reform. University Press of Kentucky. Mosley, P., J. Hudson and S. Horrell, 1987. Aid, the public sector and the market in less developed countries. Economic Journal, 97(387): 616-641. View at Google Scholar | View at Publisher Ng, S. and P. Perron, 1995. Unit root tests in ARMA models with data-dependent methods for the selection of the truncation lag. Journal of the American Statistical Association, 90(429): 268-281. View at Google Scholar | View at Publisher Nowak-Lehmann, F., A. Dreher, D. Herzer, S. Klasen and I. Martínez-Zarzoso, 2012. Does foreign aid really raise per capita income? A time series perspective. Canadian Journal of Economics/Revue Canadienned'Economique, 45(1): 288-313. View at Google Scholar | View at Publisher Österholm, P. and E. Hjalmarsson, 2007. Testing for cointegration using the Johansen methodology when variables are near-integrated (No. 7-141). International Monetary Fund. Retrieved from https://pdfs.semanticscholar.org/d92d/8bef0d79236c2c0b9684a3a35e2a69ef0615.pdf. Oxley, L. and D. Greasley, 1998. Vector autoregression, cointegration and causality: Testing for causes of the British industrial revolution. Applied Economics, 30(10): 1387-1397. View at Google Scholar | View at Publisher Papanek, G.F., 1972. The effect of aid and other resource transfers on savings and growth in less developed countries. Economic Journal, 82(327): 934-950. View at Google Scholar | View at Publisher Papanek, G.F., 1973. Aid, foreign private investment, savings, and growth in less developed countries. Journal of Political Economy, 81(1): 120-130. View at Google Scholar | View at Publisher Phillips, P.C. and P. Perron, 1988. Testing for a unit root in time series regression. Biometrika: 335-346. View at Google Scholar | View at Publisher Rajan, R.G. and A. Subramanian, 2008. Aid and growth: What does the cross-country evidence really show? Review of Economics and Statistics, 90(4): 643-665. View at Google Scholar | View at Publisher Roodman, D., 2007. The anarchy of numbers: Aid, development, and cross-country empirics. World Bank Economic Review, 21(2): 255-277. View at Google Scholar | View at Publisher Rosenstein-Rodan, P.N., 1961. International aid for underdeveloped countries. Review of Economics and Statistics, 43(2): 107-138. View at Google Scholar Sala-i-Martin, X.X., 1997a. I just ran two million regressions. American Economic Review, 87(2): 178-183. Sala-i-Martin, X.X., 1997b. I just ran four million regressions (No. w6252). National Bureau of Economic Research. Retrieved from http://j- bradford-delong.net/teaching_folder/Econ_202c/readberk/4-Patterns_of_Growth/Sala-i-Martin_4M.pdf. Toda, H.Y. and T. Yamamoto, 1995. Statistical inference in vector autoregressions with possibly integrated processes. Journal of Econometrics, 66(1): 225-250. View at Google Scholar | View at Publisher Wahab, N.T.A. and S.D. Applanaidu, 2015. An econometric analysis of food security determinants in Malaysia: A vector error correction model approach (VECM). Asian Social Science, 11(23): 1-11. View at Google Scholar | View at Publisher Wassell, C.S. and P.J. Saunders, 2005. Time series evidence on social security and private saving: The issue revisited. Ellensburg: Department of Economics, Central Washington University. Weisskopf, T.E., 1972. The impact of foreign capital inflow on domestic savings in underdeveloped countries. Journal of International Economics, 2(1): 25-38. View at Google Scholar | View at Publisher World Bank, 2017. World development indicators. Retrieved from http://databank.worldbank.org/data/reports.aspx?source=world- development-indicators [Accessed 2017 May 30]. Yeoh, M. and D. Stansel, 2013. Is public expenditure productive: Evidence from the manufacturing sector in US cities, 1880-1920. Cato Journal, 33(1): 1-28. View at Google Scholar Appendix A: Abbreviations ADF test: Augmented Dickey-Fuller test AEL: Aid effectiveness literature AIC: Akaike information criterion ECT: Error correction term FPE: Final prediction error GDP: Gross domestic product GNI: Gross national income HQ: Hannan-Quinn information criterion IMF: International Monetary Fund LDC: Less developed country LDCs: Less developed countries ODA: Official development assistance OLS: Ordinary least squares SC: Schwarz information criterion T-Y: Toda and Yamamoto WDI: World development indicators WEO: World economic outlook WW2: World War Two VAR: Vector auto regression VECM: Vector error correction modeling http://econpapers.repec.org/bookchap/oxpobooks/9780198774501.htm https://scholar.google.com/scholar?hl=en&q=Maximum%20likelihood%20estimation%20and%20inference%20on%20cointegration—with%20applications%20to%20the%20demand%20for%20money http://dx.doi.org/10.1111/j.1468-0084.1990.mp52002003.x https://scholar.google.com/scholar?hl=en&q=The%20long-run%20impact%20of%20foreign%20aid%20in%2036%20African%20countries:%20Insights%20from%20multivariate%20time%20series%20analysis http://dx.doi.org/10.1111/obes.12012 https://scholar.google.com/scholar?hl=en&q=The%20real%20exchange%20rate,%20foreign%20aid%20and%20macroeconomic%20transmission%20mechanisms%20in%20Tanzania%20and%20Ghana https://scholar.google.com/scholar?hl=en&q=Time%20series%20analysis%20in%20the%20assessment%20of%20ICT%20impact%20at%20the%20aggregate%20level–lessons%20and%20implications%20for%20the%20new%20economy http://dx.doi.org/10.1016/j.im.2004.11.005 https://scholar.google.com/scholar?hl=en&q=Are%20there%20negative%20returns%20to%20aid? https://scholar.google.com/scholar?hl=en&q=Aid%20and%20income:%20Another%20time-series%20perspective https://scholar.google.com/scholar?hl=en&q=Aid%20and%20income:%20Another%20time-series%20perspective http://dx.doi.org/10.1016/j.worlddev.2013.12.015 https://scholar.google.com/scholar?hl=en&q=Numerical%20distribution%20functions%20of%20likelihood%20ratio%20tests%20for%20cointegration http://dx.doi.org/10.1002/(sici)1099-1255(199909/10)14:5%3c563::aid-jae530%3e3.3.co;2-i https://scholar.google.com/scholar?hl=en&q=On%20the%20temporal%20causal%20relationship%20between%20energy%20consumption,%20real%20income,%20and%20prices:%20Some%20new%20evidence%20from%20Asian-energy%20dependent%20NICs%20based%20on%20a%20multivariate%20cointegration/vector%20error-correction%20approach http://dx.doi.org/10.1016/s0161-8938(96)00063-4 https://scholar.google.com/scholar?hl=en&q= http://dx.doi.org/10.1016/j.sbspro.2013.06.643 http://dx.doi.org/10.1016/j.sbspro.2013.06.643 https://scholar.google.com/scholar?hl=en&q=Aid-effectiveness:%20The%20micro-macro%20paradox http://dx.doi.org/10.1111/j.1759-5436.1986.mp17002004.x https://scholar.google.com/scholar?hl=en&q=Aid,%20the%20public%20sector%20and%20the%20market%20in%20less%20developed%20countries http://dx.doi.org/10.2307/2232927 https://scholar.google.com/scholar?hl=en&q=Unit%20root%20tests%20in%20ARMA%20models%20with%20data-dependent%20methods%20for%20the%20selection%20of%20the%20truncation%20lag http://dx.doi.org/10.2307/2291151 https://scholar.google.com/scholar?hl=en&q=Does%20foreign%20aid%20really%20raise%20per%20capita%20income?