The Linear and Nonlinear Relationship between Infrastructure and FDI in India

Abstract

The study examines the linear and nonlinear relationship between Infrastructure and FDI, to understand whether there is a significant difference or not concerning the FDI equity inflows to infrastructure projects. The ARDL and Granger causality methods to cointegration; propose the existence of long-run function in two-directional causalities between foreign direct investment and infrastructure, whereas the nonlinear autoregressive distributed lag (ARDL) validates the asymmetries in the relationship between FDI and Infrastructure. The outcomes of the study are that foreign direct investment inflows are significant to improve the infrastructure projects in various sectors, in the short-run and long run. As enlightening infrastructure is dynamic to attract FDI, outcomes will be predominantly valuable to policymakers and related to the emerging markets.

1. Introduction

The secondary information has extensively recognized the key role of infrastructure growth in fascinating FDI inflow. A sound developed infrastructure strategy boosts markets integration and entices FDI inflow in any nation [1], whereas the deficiency of comprehensive infrastructure interrupts markets relationship and herewith slowdown the foreign direct investment (FDI) inflow in particularly developing countries [2]. The obtainability of advanced infrastructure principally decreases the cost of trade, boosts the ease of doing business and invites the foreign direct investment (FDI) inflow. Infrastructure tool is used in this paper as an engine for economic growth and facilitate a comparative advantage to a developing nation in terms of foreign direct investment inflow [3]. Additionally, the secondary data has shown evidence that the nation with good infrastructure engrossed more foreign direct investment inflow [4], whereas the nation’s deficient with infrastructure development are stereotypically unsuccessful to attract the FDI inflow [5] and those nation economies also shown that the poor condition [6]. Moreover, it also determined that the impact of the infrastructure development on FDI is positive and significant in a growing economy, preceding research [7] assessed that a deficiency of Infrastructure castigates FDI inflow. The significance of the infrastructure plays a vital role in the promotion of foreign direct investment inflow. The research data extensively explore the query of how the nonexistence of infrastructure can affect foreign direct investment inflow along with the different results of foreign direct investment in the host nation. Though the literature review has given little concentration to examine the role of FDI in improving the obtainability and quality of infrastructure in developing nations’ economies. According to Pradhan et al. [8] illustrated that the foreign organizations carried progressive technology and skills to the host nation herewith encouraged new technological dissemination in the nation along with investment. FDI inflow also facilitates home organizations with an unintended opportunity to learn from the foreign firms by studying and permeating an intelligence of plenteous needed competition [9]: which develops a cumulative output of the ant nation economy. Foreign direct investment plays a significant role in economic growth [10], the positive impact of FDI inflow is not only inadequate to the transfer of better technology, in circumstance, it also needs any nation to develop the quality infrastructure [11]. As a developing nation economy like Indian have enough resources but do not advance technology to effective utilization of the resources, to improve the infrastructure facilities in India, advanced technology is required, it is required the support of overseas capital to improve their infrastructure facilities. Foreign companies cooperate in R&D in enhancing innovative technology and development of any nation, specifically in infrastructure development to bond up with various markets in the different nations. The literature review broadly examined the various determinants factors of FDI like population, political stability and institutional quality etc. [12]. As this critical point lacks in review, this paper aims to examine the causal two functional relationships between total FDI and total infrastructure and enhance the literature review on this vital singularity. Furthermore, the literature discloses that prevailing research articles on the subject matter hurt from numerous data limitations [13]. The original paper on infrastructure focuses on variables representative of infrastructure for a large nation sample during 1990–2018 but it does not formulate an index of cumulative infrastructure. Likewise, extensively the review on infrastructure projects in different sectors depend on a very inadequate description of infrastructure while examining its stimulus on different economic indicators are investment, trade, and growth. Gnangnon (2018) assessed the impact of the telecommunication infrastructure on economic growth in a developing nation like India. Chakraborty and Nunnenkamp [14] uses ITC (international telephone circuits), the inclusive road infrastructure length and the number of airways as a proxy for the infrastructure development to examine the relationship between public infrastructure and foreign capital. Hall et al. [15] investigated broader insight and apprehension of the various infrastructure components to assess the association between transportation cost and infrastructure growth.

As for the given information limitations, this research paper employs a recently established inclusive using global infrastructure index 2020 which comprehends numerous infrastructure extents for India to overcome statistics limitations in secondary information. Predominantly the global infrastructure index 2020 is grounded on an annual wide-ranging of minimum 15 indicators datasheet of the obtainability and quality of infrastructure during 1995–2018 formulated by Khan et al. [16, 17]. In this research paper, the following infrastructure parameters (like power sector, construction, transportation, telecommunication, health, finance and energy) are used. UCM (Unobserved Components Model) is employed expedient infrastructure from the sub-parameters of infrastructure development. Additionally, the paper highlights some important points According to the Reserve Bank of India, infrastructure covers the following sectors also Power, Telecommunications, Railways, Roads including bridges, Seaport and airport, Industrial parks, Urban infrastructure, Mining, exploration and refining, and Cold storage and cold room facility, including for farm level pre-cooling for the preservation or storage of agricultural and allied produce, marine products and meat.

2. Infrastructure and FDI inflow in India

India, among the worldwide five major countries in the emerging economy, has significant potential to improve rapidly and thus made up to be an appropriate endpoint for FDI inflow. Despite all difficulties, India has attracted reasonable FDI inflow comparatively with other developing economic developed issues. In the 20th century’s, policy reforms, Indian performed better and received comparatively greater FDI inflow [18]. The FDI inflow for the financial year 2009–2010 was 37,745 US million dollars, and over the ensuing period of 10 years, the FDI inflows have recovered stable growth in each year. For the year 2019–2020, the inflow was $27.1 billion higher than the annual inflows in previous years from 2010 to date. The FDI inflows reduced during the year 2011–2012 and 2013–2014 where they fell by 8 per cent and 26 per cent respectively due to some reason like slowdown of economic development issues in India. Table 1 has explained the input of specific sector FDI out of total FDI inflow in the Indian sector. The table illustrates the evocative variations in the infrastructure sectoral composite of FDI inflow in India from the last 20 years. An inclusive investigation of sector-wise FDI discloses that external investors favored in Manufacturing sectors throughout 2000–2020. The manufacturing sector has accounted for more than US$ 89.40 billion from April 2000 to March 2020. During 2020 the Government of India increased FDI in manufacturing under the automatic route from 49–74%.

