Research methods in economics and its implications for capital formation

Abstract We explore whether public or private capital augments or obstruct Foreign Direct Investment (FDI) inflows by decomposing Domestic Capital Formation (DCF) into private and public capital formation. To this end, we apply Cross-Sectional Autoregressive Distributed Lags (CS-ARDL) approach to analyze panel time-series data. Our empirical results show that public capital crowds in FDI inflows while private capital crowds out FDI inflows. However, institutional quality significantly attracts FDI inflows for less developing economies. We argue that private and public capital possess different attributes; thus, clubbing them together might result in aggregation bias. We observe a strong connection of good institutional quality with private and public capital to augment foreign capital inflows for developing countries in the long run. Besides, our empirical results suggest that returns are high with quality institutions, especially for developing regions. Our result estimations provide several policy implications.


Introduction
Foreign capital inflow is a dynamic conduit of technology transfer from developed to developing countries. Developing countries often encounter insufficient domestic capital savings; thus, FDI inflow fulfils the required amount of domestic investment. The literature argues that FDI contributes toward the prosperity and socio-economic development of the less developing economies (Ndikumana & Verick, 2008). FDI is the prime vector of technological diffusion, productivity enrichment and job creation in developing and transition economies. Besides, FDI fosters the process of globalization; eventually, it promotes economic development in the less developing nations (Quazi, 2007;Smith, 1997). In real terms, foreign capital flows increased by roughly 6% annually in the last four decades, higher than the world's GDP growth rate (Ju & Wei, 2007). According to the UNCTAD report, FDI inflows increased by twenty-nine percent in 2005 and reached the digits of nine hundred sixteen billion US dollars 1 . FDI inflows significantly increased in the case of developing countries in the last couple of decades (Ndikumana & Verick, 2008).
FDI inflows realize the rising investment needs for rapid economic development in the developing economies (North, 1981(North, , 1990). In addition, prior literature highlights the promising role of institutional quality to accrue economic gains from foreign capital inflows (OECD, 2002). Empirical and theoretical studies emphasized the role of institutional quality in attracting foreign capital inflows in the last couple of decades (Acemoglu & Johnson, 2005;IMF, 2003). Institutional quality is also associated with economic growth (Ali et al., 2010;North, 1990). Evidence shows that Russia experienced less inflow of FDI due to slowdown of institutional reform 2 . In addition, The Economist claims that poor institutional quality reduces the pace of socio-economic development and research and development activities 2 (The Economist, 2003).
Existing literature clarified different possible ways utilizing those channels the institutions influence international capital flows. Three crucial factors are highlighted, focusing on the significance of institutions in promoting foreign capital inflows (Ali et al., 2010;Buchanan et al., 2012). Firstly, North (1990) emphasized the role of institutional quality in stimulating investment and economic development. Secondly, developing and transition economies firmly focused on restructuring the institutions to attract FDI inflows due to the rapid increase of foreign capital flows in the last two decades. Thirdly, overseas investors keenly focus on the quality of institutions of the host country while deciding in which country to invest (Bevan et al., 2004). Institutions are designed to minimize and curtail the risk associated with business transactions and human exchange (North, 1990). Furthermore, North (1990) explains that parties have insufficient information about the true intentions of their business partner due to asymmetric available in the financial market.
There are different theoretical views regarding the nexus between public and private capital formation. The traditional economist claims that public capital obstructs private capital due to increased public expenditure and decreased tax collection, leading to a budget deficit. Thus, public capital sponsored by public borrowings hikes the interest rate and reduces productivity, resulting in a decrease of private capital formation in the local economy (Ameer et al. 2020;Şen & Kaya, 2014;Mohanty, 2018). In contrast, according to the Keynesian perspective, an increase in public expenditure stirs and crowds in domestic economic activities and, resultantly, stimulates private capital in the economy. In addition, the new-classical theory claims that public expenditure would neither stimulate nor impede private investment because budget deficit occurs owing to an increase in public spending and, thus, increase in the level of public spending cannot alter interest rate, therefore; it cannot influence private investment (Bernheim, 1989).
The classical theory claims that private and public capital formation typically crowds out each other (Şen & Kaya, 2014;Mohanty, 2018). Literature regards the derive of private and public investment very differently (Mohanty, 2018;Narayan, 2004;Şen & Kaya, 2014;Shah et al., 2020). In general, private and public capital formations repel and resist each other (Şen & Kaya, 2014;Mohanty, 2018). Consequently, thus, accumulating them into one composite term may cause domestic capital formation aggregation bias. A study of Amighini et al. (2017) explored the reverse causality impact of FDI inflows on gross fixed capital formation for developing countries. Also, this study has not considered the idea of bifurcation of aggregate capital formation. Henceforth, the prior studies, such as Buchanan et al. (2012) and Huynh et al. (2020), explored the impact of institutional quality (IQ) and aggregate gross domestic capital (DCF) on foreign direct investment inflows (FDI) for panel data studies but these studies also ignored the idea of bifurcation of aggregate domestic capital formation (DCF) into private and public capital formation in order to control domestic capital aggregation bias. In addition, these studies also ignored the common correlation bias which generally exists in the time series panel data studies. Although, a study of Shah et al. (2020) and Ameer et al. (2021) considered the idea of bifurcation by decomposing aggregation capital formation into private and public capital but these studies explored the reverse causality impact of FDI inflow and FDI outflow on domestic capital formation. In addition, these studies of Shah et al. (2020) and Ameer et al. (2021) particular focused on GCC regions but not specially developing regions.
Best to our knowledge, this is the first study particulary for developing countries which has addressed the issue of aggregation bias by exploring impact of aggregate capital formation on FDI inflows by decomposing aggregate capital formation into private and public capital formation. Thus, we contribute to the existing literature by decomposing aggregation capital formation into private and public capital to measure the distinct impact of private and public capital formation on foreign capital inflows (FDI) respectively to avoid aggregation domestic capital formation bias. Overall, this empirical work adds to the existing research literature on many fronts. First of all, we explore interaction effects (DCF Ã IQ) of aggregate domestic capital formation (DCF) and institutional quality in promoting FDI. Next, we measure interaction effects (PRI Ã IQ) of private capital formation and institutional quality (IQ) on FDI. We use the novel concept of CS-ARDL to hold for endogeneity and common correlation bias issues in the developing and transition regions and get consistent results. Besides, we examine interaction effects (PUBI Ã IQ) of public capital formation and institutional quality (IQ) in stimulating IFDI. In addition, we investigate combined interaction effects (PRI Ã PUBI Ã IQ) of institutional quality, private and public capital formation instantaneously on FDI for developing countries. Also, we have formulated a comprehensive index of institutional quality to capture the effects of all crucial individual governance indicators extensively into one aggregate component by aggregating six key individual governance indicators into one aggregate institutional index. Finally, many previous studies have ignored cross-sectional dependency issues to explore the impact of domestic capital formation and institutional quality on FDI inflows.
Section 2 explains the literature review. The third section of our empirical study comprises of methodology, data collection and source of a dataset. The fourth section of our empirical study sheds light on result estimations and their elaboration. Section five concludes our paper.

