Innovation spillovers, economic growth and role of absorptive ability

Abstract

Research and Development (R&D) based economic sustainability is the prime area of concern in endogenous growth framework to solve the problem of production inefficiency for attaining the economic stability. The high Total Factor Productivity (TFP) growth can be attained through green technology, reverse engineering, ‘learning by doing’ and artificial intelligence. The foreign and domestic green R&D innovation adoption and its spillovers are relying on producers’ willingness to opt the green financing practices and knowledge capital. The current research aims to address a critical literature gap by exploring the intricate linkages between green R&D spillovers, innovation, and green productivity growth in Pakistan. It investigates the mechanisms through which long-term R&D spillovers foster sustainable green growth, while distinguishing the relative impact of domestic and foreign spillovers on green innovation adoption. Further, the study quantifies the absorptive capacity of Pakistan’s work force and outlines pathways to enhance labor efficiency for advancing sustainable development. The time series data covering the period of 1972 to 2022 is used for the quantitative analysis. The Translog and Cobb Douglas Production Functions are used to measure the TFP growth and Autoregressive Distributive Lagged (ARDL) Model is applied for empirical analysis. The results indicate presence of foreign and domestic R&D innovation spillovers and adoption in Pakistan with poor absorptive ability. Moreover, it is observed that foreign R&D spillovers have an affirmative role in TFP growth as compared to domestic R&D. Based on the empirical findings, government should focus on sustainable policies related to local R&D, R&D spillovers with sufficient and sustainable R&D expenditures, their availability and accessibility of innovation to boost the resource efficacy for higher TFP growth. In the similar vein, the implementation of extension services to educate the laborers for adoption of innovation, innovative technology, and artificial intelligence (AI) to attain sustainable productivity should also be emphasized.

Introduction

Research and Development (R&D) provides a pivotal mechanism to transform the economy from resource-based to knowledge-based. In the globalization era, the role of R&D has increased multifold for the accomplishment of sustainable economic growth, as only a knowledge-based economy can magnificently compete in the international market to attain the comparative advantages. Resource efficiency relies on the level of R&D green spending, internal knowledge, and labor capacity to absorb the innovation spillovers from across the world. The R&D spillover shocks are long-term phenomenon, which infiltrate in the economy through various channels such as labor migration, international trade linkages, foreign direct investment (FDI), networking, international collaborations, and extension services. These channels are pivotal in innovation diffusion, which are generated through R&D activities across borders, state, sector, and industries. Once an economy achieves the steady economic growth, further long term sustainable growth potential can be fostered through continued engagement in green R&D-based activities and its spillovers. This involves the dissemination and early adoption of innovation across the state, provinces, and industries. Green technology adoption initiatives contribute to attaining the potential level of sustainable economic growth and competitiveness of a nation in the global market.

The economic growth measurement was initially introduced by Solow (1957), who adopted exogenous growth determinants. Subsequently, Jorgenson and Griliches (1967) elaborated the growth model and switched the conventional growth measurement process by incorporating labor and capital efficiency (quality) as crucial factors for higher economic output. Jorgenson and Griliches (1967) argued that the advancement of a country is not solely reliant on the quantity of physical capital, labor, and land; the quality of these inputs is equally essential in the production process to achieve the resource efficiency. In later developments, Griliches (1992) and Romer (1991) concluded that economic output hinges on R&D innovation, knowledge spillovers, and the ability to absorb innovation, which is reflected in labor efficiency or knowledge capital. For absorptive capacity improvement, talent is an essential factor, as the young researchers with innovative knowledge endorse the exchange of ideas and collaboration, which augments the clean R&D spillover process (Wang, 2015). Conversely, the foreign talent spillover cause the crowding-out effect for internal/existing talent, which is harmful to the internal innovation process and the sustainable inclusive growth process (Agrawal et al., 2019).

Initially, economists established fundamental connections between green R&D spillovers and sustainable economic growth by treating technological innovation as an exogenous variable. However, the importance of R&D gained as Griliches (1973) incorporated the R&D spillovers as an endogenous determinant of economic output. Within the framework of the production function, the significance of R&D innovation has grown over time through novel-oriented studies on endogenous growth theories that positioned the R&D innovation as an influential determinant of economic output (Aghion and Howitt, 1990). Furthermore, Griliches (1992) emphasized on R&D spillovers as a primary driver for sustainability output, fostering innovation and spillover shocks to cost-efficient and market-compatible products that enables firm or economy to secure comparative advantages. New growth theories heighten the role of R&D spillovers as catalysts for technological progress and innovation adoption in economic growth (Romer, 1990; Grossman and Helpman, 1991).

R&D spillovers and economic growth

Technological innovation facilitates the mapping of inputs to outputs by enhancing the product efficiency. R&D contributes distinctive and foremost innovative knowledge, which often entails strong complementary inputs, such as AI tools, materials, and energy sources. Technological spillover is the utilization of R&D generated knowledge spillover to gain higher productivity with limited resources. Empirical and theoretical studies examining R&D models consistently indicate that R&D spillovers exert a substantial influence on the productivity of manufacturing, agriculture and service sectors to minimize the environmental damages both in developed and developing countries (Coe and Helpman, 1995; Lee, 2013; Liu et al., 2015; Maria and Smulders, 2017).

Innovation spillovers are fundamental drivers in enhancing productivity, catalyzing innovation, facilitating the “learning-by-doing” process, and enhance the value addition process both in agriculture and manufacturing sectors. Furthermore, R&D spillovers act as an instrument to achieve the potential level of output to sustain the long-term economic development. International trade emerges as a key factor for knowledge spillovers and innovation adoption, which is helpful in introducing efficient product varieties across borders. International trade in technological products increases the market size through innovative commodity varieties and trade openness in R&D-based products. It plays a fundamental role in introducing novel products, providing ways to access technical knowledge and mitigating the cost of innovation (Rivera and Romer, 1991; Usman et al., 2021).

R&D spending provides an imperative path to obsolescence, withstand competition, and navigate waves of disruption. Engaging in R&D activities provides distinct advantages in terms of innovation spillovers and absorptive capacity, whether at the national level, corporate level, or individual researcher dedicated to exceptional efforts in unique knowledge and product development. The economic impact of R&D spending is manifested in progressive ways through the production process of manufacturing and the agriculture sector, which improves the knowledge efficiency of the labor force (Coe et al., 2009; Usman et al., 2021). Raza and Siddiqui (2014) suggest that spending on R&D enhances the production process in the economy. Further, it brings innovative technology and techniques in production to ensure the efficient provision of goods and services. As a result, the economy is able to produce higher-value goods and services. In the context of economic development, innovative technologies generated through R&D initiatives are characterized by increased durability, capability, and power in high-intensity production of market-compatible products, which improve the living standard in the economy and the economic development process. Moreover, the positive spillover of R&D generates innovative knowledge. The imported goods and services, developed by trade partners, also enhance the productivity growth of the host country. In the similar vein, Ho et al. (2009) argue that more open countries greater productivity gain from external R&D expenditure compared to economies with lower level of openness, which significance of R&D spending transcends national borders, fostering innovation, enhancing productivity, and contributing to overall economic development.