Similarly, the FDI inflow has significantly contributed to the above-mentioned three sectors and has shown the reforms of sectoral-FDI also account for significant variation for the time-to-time period. The distribution of the service sector out of total FDI inflow has increasingly and expansively improved in the same period. FDI equity inflow amount for services sector India FY 2015–2020. In the financial year 2020, the foreign direct investment equity inflow in the services sector in India was worth approximately 7.86 billion U.S. dollars. The foreign investment inflows have been consistently increasing over the last five years in this sector. To assess the post- and pre-reform of sector-wise FDI performance in the economy of India, this paper calculated the FDI performance index sector level that indicates the share of FDI sector-wise, comparative to its influence to aggregates of the India GDP. A value higher than 1 presents that the specific sector has recognized additional FDI inflow than its comparative economic size while a value less than 1 suggests that the specific sector received less FDI- inflow than its relative contribution; the below method was also used by Shah et al. [19].

2.1 Rural infrastructure

Rural infrastructure in the country is crucial for agriculture, agro-industries and poverty alleviation in the rural areas. Rural infrastructure provides essential production conditions which are required for social and economic growth and for promoting the quality of life in rural areas. As per the government statistics clean tap water is available to only 24% rural households. About 56% of rural households had electricity connections. Centre and state government have over all estimated a total capital expenditure of Rs. 7,73,915 crore between fiscals 2020 and 2025 on rural infrastructure development in India.

According to the Department for Promotion of Industry and Internal Trade (DPIIT), the Indian food processing industry in rural has cumulatively attracted Foreign Direct Investment (FDI) equity inflow of about US$ 10.24 billion between April 2000 and December 2020.

In the year 2021 infrastructure activities accounted for 13% share of the total FDI inflows of US$ 81.72 billion. The government invested US$ 1.4 trillion in infrastructure development as of July 2021.

Department of Drinking Water and Sanitation will be implementing the Jal Jeevan Mission to provide functional household tap connection to every rural household i.e., “Har Ghar Nal se Jal” by 2024. The program will be implemented at an estimated total capex of Rs. 3,60,000 crore shared between states and center as follows: Rs. 2,48,626 crore would be invested in rural housing under PMAY Gramin and about Rs 162,329 crore would be invested to improve rural roads under PMGSY. Improving the rural road connectivity by providing all-weather roads to connect eligible habitations in rural areas. As on December 31, 2019, road length worth Rs. 2.9 lakh crore had been sanctioned and expenditure of Rs. 2.17 lakh crore incurred. World Bank sanctioned about INR 2462 billion (US$ 37 billion) through its Country Assistance Strategy committed to a series of loans/credits to support “Pradhan Mantri Gram Sadak Yojana (PMGSY) to complete 165,411 Road projects in rural areas. The total projected rural infrastructure investment from 2020 to 2025 is given in the Table below.

From the table given above it can be understood that, the rural infrastructure investment is 7% in the total infrastructure investment in India. The projected cumulative investment from 2020 to 2025 is 773,915 million rupees.

Sector-wise break-up of capital expenditure of Rs. 111 lakh crore during fiscals 2020–2025.

from the above diagram it can be understood that, energy sector 24%, roads sector 18%, railways 12%, ports 1%, Airports 1%, urban infrastructure 17%, digital infrastructure 3%, irrigation 8%, rural infrastructure 7%, agriculture & food processing 2%, social infrastructure 4% and industrial infrastructure 3%. Hence, it is concluded that, the total share of the rural infrastructure in total FDI is 7%.

$$\text{Present}\mathrm{FDI}\text{inflow}=\frac{{\mathrm{FDI}}_{\mathrm{t}}/{\mathrm{FDI}}_{\mathrm{i}}}{{\mathrm{GDP}}_{\mathrm{t}}/{\mathrm{GDP}}_{\mathrm{i}}}$$

From the above equation used for the determination of present FDI inflow, whereas, FDI_i inflow in the infrastructure sector I; FDI_t is cumulative FDI inflow, GDP_i&t indicates GDP of the infrastructure sector I and overall value of GDP is t.

Table 2 has shown the variance between the infrastructure project performance during pre-and post-reforms periods of sector-wise FDI growth and better performance indices. The performance indexes illustrate that during the pre-and post-reforms era, the major and important sectors are gas, oil, power sector, transportation, construction and mining sectors, which attracted FDI inflow and contributed to GDP growth. In the present situation, the Indian industries have overcome the shortage of electricity and the deficiency of proper infrastructure facilities. Both private and public manufacturing sectors are facing low-level problems against the lack of infrastructure issue, it looks like the latter is winning. Based on the literature review, the paper has tested the following two hypotheses.

Years	Service sector	Manufacturing sector	Primary sector
2000–2005	0.086	0.983	27.341
2005–2010	0.193	0.671	18.037
2010–2015	1.386	1.472	24.726
2015–2020	1.047	1.057	9.163

Table 1.

Index of sector-level FDI performance.

Source: Calculations of authors’.

Department	FY20	FY21	FY22	FY23	FY24	FY25	No phasing	FY20-FY25
Rural infrastructure	103,555	116,306	109,930	27,055	27,055	27,055	0	410,955
Water and sanitation	36,758	60,497	100,881	84,822	80,002	0	0	362,960
Total rural infrastructure	140,313	176,803	210,811	111,877	107,057	27,055	0	773,915
Total infrastructure	1,442,131	2,153,779	2,132,274	1,647,122	1,540,813	1,315,091	899,218	11,130,428

Table 2.

Table shows the projected investment in rural infrastructure in India from 2020 to 2025. (rupees in crores).

Null Hypothesis (H0): There is no significant difference in FDI equity inflows to Infrastructure projects.

Alternative Hypothesis (H1): There is a significant difference in FDI equity inflows to Infrastructure projects.

3. Data and methodology

3.1 Explanation of variables and data gathering

To assess the relationship between infrastructure and FDI inflow from 2000 to 2020, the paper depends on the global infrastructure index 2020 (GII-2020) a compound index and also sub-sector of infrastructures such as transportation (TI), telecommunication (CI), power sector (PI) and energy sector (EI) and financial sector (FI) recognized on data collected from various sources (RBI, world bank and Global infrastructure index and CMIE reports).