Literature review
Existing empirical research intensely emphasized institutional quality's effects on FDI inflows (Ali et al., 2010;Buchanan et al., 2012). MNCs preferences are changing from resource and market seeking to efficiency-seeking; thus; consequently, good governance and economic freedom have emerged as rising determining factors of FDI in the last decades (Dunning, 2002). Non-traditional determinants of FDI inflows, for instance; good governance and economic freedom, are emerging more serious determining factors of foreign capital inflows in the recent decades while more traditional FDI determining factors, such as low labour costs and natural resources, are deemed to less valuable compare to the traditional determinants of foreign capital flows in the recent era (Addison & Heshmati, 2003;Becchetti & Hasan, 2004;Noorbakhsh et al., 2001). MNCs also consider law and order situation seriously while investing abroad when courts cannot enforce the contracts successfully. Public officials easily approach the courts to influence political decisions (Drabek & Payne, 2002). Property rights protection, sound political environment and control of corruption are critical institutional indicators to attract multinational investments in developing countries (Jensen, 2003;Richards & Nwankwo, 2005). In the case of seventeen Latin American countries, Judicial competency and supremacy of the rule of law attract foreign capital inflows (Staats & Biglaiser, 2012).
The quality of institutions assesses the risk premium. The risk premium is influenced by the protection of property rights issues, enforceability of the contract, and probability of the third party (North, 1990). In addition, some scholars argue that multinational corporations (MNCs) face expropriation risks in those countries where protection of property rights are pretty poor (Henisz, 2000;Henisz & Williamson, 1999). Survey investment reports claim that corruption impedes foreign capital inflows (Asiedu & Villamil, 2000;Gastanaga et al., 1998). Overall, more corrupt countries receive lesser foreign capital inflows. The lower level of corruption index attracts FDI inflows in the host country (Cuervo-Cazurra, 2006, 2008. Strong protection of property rights attracts foreign capital inflows, mainly; when other institutional factors influence foreign capital inflows indirectly through property rights protection (Ali et al., 2010). Quality institutions minimize running business and production costs (North, 1990) and thus, consequently, flourish as well as upsurge business activities; however, weak institutional structure increases risk premium, running business costs, and production costs (Cuervo-Cazurra, 2006, 2008. Good governance has higher returns for developing countries if we compare it with that of other countries in their study sample (Globerman & Shapiro, 2002). The principal opinion is that countries with solid institutional quality can attract more FDI inflows (Gani, 2007;Globerman & Shapiro, 2002) whereas bad institutions cannot protect the investments (Globerman & Shapiro, 2003). Quality institutions attract FDI inflows while bad institutional quality impedes FDI inflows. Weak institutional quality upsurges all types of investment uncertainties, including FDI inflows (Ali et al., 2010). Also, Buchanan et al. (2012) explored the impact of institutions and domestic capital formation on FDI inflows for a large panel of 164 countries and concluded that quality institutions attract FDI inflows. Jude and Levieuge (2013) concluded that lack of institutional structure is the cause of lower per capita income, lower productivity, sluggish investment opportunities and lower economic growth. Peres et al. (2018) concluded that institutional quality positively stimulates FDI inflows for developed countries and its effects are neutral in the case of developing countries. In addition, governance indicators, such as control of corruption and the rule of law, are significant institutional indicators to stimulate foreign capital inflows.
Quite lot of empirical studies concluded that public capital formation positively stimulates private capital formation in the case of developed and developing economies (Andrade & Duarte, 2016;Ang, 2009). In contrast, a lot of empirical research studies refuted the arguments that public capital formation stirs private capital formation and found unconditionally different empirical findings that public investment crowds out private investment (Atabaev et al., 2018;Mountford & Uhlig, 2005;Xu & Yan, 2014). Conversely, some empirical studies claimed that there exists a neutral relationship between private capital and public spending (Kollamparambil & Nicolaou, 2011;Narayan, 2004) or stimulates each other in the short-run and they obstruct each other in the long-run (Nguyen & Trinh, 2018). Scholars and policy makers worldwide keenly focused and paid lot of attention to this theoretical idea. The empirical justification of this theory significantly differs in views (Andrade & Duarte, 2016;Ang, 2009). Henceforth, a study of Argimon et al. (1997) explored nexus between public expenditure and private expenditure for fourteen OECD states. Their empirical evidence suggest that public capital stimulates or crowds in private investment because of positive effect of infrastructure on private capital efficiency (Argimon et al., 1997). In addition, a study of Mahmoudzadeh et al. (2013) comprise of 23 developed and 15 developing economies; they concluded that public capital impedes private capital for developed economies and the public capital stimulates private capital in case of developing economies (Mahmoudzadeh et al., 2013).
As per above discussed empirical literature, we infer that only studies of Buchanan et al. (2012) and Huynh et al. (2020) have studied impact of aggregate domestic capital (DCF) on FDI infows for developed or developing countries but these studies have not considered idea of decomposition of aggregate domestic capital formation. Additionally, we find that few of existing studies, such as Ameer et al. (2021) and Shah et al. (2020), explored the reverse causality impact of FDI outflows and inflows simultaneously on DCF by bifurcation of aggregate capital formation in to private and public capital and these two studies particularly focused on GCC region but not developing regions. After reading the relevant literature, we have contributed to the existing literature by addressing the issue of aggregation bias by exploring the impact of aggregate domestic capital formation on FDI inflows by decomposing aggregate capital formation into private and public capital formation particularly in case of developing countries. This paper aims at specifically filling this gap.