%20A%20time%20series%20perspective http://dx.doi.org/10.1111/j.1540-5982.2011.01696.x http://dx.doi.org/10.1111/j.1540-5982.2011.01696.x https://scholar.google.com/scholar?hl=en&q=Vector%20autoregression,%20cointegration%20and%20causality:%20Testing%20for%20causes%20of%20the%20British%20industrial%20revolution http://dx.doi.org/10.1080/000368498325002 https://scholar.google.com/scholar?hl=en&q=The%20effect%20of%20aid%20and%20other%20resource%20transfers%20on%20savings%20and%20growth%20in%20less%20developed%20countries http://dx.doi.org/10.2307/2230259 https://scholar.google.com/scholar?hl=en&q=Aid,%20foreign%20private%20investment,%20savings,%20and%20growth%20in%20less%20developed%20countries http://dx.doi.org/10.1086/260009 https://scholar.google.com/scholar?hl=en&q=Testing%20for%20a%20unit%20root%20in%20time%20series%20regression http://dx.doi.org/10.1093/biomet/75.2.335 https://scholar.google.com/scholar?hl=en&q=Aid%20and%20growth:%20What%20does%20the%20cross-country%20evidence%20really%20show? http://dx.doi.org/10.1162/rest.90.4.643 https://scholar.google.com/scholar?hl=en&q=The%20anarchy%20of%20numbers:%20Aid,%20development,%20and%20cross-country%20empirics http://dx.doi.org/10.1093/wber/lhm004 https://scholar.google.com/scholar?hl=en&q=International%20aid%20for%20underdeveloped%20countries https://scholar.google.com/scholar?hl=en&q=International%20aid%20for%20underdeveloped%20countries http://j-bradford-delong.net/teaching_folder/Econ_202c/readberk/4-Patterns_of_Growth/Sala-i-Martin_4M.pdf http://j-bradford-delong.net/teaching_folder/Econ_202c/readberk/4-Patterns_of_Growth/Sala-i-Martin_4M.pdf https://scholar.google.com/scholar?hl=en&q=Statistical%20inference%20in%20vector%20autoregressions%20with%20possibly%20integrated%20processes http://dx.doi.org/10.1016/0304-4076(94)01616-8 https://scholar.google.com/scholar?hl=en&q=An%20econometric%20analysis%20of%20food%20security%20determinants%20in%20Malaysia:%20A%20vector%20error%20correction%20model%20approach%20(VECM) http://dx.doi.org/10.5539/ass.v11n23p1 https://scholar.google.com/scholar?hl=en&q=The%20impact%20of%20foreign%20capital%20inflow%20on%20domestic%20savings%20in%20underdeveloped%20countries http://dx.doi.org/10.1016/0022-1996(72)90043-8 http://databank.worldbank.org/data/reports.aspx?source=world-development-indicators http://databank.worldbank.org/data/reports.aspx?source=world-development-indicators https://scholar.google.com/scholar?hl=en&q=Is%20public%20expenditure%20productive:%20Evidence%20from%20the%20manufacturing%20sector%20in%20US%20cities,%201880-1920 Asian Journal of Economics and Empirical Research, 2017, 4(2): 75-90 85 Appendix B: The Data Year GDP per capita in US $ (GDP) ODA(percent of GNI) Gross capital formation (percent of GDP) (CAPITAL) Population growth (POPLG) 1973 117.7819065 5.198165 8.712006898 1.585485524 1974 179.1641755 4.243359853 7.374857223 1.703316829 1975 272.9701785 5.512471456 6.147905815 1.997715897 1976 138.7232244 4.927019983 9.911362042 2.334804116 1977 128.942513 8.162886773 11.5232178 2.596271472 1978 172.6062003 7.5161892 11.54679855 2.766916511 1979 196.6780059 7.48378619 11.20387213 2.810825619 1980 222.9242646 7.08665606 14.4393913 2.769204023 1981 242.2224312 5.337540043 17.15576644 2.710344222 1982 215.7421858 7.096030945 17.36327909 2.677536855 1983 199.6916194 5.751979043 16.56273677 2.658002448 1984 208.9325984 6.100986381 16.48425757 2.661362183 1985 239.5138363 4.972468716 15.8309437 2.675519221 1986 227.8791364 6.432029907 16.17645483 2.689529516 1987 247.5620475 7.208769256 15.47344203 2.683137929 1988 263.7341157 5.938576105 15.73598307 2.64460664 1989 278.3516037 6.116851021 16.12091443 2.567501631 1990 298.144992 