The global infrastructure index 2020 (GII-2020) encompasses different quality and quantity magnitudes of infrastructure for India. The GII-2020 is created every year on a comprehensive range of infrastructure development parameter datasets of the accessibility and quality of infrastructure throughout 2000–2020. Besides, the paper used the institutional quality component, trade openness and human capital factors as control variables.

3.2 Research methodology

The present research investigates the two functional short and long-run causal dynamic relationships between infrastructure and FDI inflow, employing granger causality, ARDL (autoregressive distributed lag), and NARDL (Nonlinear autoregressive distributed lag) estimators to cointegration. This method is recognized in the case when the carefully chosen indicator is integrated either at the 1(0) level or the first difference I (1).

Moreover, from the simple linear transformation, the error ECM (−1) correction model easily may originate [16, 17]. To calculate the relationship between FDI and infrastructure the autoregressive distributed lag model assesses the following unlimited error correction model:

$$\begin{array}{l}\mathrm{\Delta }{\mathrm{FDI}}_{\mathrm{t}}={\mathrm{\alpha }}_0\mathrm{fdi}+\sum _{\mathrm{i}=\mathrm{t}}^{\mathrm{p}}{\partial }_{\text{fdii}}\mathrm{FDI}\_{inf}_{\mathrm{t}-\mathrm{i}}+\sum _{\mathrm{i}=1}^{\mathrm{p}}{\in }_{\text{fdii}}\mathrm{\Delta HC}\_{inf}_{\mathrm{t}-1}+\sum _{\mathrm{i}=1}^{\mathrm{p}}{\mathrm{\beta }}_{\text{fdii}}\mathrm{\Delta }\text{TO}\_{inf}_{\mathrm{i}=\mathrm{t}}\\ +\sum _{\mathrm{i}=1}^{\mathrm{p}}{\mathrm{\gamma }}_{\text{fdii}}\mathrm{\Delta IQ}\_{inf}_{\mathrm{t}=\mathrm{i}}+\sum _{\mathrm{i}=1}^{\mathrm{p}}{\mathbf{\varnothing }}_{\text{fdii}}\mathrm{\Delta GI}\_{inf}_{\mathrm{I}=1}+{\mathrm{\mu }}_{1\text{fdii}}\mathrm{FDI}\_{inf}_{\mathrm{t}=\mathrm{i}}+{\mathrm{\mu }}_{2\text{fdii}}\mathrm{\Delta HC}\_{inf}_{\mathrm{t}-1}\\ +{\mathrm{\mu }}_{3\text{fdii}}\mathrm{\Delta }\text{TO}\_{inf}_{\mathrm{i}=\mathrm{t}}+{\mathrm{\mu }}_{4\text{fdii}}\mathrm{\Delta IQ}\_{inf}_{\mathrm{t}=\mathrm{i}}+{\mathrm{\mu }}_{5\text{fdii}}\mathrm{\Delta GI}\_{inf}_{\mathrm{I}=1}+{\mathrm{D}}_{\mathrm{t}}+{\forall }_{11}\end{array}$$E1

$$\begin{array}{l}\mathrm{\Delta }\mathit{HC}{\_inf}_{\mathrm{t}}={\mathrm{\alpha }}_0\mathrm{fdi}+\sum _{\mathrm{i}=1}^{\mathrm{p}}{\in }_{\text{fdii}}\mathrm{\Delta HC}\_{inf}_{\mathrm{t}-1}+\sum _{\mathrm{i}=\mathrm{t}}^{\mathrm{p}}{\partial }_{\text{fdii}}\mathrm{FDI}\_{inf}_{\mathrm{t}-\mathrm{i}}+\sum _{\mathrm{i}=1}^{\mathrm{p}}{\mathrm{\beta }}_{\text{fdii}}\mathrm{\Delta }\text{TO}\_{inf}_{\mathrm{i}=\mathrm{t}}\\ +\sum _{\mathrm{i}=1}^{\mathrm{p}}{\mathrm{\gamma }}_{\text{fdii}}\mathrm{\Delta IQ}\_{inf}_{\mathrm{t}=\mathrm{i}}+\sum _{\mathrm{i}=1}^{\mathrm{p}}{\mathbf{\varnothing }}_{\text{fdii}}\mathrm{\Delta GI}\_{inf}_{\mathrm{I}=1}+{\mathrm{\mu }}_{1\text{fdii}}\mathrm{FDI}\_{inf}_{\mathrm{t}=\mathrm{i}}+{\mathrm{\mu }}_{2\text{fdii}}\mathrm{\Delta HC}\_{inf}_{\mathrm{t}-1}\\ +{\mathrm{\mu }}_{3\text{fdii}}\mathrm{\Delta }\text{TO}\_{inf}_{\mathrm{i}=\mathrm{t}}+{\mathrm{\mu }}_{4\text{fdii}}\mathrm{\Delta IQ}\_{inf}_{\mathrm{t}=\mathrm{i}}+{\mathrm{\mu }}_{5\text{fdii}}\mathrm{\Delta GI}\_{inf}_{\mathrm{I}=1}+{\mathrm{D}}_{\mathrm{t}}+{\forall }_{1\mathrm{t}}\end{array}$$E2

The measuring the long-run relationship between FDI and infrastructure this paper employs the bound testing techniques. The process of bound testing technique analysis of the hypothesis of no cointegration between the chosen indicator and the existence of cointegration between the indicators of study interest. The lower and upper bound critical values are significant role-plays as a determinant for the cointegration test [20]. If the calculated F-statistic value is higher than the upper bound critical value, then the H0 (Null hypothesis) is rejected. If the F-statistic value is lower than the lower bound critical value,

