Urban Resilience Amid Supply Chain Disruptions: A Causal and Cointegration-Based Risk Model for G-7 Cities Post-COVID-19

Abstract

The COVID-19-induced strain on global supply chains led to significant market imbalances and unprecedented inflation, particularly affecting urban economies. Containment policies and stimulus packages resulted in unpredictable demand shifts, challenging urban supply chain planning and resource distribution. These disruptions underscored the need for robust risk management models, especially in cities where economic activity and population density exacerbate supply chain vulnerabilities. This study develops a comprehensive risk model tailored for G-7 urban economies, analyzing the causal and cointegration relationships between key economic indicators. Using Granger causality tests and a factor-augmented vector autoregression (FAVAR) approach, the study examines complex time series and high-dimensional variables, focusing on urban-specific indicators such as the composite leading indicator (CLI) and business confidence indicator (BCI). Our results indicate strong causal relationships among these indicators, validating CLI as a reliable early predictor of urban economic trends. The findings confirm the viability of this urban supply chain risk management model, offering potential pathways for strengthening urban resilience and economic sustainability in the face of future disruptions. This approach positions the study within the context of urban science, emphasizing the impacts on cities and how urban economies can benefit from the developed risk model.

1. Introduction

The global business landscape, facing constant threats from disruptions like the ongoing COVID-19 pandemic, grapples with supply chain challenges, including shortages, financial losses, and demand–supply imbalances. Proactive risk mitigation, through strategic risk analysis and resilient supply chain development, as well as post-crisis recovery [1], is crucial. Learning from past disruptions is vital, necessitating companies to analyze incidents for enhanced resilience. Governments collaborate with businesses to formulate effective risk management plans, emphasizing the importance of seamless public–private sector collaboration. During crises, governments implement varying stimulus packages, underscoring the need for careful planning to prevent supply–demand imbalances and inflation.

To address these challenges, it is vital to classify disruptions based on their origin, such as supply-side, demand-side, or logistics-side disruptions [2]. Various external events can disrupt supply chains, including environmental, geopolitical, economic, and technological factors. In light of these challenges, this paper aims to propose a comprehensive model addressing various components simultaneously using the dataset developed for G7 urban economies (Canada, France, Germany, Italy, Japan, the United Kingdom, and the United States). This model considers the interdependencies among varied factors affecting supply chains. Additionally, the paper incorporates an econometric analysis to study the relationships between the model’s components. By developing a comprehensive approach, this research contributes to an understanding of supply chain vulnerabilities and resilience strategies in the face of disruptions.

To tackle challenges effectively, it is crucial to categorize disruptions by their origin, namely supply-side, demand-side, or logistics-side [2]. Supply chains face disruptions from diverse external events, spanning environmental, geopolitical, economic, and technological factors. This paper proposes a holistic model that addresses multiple components concurrently, recognizing the interdependencies among factors affecting supply chains. Utilizing econometric analysis, the paper explores the relationships between the model’s components. Through this comprehensive approach, the research enhances the understanding of supply chain vulnerabilities and resilience strategies amid disruptions.

Supply chain disruptions, particularly during global crises like the COVID-19 pandemic, have profound effects on economic stability, especially in the urban centers where economic activity is concentrated [3]. The majority of urban cities are economically dominated by the consumer business and transportation and manufacturing sectors [4], which can magnify the impact of such crises on economic stability. Urban economies are more vulnerable to disruptions due to their dependence on global supply chains for goods and services [5]. Previous research highlights the challenges faced by urban areas in managing supply chain risks, exacerbated by population density and logistical constraints [6], pointing out the importance of integrating sustainable practices and urban planning principles to enhance transportation security and supply chain efficiency within urban environments amid global disruptions [7].

Risk management models have increasingly focused on supply chain resilience, emphasizing the importance of real-time data, early warning indicators, and adaptive strategies [8]. Studies on the role of government policies, such as stimulus packages and containment measures, reveal their unintended consequences on supply chains, further complicating risk management efforts [9]. The integration of advanced econometric models, such as Granger causality and factor-augmented vector autoregression (FAVAR), provides valuable insights into the dynamic relationships between economic indicators, helping predict and mitigate future disruptions [10].