6.492388153 16.45867552 2.466950281 1991 285.296976 5.946636189 16.89594746 2.355938926 1992 285.6978098 5.598726634 17.30502928 2.257783657 1993 292.3645263 4.060145962 17.94683201 2.187760068 1994 291.3258679 5.004785042 18.40255619 2.155122135 1995 320.3619277 3.27837883 19.11979582 2.1457187 1996 383.8299551 2.577291706 20.7299506 2.138090473 1997 390.4079054 2.04049926 21.81621451 2.115690607 1998 396.1696495 2.26168444 22.12141282 2.078586608 1999 398.2295463 2.307716612 22.7213703 2.021669268 2000 406.5317405 2.128498674 23.80856257 1.94944844 2001 403.5945462 1.876225243 24.17430673 1.882916186 2002 401.7081533 1.592481356 24.34141614 1.816606212 2003 434.0465632 2.228824518 24.67918886 1.726004223 2004 462.2748798 2.08147327 24.99183394 1.605803333 2005 485.8528881 1.818585047 25.83043551 1.47034775 2006 495.8537802 1.609564116 26.14414575 1.326957091 2007 543.0822631 1.788530336 26.17849707 1.203348026 2008 618.0758836 2.098240471 26.2022714 1.125881485 2009 683.6144223 1.108309467 26.20605702 1.109061795 2010 760.3319352 1.126595014 26.24665618 1.134879634 2011 838.5478017 1.074870504 27.42097337 1.172933905 2012 858.9333626 1.485229114 28.26233501 1.199882864 2013 954.3963997 1.622223223 28.38962075 1.216351172 2014 1086.800087 1.31122154 28.57787571 1.214377385 Source: World Bank World Development Indicators 2017 Appendix C: Data Description Variable Description GDP GDP per capita is gross domestic product (current prices in US $) divided by midyear population. ODA Net official development assistance (ODA) consists of disbursements of loans made on concessional terms and grants by official agencies of the members of the Development Assistance Committee (DAC), multilateral institutions, and non-DAC countries to promote economic development and welfare in countries and territories in the DAC list of ODA recipients, expressed at percentage of gross national income (GNI). Capital (CAPITAL) Capital is the gross capital formation expressed in percentage of GDP consists of outlays on additions to the fixed assets of the economy plus net changes in the level of inventories. Population (POPLG) Annual population growth rate for year t is the exponential rate of growth of midyear population from year t-1 to t, expressed as a percentage. Source: World Bank World Development Indicators 2017 Asian Journal of Economics and Empirical Research, 2017, 4(2): 75-90 86 Appendix D: Johansen Cointegration Test Date: 06/04/17 Time: 9:49 Sample (adjusted): 1978 2014 Included obervations: 37 after adjustments Trend assumption: Linear deterministic trend (restricted) Series: GDP ODP CAPTIAL POPLG Lags interval (in first differences): 1 to 4 Unrestricted Cointegration Rank Test (Trace) Hypothesized No. of CE(s) Elgenvalue Trace statistic 0.05 Critical Value Prob.** None * 0.807724 119.5347 47.85613 0.0000 At most 1* 0.642178 58.52829 29.79707 0.0000 At most 2* 0.362653 20.50268 15.49471 0.0081 At most 3* 0.098491 3.836339 3.841466 0.0501 Trace test indicates 3 cointegrating eqn (s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon et al. (1999) p-value Unrestricted Cointegration Rank Test (Maximum Eigenvalue) Hypothesized No. of CE(s) Elgenvalue Max-Eigen Statistic 0.05 Critical Value Prob.** None * 0.807724 61.00638 27.58434 0.0000 At most 1* 0.642178 38.02562 21.13162 0.0001 At most 2* 0.362653 16.66634 14.26460 0.0205 At most 3* 0.098491 3.836339 3.841466 0.0501 Max-eigenvalue test indicates 3 cointegrating eqn (s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon et al. (1999) p-value Date: 06/04/17 Time: 10:03 Sample (adjusted): 1978 2014 Included obervations: 37 after adjustments Trend assumption: Linear deterministic trend (restricted) Series: GDP ODP CAPTIAL POPLG Lags interval (in first differences): 1 to 4 Unrestricted Cointegration Rank Test (Trace) Hypothesized No. of CE(s) Elgenvalue Trace statistic 0.05 Critical Value Prob.