The Granger causality model using the I(I) of variables all over a VAR may cause uncertainty in the results in the existence of cointegration among selected variables. Hence, an advanced form of traditional Granger causality model relating the error correction method (ECM) is articulated in VECM as follow:

$$\begin{array}{l}\mathrm{\Delta }{\mathrm{FDI}}_{\mathrm{t}}={\mathrm{\alpha }}_0\mathrm{fdi}+\sum _{\mathrm{i}=\mathrm{t}}^{\mathrm{p}}{\partial }_{\text{fdii}}\mathrm{FDI}\_{inf}_{\mathrm{t}-\mathrm{i}}+\sum _{\mathrm{i}=1}^{\mathrm{p}}{\in }_{\text{fdii}}\mathrm{\Delta HC}\_{inf}_{\mathrm{t}-1}+\sum _{\mathrm{i}=1}^{\mathrm{p}}{\mathrm{\beta }}_{\text{fdii}}\mathrm{\Delta }\text{TO}\_{inf}_{\mathrm{i}=\mathrm{t}}\\ +\sum _{\mathrm{i}=1}^{\mathrm{p}}{\mathrm{\gamma }}_{\text{fdii}}\mathrm{\Delta IQ}\_{inf}_{\mathrm{t}=\mathrm{i}}+\sum _{\mathrm{i}=1}^{\mathrm{p}}{\mathbf{\varnothing }}_{\text{fdii}}\mathrm{\Delta GI}\_{inf}_{\mathrm{I}=1}++\mathrm{\Omega }{\mathrm{ECM}}_{\mathrm{t}-1}+{\mathrm{D}}_{\mathrm{t}}+{\mathrm{\mu }}_{3\mathrm{t}}\end{array}$$E3

$$\begin{array}{l}\mathrm{\Delta }\mathit{HC}{\_inf}_{\mathrm{t}}={\mathrm{\alpha }}_0\mathrm{fdi}+\sum _{\mathrm{i}=1}^{\mathrm{p}}{\in }_{\text{fdii}}\mathrm{\Delta HC}\_{inf}_{\mathrm{t}-1}+\sum _{\mathrm{i}=\mathrm{t}}^{\mathrm{p}}{\partial }_{\text{fdii}}\mathrm{FDI}\_{inf}_{\mathrm{t}-\mathrm{i}}+\sum _{\mathrm{i}=1}^{\mathrm{p}}{\mathrm{\beta }}_{\text{fdii}}\mathrm{\Delta }\text{TO}\_{inf}_{\mathrm{i}=\mathrm{t}}\\ +\sum _{\mathrm{i}=1}^{\mathrm{p}}{\mathrm{\gamma }}_{\text{fdii}}\mathrm{\Delta IQ}\_{inf}_{\mathrm{t}=\mathrm{i}}+\sum _{\mathrm{i}=1}^{\mathrm{p}}{\mathbf{\varnothing }}_{\text{fdii}}\mathrm{\Delta GI}\_{inf}_{\mathrm{I}=1}++\mathrm{\Omega }{\mathrm{ECM}}_{\mathrm{t}-1}+{\mathrm{D}}_{\mathrm{t}}+{\mathrm{\mu }}_{3\mathrm{t}}\end{array}$$E4

3.3 The non-linear auto-regressive distributive lag model (NARDLM)

According to Pesaran et al. [20] the cointegration test makes available proof of a linear relationship among the chosen variables. The current research paper also uses the NARDL [19] model to examine the existence of an association between FDI inflow and infrastructure in India. The non-linear auto-regressive distributive lag model [21] is a nonlinear extended form of the autoregressive distributive lag model for consistent impeding both short and long-run irregularity in the autoregressive distributive lag model.

The non-linear auto-regressive distributive lag model is calculated in the current paper that determines the short run and long run of the positive and negative partial sums. Thus, the non-linear auto-regressive distributive lag model contemplates the form of the resulting equation:

$$\begin{array}{l}\mathrm{\Delta }{\mathrm{FDI}}_{\mathrm{t}}={\mathrm{\alpha }}_0\mathrm{fdi}+\sum _{\mathrm{i}=\mathrm{t}}^{\mathrm{p}}{\partial }_{\text{fdii}}\mathrm{GII}\_{inf}_{\mathrm{t}-\mathrm{i}}+\sum _{\mathrm{i}=1}^{\mathrm{p}}{\in }_{\text{fdii}}\mathrm{\Delta HC}\_{inf}_{\mathrm{t}-1}+\sum _{\mathrm{i}=1}^{\mathrm{p}}{\mathrm{\beta }}_{\text{fdii}}\mathrm{\Delta }\text{TO}\_{inf}_{\mathrm{i}=\mathrm{t}}\\ +\sum _{\mathrm{i}=1}^{\mathrm{p}}{\mathrm{\gamma }}_{\text{fdii}}\mathrm{\Delta IQ}\_{inf}_{\mathrm{t}=\mathrm{i}}+\sum _{\mathrm{i}=1}^{\mathrm{p}}{\mathbf{\varnothing }}_{\text{fdii}}\mathrm{\Delta GI}\_{inf}_{\mathrm{I}=1}+{\mathrm{\mu }}_{1\text{fdii}}\mathrm{FDI}\_{inf}_{\mathrm{t}=\mathrm{i}}\\ +{\mathrm{\mu }}_{2\text{fdii}}\mathrm{\Delta GII}\_{inf}_{\mathrm{t}-1}+{\mathrm{\mu }}_{3\text{fdii}}\mathrm{\Delta }\text{TO}\_{inf}_{\mathrm{i}=\mathrm{t}}+{\mathrm{\mu }}_{5\text{fdii}}\mathrm{\Delta }{\mathrm{HC}}_{\mathrm{I}=1}+{\mathrm{D}}_{\mathrm{t}}+{\forall }_{1\mathrm{t}}\end{array}$$E5