Methodology and data
Our empirical study includes a comprehensive panel of seventy-three (73) developing and transition economies from 1996 to 2017 annually. For developing countries, we have cross-country studies. i.e., (N 73) and several years i.e., (T 23) in our study. There is a possibility of common correlation bias (CD) when cross-section (N) is relatively larger than number of years (T). It is possible that FDI inflows by one developing country can influence the FDI inflows of other developing economies. Also, when we have a large cross-section and relatively less time span (N>T), it is highly expected that institutional structure of one developing country depend or influenced by other's developing countries institutional policy structure due to the rising wave of globalization and technology advancement. Developing economies are strongly interconnected with each other and follow mutual economic as well as cultural policies, thus; probability of cross-sectional dependency in particular case of developing countries is quite high. Henceforth, cross-sectional dependency bias issues usually occur in the cross-country panel dataset due to spill-over effects, omitted variable bias and mutual interconnectedness with in socio-economic network (Pesaran & Tosetti, 2011). We test our null hypothesis that there does not exist cross-sectional dependency issues in our variables of study against the alternative hypothesis of cross-sectional dependence. Our empirical work follows the methods of Pesaran (2004).
Theq ij denotes the pair-wise common correlation coefficient of the residuals which is derived from ADF regression. N and T denote for cross-section and time dimensions, respectively. We have reported and clarified our baseline model regression equations as following: whereas i ¼ 1 … … . i, which signifies cross-sectional dimension; and t ¼ 1 … … .t represent period and ai denotes country-specific effects. PRI stands for private capital formation, and PUBI denotes public capital formation. To gauge the effects of DCF and IQ on FDI inflows more precisely and accurately, control variables are added to equations (2,3,4 & 5), respectively. The selection of explanatory or control variables is based on current empirical literature and is symbolized by 'x'. Our extended models are reported as: The extended models in equations (6,7,8 & 9) follow the same characteristics of error terms and coefficients of our baseline models reported in equations (2,3,4&5). Henceforth, we have added additional explanatory variables such as interactive proxy variables (DCF Ã IQ) or (PRI Ã IQ) or (PUBI Ã IQ) or (PRI Ã PUBI Ã IQ) and inflation rate (INFLATION) in equations (6,7,8 & 9) respectively to measure the impact of DCF and IQ on FDI inflows more accurately and have a robust check of our empirical findings of our baseline models. Equation (6) captures the effects of DCF, IQ and other control variables on foreign capital inflows. Equation (7) captures the effects of private capital formation, IQ and other control variables on foreign capital inflows. Equation (8) captures the impact of public capital formation, IQ and other control variables on foreign capital inflows. Also, Equation (9) captures the simultaneous impact of PRI, PUBI, IQ and other control variables on foreign capital inflows for developing countries.