** None * 0.816421 160.87610 63.87610 0.0000 At most 1* 0.732390 42.91525 42.91525 0.0000 At most 2* 0.585806 25.87211 25.87211 0.0000 At most 3* 0.362633 12.51798 12.51798 0.0096 Trace test indicates 4 cointegrating eqn (s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon et al. (1999) p-value Unrestricted Cointegration Rank Test (Maximum Eigenvalue) Hypothesized No. of CE(s) Elgenvalue Max-Eigen Statistic 0.05 Critical Value Prob.** None * 0.816421 62.71900 32.11832 0.0000 At most 1* 0.732390 48.77429 25.82321 0.0000 At most 2* 0.585806 32.61259 19.38704 0.0000 At most 3* 0.362633 16.66513 12.51798 0.0096 Max-eigenvalue test indicates 4 cointegrating eqn (s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon et al. (1999) p-value Appendix E 1 Vector Error Correction Estimates Date: 04/06/17 Time: 14:15 Sample (adjusted): 1978-2014 Included observations: 37 after adjustments Standard errors in ( ) & t-statistics in [ ] CointegratingEq: CointEq1 GDP (-1) 1.000000 ODA (-1) 124.4875 (154.249) [0.80705) CAPITAL (-1) 92.06700 (78.0954) [1.17890] POPULATION (-1) 2489.280 (408.444) [6.09454] C -7928.584 Error Correction D (GDP) D (ODA) D (CAPITAL) D (POPLG) CointEq1 -0.018332 (0.01108) [-1.65402] -0.000722 (0.00029) [-2.50244] -0.000296 (0.00023) [-1.31052] -5.76E-07 (5.1E-06) [-0.11193] Asian Journal of Economics and Empirical Research, 2017, 4(2): 75-90 87 D (GDP(-1)) 0.192055 (0.25827) [0.74363] -0.010328 (0.00673) [-1.53548] 0.005085 (0.00527) [0.96510] -4.77E-05 (0.00012) [-0.39738] D (GDP(-2)) -0.132601 (0.21960) [-0.60382] -0.003558 (0.00572) [-0.62202] -0.005496 (0.00448) [-1.22676] -2.01E-06 (0.00010) [-0.19708] D (GDP(-3)) 0.326056 (0.18789) [1.73531] -0.006538 (0.00489) [-1.33610] 0.003398 (0.00383) [0.88644] 0.000121 (8.7E-05) [1.38744] D (GDP(-4)) -0.021262 (0.20464) [-0.10390] 0.011214 (0.00533) [2.10410] -0.008723 (0.00417) [-2.08938] -3.52E-05 (9.5E-05) [-0.36988] D (ODA(-1)) 0.944206 (8.25877) [0.11433] -0.819793 (0.21510) [-3.81128] -0.237344 (0.16848) [-1.40873] 0.001366 (0.00384) [0.35597] D (ODA(-2)) 2.950476 (11.3903) [0.25904] -0.818083 (0.29666) [-275769] -0.163204 (0.23236) [0.70237] 0.005637 (0.00529) [1.065081] D (ODA(-3)) 4.675114 (9.96808) [0.46901] -0.606285 (0.25962) [-2.33532] -0.204697 (0.20335) [-1.00662] 0.003029 (0.00463) [0.65406] D (ODA(-4)) 0.230430 (7.17290) [0.03213] -0.351906 (0.18682) [-1.88371] -0.038276 (0.14633)[- [0.026157] 0.002578 (0.00333) [0.77349] D (CAPITAL(-1)) -8.834268 (10.6821) [-0.82702 -0.717825 (0.27821) [-2.58015] 0.350906 (0.21792) [1.61028] 0.004207 (0.00496) [0.84761] D (CAPITAL(-2)) -7.986122 (9.11581) [-0.87607] -0.214859 (0.23742) [-0.90498] -0.358030 (0.18596) [-1.92526] 0.004375 (0.00424) [1.03290] D (CAPITAL(-3)) 2.340438 (7.62624) [0.30689] -0.557906 (0.19862) [-2.80887] 0.076628 (0.15558) [0.49254] -0.005680 (0.00354) [-1.60306] D (CAPITAL(-4)) 0.218031 (6.77971) [0.03216] -0.333128 (0.17658) [-1.88661] -0.006779 (0.13831) [-0.04901] 0.008697 (0.00315) [2.76098] D (POPULATION(- 1)) 574.9397 (414.181) [1.38814] -16.34547 (10.7872) [-1.51527] -14.58656 (8.44938) [1.72635] 1.993824 (0.19245) [10.3604] D (POPULATION(- 2)) -917.3912 (899.247) [-1.02018] 41.35613 (23.4206) [1.76580] 30.92362 (18.3448) [1.68568] -1.439530 (0.41783) [-3.44527] D (POPULATION(- 3)) 682.4348 (877.375) [0.77781] -37.31820 (22.8509) [2.33422] 11.24026 (8.24197) [1.36378] 0.349115 (0.40767) [0.85638] D (POPULATION(- 4)) -136.3971 (404.014) [-0.33761] 24.56161 (10.5224) [2.33422] 0.496043 (0.36332) [1.36378] -0.001850 (0.18772) [-0.00986] C 32.67681 (17.8097) [1.83477] 0.876607 (0.46385) [1.88986] 0.496043 (0.36332) [1.365301] -0.007797 (0.00828) [-0.94217] R-squared 0.692773 0.624266 0.765374 0.980194 Adj. R-squared 0.417886 0.288082 0.555446 0.962473 Sum sq. resids 12619.18 8.559883 5.251719 0.002724 S.E. equation 25.77144 0.671208 0.525744 0.011975 F-statistic 2.520211 1.856919 3.645887 55.31306 Log Likelihood -160.3937 -25.41984 -16.38202 123.5532 Akaike A/C 9.642906 2.347019 1.858488 -5.705580 Schwarz SC 10.42659 3.130708 2.642177 -4.921890 Mean Dependent 25.88804 -0.185180 0.460937 -0.037348 S. D. Dependent 33.77807 0.795504 0.788518 0.061814 Determinant resid covariance (dof adj.) 0.002483 Determinant resid covariance 0.000173 Log Likelihood -49.71323 Akaike information criterion 6.795310 Schwarz criterion 10.10422 Asian Journal of Economics and Empirical Research, 2017, 4(2): 75-90 88 2. Vector Error Correction Estimates Appendix F: VEC Granger Causality/ Block Exogeneity Wald Tests Dependent Variable: D(GDP) Method: Least Squares (Gauss-Newton / Marquardt steps) Date: 05/30/17 Time: 13:21 Sample (adjusted): 1978 2014 Included observations: 37 after adjustments D(GDP) = C(1)*( GDP(-1) + 124.487483696*ODA(-1) + 92.0669986939 *CAPITAL(-1) + 2489.28043071*POPLG(-1) - 7928.5843028 ) + C(2) *D(GDP(-1)) + C(3)*D(GDP(-2)) + C(4)*D(GDP(-3)) + C(5)*D(GDP(-4)) + C(6)*D(ODA(-1)) + C(7)*D(ODA(-2)) + C(8)*D(ODA(-3)) + C(9) *D(ODA(-4)) + C(10)*D(CAPITAL(-1)) + C(11)*D(CAPITAL(-2)) + C(12) *D(CAPITAL(-3)) + C(13)*D(CAPITAL(-4)) + C(14)*D(POPLG(-1)) + C(15)*D(POPLG(-2)) + C(16)*D(POPLG(-3)) + C(17)*D(POPLG(-4)) + C(18) Coefficient Std. Error t-Statistic Prob. C(1) -0.018332 0.011084 -1.654018 0.1146 C(2) 0.192055 0.258265 0.743635 0.4662 C(3) -0.132601 0.219603 -0.603823 0.5531 C(4) 0.326056 0.187894 1.735313 0.0989 C(5) -0.021262 0.204640 -0.103901 0.9183 C(6) 0.944205 8.258765 0.114328 0.9102 C(7) 2.950476 11.39025 0.259035 0.7984 C(8) 4.675114 9.968084 0.469008 0.6444 C(9) 0.230430 7.172901 0.032125 0.9747 C(10) -8.834268 10.68205 -0.827020 0.4185 C(11) -7.986122 9.115808 -0.876074 0.3919 C(12) 2.340438 7.626244 0.306893 0.7623 C(13) 0.218031 6.779708 0.032159 0.9747 C(14) 574.9397 414.1807 1.388137 0.1812 C(15) -917.3912 899.2467 -1.020177 0.3205 C(16) 682.4348 877.3752 0.777814 0.4463 C(17) -136.3971 404.0136 -0.337605 0.7394 C(18) 32.67681 17.80975 1.834772 0.0822 R-squared 0.692773 Mean dependent var 25.88804 Adjusted R-squared 0.417886 S.D. dependent var 33.77807 S.E. of regression 25.77144 Akaike info criterion 9.642905 Sum squared resid 12619.18 Schwarz criterion 10.42659 Log likelihood -160.3937 Hannan-Quinn criter. 9.919192 F-statistic 2.520211 Durbin-Watson stat 1.891938 Prob(F-statistic) 0.027249 VEC Granger Causality/Block Exogeneity Wald Tests Date: 05/30/17 Time: 14:10 Sample: 1973 2014 Included observations: 37 Dependent variable: D(GDP) Excluded Chi-sq df Prob. D(ODA) 0.454714 4 0.9778 D(CAPITAL) 2.913232 4 0.5724 D(POPLG) 3.250685 4 0.5168 All 10.42330 12 0.5789 Dependent variable: D(ODA) Excluded Chi-sq df Prob. D(GDP) 6.991891 4 0.1363 D(CAPITAL) 15.11521 4 0.0045 D(POPLG) 13.57706 4 0.0088 All 22.25028 12 0.0348 Dependent variable: D(CAPITAL) Excluded Chi-sq df Prob. D(GDP) 6.078254 4 0.1934 D(ODA) 3.926476 4 0.4160 D(POPLG) 7.677406 4 0.1041 All 31.27932 12 0.0018 