$$\begin{array}{l}\mathrm{\Delta }{\mathit{GII}}_{\mathrm{t}}={\mathrm{\alpha }}_0\mathrm{fdi}+{\sum }_{\mathrm{i}=\mathrm{t}}^{\mathrm{p}}{\partial }_{\text{fdii}}\mathrm{GII}\_{inf}_{\mathrm{t}-\mathrm{i}}+\sum _{\mathrm{i}=1}^{\mathrm{p}}{\in }_{\text{fdii}}\mathrm{\Delta }{\mathrm{FDI}}_{\mathrm{t}-1}+\sum _{\mathrm{i}=1}^{\mathrm{p}}{\mathrm{\beta }}_{\text{fdii}}\mathrm{\Delta }{\mathrm{FDI}}_{\mathrm{i}=\mathrm{t}}\\ +\sum _{\mathrm{i}=1}^{\mathrm{p}}{\mathrm{\gamma }}_{\text{fdii}}\mathrm{\Delta IQ}\_{inf}_{\mathrm{t}=\mathrm{i}}+\sum _{\mathrm{i}=1}^{\mathrm{p}}{\mathbf{\varnothing }}_{\text{fdii}}\mathrm{\Delta }{\mathrm{HC}}_{\mathrm{I}=1}+\sum _{\mathrm{i}=1}^{\mathrm{p}}{\mathrm{\beta }}_{\text{fdii}}\mathrm{\Delta }\text{TO}\_{inf}_{\mathrm{i}=\mathrm{t}}\\ +{\mathrm{\mu }}_{2\text{fdii}}\mathrm{\Delta GII}\_{inf}_{\mathrm{t}-1}+{\mathrm{\mu }}_{3\text{fdii}}\mathrm{\Delta }\text{TO}\_{inf}_{\mathrm{i}=\mathrm{t}}+{\mathrm{\mu }}_{5\text{fdii}}\mathrm{\Delta }{\mathrm{HC}}_{\mathrm{I}=1}+{\mathrm{D}}_{\mathrm{t}}+{\forall }_{1\mathrm{t}}\end{array}$$E6

4. Empirical outcomes and argument

4.1 Descriptive statistics and unit-root testing

Table 3 explains descriptive statistics value, this table helps to highlight the how data descriptive statistics like. Descriptive statistics values comprise of several observations with determined values, mean, minimum, maximum, central value and standard deviation point with corresponding variables to transportation infrastructure (T_inf), telecommunication infrastructure (Te_inf), energy sector infrastructure (E_inf), Financial sector infrastructure (F_inf), global infrastructure index 2020 (G_inf-2020), quality in institutional approach (IQ_inf), the primary sector of FDI inflow (PFDII), FDI inflow service sector (FDIIS), export and import to GDP or trade openness in infrastructure (T_inf) and human capital (H-inf).

Years	α	β	∅	μ	∂	γ
2000–2005	17.845	19.462	7.374	7.562	6.461	2.479
2005–2010	9.351	24.522	23.538	22.218	9.704	7.483
2010–2015	27.361	21.580	17.650	31.492	16.739	14.695
2015–2020	39.720	31.301	6.361	38.572	29.537	27.968

Table 3.

Shares’ of different economic groups in % of cumulative FDI inflow in India.

Source: calculations of authors. The data has been collected from RBI.

Ouattara (2004) illustrated that the level of stationary among all the chosen variables of the study was of interest to observe the probable variables of FDI inflow in infrastructure sectors wise during the long run and short run. Due to the circumstance that if the factors of the study interest are stationary at I (2) the estimated F-test value will not be significant. In the current paper, use the two types of tests are structural break analysis which is (1) and (1) contemplate the structural break in the given timer series data to examine the order of integration among the selected variables.

Table 4 explore that each variable is integrated either at I(1) OR I(0) order and none of the indicators is stationary at I(2) order, According to (1) in this condition, the auto-regressive distributive lag model is suitable moderately another cointegration process. To assess the existence of a long-run relationship among chosen variables, this paper used auto-regressive distributive lag model and error correction model techniques to cointegrate by using equations no 1&2. The study calculates the regressions techniques that FDI is substituted by sectoral FDI inflow (like by FDI in the primary sector, FDI in the service sector, and FDI in manufacturing and trading) to evaluate the probable long-run association regarding FDI inflow and cumulative infrastructure. As this paper investigates the two functional causalities between infrastructure and FDI inflow sector (like by FDI in the primary sector, FDI in the service sector, and FDI in manufacturing and trading), so for this determination of inverse impact, the study also take infrastructure as a dependent variable and then substitute the infrastructure into sub-indices of infrastructure (such as (T_inf), (Te_inf), (E_inf), (F_inf), (G_inf-2020), (IQ_inf), (PFDII), (FDIIS), (T_inf) (H-inf)). The optimum lag length is grounded on AIC for measuring the present models of interest.

Variable	N	Mean	Std.dev	Min	Max
T_inf	37	−.765	.026	−.967	−.644
Te_inf	37	−.564	.531	−.931	−.854
E_inf	37	−.786	.201	−.2.872	−.117
F_inf	37	.043	.746	−.797	.708
G_inf-2020	37	−0.069	2.836	−1.417	−.835
IQ_inf	37	213.962	21.690	−2.630	2.648
PFDII	37	231.067	214.495	141.759	241.640
FDIIS	37	146.947	732.571	−.138.503	271.492
FDI	37	214.057	261.837	127.395	382.708
TO-inf	37	0.056	0.073	.352	.893
HC-inf	37	31.672	2.873	41.153	32.163

Table 4.

Descriptive statistics value.

Source: calculations of authors.

5. Linear cointegration outcomes (autoregressive distributed lag-ARDL)

From Table 5, the significant level calculated with help of the F-statistics values, the Ho (Null hypothesis) rejected the there is no cointegration and Table 5 suggested that there is a possible relationship between the FDI inflow, Infrastructure and all other control variables (such as Trade openness (export and import), Infrastructure intuitional quality and Human capital in infrastructure projects) exist in long-run. From equation no 1, the calculated F-statistics values are the upper bound critical value at 5% and 1% significant level with control variables. The outcomes are in the same order with preceding research studies [22, 23]. Furthermore, it was also examined in Table 4, the probable association exit in the long run between FDI, Infrastructure and control variables. From equation no 2, the calculated F-statistics value is higher than the upper bound critical factor value at 5% and 1% significant level without considering the control variables of human capital and quality in infrastructure institutional body). The experiential outcomes of the certain test for equation no 1&2, the H1 (alternative hypothesis) accepted, the existence of cointegration between the chosen variables and Ho (Null hypothesis) rejected, due to no cointegration between the selected variables, according to Asiedu [24]. The study also checked the robustness for the determination of the long-run relationship between FDI and infrastructure projects. The study also used the depended-on variables with and without control variables, indicates in Table 6 which gives constant outputs in both the cases (with control variables and without control variables).