The empirical results of Liu et al. (2016) suggest that contribution of R&D spillover, both from foreign and domestic sources, significantly influences economic growth, which is directed to enhance the development and living standard of the economy. In addition, Gorkey (2014) delves into the long-term repercussions of technological spillover on economic and environmental conditions; findings reveal that R&D spillovers play a pivotal role in improving the domestic output while minimizing environmental damages. The interdependence of a host country's R&D spillover and innovation capacity is dependent on various factors, such as innovative thinking, knowledge capital, “learning by doing”, learning through experiences, and the absorptive capacity for foreign knowledge (Castle et al., 2014; Richard et al., 2023). Furthermore, comparative advantage and profit margin through investment in R&D spillover, improve the strategic partnership between research institutes and domestic firms, which accelerates the way of innovative thinking and domestic R&D spillovers process. Such collaborations contribute to the creation of unique new products in competitive markets, subsequently leading to increased customer satisfaction, improved performance, and a comparative advantage for selling products globally.

Inclusive and exclusive R&D spillovers-driven growth plays a pivotal role in shaping modernization and societal development. However, it is important to note that not all forms of growth can be attributed to technological advancement, improved allocation and scale economies. Economic development resulting from R&D spillovers brings knowledge acquisition about significant improvement in living standards, life expectancy, quality of essential services, and mitigates adverse poverty shocks. R&D spillovers beneficial to a selected group of original, driven minds, and skilled individuals who push technological progress. Successive technology creates new demands, thereby generating further interest in endogenous R&D activities (Sulehri et al., 2023). Conversely, the development of novel practices can be spearheaded by highly skilled engineers, scientists, and researchers who have immediate access to pertinent propositional knowledge; the ingenuity serves as a driving force behind continuous progress (Xu and Khan, 2023).

Economic theories propose two primary drivers of economic growth in the current situation, such as the accumulation of R&D and human capital development (Asim and Sorooshian, 2021). Both human capital and R&D perform an incremental role in productivity across all sectors of the economy. Research fosters knowledge creation, while R&D serves as the mechanism through which researchers generate new knowledge, formulas, technology, techniques, products, or services in both national and international markets (Usman et al., 2021; Stads et al., 2015). R&D-based innovation is utilized individually or offered at the marketplace to produce efficient and market-oriented goods and services to earn higher profits. Innovative technology allows producers to either maintain output with fewer resources or increase output with the available resources (cost minimization or profit maximization process). Undoubtedly, the reliable research and timely adoption dynamically contributes in the economy to generate tangible benefits, promote stable economic growth, and cope with risks aimed at rapid economic integration. The R&D process at the firm or country level typically encompasses seven fundamental stages: knowledge generation, idea screening, development and testing (including patenting), strategy formulation, product development implementation, market testing based on practical applications and finally commercialization or the sale of innovative patents (Sulehri et al., 2023).

Incorporating empirical evidence strengthens the theoretical claims of this study by analyzing Pakistan’s experience within broader global debates on R&D spillovers and sustainable growth. Evidence from Pakistan shows that while the country benefits from technology transfer through trade and FDI, its weak absorptive capacity—stemming from low R&D investment, limited human capital efficiency, and institutional constraints—restricts the effective utilization of spillovers (Lee and Kim, 2022). In contrast, China demonstrates how deliberate policies to enhance absorptive capacity, particularly through sustained R&D spending and targeted green innovation initiatives, have amplified the impact of both domestic and foreign spillovers on sustainable growth (Ramanathan, and Li 2025). Similarly, South Korea’s innovation-driven development highlights how heavy investment in education, R&D intensity, and institutional reforms enabled the country to internalize spillovers, fostering rapid industrial upgrading and long-term growth (Lee, and Kim 2022). The aforementioned scenarios are consistent with cross-country evidence, which shows that the growth effects of R&D spillovers are highly contingent on absorptive capacity, with countries possessing stronger human capital and institutional systems capturing the greatest benefits (Crespi and Zuniga, 2012). Together, these findings reinforce the argument that Pakistan must enhance its innovation systems, educational base, and institutional quality in order to transform external and domestic knowledge into productivity gains and environmentally sustainable growth (Table 1).

Table 1 Theoretical revolution in exogenous growth models and R&D innovation.

Innovation index of Pakistan

Innovation index captures national elements which measure the domestic innovation activities, consists of five inputs pillars and two output pillars. The input elements are human capital and research, research institutions, infrastructure, sophisticated business, and market while output pillars are unique new products and knowledge- based outputs (Global Innovation Index, 2020). The average value of the innovation index of Pakistan from 2011 to 2020 is 23.85 points, the maximum value of the innovation index is 26.8 during 2011, and the minimum value is 22.3 during 2020 (Global Innovation Index, 2020). In the global innovation index ranking, Pakistan is at 108 among 131 countries (Global Innovation Index, 2020).

R&D expenditures of Pakistan

In Pakistan, the public sector carries the utmost proportion of expenditures allocated to R&D through investment in higher education, while universities are considered as the principal research institutions. Higher education R&D expenditures in Pakistan do not produce significant effects on new knowledge creation (Khan and Khattak, 2014). R&D spending and economic growth have a two-way relationship as an increase in economic growth leads to incremental R&D expenditures. Conversely, the rise in R&D spending leads to increased economic growth. Similarly, Ildırar et al. (2016) observe the bidirectional causality between economic growth and R&D spending. The expenditures on R&D capital highlight the country’s priority for science and technology, innovation, and knowledge spillovers, which lead to economic development in the long run.

R&D spending of a country aims to design, develop, and enhance its unique services, products, technology, formula, or processes. R&D spending as a proportion of GDP of Pakistan includes both current and capital expenditures, comprising of four main dimensions, such as business enterprises' expenditures for innovation, government expenditure on innovation, higher education spending and contributions from private non-profit sectors expenditures. In Pakistan, the percentage share of R&D spending is very low. Surprisingly, in 2007, the percentage share of R&D considered as high, was only 0.63 percent of the GDP. The government's R&D spending as a percentage of GDP is not satisfactory, as more funds are required for the internal research and innovation process. In 2017, the percentage of R&D spending to GDP was 0.236 percent as compared to 0.246 percent from the previous year. The lowest R&D expenditures were during 1998, with a percentage share of GDP was 0.109 percent. The R&D structure in Pakistan is not well established, and the government, firms, individuals and researchers are not familiar with the importance of R&D innovation to acquire a competitive advantage in science & technology.

Drawing insights from both international and domestic literature, the current research concludes that the contribution of R&D innovation to the economic growth of a country is ambiguous. A comprehensive review of studies suggests that R&D diffusion produces positive externalities and technological transformation, labor migration and knowledge shocks are the key determinants to achieve the long run economic growth (Griliches, 1992; Keller, 2021; Rismawan et al., 2021). Conversely, many studies argue that R&D spillovers produces negative externalities, such as increased unemployment, elevated comparative cost of the industry, heightened income inequality, elevated water and air pollution, reduced availability of organic food, and declining the domestic productivity (Aitken and Harrison, 1999; Ahmad, et al., 2020; Lucking et al., 2018; Adetutu and Ajayi, 2020).