Dependent variable: D(POPLG) Excluded Chi-sq df Prob. D(GDP) 2.178736 4 0.7029 D(ODA) 1.822800 4 0.7683 D(CAPITAL) 11.49740 4 0.0215 All 27.84601 12 0.0058 Asian Journal of Economics and Empirical Research, 2017, 4(2): 75-90 89 Appendix G: Residual Diagnostics 1 Breusch-Godfrey Serial Correlation L M Test 2. Heteroskedasticity Tests Breusch-Pagan-Godfrey Breusch-Godfrey Serial Correlation LM Test: F-statistic 0.926414 Prob. F(4,15) 0.4746 Obs*R-squared 7.329830 Prob. Chi-Square(4) 0.1195 Test Equation: Dependent Variable: RESID Method: Least Squares Date: 05/30/17 Time: 14:13 Sample: 1978 2014 Included observations: 37 Presample missing value lagged residuals set to zero. Variable Coefficient Std. Error t-Statistic Prob. C(1) 0.018832 0.070014 0.268982 0.7916 C(2) 0.760697 3.267906 0.232778 0.8191 C(3) -0.169576 0.822695 -0.206123 0.8395 C(4) 0.256660 0.646442 0.397035 0.6969 C(5) -0.162085 1.089713 -0.148741 0.8837 C(6) -6.310117 9.289973 -0.679240 0.5073 C(7) -7.948015 14.58463 -0.544958 0.5938 C(8) -6.127644 12.02688 -0.509496 0.6178 C(9) -5.035852 12.79780 -0.393494 0.6995 C(10) -6.649461 13.64556 -0.487298 0.6331 C(11) 6.855772 34.09074 0.201104 0.8433 C(12) 7.840021 31.75620 0.246882 0.8083 C(13) 0.465407 7.692474 0.060502 0.9526 C(14) 15.23944 438.5801 0.034747 0.9727 C(15) -726.7694 1913.512 -0.379809 0.7094 C(16) 1024.182 2425.276 0.422295 0.6788 C(17) -530.9792 1511.716 -0.351243 0.7303 C(18) -32.49555 118.4548 -0.274329 0.7876 RESID(-1) -0.920582 3.344450 -0.275257 0.7869 RESID(-2) -0.190278 0.381904 -0.498237 0.6255 RESID(-3) -0.509558 0.390503 -1.304876 0.2116 RESID(-4) -0.480914 0.401685 -1.197243 0.2498 R-squared 0.198104 Mean dependent var 0.000000 Adjusted R-squared -0.924552 S.D. dependent var 18.72252 S.E. of regression 25.97341 Akaike info criterion 9.638346 Sum squared resid 10119.27 Schwarz criterion 10.59619 Log likelihood -156.3094 Hannan-Quinn criter. 9.976030 F-statistic 0.176460 Durbin-Watson stat 2.082360 Prob(F-statistic) 0.999818 Heteroskedasticity Test: Breusch-Pagan-Godfrey F-statistic 1.047583 Prob. F(20,16) 0.4686 Obs*R-squared 20.97907 Prob. Chi-Square(20) 0.3984 Scaled explained SS 7.501930 Prob. Chi-Square(20) 0.9947 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 05/30/17 Time: 14:16 Sample: 1978 2014 Included observations: 37 Variable Coefficient Std. Error t-Statistic Prob. C -4022.146 5353.060 -0.751373 0.4633 GDP(-1) -2.295792 6.225320 -0.368783 0.7171 ODA(-1) -186.8592 194.6259 -0.960094 0.3513 CAPITAL(-1) 170.4243 278.9498 0.610950 0.5498 POPLG(-1) -647.3674 9708.019 -0.066684 0.9477 GDP(-2) -2.677819 7.849666 -0.341138 0.7374 GDP(-3) 7.695602 6.487008 1.186310 0.2528 GDP(-4) -6.905654 7.133606 -0.968045 0.3474 GDP(-5) 7.919689 5.455991 1.451558 0.1660 ODA(-2) 128.1970 217.4604 0.589519 0.5637 ODA(-3) -115.4529 222.4529 -0.518999 0.6109 ODA(-4) 219.5739 192.0088 1.143562 0.2696 ODA(-5) 238.5780 186.6494 1.278215 0.2194 CAPITAL(-2) -234.5552 311.9238 -0.751963 0.4630 CAPITAL(-3) 228.8284 257.3921 0.889027 0.3872 CAPITAL(-4) -202.2138 240.7063 -0.840085 0.4132 CAPITAL(-5) 151.7398 157.2671 0.964854 0.3490 POPLG(-2) 354.0182 28946.88 0.012230 0.9904 POPLG(-3) 7822.916 38353.49 0.203969 0.8409 POPLG(-4) -10393.10 27361.20 -0.379848 0.7091 POPLG(-5) 2810.952 8827.230 0.318441 0.7543 R-squared 0.567002 Mean dependent var 341.0588 Adjusted R-squared 0.025754 S.D. dependent var 569.4236 S.E. of regression 562.0433 Akaike info criterion 15.79784 Sum squared resid 5054283. Schwarz criterion 16.71215 Log likelihood -271.2601 Hannan-Quinn criter. 