Augmented dickey fuller test (ADF)				DF-GLS Test	Zivot-Andrews
Variables	I (0)	I (1)	I (0)	I (1)	I (1)	Break	I (0)	Break
T_inf	−1.847	−3.849***	−2.401	−4.842**	−1.372	2003	−2.390**	2010
Te_inf	−2.673***	−4.283***	−3.207***	−2.194***	−3.408	2005	−3.490***	2008
E_inf	−3.670***	−6.381***	−1.869	−5.784***	−4.784***	2010	−1.539***	2012
F_inf	−1.934	−5.298**	−2.301***	−4.483***	−4.389	2013	−4.382***	2007
G_inf-2020	−2.873	−2.602***	−1.403	−6.492***	−1.950**	2016	−2.367***	2014
IQ_inf	−3.438***	−4.391***	−2.672*	−3.502***	−3.041	2014	−5.361***	2015
PFDII	−5.785***	−2.428***	−1.069	−5.302***	−3.361***	2017	−6.351***	2017
FDIIS	2.480	−4.406***	−2.301	−3.401***	−2.701	2018	−4.287***	2006
FDI	3.561***	−3.371***	−1.285**	−4.295***	−1.361	2020	−6.351**	2008
T0-inf	1.015	−5.103**	−3.40***	−2.491***	−2.730	2012	−3.537***	2008
HC-inf	2.638**	−2.502**	−1.289	−3.089***	−1.308	2008	−1.628**	2009

Table 5.

Unit root test outcomes.

***,**, and * indicates significance level at per cent of “10%”, “5%” and “1%” correspondingly. The “critical values” of intercept are −2.701, −2.730, −1.950 significant level at 1%, 5% and 10% correspondingly, where the “critical values” for Zivot-Andrews are −3.490, −6.351, −6.351 significant level at 1%, 5% and 10% ‘correspondingly.

Cumulative Global Infrastructure Index 2020 to cumulative and disaggregate FDI inflow
Variables	FDI_I		FDI_P		FDI_S		FDI_M
	F-Sta	ECM	F-Sta	ECM	F-Sta	ECM	F-Sta	ECM
FDI/GII	2.65*	−3.10	3.51	−3.01***	6.84***	−1.84	6.56**	−3.98
FDI/GII/IQI	2.04*	−4.31**	3.47	−4.31	6.56***	−3.05	4.62	−379
FDI/GII/IQI/TO	4.35	−5.71**	4.23***	−4.28	3.43	−5.40**	3.69	−4.37
FDI/GII/IQI/TO/HC	7.69***	−2.82***	7.06	−5.14***	8.35***	−6.57***	6.24**	−6.45***
FDI/GII/IQI/TO/HC/	3.71***	−4.52***	10.75***	−9.56***	5.40	−5.83**	7.62***	−747***

Aggregate and disaggregate FDI Inflow to Cumulative Global Infrastructure Index 2020
Variables	FDI_I		FDI_P		FDI_S		FDI_M
	F-Sta	ECM	F-Sta	ECM	F-Sta	ECM	F-Sta	ECM
FDI/GII	7.13***	−3.76	6.74***	−4.17***	2.93	−2.14	2.98	−4.91
FDI/GII/IQI	6.36***	−3.42	3.68***	−4.38***	3.52	−2.21	3.53	−4.13
FDI/GII/IQI/TO	3.61	−2.28	4.35**	−3.57	3.21	−3.75**	3.89	−5.52**
FDI/GII/IQI/TO/HC	4.39	−7.01***	3.78*	−2.18	4.89**	−4.27**	4.27**	−5.63**
FDI/GII/IQI/TO/HC/	5.31**	−5.39**	4.05**	−5.37***	4.14	−3.19	3.52	−5.53**

Table 6.

Cointegration outcomes (ARDL constraints test and error correction model result).

***, **, and * Indicates significance level at “10%”, “5%” and “1%” correspondingly.

Table 6 illustrated that the association among the aggregates infrastructure, manufacturing sector and FDI inflow in the long run. Based on Table 6, the outcomes show the expected positive relationship among the chosen variables in the long run. The calculated F-statistics values are lower than higher bound critical factor value and significant at 5 per cent level with control variables are infrastructure institutional quality, human capital and export and import trade openness, while on the other side (i.e., opposite causality) the pragmatic outcomes of the bound test have advised robust relationship between total infrastructure and FDI inflow in the manufacturing sector (column 5–6). The predictable F-statistic value is higher than the upper bounds critical factor value at 5% and 1% correspondingly. Thus, the described outcomes disclose the existence of two functional associations between total infrastructure and manufacturing FDI. In this connection, the null hypothesis was rejected because there is no positive relationship between the selected variables. The current paper showed that two functional associations between total infrastructure FDI inflow in the primary sector in the long run in the column no 4 and 8. The empirical outcomes explored the positive association among the infrastructure, FDI in the primary sector in the long run and all the selected variables of the paper. The F-statistics is higher than the upper bound critical factor value at a 1 per cent significance level with consideration of with and without control variables.

Table 6 indicates the two-function association between FDI inflow in the service sector and infrastructure in columns 4 and 8. The outcomes show the existence of two functional relationships between FDI and infrastructure development in India. The F-statistics values are greater than higher bound critical factor values in the case of with and without control variables of column 4. On the other hand, the Aggregate infrastructure to FDI services the values of assessed F-statistics are lesser than the greater bound critical factor values in case of without control variables and experiential greater than higher bound critical factor values at 10% significance level.

6. Granger causality method

The granger causality test determines the long-run relationship between the condition for causality and the selected variables of the study according to Morley [22, 23]. The Confirmation of long-run existence between the variables indicators shows that there should be the minimum non-functional causality between the selected variables for this research [25]. Henceforth, VECM is employed to calculate the function of the long run and short-run causality relationship between total infrastructure and FDI inflow with the consistency of the service sector, manufacturing sector and the primary sector.

Table 7 illustrates the long and short-run granger causality relationship from FDI inflow in different sectors and total infrastructure in Indian, the results show that the coefficient of error correction in long run period and the CEC term is strongly significant when cumulative FDI inflow FDI in the manufacturing sector, FDI in the primary sector and FDI in the service sector are used as dependent variables. Whereas the F-statistics value does not indicate a significant impact on the selected variables during the short run, i.e., FDI inflow in selected sectors to total infrastructure. The empirical output of the Granger causality method estimator promoted the long-run causality exists from the study variables (FDI_I, FDI_T, FDI_M, FDI_S) to total infrastructure which advises the infrastructure play a significant role to attract FDI inflow in service sectors, primary sectors, and manufacturing sectors of India (1). However, there is no causality existing in the short-run (from FDI_I, FDI_T, FDI_M, FDI_S to total infrastructure) which discloses that the total infrastructure does not affect the ability to attract FDI inflow in sectors wise in the short run. The results in Table 7 also indicates the short and long-run causality from total infrastructure to total FDI inflow. The output indicates that the long and short-run causality in current and significant level at 5 per cent. It means that in Indian total FDI inflow affects the availability of infrastructure and quality level.