The research makes a significant contribution to the existing knowledge on R&D and its spillovers in Pakistan through several ways. First, it represents one of the initial endeavors to systematically investigate R&D spillover effects on economic success in Pakistan. Second, the study explores the mechanism through which R&D spillovers are evident, emphasizing both domestic and foreign sources, such as trade and FDI, as an important channel for R&D spillover dynamics. Third, the research employs robust methodologies to calculate the TFP adopting both the Translog and Cobb-Douglas production functions. Fourth, the existing literature regarding R&D spillovers predominantly adoptes cross-section or panel data, like cross country or regions, this research pioneers a time series analysis approach for a more nuanced and carried analysis for country specific. Additionally, the investigation not only focuses on R&D spillover tools, but also incorporates an assessment of the laborer absorptive capacity in Pakistan. Fifth, the existing literature on adoption of technology in Pakistan (Akhtar and Pirzada, 2014; Ali, 2013; Chavas and Nauges, 2020; Raza et al., 2017; Wang et al., 2020), rarely focus on examining the impact of manufacturing and agri-inputs through FDI. This research stands out as a unique contribution, systematically measuring TFP growth and investigating the intricate association between the adoption of R&D and absorptive capacity in influencing economic growth. By addressing these gaps, this study significantly advances the understanding of the complex dynamics surrounding R&D diffusions and its contribution to productivity growth in Pakistan.

This research applies and extends endogenous growth theory to the context of Pakistan through examining the R&D-based innovation and its spillovers contribution to economic growth from both domestic and foreign sources. Endogenous growth theory emphasizes that sustainable growth depends not only on external factors but also on internal factors such as human capital, knowledge capital, intellectual capital, and innovation. The current research empirically tests the theoretical concept that knowledge is capable of diffusing from developed to developing countries. Further, this study adds to the innovation spillover literature, specifically the diffusion of technology or knowledge capital. The novelty of this research lies in introducing absorptive capacity as a key indicator for a developing country like Pakistan. The benefits of R&D spillovers depend on a country’s absorptive ability to recognize and assimilate by applying external knowledge. This approach refines the theoretical framework by demonstrating that the mere presence of R&D is not sufficient without adequate institutional and human capital capacity to utilize it effectively.

Based on the diverse literature gap in the context of the Pakistan economy, this research aims to address the following central questions. To what extent the domestic and foreign R&D spillovers contribute to green technology adoption and to productivity gains and environmentally sustainable economic growth in Pakistan? Does a domestic and foreign R&D spillover catalyze green technology adoption in Pakistan through efficient absorptive ability? What is the role of R&D and its spillovers in the green growth of Pakistan? Does the absorptive ability exist within the Pakistani labor force? Does domestic R&D spillover has a crucial influence in promoting green growth compared to foreign R&D spillover or vice versa? By addressing the aforementioned questions, the study endeavors to increase the comprehension of the nuanced relationship between R&D spillovers, innovation, and productivity growth in the context of Pakistan. This research purposes to uncover the understanding of the mechanisms through which R&D innovation spillovers in long-term green growth. Moreover, it examines the relative contributions of domestic and foreign R&D spillovers for green innovation adoption for sustainable growth. Likewise, the current study not only quantifies the knowledge absorptive ability of the Pakistani labor force but also analyzes the influence of domestic R&D spillover in promoting green growth compared to foreign R&D spillover and vice versa. This research tests the threshold level of absorptive capacity required for domestic R&D spillovers to become more influential than foreign R&D spillovers in promoting sustainable economic growth.

Materials and methods

Research in technological innovation is a major driving force in economic success and economic integration across boundaries. Neoclassical economics consider technological innovation as exogenous and focus on factor accumulation (like labor, capital, and land) as a source of economic output (Solow, 1957; Cass, 1965; Koopmans, 1965). Standardized technology modernizes the country and provides an alternative competing system for development, and coalitions with other stakeholders to innovate. The endogenous economic growth models integrate technological innovation and consider the knowledge and R&D spillovers within the growth model (Romer, 1990; Grossman and Helpman, 1991). The total factor productivity and economic output are dependent on domestic R&D and its spillover shocks from foreign sources.

R&D spillovers have a similar process that benefits trading partners (Griliches, 1998), while knowledge diffusion has causal roots in non-competitiveness and exclusive technology (Romer, 1991). The knowledge spillover extends up to 300 km (Bottazzi and Peri, 2007). However, today in the globalization era, transportation advancement, communication, and IT have amplified spillovers impact across the globe, especially when the host country is efficient in absorptive ability of innovative knowledge. Typically, the knowledge generation process spreads through face-to-face interactions among researchers, policymakers and field workers. Absorptive capacity creates hurdles in disseminating knowledge in distant areas, particularly for unskilled laborers. The effectiveness of knowledge spillover is reliant on the absorptive ability of a country, which reduces the innovation cost, transmission cost and time horizon (Hauser et al., 2007). R&D spillovers are positively associated with TFP growth, the output elasticity ranges between 10 and 30 percent for firms operating within the same industry. Both government and firm R&D spending contribute positively to TFP growth. TFP growth is contingent upon the size and distribution of funds towards R&D and innovation activities (Bronzini and Iachini, 2014). Moreover, Guellec and de la Potterie (2001) reveal an inverse synergy among defense-related R&D compared to civilian R&D spending’s on TFP. Similarly, Ho et al. (2009) observe a protracted elasticity of R&D spending contribution to TFP growth to be 0.091 in the case of Singapore. Both R&D and TFP growth are complementary goods (Cin et al., 2017; Czarnitzki and Hussinger, 2018; Bye et al., 2019).

This study builds its theoretical foundation on the intersection of endogenous growth theory, ecological economics, and innovation studies to explain the role of R&D spillovers, absorptive capacity, and green technology adoption in fostering sustainable economic growth. Endogenous growth theory posits that long-run growth is primarily driven by internal factors such as human capital, knowledge accumulation, and innovation, with knowledge being a non-rival good that can diffuse across economies (Romer, 1990; Lucas, 1988). This provides the basis for analyzing how domestic and foreign R&D spillovers contribute to productivity gains in Pakistan. Complementing this, the Porter Hypothesis (Porter and van der Linde, 1995) suggests that stringent but well-designed environmental regulations can stimulate innovation that simultaneously enhances competitiveness and reduces environmental harm, thus linking green innovation directly to growth.

The eco-innovation framework (Rennings, 2000; Kemp and Pearson, 2007) further reinforces this perspective by emphasizing that the diffusion and adoption of environmentally friendly technologies are shaped not only by technological progress but also by absorptive capacity and institutional support. Moreover, ecological modernization theory (Mol and Sonnenfeld, 2000) argues that economic development and environmental sustainability can mutually reinforce when supported by strong institutions and policies that enable societies to decouple growth from ecological degradation. Finally, the national innovation systems perspective (Lundvall, 1992; Nelson, 1993) underlines the systemic interactions among firms, universities, government, and institutions, highlighting that spillovers can only translate into growth when supported by effective knowledge networks and absorptive capacity at the national level. Together, these theoretical perspectives extend the standard endogenous growth framework by embedding sustainability concerns and institutional dynamics, thereby providing a comprehensive lens to analyze how innovation spillovers and absorptive ability drive both economic and environmental outcomes in Pakistan.