Panel CS-ARDL and unit-root test methods
The traditional panel unit root test methods consider cross-sectional independence across the time series units (Im et al., 2003;Levin et al., 2002;Maddala & Wu, 1999). However, the newly introduced panel unit root test methods not only solve the issue of common correlation effect bias (CD) cross the units but they also control the structural breaks issues that usually exist in the time series panel dataset (Bai & Ng, 2004;Choi, 2006;Moon & Perron, 2004;Pesaran, 2007;Smith et al., 2004). To control cross-sectional dependency biases in the variables of our study, we have applied cross-sectional augmented Dickey-Fuller (CADF) Panel unit root test, which is reported in Equation (10): Where as t ¼ 1, . . . :, T, i ¼ 1, . . . :, N and y t denotes the cross-sectional mean of y it which is derived from y t ¼ N À1 P N i¼1 y it : The study of Pesaran (2007) provides the crosssectional augmented panel unit root (CIPS) test statistic as reported in Equation (11): (7) signifies t-statistic for b i : After applying the CD test among the set of variables individually, we found common correlation effects (CD) among the units. Henceforth, it is best fitted and suitable to apply CS-ARDL methods for this empirical study which is reported in Equation (12). Where u i stands for error correction term (ecm) that explains adjustment of short-run disequilibrium after economic shock towards long-run equilibrium. Y tÀ1 denotes unobserved temporal factors of lagged dependent variable in the long run and X tÀ1 stands for unobserved temporal factors of lagged independent variables in the long run while DY t and DX t In the short run, denote unobserved temporal factors for dependent and explanatory variables, which is reported in the above paragraph in Equation (12).