	F-Statistics (Short-run)				ECMt-1 (Long run)				A/R
FDI inflow to total Infrastructure
∆FDI_I	∆GII	∆IQ	∆TOE&I	∆HC	∆GII	∆IQ	∆TOE&I	∆HC	H1:A
	1.62	0.23	6.694	0.64***	−0.31***	−0.63***	−0.34***	−0.52***
FDI inflow in Primary sector to total Infrastructure
∆FDI_P	∆GII	∆IQ	∆TOE&I	∆HC	∆GII	∆IQ	∆TOE&I	∆HC	H1:A
	0.56	0.023	3.75	7.05***	−0.65***	−0.23***	−0.76***	−0.78***
FDI inflow in the Manufacturing sector to total Infrastructure
∆FDI_M	∆GII	∆IQ	∆TOE&I	∆HC***	∆GII	∆IQ	∆TOE&I	∆HC	H1:A
	2.01	3.04	3.05	1.72	−0.32**	−0.15**	−0.37**	−0.28***
FDI inflow in Services sector to total Infrastructure
∆FDI_S	∆GII	∆IQ	∆TOE&I	∆HC	∆GII	∆IQ	∆TOE&I	∆HC	H1:A
	2.49	0.67	2.25	0.72	−0.67***	−0.15***	−0.71***	−0.19***
Total infrastructure and FDI inflow (Opposite causality)
∆GII	∆FDI_I	∆IQ	∆TOE&I	∆HC	∆FDI_I	∆IQ	∆TOE&I	∆HC	H1:A
	4.78***	0.84	2.46	0.04**	−0.51***	−0.42**	−0.71***	−0.91***

Table 7.

Granger causality test output.

***, **, and * Indicates significance level at “10%”, “5%” and “1%” correspondingly.

Source: calculations of author.

Whereas the transportation infrastructure, telecommunication infrastructure, energy infrastructure, infrastructure in the power sector and financial infrastructure variables are used in this paper as dependent variables. This empirical output shows that total FDI inflow causes aggregates and sub-indices of infrastructure in the long run. The finding of the study reveals that inverse causality in FDI inflows indicates positive and significant effects on overall infrastructure sub-indices in the long-run period. Furthermore, the outcomes show that the sectors are FDI_P, FDI_S and FDI_M are used as descriptive variables. The output demonstrated that the error correction model is significant at the level of 5 per cent while FDI_P, FDI_S and FDI_M are used as independent variables. The outcomes also indicate that in the long run extension of FDI inflow, it can grow infrastructure quality and availability (1). Can grow infrastructure quality and availability (1).

Null hypothesis: The Diagnostic tests are not affected by the mention Econometric problem. Alternative: The Diagnostic tests are affected by the mention Econometric problem.

Table 8 illustrates the determined causal relationship between GII and FDIP in the long run, in the same order where FDI_S is used as a dependent variable. The fact that FDI_ S is used as a dependent variable. This indicates that the impact of total infrastructure is positive but insignificant in the long run without considering the control variables, while significant considering the control variable. The empirical outcomes indicate that the spill-over effect of FDI inflow is more than infrastructure in the long run in Indian. The model’s constancy is established by recursive estimation. They recommend that statistically valid inference can be drawn from the selected models. The rest of the diagnostic tests are indicated in Table 8.

Econometric problem	F-statistics	P-values	Test	Hypothesis A/R	Support equation
Heteroscedasticity	0.0471	0.0378	Breusch-Pagan-Godfrey	Accepted	Equation no 1
Specification	2.4914	0.0121	Ramsey RESET	Accepted
Serial Correlation	0.4891	0.3861	Breusch-Godfrey LM	Accepted
Normality	1.0382	0.0137	Jarque-Bera
Heteroscedasticity	1.0381	0.0027	Breusch-Pagan-Godfrey	Accepted	Equation no −2
Specification	3.2037	0.0271	Ramsey RESET	Accepted
Serial Correlation	0.4891	0.0461	Breusch-Godfrey LM	Accepted
Normality	0.8325	0.0294	Jarque-Bera	Accepted

Table 8.

Diagnostic tests.

7. Nonlinear cointegration test

There may be a nonlinear relationship exist of time series variables, thus, after the newest methodology proposed by Shin et al. [21], this paper tested the cointegration method by exempting the linear relationship restriction. The outcomes are described in Table 9, which authorizes the cointegration relationship (attained negative and significant statistics of Error correction model) among the FDI_I, FDI_S, FDI_P, FDI_M and G_I_INF. Though, the co-movement of FDI_I, FDI_S, and G_I_INF is maintained by a significant PSS test. The feature that differentiates the non-linear auto-regressive distributive lag mode [25] from the traditional autoregressive distributive lag mode is the asymmetries testing. Fascinatingly, the outcomes illustrate that in the case of equation no 1 there is an indication of SR asymmetries, and in equation no 3 there exist LR asymmetries.