Data framework

The current research employs a time series analysis to investigate the effectiveness of both domestic and foreign R&D spillover shocks on total factor productivity (TFP) growth in Pakistan over the period 1972–2022. The data were collected from multiple credible national and international sources, including the Pakistan Bureau of Statistics (PBS), Pakistan Economic Survey, State Bank of Pakistan, Ministry of Finance, Penn World Table (version 10.01), and World Development Indicators (WDI). Gross expenditure on R&D (GERD), domestic patents, and higher education R&D investments are used as proxies of Domestic R&D spillovers, while foreign spillovers are measured through trade-weighted foreign R&D stock and FDI inflows. TFP growth is derived from Translog and Cobb-Douglas production functions. To capture the short and long-run dynamics, the Autoregressive Distributed Lag (ARDL) model is applied to capture the short and long-run dynamics along with the diagnostic and stability tests.

Analytical framework

The R&D expenditures and early adoption of innovation performs a valuable contribution to the economic production of the economy. R&D investment carries innovation, new technology, and unique product varieties to earn comparative advantages and global exchange exports revenue. R&D spillovers perform vital role in influencing the education, knowledge, financial capacity, management skill, practical experience, readiness to choose novelty and capacity to absorb the new knowledge of firms, farmers, and individuals, thereby shaping their ability to adopt the innovation earlier. The results indicate that the R&D spending rate of return is higher, and investment for innovative technology, product varieties, new seeds and fertilizers provides a significantly higher output from manufacturing and agriculture sectors (Chandio et al., 2021). Numerous methods are available for calculating the TFP growth, including indexing approach, Cobb-Douglas production function, stochastic frontier, OLS, etc. However, such methods are not pertinent in this research because of data limitations (Sharif et al., 2021).

For the Pakistan economy, the TFP growth is calculated via Cobb-Douglas production function because of constraints. Furthermore, the TFP growth is measured at the cumulative level through the Cobb-Douglas production function, which makes sense for estimating the TFP growth using traditional yearly time series data that is dependent on capital and labor inputs. The assumption of constant return to scale was included in the Cobb-Douglas production function with respect to capital and labor (Coe and Helpman, 1995; Coe et al., 2009). The Translog and Cobb-Douglas production functions are applied to measure the TFP growth by adopting the Hicks neutral (Constantin et al., 2021).

$${{\rm{Y}}}_{{\rm{t}}}={{\rm{A}}}_{{\rm{t}}}{{\rm{K}}}_{{\rm{t}}}^{{\rm{\alpha }}}{{\rm{L}}}_{{\rm{t}}}^{{\rm{\beta }}}$$

(1)

In model 1, output is denoted by Y_t, labor by L_t, capital stock by K_t, and A_t is the TFP (Salim and Islam, 2010). Whereas “t” shows time series, while α and β represent the elasticity of both capital stock and labor force. Taking logarithm on both in Eq. 1, and converting it into input-output model, the Eq. 3 is used to calculate the TFP growth. By applying the properties of logarithms, the final equation for measurement of TFP growth is as follows:

$${{\rm{TFP}}}_{{\rm{t}}}={{\rm{Y}}}_{{\rm{t}}}/{{\rm{K}}}_{{\rm{t}}}^{{\rm{\alpha }}}{{\rm{L}}}_{{\rm{t}}}^{{\rm{\beta }}}$$

(2)

$${\mathrm{ln}{\rm{TFP}}}_{{\rm{t}}}={\mathrm{ln}{\rm{Y}}}_{{\rm{t}}}-({{\rm{\alpha }}\mathrm{ln}{\rm{K}}}_{{\rm{t}}}+{{\rm{\beta }}\mathrm{ln}{\rm{L}}}_{{\rm{t}}})$$

(3)

By adopting the equation 3, TFP_t growth is calculated, where the inputs are capital and labor. Moreover, the net capital stock K_t is measured for the economy, the perpetual inventory method is adopted as given in Eq. 4 (Coe et al., 2009; Lapple et al., 2016).

Net capital stock

Gross capital formation, which is measured through the entire amount of capital expenditure made by the economy, is the increase in the stock of capital. Net investment in the economy is defined as gross capital formation after inflationary effects and depreciation is subtracted. The depreciation is referred to as the difference between gross capital formation and fixed capital consumption, is the net capital stock. The wear and tear costs incurred by fixed capital to keep capital stock in its initial state are referred to as the depreciation rate. According to Kuo and Yang (2008), the average life of machinery (capital equipment) is used to calculate depreciation.

The net capital stock is determined using the Perpetual Inventory Methodology (PIM) technique, which is based on Griliches (1979) and Barro and Sala-i-Martin (2004). This method includes the approximation of the growth rate, depreciation, and initial capital stock. Each sector’s growth rate for the preceding period is taken to be the current capital growth rate (Sharif et al., 2021). The following are the estimated formulations:

$${{\rm{K}}}_{{\rm{t}}+1}={{\rm{I}}}_{{\rm{t}}}+(1-{\rm{d}}){{\rm{K}}}_{{\rm{t}}}$$

(4)

In Eq. 4, “t” stands for time, “K_t+1” for net capital stock, “d” for the depreciation rate and I_t for gross capital stock. Although the initial capital formation was determined using gross fixed capital formation, the study’s primary focus was on quantifying net capital stock. The following is the methodology for calculating the beginning capital:

$${{\rm{I}}}_{{\rm{o}}}=\frac{{{\rm{I}}}_{{\rm{i}}}}{{{\rm{g}}}_{{\rm{i}}}+{\rm{d}}}$$

(5)

In Eq. 5, I_o is the starting level gross capital stock, and g_i is the capital formation growth rate. To measure the capital stock, GDP growth from the prior era was used as a proxy (Sharif et al., 2021) of growth in capital formation. To calculate the net capital stock, depreciation data is taken from Penn World Table 10.01. It is necessary to interpret the growth of capital stock as “g” as the average growth of capital stock over the sample range.

Model for R&D capital and economic growth

Comprehensive research has been conducted in the literature relevant to economic performance and the role of R&D spillover at international forums. Würtenberger et al. (2012) highlights the issue related to R&D spillover and its role in economic growth and argue that technological spillover is a key factor to boost long-run economic growth. Available studies adopted diverse mechanisms for capacity to absorb the innovation, whereas few studies concentrate on educational expenditures and human capital (Criscuolo and Narula, 2008; Keller, 2004), while others are focused on R&D investment and emphasized new knowledge adoption (Wang et al., 2010), and technological infrastructure (Chuang and Hsu, 2004). The prior literature explains the absorption ability in the form of national, social and innovative culture, infrastructure, orientation, and government inducement on the adoption of new knowledge. The production function in the form of Cobb-Douglas is as follows:

$${Y}_{t}=TF{P}_{t}{L}_{t}^{\alpha }{K}_{t}^{\beta }$$

(6)

In Eq. 6, Y_t is productivity output, while ${\mathrm{TFP}}_{t}{,\,L}_{t\,}^{\alpha }\,{and}\,{K}_{t}^{\beta }$ are total factor productivity, labor force and capital stock, respectively. So TFP is dependent on knowledge spillover (A_t) human capital index (HC) and R&D activities (RD), both domestic and foreign.

$$TF{P}_{t}={A}_{t}H{C}_{{t}}^{{\gamma }}R{D}_{{t}}^{{d}}R{D}_{{t}}^{{f}}$$

(7)

The knowledge spillover is depending on technological changes (TC) and fixed technology (FT)

$${A}_{t}=T{C}_{{t}}F{T}_{{t}}$$

(8)