Data description and source
Foreign capital inflows (%GDP) is the dependent variable while DCF, IQ and other control variables are explanatory variables of our empirical study. Figure 1 reports the distribution of FDI inflows across our sample countries and over time.
The key solution is to sum all the individual governance indexes into one aggregate composite term which denotes all six individual governance indicators in to one aggregate index (Daude & Stein, 2007). Accordingly, we have applied principal component analysis (PCA) methodology, termed it 'institutional quality'. We are considering six individual governance indicators 3 to formulate composite index of institutional quality. Governance indicators are normally highly correlated with each other, it might cause multicollinearity among the individual institutional indicators and might reduce the extent to which the relevance of each individual governance indicator can be measured (Mauro, 1995). Table 1 reports our variables, definitions and sources.

Descriptive statistics
The results are reported in Table 2. For developing countries, the mean value of DCF (%GDP) is 23.69. The mean value of PUBI (% GDP) is 10.24, while the mean value

Cross-Sectional dependency order of integration and slope homogeneity tests
The first-generation panel unit root tests assume cross-sectional independence across the units. They might lose a degree of freedom if these unit root methods are applied for the dataset that suffers from cross-sectional dependence (Sadorsky, 2013). Henceforth, we apply the CD test to check for common correlation bias in the dataset. Accordingly, we will apply Pesaran (2004) CD test to check for cross-sectional dependency across the units in our panel dataset. CD test produces unbiased results as the cross-country units increase and reach infinity (Pesaran, 2004). We have reported our CD test results in Table 3, which exhibits the presence of crossdependency in the variables of our study. Henceforth, we reject our null hypothesis of cross-sectional independence among the study variables and accept the alternative hypothesis of cross-sectional dependence among the variables of our study. Due

PUBI Public Capital Formation
The traditional economist claims that public capital obstructs private capital due to an increase in public expenditure and a decrease in tax collection, giving rise to budget deficit (Mohanty, 2018;Narayan, 2004;Şen & Kaya, 2014). In contrast, according to the Keynesian perspective, an increase in public expenditure stirs and crowds in domestic economic activities and, resultantly, stimulates private capital in the economy (Bernheim, 1989  to the presence of cross-sectional dependency, we have applied used Pesaran's (2007) cross-sectionally augmented panel unit root test (CIPS) and Z(t-bar)). We have estimated unit root tests with a constant term. Panel unit root test results show that the variables are stationary at first difference. Correlation (q) across the variables and result estimations for testing of slope heterogeneity are reported in Table 3. As per value of Delta, we reject the null hypothesis that slope coefficients are homogenous and accept the alternative hypothesis that slope coefficients are heterogenous.
In this study, we have applied CS-ARDL approach to address the issue of endogeneity and common correlation bias in our empirical study for developing economies. CS-ARDL imposes short-term heterogeneity and long-term homogeneity on estimated parameters and it is executed under the error correction mechanism.

