Frequency domain analysis of foreign direct investment and economic growth dynamics

This study explores the dynamic, frequency-dependent causal relationship between Foreign Direct Investment (FDI) and Pakistan’s gross domestic product (GDP) over the period 1972–2022. Contrary to the conventional time-domain analyses, it applies the Frequency Domain Spectral Granger Causality approach to capture cyclical patterns and time-varying interactions—an underexamined dimension in Pakistan’s economic literature. The analysis is conducted initially under controlled conditions, excluding key confounding variables, and subsequently extended to incorporate them. The empirical findings yield three key insights. First, FDI exerts a dominant influence on GDP during long-term (> 10-year) and high-frequency (< 3-year) cycles, whereas GDP significantly affects FDI primarily within medium-term (4–9-year) business cycles and periods of economic shocks. Second, the growth dividends of FDI approximately double in contexts of robust financial depth, savings, and labour force participation, but deteriorate sharply when these fundamentals are weak, which highlights the conditional nature of spillover effects. Third, the intensity of causality shifts across frequencies in response to policy and external shocks helped explain inconsistencies in prior linear models. Robustness checks using two-lag MWALD and Toda–Yamamoto VAR models affirm these results. This paper offers the first frequency-specific evidence of FDI–growth dynamics in Pakistan, reconciling previous empirical discrepancies and delivering actionable, time-sensitive policy recommendations: sustain macroeconomic stability and legal frameworks to attract long-cycle FDI; strengthen financial systems and human capital to convert mid-cycle growth into sustained investment; and deploy targeted interventions to mitigate short-cycle volatility.