While much of the literature addresses national and global scales, fewer studies focus on urban-specific challenges, particularly regarding how city-level economies respond to supply chain shocks. This paper addresses this gap by developing a comprehensive supply chain risk management model, tailored to urban economies in G-7 countries, using key indicators like the composite leading indicator (CLI) and the business confidence indicator (BCI) as predictors of urban economic movements. This study’s innovation lies in its use of Granger causality tests and a factor-augmented vector autoregression (FAVAR) approach to manage high-dimensional urban data, enabling a nuanced detection of the causal relationships among urban-specific indicators. This methodology provides predictive insights and validates CLI as a reliable early indicator for urban economic trends, offering a novel risk management approach designed to strengthen urban resilience in future disruptions.

2. Materials and Methods

2.1. Supply Chain Risk Management Model

Business and government leaders have rarely faced such a dynamic and complex set of volatile conditions in a number of fields simultaneously. This fact creates the necessity to develop a model to help decision-makers design supply chain resilience strategies that consider many interrelated factors. Within the scope of this methodology, the following research question needs to be answered:

Research Question: what is the causal relationship between supply chain resiliency, economic environment, risk management, and infrastructure?

Figure 1 depicts the framework developed in this study to illustrate the complex environment in which decision-makers have to operate while overcoming supply chain challenges in the face of disruptors.

Effective supply chain risk management involves predicting and preventing incidents, addressing risk quantification, information sharing, and enhancing security. Economic policies and government responses add uncertainty, which is integral to risk models. External shocks, like pandemics, underscore the need for preparedness and integrated risk management. Proactive policies targeting supply chain resilience are crucial. Assessing causality relations among the model’s factors in Figure 1 is critical. This study employs a Granger causality test and a factor-augmented vector autoregression (FAVAR) for the nuanced detection of nonlinear, high-order causality and a simultaneous analysis of direction and dynamic connectedness.

To assess the relationships among the model factors, vector autoregression (VAR) on the level and VAR in difference models are utilized for cointegration and causality analysis. The VAR model can be expressed as below:

$$x_t=\alpha +{\varnothing }_1{x}_{t-1}+{\dots +\varnothing }_n{x}_{t-n}+w_t$$

(1)

The classical VAR model becomes challenging even with moderately large dimensions (N and P) [11]. To draw inferences from the high-dimensional VAR model, limiting the parameter space (Equation (1)) to a feasible number of degrees of freedom is essential. However, time-series data exhibit significant temporal and cross-sectional dependency, impacting the accuracy of regularized estimation. To mitigate this, reducing the dimensionality of the model (Equation (1)) is essential. In this study, we implement a factor-augmented method for dimensionality reduction.

2.2. TVP Factor-Augmented Vector Autoregression (FAVAR)

In FAVAR, observable and unobservable factors follow a vector autoregressive process, driving the co-movement of numerous observable variables [12,13]. This method addresses the omitted variable problem and enables the estimation of internally consistent structural impulse response functions (SIRFs) for a wide range of variables.

Researchers have utilized FAVAR in assorted studies. Ramsauer et al. (2019) extended FAVAR to mixed frequency and incomplete panel data, measuring the monetary policy impact on financial markets and the real economy [14]. Wang et al. (2017) used FAVAR with stochastic volatility and time-varying coefficients to create a financial conditions index, analyzing the relationship between future inflation and a composite index of financial indicators [15]. Vargas-Silva (2008) explored the relationship between monetary policy and the housing market using impulse response functions obtained from a FAVAR model [16].

In this study, for the slow-R-fast scheme, certain assumptions are made. COVID-19 effects or news/financial shocks do not immediately affect slow-moving variables such as long-term interest rates, employment, and trade in goods within a given period. Fast-moving variables, such as industrial production and consumer confidence indicators, respond to all types of shocks, including COVID-19 shocks, which are reflected solely in these variables. If multivariate stochastic volatilities are allowed to exist in the factors, then we have a FAVAR model.

The FAVAR model [11] describes the relationship between the observed variables $Y_t$, the unobserved factors $F_t$, and the observable economic variables $X_t$.

$$Y_t={\mathsf{\Phi }}^f{F}_t+{\mathsf{\Phi }}^x{X}_t+{\epsilon }_t$$

(2)

$$\left[\begin{array}{c}{F}_t\\ X_t\end{array}\right]=\psi \left(L\right)\left[\begin{array}{c}{F}_{t-1}\\ X_{t-1}\end{array}\right]+v_t$$

(3)

The model captures the relationship between $Y_t$, $F_t$, and $X_t$ through the lagged relationships represented by $\psi \left(L\right)$. The factor $F_t$ summarizes additional economic information not fully captured by the observable variables $X_t$. The matrices ${\mathsf{\Phi }}^f$ and ${\mathsf{\Phi }}^x$ capture how these factors and observable variables contribute to the observed variables $Y_t$. The model allows for a richer representation of the underlying economic dynamics by incorporating unobserved factors $F_t$, making it more flexible than the traditional VAR models that are based solely on observable variables $X_t$.