The impact of private Capital formation and institutional quality on FDI inflows for developing countries
The empirical estimations of our baseline model (M1.1) and extended models (M1.2 & M1.3) show that aggregate domestic capital formation (DCF) crowds in foreign capital inflows in the long run for developing countries. The result estimations are displayed in Table 4. Among the other variables, institutional quality (IQ) attracts FDI inflows for developing countries. Quality institutions decrease the cost of production and running cost of business, thus giving rise to profitability and upsurge economic activities. Conversely, bad institutional quality increases uncertainty in addition to running cost of the business and thus, in turn, impedes economic activities. Our results estimation is consistent with those of Ali et al. (2010), North (1990), Buchanan et al. (2012) and Huynh et al. (2020) which argue that strong institutions promote FDI inflows while poor institutional quality crowds out FDI inflows. The sign of interaction term (DCF Ã IQ) of domestic capital formation and institutional quality show that institutional quality and domestic capital formation are adversely interconnected and as a result, obstruct FDI inflows in our extended model (M1.2), or it does not contribute to FDI inflows for our extended model (M1.3) in the long run. The coefficient of error correction term (EC) in the M1.1, M1.2 and M1.3 show a long-run relationship between foreign capital inflows and other variables of interest Variable of interaction effects (DCF Ã IQ) and inflation rate assert insignificant impact on FDI inflows in the short and long run for developing countries. We will explain the short-run results of our model, and we found that DCF and IQ augment FDI inflows in the short run. However, the signs of coefficients of the variable of interaction effects (DCFˣIQ) and the inflation rate are insignificant. They do not contribute to FDI inflows in the short run and long run. The signs of coefficients of the variable of interaction effects (DCFˣIQ) and inflation rate are contrary to expectations in the short run and long run. The insignificant and unexpected result in Table 4 indicates aggregation bias and demand deep down sectoral by decomposing the aggregate domestic capital formation (Private and Public Capital).

The impact of private Capital formation and institutional quality on FDI inflows for developing countries
In Table 5, we investigate the influence of PRI, IQ, and other variables of interest on FDI inflows in the long and short run. Our result estimations show that private capital formation (PRI) crowds out foreign capital inflows in the long run for developing countries in our extended models (M1.2 & M1.3). One unit increase in PRI decreases significantly FDI inflows in the developing countries; this negative linkage between PRI and foreign capital inflows might be attributable to the fact that FDI inflows are significantly utilized for public sector development with less focused on the development of private sector in the developing countries. Our empirical results show that institutional quality (IQ) give rise to FDI inflows in our baseline (M1.1) and extended models (M1.2 & M1.3). Thus, quality institutions decrease the business's running and operating costs and augment FD inflows. Quality institutions also protect a firm's intellectual property rights, which ultimately boosts investor confidence in the commercial setup. The sign of interaction term (PRI Ã IQ) of private capital and institutional quality show that IQ and PRI are unfavourably interconnected and thus, hinder FDI inflows in our extended model (M1.3), or it does not contribute to FDI inflows for our extended model (M1.2) in the long run. Conversely, in our extended model (M1.3), other variables such as the inflation rate do not stimulate foreign capital inflows in the long run.
The coefficient of error correction term (EC) in the M1.1, M1.2 and M1.3 shows a long-run relationship between foreign capital inflows and other variables of interest of our study. Our short-run rate of adjustment towards long-run equilibrium is 60.69%, 62.41% and 58.91%, respectively in the M1.1, M1.2 and M1.3. Looking into the short-run results in Table 5, we analyse the influence of PRI and IQ and other variables of interest on FDI inflows in the short run, and we found that PRI, IQ and other variables of interest have an insignificant effect on FDI inflows except for inflation rate because variables can behave differently in the short run due to difference of period if we compare with the long run.