For substituting the value of A_t and TFP_t, the Eqs. 6 and 7 become,

$${Y}_{t}={{TC}}_{t}{{FE}}_{t}{{HC}}_{t}^{\gamma }{{RD}}_{t}^{f}{{RD}}_{t}^{d}{L}_{t}^{\alpha }{K}_{t}^{\beta }$$

(9)

$${{TFP}}_{t}\,=\,{{TC}}_{t}{{FE}}_{t}{{HC}}_{t}^{\gamma }{{RD}}_{t}^{f}{{RD}}_{t}^{d}$$

(10)

To quantify the role of R&D spillover and its impact on economic growth, this research takes the log and adds the intercept and residual terms in Eqs. 9 and 10. This gives the final estimated model in the form of economic growth and TFP growth. FDI inflows effects are productivity-driven and dominant on TFP growth per worker, so the FDI inflows privileges are subordinate to the host country’s absorptive capacity. To sustain long-run economic growth, countries require knowledge-driven, quality institutions, and skilled-based human capital (Ahmed and Kialashaki, 2019; Le et al., 2021). The transformed growth is as follows:

$$\begin{array}{l}{{l}{n}{Y}}_{{t}}={\beta }_{{0}}+{{\beta }_{{1}}lnTC}_{t}+{\beta }_{{2}}{lnFT}_{t}+{\beta }_{{3}}{{l}{n}{H}{C}}_{{t}}+{\beta }_{{4}}R{D}_{t}^{f}\\ \,\,\,\,\,\,\,\,\,\,+{\beta }_{{5}}R{D}_{t}^{d}+{\beta }_{{6}}ln{L}_{t}+{\beta }_{{7}}ln{K}_{t}+{\beta }_{{8}}{{l}{n}{H}{C}}_{t}* R{D}_{{t}}^{{f}}+\,{{\in }}_{{t}}\end{array}$$

(11)

Currently, the researchers are more enthusiastic about multidisciplinary and multidimensional knowledge skills, which increase the absorptive ability as well as convert the economy from resource-based to knowledge-based. The collaboration among stakeholders (like universities, research institutions, and industries) can improve the absorptive ability, which plays a mediating role in innovative capabilities and industrial performance (Asplund and Bengtsson, 2020; Zhai et al., 2018). The final estimated model is as follows:

$$\begin{array}{l}{lnTFP}_{t}={\beta }_{0}+{{\beta }_{1}lnTC}_{t}+{\beta }_{2}{lnFT}_{t}+{\beta }_{3}{lnHC}_{t}+{\beta }_{4}R{D}_{t}^{f}\\ +{\beta }_{5}R{D}_{t}^{d}+{\beta }_{6}ln{L}_{t}+{\beta }_{7}ln{K}_{t}+{\beta }_{8}{lnHC}_{t}* R{D}_{t}^{f}+\,{{\in }}_{t}\end{array}$$

(12)

The estimated model of R&D spillovers and absorptive ability impact on output growth in Pakistan using ARDL is as follows:

$$\begin{array}{l}\Delta {\text{ln}}{\left(\mathrm{TFP}\right)}_{{\rm{t}}}={{\rm{\beta }}}_{0}+\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\beta }}}_{1}\Delta {\text{ln}}{\left(\mathrm{EMP}\right)}_{{\rm{t}}-1}+\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\beta }}}_{2}\Delta {\text{ln}}{\left(\mathrm{HC}\right)}_{{\rm{t}}-1}+\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\beta }}}_{3}\Delta {\text{ln}}{\left(\mathrm{ECI}\right)}_{{\rm{t}}-1}\\ +\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\beta }}}_{4}\Delta {\text{ln}}{\left(\mathrm{TOP}\right)}_{{\rm{t}}-1}+\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\beta }}}_{5}\Delta {\text{ln}}{(\mathrm{Tech\_Imp})}_{{\rm{t}}-1}+\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\beta }}}_{6}\Delta {\text{ln}}{(\mathrm{UT})}_{{\rm{t}}-1}+\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\beta }}}_{7}\Delta {\text{ln}}{(\mathrm{Tech\_Exp})}_{{\rm{t}}-1}\\ +\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\beta }}}_{8}\Delta {\text{ln}}{(\mathrm{Uni})}_{{\rm{t}}-1}++\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\beta }}}_{9}\Delta {\text{ln}}{(\mathrm{RD\_OECD})}_{{\rm{t}}-1}+\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\beta }}}_{10}\Delta {\text{ln}}{(\mathrm{RD\_USA})}_{{\rm{t}}-1}+\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\beta }}}_{11}\Delta {\text{ln}}{(\mathrm{RD\_China})}_{{\rm{t}}-1}\\ +\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\beta }}}_{12}\Delta {\text{ln}}{({\rm{R}}\& D\_W)}_{{\rm{t}}-1}+\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\gamma }}}_{1}\mathrm{ln}{\left(\mathrm{EMP}\right)}_{{\rm{t}}-1}+\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\gamma }}}_{2}\mathrm{ln}{\left(\mathrm{HC}\right)}_{{\rm{t}}-1}+\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\gamma }}}_{3}\mathrm{ln}{\left(\mathrm{ECI}\right)}_{{\rm{t}}-1}+\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\gamma }}}_{4}\mathrm{ln}{\left(\mathrm{TOP}\right)}_{{\rm{t}}-1}\\ +\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\gamma }}}_{5}\mathrm{ln}{(\mathrm{Tech\_Imp})}_{{\rm{t}}-1}+\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\gamma }}}_{6}\mathrm{ln}{(\mathrm{UT})}_{{\rm{t}}-1}+\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\gamma }}}_{7}\mathrm{ln}{(\mathrm{Tech\_Exp})}_{{\rm{t}}-1}+\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\gamma }}}_{8}\mathrm{ln}{(\mathrm{Uni})}_{{\rm{t}}-1}++\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\gamma }}}_{9}\mathrm{ln}{(\mathrm{RD\_OECD})}_{{\rm{t}}-1}\\ +\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\gamma }}}_{10}{\text{ln}}{(\mathrm{RD\_USA})}_{{\rm{t}}-1}+\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\gamma }}}_{11}{\text{ln}}{(\mathrm{RD\_China})}_{{\rm{t}}-1}+\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\gamma }}}_{12}{\text{ln}}{({\rm{R}}\& D\_W)}_{{\rm{t}}-1}+\mathop{\sum }\limits_{{\rm{t}}=1}^{{\rm{n}}}{{\rm{\delta }}}_{1}\mathrm{ln}{(\mathrm{HC}* \mathrm{FDI})}_{{\rm{t}}-1}\\ +\,{{\rm{\delta }}}_{2}\mathrm{ln}{(\mathrm{HC}* \mathrm{TOP})}_{{\rm{t}}-1}+{{\rm{\delta }}}_{3}\mathrm{ln}{(\mathrm{HC}* \mathrm{RD\_Tech\_Imp})}_{{\rm{t}}-1}+\,{{\rm{\delta }}}_{4}ln{(\mathrm{HC}* \mathrm{RD\_OECD})}_{{\rm{t}}-1}+{{\rm{\delta }}}_{5}\mathrm{ln}{(\mathrm{LRD}* \mathrm{RD\_USA})}_{{\rm{t}}-1}\\ +\,{{\rm{\delta }}}_{6}\mathrm{ln}{(\mathrm{HC}* \mathrm{RD\_China})}_{{\rm{t}}-1}+{{\rm{\delta }}}_{7}\mathrm{ln}{(\mathrm{HC}* \mathrm{RD\_W})}_{{\rm{t}}-1}+\,{{\rm{\delta }}}_{8}\mathrm{ln}{(\mathrm{HC}* \mathrm{FDI})}_{{\rm{t}}-1}+{{\rm{\varepsilon }}}_{{\rm{t}}}\end{array}$$