Variables	FDI_I	FDI_P	FDI_S	FDI_M
SR dynamic
∆FDI_I	0.481**	0.361	0.732	0.301
∆GII_PS	0.701	1.332*	−5.952	2.639
∆GII_PSt-1	0.427	2.549	−7.603	12.812
∆GII_NG	−2.481*	0.367	3.225	−9.374
∆GII_NGt-1	−1.302**	−1.837	6.361	−11.371
∆H_C	9.326***	−7.418	−37.291	−26.385*
∆H_Ct-1	7.589***	−11.720**	−16.320*	−35.679**
∆I_Q	0.375	0.211*	−0.391**	0.581
∆I_Qt-1	0.017	−0.417	−2.438	0.793
∆T_O	−2.940	−3.491	−4.210	3.482
∆T_Ot-1	−0.013	−0.036	−7.364	−1.596
∆DM_GII	1.058*	2.972	−4.647	4.795
∆DM_GIIt-1	0.381	3.285	−2.431	3.061
LR dynamics
GII-PS	0.503	−0.602	2.442	−0.640
GII_NG	−0.186	−3.673	8.927	−6.582
H_C	12.036***	9.027	23.183***	36.284**
I_Q	2.748**	5.327***	−0.947	4.473
T_O	6.274**	−0.390**	5.963	9.739
DM_GII	−2.491	−0.283	13.327	−3.406
PSS F-Stat	8.384**	4.372***	0.113**	1.728***
ECMt-1	−3.374**	−1.361**	0.341***	−3.273**
Constant	−107.849	−52.286***	−103.325***	−178.957***
N	57	57	57	57
R^2	0.749	0.702	0.821	0.384
Adj. R^2	0.853	0.731	0.873	0.648
SR asymmetries	3.593	0.668	0.703**	0.478**
LR asymmetries	0.472***	0.004***	3.251	0.561

Table 9.

Nonlinear effect of global infrastructure index on aggregate and disaggregate FDI inflow in India.

Note: * DU_FDI is time dummy variable confirmed for operational break in FDI_I, FDI_S, FDI_P, and FDI_M. ***p < 0.01, ** p < 0.05, * p < 0.1.

Likewise, Table 10 explores the dependent variable is exchanged with an independent variable and the non-linear auto-regressive distributive lag model is assessed. The outcome of the paper is that cointegration exists when FDI inflow and FDI in the services sector are taken as descriptive variables, while unpredictably, the PSS F-Test does not sustain to Error correction term or model. Concerning the asymmetric relationship, only equation no 1 shows the existence of SR asymmetries, which is confirmation of the outcomes stated in Table 9. Thus, the paper infers that in the relationship of FDI and G_I_INF, traditional auto-regressive distributive lag may not be acceptable to rely upon and to articulate effective strategies, as it proceeds from asymmetric circumstances, which may lead to unsuitable policy measures. Hence, it is suggested to contemplate the non-linearities that may exist while testing linear modeling between the variables.

Variables	FDI_I	FDI_P	FDI_S	FDI_M
SR dynamic
∆GII_I	0.052	0.034	−0.081	−0.342
∆FDI-PS	−0.512	0.164*	0.051	0.892
∆FDII_PSt-1	−0.901*	0.522	0.073	0.036
∆FDI_NG	−0.541	−0.701	0.067	0.307
∆FDI_NGt-1	−0.062	0.381	0.097	0.431
∆H_C	21.983*	0.821	−6.842	−8.031
∆H_Ct-1	2.092	−5.057	0.462	−0.582
∆I_Q	−0.037*	−0.371	2.092	0.482
∆I_Qt-1	−0.361*	−0.781	0.879	1.462
∆T_O	3.267	4.381	0.956	1.549
∆T_Ot-1	2.471	4.381	0.472	5.391
∆DM_FDI	0.302	−0.613	0.462	−0.945
∆DM_FDIt-1	−0.461	−0.203	0.034	−0.126
LR dynamics
FDI-_PS	0.705***	−0.027	−0.231	−0.479
FDI_NG	0.523***	0.916	−0.362	−0.253
H-C	−16.538	−7.527	16.437	27.481
I_Q	0.567	0.937	0,371	0,738
T_O	−3.601	−1.385	−0.482	−2.481
DM-FDI	0.471**	0.681	−0.385	0.462
PSS F-Stat	1.372	0.375*	−0.471***	0.463
ECMt-1	−0.472*	−0.638	−0.617**	−0.739**
Constant	97.153**	32.230**	−17.926	−27.631
N	57	57	57	57
R^2	0.471	0.746	0.857	0.431
Adj. R^2	0.521	0.648	0.427	0.172
SR asymmetries	2.461***	0.374	1.046	0.597
LR asymmetries	0.031	0.204	0.381	0.046

Table 10.

Nonlinear effect of aggregate and disaggregate foreign direct investment inflow on global infrastructure index.

Note: * DU_FDI is time dummy variable confirmed for operational break in FDI_I, FDI_S, FDI_P, and FDI_M. ***p < 0.01, ** p < 0.05, * p < 0.1.

8. Conclusion

The current paper determined to examine the linear and nonlinear cointegration between FDI inflow and total infrastructure, together with various sub-indices of infrastructure and sectoral FDI inflows of India. To accomplish this objective, the paper used Granger causality to determine the causal relationship between FDI inflow and infrastructure, while linear and nonlinear situations are used to find the cointegration relationship. The observation of the findings confirms the existence of the linear and nonlinear cointegration between the cumulative as well as sub-indices of infrastructure and aggregated and disaggregated FDI inflow. Additionally, the findings of asymmetric testing are motivating, which article mix outcomes in terms of the existence of SR and LR asymmetries in the appropriate manner as stated in Tables 9 and 10. So, we infer that in the fitting together of FDI and Global infrastructure index, traditional ARDL may not be acceptable to depend on and to articulate effective policies, as it proceeds from asymmetric circumstances, which may lead to a weedy policy assertion. Hence, it is suggested to study the non-linearities that may exist while testing linear modeling. Furthermore, the conclusions elaborate that to make the economy attract more FDI, the government shall further expand the system of infrastructure in education, quality of the institution and to promote the exports. Furthermore, the empirical results advise that improved quality and availability of infrastructure stocks are the most to attract high FDI inflow in the primary sector, services sector and manufacturing sector of India’s economy in the long run. Hence, the emphasis of policies should be to progress both infrastructure facilities and to make available a conducive atmosphere for global investors to obtain high FDI because FDI inflows indicate to improve the quality and availability of infrastructure. This research concludes that, the current study offers a worthwhile understanding to policymakers and supervisors to consider the sectoral level FDI inflow in India, as an alternative of planning policies exclusively based upon aggregate FDI. Likewise, the study brings into the argument an exceptional measure of infrastructure index (G_I_I) that incorporates the broader aspects together with telecommunication, energy, transportation and financial infrastructure. On the other hand, the previous secondary information deeply depends on only the telecommunication and IT infrastructure which may not be acceptable to represent the sundry dimensions of the infrastructure, reported by the Global Infrastructure Index 2020.