The impact of public Capital formation and institutional quality on FDI inflows for developing countries
In Table 6, we investigate the influence of PUBI, IQ and other variables of interest on FDI inflows for developing countries in the long and short-run. As a result,  Table 6, we analyse the effects of PRI, IQ and other variables of interest on FDI inflows. In short, we found that PRI, IQ and other variables of interest have an insignificant impact on foreign capital inflows except for the inflation rate.  (Tables 5 and 7) and the positive influence of public capital formation on FDI inflows (Tables 6 and 7) show that capital markets are weaker in the developing countries, and significant sectors of the economy are strongly controlled by government by the larger extent. In our baseline and extended models, public capital formation crowds in FDI inflows in the long run. Institutional Quality (IQ) attract foreign capital inflows in the long run in our models. In our extended models, the interaction term (PRI Ã PUBI Ã IQ) of private capital, public capital and institutional quality are favourably interconnected attract to FDI inflows (IFDI) in the long run. Our finding is exciting that there is a strong positive link between private capital formation, public capital formation and institutional quality to promote FDI inflows in the long run. Quality institutions are strongly linked with private capital and public capital formation to crowd FDI inflows in developing countries. Empirical estimations suggest that higher level of institutional quality is strongly interrelated with private and public capital to promote FDI inflows. Conversely, in case of weak institutional quality, MNCs would be reluctant to invest across the borders due to expropriation risk from the government or disadvantageous rules changes after investment. Empirical results suggest that MNCs will be reluctant to invest in these countries with corrupt institutional quality even though developing countries are financially open for foreign capital inflows or freely liberalise their borders for international capital inflows. The coefficient of error correction term (ECT) in the M1.1, M1.2 and M1.3 show a long-run relationship between foreign capital inflows and other variables of interest of our study. Our short-run rate of adjustment towards long-run equilibrium is 62.17%, 67.48% and 64.26%, respectively, in the M1.1, M1.2 and M1.3. Looking into the short-run results in Table 7, we investigate the short-run impact of PRI, PUBI, IQ and other variables of interest on FDI inflows in the case of developing economies, we found that PRI, PUBI, IQ and other variables of interest have an insignificant effect on FDI inflows because variables can behave differently in the short run if we compare with the long run due to short span in the short run. However, the signs of coefficients of the variable of interaction effects (PRIˣ PUBIˣ IQ) significant and positively contribute to foreign capital inflows in the short run in our extended models. Other variables such as INFLATION have an insignificant influence on foreign capital inflows in the long and short run.
We have applied Dumitrescu and Hurlin (2012) Granger non-causality test as a robustness check. Table 8 reports that there is bidirectional causality exist between DCF and IFDI (DCF$IFDI). Additionally, we notice that there is also bidirectional causality exist between private capital formation and IFDI (PRI$IFDI). Furthermore, there also bidirectional relationship exist between IFDI and public capital formation (PUBI$IFDI). In sum, our granger causality result estimations strongly support the long run impact of aggregate domestic capital formation of FDI inflows and validate our result estimations of CS-ARDL methods by providing the robust checks.

Conclusion and recommendations
Our empirical study investigates the short-run and long-run impact of DCF and IQ on FDI inflows in developing countries. Given the common correlation of our variables across the sampled developing economies, we applied CS-ARDL methods to control endogeneity and remove cross-sectional dependency issues in the variables of our empirical study. Our results show that public capital crowds in while private capital crowds out FDI inflows. Our empirical findings infer that the nature of private and public capital functions differently to macro-economic variables; thus, aggregating them together might incur bias. Furthermore, our result estimations show that institutional quality spurs FDI inflows in the long-run economies of developing countries. The interaction of Domestic capital formation and institutional quality (DCF Ã IQ) insignificantly affect FDI inflows. However, the sign of the coefficient of the interaction term (PRI Ã PUBI Ã IQ) of PRI, PUBI and IQ turned to be significant and positive when we split DCF into public and private capital in our extended models. Public capital formation attracts FDI inflows in developing countries, and private capital formation obstructs FDI inflows. The positive linkage between public investment and FDI inflows implies that PUBI might complement attracting FDI inflows.
Our empirical investigation also manifests that institutional quality plays a crucial role in elevating FDI inflows in the long run. Quality institutions promote private and public capital, and consequently, thus; an increase of private and public capital formation stimulate FDI inflows in the long run for developing countries. Out of many components of institutional quality, existing empirical literature suggest that rule of law and control of corruption are prime factors in promoting FDI inflows. As per empirical results, we notice that institutional quality significantly contribute to attract FDI inflows in all models of our study and we infer from empirical findings that a high level of corrupt business practices and the fragile rule of law are counterproductive with MNCs investment decisions. Positive parameters of public investment and institutional quality reinforce their importance in fostering FDI inflows.
Our findings may not be generalized in the context of developed and emerging countries. Therefore, our study creates a new avenue to conduct a comprehensive study considering different income stratifications.

Notes Funding
No specific project funding available for this project.

Ethics statement
N/A