(13)

Equation 13 represents the short and long term dynamics of ARDL model, whereas ${\beta }_{0},\,{\beta }_{1},\,\ldots \ldots \ldots \ldots \,{\beta }_{12}$, are short-run parameters, while parameters ${\gamma }_{1},\,{\gamma }_{2},\ldots \ldots \ldots \ldots \ldots {\gamma }_{12}$ represent long term association and ${\varepsilon }_{t}$ represents the error term. In addition, ${\delta }_{1},\,{\delta }_{2},\ldots \ldots \ldots \ldots \ldots {\delta }_{8}$ represent interactive terms to capture the labor force absorptive ability in case of Pakistan.

Results and discussion

R&D spillovers and TFP growth

Green R&D spillovers perform an essential role in manufacturing, agricultural and services sector growth through the channels of innovation adoption, technological transformation and knowledge capital. An economic R&D consists of factors including innovation expenditures, either domestic or foreign, trade openness, FDI, technology imports and exports. The non-economic factors consist of R&D structures, the incentive system, innovation environment, and factors related to absorptive ability. Analysis techniques are adopted according to the nature and limitations of data, model requirements, and assumptions of the study. Different data cleaning and screening tools are applied to avoid unbiased, spurious, and inconsistent analysis. For empirical analysis, this research adopts the unit root test, the ARDL model, the Cobb-Douglas (CD), and the Translog production function. For results, accuracy and cleaning, several residual diagnostic tests and remedial tests are also applied. The CD production function is appropriate for measuring TFP growth using conventional time series data of aggregate inputs like labor and capital.

Figure 1 shows the computed plot of TFP growth in Pakistan. The TFP increase exhibits a favorable rising trend. In 2020, the TFP growth remained at 2.01 percent, which is less than the 2.90 percent global TFP growth (World Bank, 2021). To ensure the efficiency of the full-employment level, the calculated value of TFP with the total labor force is 2.21, while TFP growth with the employed labor force is 2.01. The gap in TFP growth shows that Pakistan has the potential to achieve higher productivity through a reduction in unemployment. The higher TFP growth can be achieved through spending in R&D and knowledge capital to improve the innovation and human capital efficiency.

Fig. 1: TFP growth of Pakistan.

Source: Author own estimation.

Unit root test

The trending behavior of the time series data analysis may cause the problem of spurious analysis. This problem can be resolved through examining the stationarity behavior and adopting the suitable analysis techniques in light of unit root results. The augmented Dickey–Fuller (ADF) technique is applied to identify the stationary level of given variables, the outcomes shown in Table 2. According to ADF outcomes, the explained variable is integrated at the first difference, while the independent variables have mixed stationarity behavior; some variables are integrated at the level, and a few variables are integrated at the first difference. This demonstrated that the adoption of R&D from earlier periods and skilled-based knowledge capital is crucial for Pakistan’s TFP growth. For optimal lag selection, the Akaike Information Criterion (AIC) provides robust results compared to Schwarz–Bayes Criterion (SBC) and Hannan–Quinn Criterion (HQC), as the results emphasized that lag 2 is the optimal lag and suitable for the given sample size.

Table 2 ADF test results of R&D spillovers and TFP growth.

Long-term coefficient of R&D Spillover on TFP Growth

The long-term analysis uses time series data to figure out what’s going on with trends and what might be wrong with an analysis. In order to avoid spurious analysis, the problem of multicollinearity is found during the data-cleansing process. Due to interacting terms and tighter proxies of R&D spillovers, the problem of multicollinearity emerged. For this reason, many models’ estimates include the addition of R&D adoption proxies. The ARDL method of cointegration is applicable for the final empirical results since the outcomes of the ADF test demonstrate that all the selected variables are integrated at the level or first difference (I(0) or I(1)). To prevent multicollinearity, seven models are estimated through the dynamic autoregressive distributive lag (ARDL) technique. The analysis outcomes of all estimated models are given in Table 3.

Table 3 Long-run results TFP growth and R&D spillovers model.

The long-run estimated results of all models show that R&D penetration creates positive externalities for TFP growth in Pakistan. The results highlight that international R&D has more magnitude with a positive spillover shock as compared to local R&D to enhance the TFP growth. The calculated values of R&D absorptive ability indicate negative and significant, which emphasizes that the Pakistani labor force has less knowledge capital with poor absorption capacity. The empirical results of R&D expenditures across the globe have positive spillover shocks in Pakistan TFP growth, while R&D expenditure from OECD countries is creating negative externalities for TFP growth. In all seven specifications, the Human Capital (HC_t) and Employment (EMP_t) are considered as control variables. The estimated value of HC_t in all estimated models shows mixed results; in three models, HC_t has positive and significant results, while in four models, HC_t has insignificant results.

In the first estimated model, the explained variable is TFP growth (TFP_t), while predictor variables are employment (EMP_t), human capital (HC_t), Foreign Direct Investment (FDI_t), University Teachers (UT_t), and the interaction term of HC with FDI (HC*FDI). The EMP_t and HC_t are control variables, while FDI is a proxy of foreign R&D and UT_t is a proxy of domestic R&D. The calculated value of EMP_t has a significant impact on TFP_t with positive elasticity; the calculated value of EMP_t shows one percent increase in employment has a 17 percent contribution to the TFP growth of Pakistan. Further, Moreno-Galbis (2012) conclude that TFP growth accelerates the job markets, increases the trained, skilled, and intensive to update job-specific technology.

The efficient and knowledgeable workforce has a productive impact on TFP growth. The coefficient value of HC_t demonstrate a positive and significant influence on TFP growth of Pakistan; this is due to the youth, energetic, and abundant labor in the country. The coefficient value of HC_t shows a 34 percent share in TFP growth in Pakistan. The study findings are aligned with the findings of Moreno-Galbis (2012), who argue that human capital magnifies the impact on growth through heterogeneous skilled labor, trained workers, and complementary association between skills and technological innovation.

In first model, the foreign R&D spillovers is captured through FDI_t, the analysis results of external R&D adoption indicate significant affirmative effect on TFP growth in Pakistan. The coefficient elasticity of FDI_t, is 2.3 percent. Additionally, the advantages of FDI spillovers can be attained through effective human capital, skilled and efficient labor, and early adoption of foreign R&D innovation, for this, domestic factors, institutional development, and extension policies are crucial tools. Technology transfer from outside sources has made a significant contribution to TFP growth. Adopting R&D innovation is the first step towards increasing productivity, but for most developing nations, access to affordable new technology is a key problem (Abdullahi et al., 2015). The results are aligned with the findings of Ahmed et al. (2017), who observed the positive association between FDI inflow and TFP growth. Khan et al. (2017) and Lapple et al. (2016) argue that R&D spending on foreign R&D and innovative technology has a positive impact on TFP growth.