16.12018 F-statistic 1.047583 Durbin-Watson stat 2.471773 Prob(F-statistic) 0.468576 Asian Journal of Economics and Empirical Research, 2017, 4(2): 75-90 90 3. Harvey 4. ARCH 5. Hisgram –Normality Test Appendix H: Wald Test Null Hypothesis: ΔODAt-1 = ΔODAt-2 = ΔODAt-3 = ΔODAt-4 =0 Test Statistic Value df Probability F-statistic 0.113678 (4,19) 0.9761 Chi-square 0.454714 4 0.9778 Null Hypothesis Summary Normalised Restriction (= 0) Value Std. Err. ΔODAt-1 0.944205 8.258765 ΔODAt-2 2.950476 11.39025 ΔODAt-3 4.675114 9.968084 ΔODAt-4 0.230430 7.172901 Restrictions are linear in coefficient Asian Online Journal Publishing Group is not responsible or answerable for any loss, damage or liability, etc. caused in relation to/arising out of the use of the content. Any queries should be directed to the corresponding author of the article. Heteroskedasticity Test: Harvey F-statistic 1.661351 Prob. F(20,16) 0.1532 Obs*R-squared 24.97409 Prob. Chi-Square(20) 0.2024 Scaled explained SS 30.42615 Prob. Chi-Square(20) 0.0632 Test Equation: Dependent Variable: LRESID2 Method: Least Squares Date: 05/30/17 Time: 14:23 Sample: 1978 2014 Included observations: 37 Variable Coefficient Std. Error t-Statistic Prob. C 8.244155 20.24627 0.407194 0.6893 GDP(-1) -0.028725 0.023545 -1.219967 0.2402 ODA(-1) -1.458669 0.736111 -1.981589 0.0650 CAPITAL(-1) -0.665133 1.055040 -0.630434 0.5373 POPLG(-1) 23.59535 36.71753 0.642618 0.5296 GDP(-2) -0.003045 0.029689 -0.102576 0.9196 GDP(-3) 0.051833 0.024535 2.112591 0.0507 GDP(-4) -0.027703 0.026981 -1.026779 0.3198 GDP(-5) 0.027118 0.020636 1.314139 0.2073 ODA(-2) -1.134605 0.822475 -1.379500 0.1867 ODA(-3) 0.863611 0.841358 1.026449 0.3199 ODA(-4) 1.260613 0.726213 1.735873 0.1018 ODA(-5) -0.210078 0.705943 -0.297585 0.7698 CAPITAL(-2) -1.180052 1.179754 -1.000253 0.3321 CAPITAL(-3) 1.879983 0.973505 1.931149 0.0714 CAPITAL(-4) -1.179576 0.910396 -1.295674 0.2135 CAPITAL(-5) 0.808679 0.594813 1.359551 0.1928 POPLG(-2) -86.76647 109.4825 -0.792515 0.4397 POPLG(-3) 140.1535 145.0600 0.966176 0.3483 POPLG(-4) -100.6748 103.4851 -0.972843 0.3451 POPLG(-5) 24.21549 33.38622 0.725314 0.4787 R-squared 0.674975 Mean dependent var 4.061506 Adjusted R-squared 0.268694 S.D. dependent var 2.485783 S.E. of regression 2.125752 Akaike info criterion 4.642934 Sum squared resid 72.30115 Schwarz criterion 5.557239 Log likelihood -64.89428 Hannan-Quinn criter. 4.965270 F-statistic 1.661351 Durbin-Watson stat 2.415947 Prob(F-statistic) 0.153242 Heteroskedasticity Test: ARCH F-statistic 0.843695 Prob. F(4,28) 0.5094 Obs*R-squared 3.549594 Prob. Chi-Square(4) 0.4704 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 05/30/17 Time: 14:27 Sample (adjusted): 1982 2014 Included observations: 33 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 280.1903 160.9962 1.740353 0.0928 RESID^2(-1) 0.302805 0.193264 1.566797 0.1284 RESID^2(-2) -0.015255 0.202813 -0.075215 0.9406 RESID^2(-3) 0.227692 0.255746 0.890306 0.3809 RESID^2(-4) -0.228803 0.258363 -0.885588 0.3834 R-squared 0.107563 Mean dependent var 378.9030 Adjusted R-squared -0.019927 S.D. dependent var 592.5022 S.E. of regression 598.3766 Akaike info criterion 15.76505 Sum squared resid 10025528 Schwarz criterion 15.99179 Log likelihood -255.1232 Hannan-Quinn criter. 15.84134 F-statistic 0.843695 Durbin-Watson stat 1.944376 Prob(F-statistic) 0.509383 0 2 4 6 8 10 12 14 -50 -40 -30 -20 -10 0 10 20 30 40 50 Series: Residuals Sample 1978 2014 Observations 37 Mean 0.000000 Median -1.413219 Maximum 45.46958 Minimum -46.67750 Std. Dev. 18.72252 Skewness 0.102723 Kurtosis 3.712146 Jarque-Bera 0.846931 Probability 0.654774