The variable of University Teachers (UT_t) is used to measure the domestic R&D spillovers, as the university faculty is considered a fundamental source of knowledge spillovers across the country. The calculated coefficient value of UT_t is insignificantly negative. The insignificant value of UT_t directed that domestic R&D spillover has not performed any fundamental contribution in TFP growth. The reason for insignificant impact of UT_t is that the university faculty is neather up to date nor generating the knowledge and its spillovers shocks for the society to boost the TFP growth in long-term. In addition, Martin (1998) concludes that the university research accelerates the TFP growth through the development of new products, country support in favorable knowledge-intensive products and innovative products competitive at marketplace globally.

Through the interactive term of human capital (HC_t) with FDI_t, the researcher captures the absorptive ability of the Pakistani workforce. The efficiency of R&D spillover is reliant on the absorbent ability of the host country, and knowledge-based labor can utilize the foreign R&D efficiently (Coe et al., 2009). The interaction term’s (HC*FDI)_t negative, significant result suggests that the labor force’s absorptive capacity is lower. The labor force in Pakistan is incapable of effectively using foreign technology. The results of the interacting term indicate that either educated labor is not readily available or that knowledge capital is insufficiently efficient to absorb foreign innovation. The findings are in line with those of Nadeem et al. (2013), Chandio et al. (2016), and Khan et al. (2017), who discovered that the lack of absorption ability makes human capital, experience, and training have little bearing on productivity. To achieve better TFP growth through technology spillover, human capital investment is necessary to boost labor productivity.

In the second specification, the explained variable is TFP growth (TFP_t), whereas explanatory variables are Employment (EMP_t), Human Capital (HC), Trade openness (TOP_t), Technology Exports (Tech_exp_t), and the interaction term of HC with TOP_t (HC*TOP). The EMP_t and HC_t are control variables, while TOP_t is proxy of international R&D and Tech_exp_t is a proxy of domestic R&D. The calculated coefficient value of EMP_t has a significant impact in TFP_t with positive elasticity and has similar impact as in first model. However, the coefficient value of HC_t shows a positive and insignificant impact on TFP growth in the second specification.

The foreign R&D spillovers are captured through TOP_t, the analysis results indicate that TFP growth is positively affected by external R&D adoption in Pakistan. The coefficient elasticity of TOP_t is 0.3 percent. Further, the TOP_t has less foreign R&D spillover shocks as compared to FDI in the case of Pakistan. The TOP_t spillovers can boost through more open economy, especially trade liberalization with the technologically advanced countries and improvements of internal knowledge diffusion. The TOP_t benefits can be attained through efficient human capital, skilled and efficient labor, and early adoption of foreign innovative technology; for this, the domestic factors, institutions development, and extension policies are important instruments to enhance the long-term TFP growth. The adoption of R&D innovation is the initial step to enhance productivity; however, the affordability of new technology is a key issue for most of the developing economies (Abdullahi et al., 2015). The outcomes are aligned with the findings of Lapple et al. (2016) and Khan et al. (2017), who argue that R&D spending on foreign technology and more open economies can attain larger benefits from innovation spillovers.

The coefficient value of Tech_exp_t shows a positive and significant contribution to TFP growth in Pakistan. The Tech_exp_t has a 0.3 percent contribution to TFP growth in Pakistan. A small coefficient value highlights that Tech_exp_t has a small contribution to innovation exports. The export of technological products has a minor share of GDP growth in Pakistan, which is a central reason of inadequate contribution technological exports in TFP growth. The results are aligned with the findings of Bolosha et al. 2022 concluded that technology exports and innovation management have a productive impact on TFP growth.

The interaction term (HC*TOP)_t yields a substantial negative result, indicating that the labor force’s absorptive capacity is lower. The labor force in Pakistan lacks the skills necessary to effectively use foreign technologies. According to the interactive-term outcomes, either there is a lack of trained workers or the knowledge capital is inefficient enough to absorb foreign innovation. The outcomes are aligned with the outcomes of Nadeem et al. (2013), Chandio et al. (2016) and Khan et al. (2017), i.e., the human capital, experience, and training has insignificant impact on productivity due to poor absorption capacity.

In the third estimated model, the explained variable is TFP growth (TFP_t), whereas the predictors are employment (EMP_t), human capital (HC), economic complexity index (ECI_t), technology imports (Tech_imp_t), no of universities (Uni_t), and the interaction term of HC with Tech_imp_t (HC*Tech_Imp). The EMP_t and HC_t are control variables, while Tech_imp_t is a proxy of foreign R&D, and Uni_t is a proxy of local R&D. The ECI_t is used to measure a country's current production capability and efficiency. The estimated value of EMP_t has an insignificant impact on TFP_t with positive elasticity. The coefficient value of HC_t has a similar outcome with a minor change in coefficient magnitude as given in the first specification.

The foreign R&D spillovers is captured through Tech_imp_t, the analysis results of external R&D adoption show a significantly positive effect on TFP growth in Pakistan. The coefficient elasticity of Tech_imp_t is 44 percent. Additionally, the advantages of the Tech_imp_t spillovers can be attained through effective human capital, skilled and efficient labor, and early adoption of foreign R&D innovations; for this, domestic factors, institutional development, and extension policies are crucial tools. Technology imports from abroad perform a noteworthy impact on TFP growth. Adopting R&D-based new technology is the first step to increasing productivity, but for most developing nations, access to affordable new technology is a major problem (Abdullahi et al., 2015). The results are aligned with the findings of Ahmed et al. (2017), who investigate the positive association between FDI inflow and TFP growth. Lapple et al. (2016) and Khan et al. (2017) argued that R&D spending on foreign R&D and innovative technology has an optimistic impact on TFP growth.

The calculated value of the Uni_t shows a positive and significant contribution to enhance the TFP growth. The Uni_t has 18 percent contribution in TFP growth. The coefficient value of Uni_t highlights the increasing number of universities performing a productive role in TFP growth and innovation spillovers across the country. Pakistan is at an initial stage of development, and an increasing number of universities perform productive role in increasing the literacy rate and human capital development. The estimated results indicate that Pakistan has to focus on university development through assuring the quality education. In addition, Martin (1998) concluded that the university research accelerates the TFP growth through the development of new products, country support in favorable knowledge-intensive products and innovative products competitive at marketplace globally.

The estimated outcomes highlighted that ECI_t has a significantly negative contribution to TFP growth. The estimated coefficient of ECI_t has a negative and significant contribution in TFP having coefficient value of -0.012. This specifies that the knowledge accumulated by the Pakistani population is not translated into the production process. Further, the innovative ideas and unique research activities are not appreciated in the inclusive research and production process. The ECI_t results indicate that the knowledge generation system is very complex and not translated into innovative activities. The industrial production structure is not developed and does not produce innovative outputs to compete in the international market. The research outcomes are aligned with Pazham and Salimifar (2016), who found the negative association between GDP growth and ECI_t of chosen panel countries. The interactive term outcomes are consistent with the findings of the first model, which shows that technology imported from foreign sources is not absorbed efficiently.

In fourth, fifth, sixth, and seventh models, the independent variables are employment (EMP_t), human capital (HC), trade openness (TOP_t), ECI_t, R&D expenditures did by USA (RD_USA_t), R&D spending did by OECD economies (RD_OECD_t), R&D spending did by China (RD_China_t), and world R&D expenditures (RD_W_t) and their interactive terms with Human Capital (HC_t) of Pakistan. The TOP_t is a proxy of foreign R&D, and ECI_t is a proxy of local R&D, while the other countries' expenditures on R&D is utilized to capture the innovation spillovers shocks towards Pakistan. The estimated results of control variables and the proxies of domestic and foreign R&D are consistent with previously estimated models. The results of different interactive terms with other countries' R&D spending shows adverse and noteworthy effect on TFP growth of Pakistan. This shows that the knowledge generated by the developed countries is not absorbed in Pakistan. The Pakistani labor force does not have the efficiency and knowledge capital for the effective use of foreign innovation.

The results of proxies of foreign R&D show positive spillover shocks and are helpful in the TFP growth of Pakistan. The estimated coefficient value of RD_USA_t, RD_China_t and RD_W_t shows a significantly positive contribution to enhance the TFP growth of Pakistan. The R&D expenditures did by the USA, China and the World is creating positive externalities for TFP growth in Pakistan, which is helpful in bringing innovation and new production techniques through positive spillover shocks. However, the R&D expenditures incurred by OECD countries (RD_OECD_t) shows significantly negative contribution to reduce the innovation process and TFP growth of Pakistan. This signifies that innovation expenditures of OECD countries are creating negative externalities for Pakistani TFP growth.

Cointegration and diagnostic estimates

The CUSUM and CUSUMQ tests are graphical analysis of the cointegration equation (called the ECM model), which is estimated in the ARDL model. The calculated values of CUSUM analysis and CUSUMQ tests lies within 5 percent bounds which is confirmation of the existence a long-run association with selected variables and show the stability in estimated coefficients (Alimi et al., 2014; Ali et al., 2019). To ascertain whether a relationship of cointegration exists, the bound test of ARDL is utilized (Pesaran et al., 2001). The calculated value of the ARDL bound test shows that the F-statistics are greater than the upper bound in all estimated models, indicating that the hypothesis of no long-run association is rejected significantly (Table 4). The estimates of the ARDL model show R&D spillover indicators have an extended effect on TFP growth. The empirical results are fairly matching with the findings of (Liu et al., 2016).

Table 4 ARDL bound test and diagnostic estimates of TFP growth models.

Short-run analysis and ECM results

The estimates of short-term coefficients are given in Table 5. Since the estimated models are time series multivariate, so, the error correction model (ECM) is used to determine how stochastic trends will behave and how quickly the dependent variable will converge to equilibrium. The error correction mechanism ECM (-1) coefficient has significantly negative sign at 1 percent level in all estimated models, which shows that variables in estimated models are cointegrated in long-run. The coefficient of ECM implies that deviation from the steady-state position in R&D spillovers in estimated models is corrected with a fast speed of adjustment (Shittu, $ Yemitan, 2012). Disequilibrium can be corrected through R&D spillovers, that shocks can be modified with faster speed and R&D spillovers perform important role in TFP growth to bring at its steady-state position (Shita et al., 2019; Ali et al., 2020).

Table 5 Short-run and ECM estimates of TFP growth models.

Conclusion and policy suggestions

The current research aims to investigate the impact of R&D spillovers and absorption capacity of foreign knowledge on TFP growth in Pakistan. It also examines the labor force efficiency for progenitive utilization of R&D innovation. The quantitative analysis is carried out through the yearly time series data from 1972 to 2022. The translog and Cobb-Douglas production functions are employed to measure the TFP growth and the autoregressive distributive lagged (ARDL) Model is applied for empirical results. The long-run estimated results of all models indicate that R&D penetration creates positive externalities for TFP growth in Pakistan. The results highlight that global R&D spending has an optimistic spillover shock as compared to internal R&D shocks to enhance the TFP growth. The negative and significant values of R&D absorptive ability indicates that the Pakistani labor force has less knowledge capital with poor absorption capacity. The empirical results of R&D expenditures across the globe have positive spillover shocks in Pakistan TFP growth, while R&D expenditure from OECD countries is creating negative externalities for TFP growth. Based on quantitative analysis, it is concluded that the global R&D is more appropriate for economic growth as compared to domestic R&D, and the Pakistani labor force has less absorptive ability.

The innovation index highlights that Pakistan is lacking good research institutions, knowledge capital, technological innovation and infrastructure, and an environment for research, which is incredibly important for the socio-economic development of the economy. The statistical and graphical data representation of domestic and foreign R&D drivers highlight that Pakistan has the potential to acquire benefits from both the internal and external spillover shocks of R&D. In terms of global R&D spillovers, Pakistan has the potential to attract foreign innovation through FDI, trade openness, and technology imports, but the domestic knowledge capital has a significant problem in absorbing the external innovation. Now, it is time to realize and move on to the importance of R&D expenditures for both private and public sectors. A combined strategy is required to focus on inclusive innovation and spillovers of foreign knowledge. Internal innovation can improve due to an increase in domestic R&D expenditure, better research culture, an incentive-based system, collaboration and networking. Based on quantitative analysis, this study has suggested the following workable policies:

• The government should focus on sustainable policies related to internal R&D, R&D spillovers with sufficient and sustainable R&D expenditures.

• The Pakistani government needs to develop an institutional structure and ecosystem for R&D spillovers.

• A combined strategy is required to focus on domestic and foreign R&D innovation spillovers both in the public and private sectors.

• Domestic knowledge spillovers can be enhanced through an increase in domestic R&D expenditure, research culture, incentive system, collaboration, and networking within and across the sectors.

• Research alliances are required among research institutions, public and private corporations, which is direly needed to design the incentive and protection mechanism for private sector innovation to encourage future R&D spillovers.

• Linkages among research institutions, industries and extension agents are required to boost the adoptability and capacity to absorb (knowledge capital).

• The government ought to concentrate on the R&D spending, human capital development, and attain a full-employment rate to boost the TFP growth.

Limitations and future research

This study provides valuable insights into the role of R&D spillovers, absorptive capacity, and their impact on sustainable economic growth in Pakistan.

However, it has certain limitations. Firstly, the analysis relies on aggregate national-level data, which may obscure sectoral or firm-level heterogeneities in R&D investment and innovation diffusion. Secondly, data availability restricts the scope of variables, particularly regarding direct measures of absorptive capacity (such as firm-level R&D collaboration, patent data, or innovation outputs), which could have provided deeper insights. Thirdly, the time series approach, although robust, is subject to limitations related to structural breaks, policy shocks, and measurement inconsistencies across different data sources. Finally, the study focuses primarily on the Pakistani context, which may limit the generalizability of findings to other developing economies with distinct institutional and economic structures.

For future research, several promising avenues can be taken into consideration. For instance, sector-specific or firm-level analyses could shed light on how R&D spillovers vary across industries and whether certain sectors (e.g., manufacturing, ICT, or renewable energy) are more effective at leveraging spillovers for productivity and sustainability gains. Comparative cross-country studies, particularly within South Asia, could further illuminate regional differences in absorptive capacity and innovation dynamics. Methodologically, future studies could integrate micro-level survey data, patent statistics, or machine-learning–based approaches to capture hidden patterns in spillover effects. Finally, researchers may also examine the role of institutional reforms, digital transformation, and public–private partnerships in enhancing absorptive capacity and accelerating the transition toward sustainable growth.