3. Empirical Findings

3.1. Data

Cross-country data obtained from the OECD database from February 2010 to September 2022 are used to investigate the causality and cointegration between the factors of the supply chain risk model explained below.

Table 1. Summary of indicators.

	Explanation	Measurement
Industrial production (IP)	Output of industrial establishments.	Change in volume of production output
Unemployment (HUR)	Provides an indication of the economic activity.	Number of unemployed people as a percentage of the workforce
Composite leading indicator (CLI)	Provides early signs of future economic movements.	Amplitude adjusted.
Business confidence indicator (BCI)	Provides insights about future expectations of businesses, measured by surveys.	BCI > 100 suggests an increased confidence in business performance.
Consumer confidence indicator (CCI)	An indication of how consumers feel about their future financial situation.	CCI > 100 indicates an increase in confidence in the future financial situation.
Long-term interest rate	Government bonds maturing in 10 years.	Averages of daily rates, measured as a percentage
Producer price indices (PPI)	Measures the rate of change in product prices as they leave the producer.	Measured in terms of the annual growth rate and index.
Trade in goods (TRG)	All goods which add to or subtract from the stock of material resources of a country through exports or imports.	Measured in million USD

summarizes the indicators and their explanations for the data spanning 56 dimensions.

The selection of the three key indicators, namely the composite leading indicator (CLI), the business confidence indicator (BCI), and the unemployment rate (HUR), reflects their critical roles in capturing early signals, confidence levels, and economic stability, which are essential for managing supply chain risks and urban resilience. The CLI is widely used as an early warning signal for economic shifts, making it valuable for preemptive risk management in volatile urban environments [17]. By signaling future economic trends, CLI can help urban policymakers and businesses anticipate supply chain issues before they fully develop, allowing for more proactive response strategies. The BCI reflects the expectations of businesses about the economy’s near-term future, which is crucial for supply chain resilience [18]. High business confidence can indicate readiness to invest and sustain operations, while low confidence suggests potential contractions and hesitancy in decision-making, which could strain supply chains and affect urban economies more broadly. The BCI is particularly valuable for understanding the psychological and behavioral components that impact economic stability and resilience. Unemployment (HUR) is a fundamental indicator of economic health and stability. High unemployment often indicates reduced economic resilience [19], as consumer demand declines and social instability may increase, affecting urban supply chains. Unemployment levels also impact labor availability, which is directly tied to supply chain efficiency and resilience, particularly in labor-dependent sectors like manufacturing and logistics. These indicators collectively offer a broad, yet targeted, view of economic trends, business sentiment, and labor dynamics. Together, they help capture the multifaceted challenges that urban economies face during disruptions, enabling a more comprehensive approach to modeling resilience.

3.2. Results

This section initiates by illustrating the causal relationships among the indicators listed in Table 1. The model summary for the G7 countries is detailed in

Table 2. Model summary.

	BCI	CCI	CLI	HUR	PPI	TRG
BCI.l1	(0.166) ***	(0.185) ***	(0.249) *	(0.212) ***
CCI.l1	(0.140) ***		(0.210) **
CLI.l1		(0.150) *
HUR.l1					−1.001 ***	−3.589 ***
PPI.l1		(0.037) *			(0.228) ***	(0.818) ***
TRG.l1				(0.010) **	(0.051) ***	(0.183) ***
BCI.l2	(0.169) ***		(0.253) *
CCI.l2
CLI.l2					(0.919) *	−3.293 **
HUR.l2	(0.165) ***	(0.184) **	(0.247) ***
PPI.l2	(0.034) ***	(0.038) **	(0.052) ***
TRG.l2	(0.008) ***		(0.012) **
BCI.l3					−1.155 *
CCI.l3
CLI.l3	(0.127) **	(0.141) *	(0.190) *		(0.862) *
HUR.l3	(0.135) ***	(0.150) ***	(0.202) ***		(0.915) **	−3.280 *
PPI.l3		(0.037) *
TRG.l3
const	−31.456 ***		−47.133 ***	−40.145 *
R2	0.626	0.755	0.492	0.739	0.765	0.713
Adj. R2	0.574	0.721	0.422	0.702	0.733	0.673

p values. *** at 1%, ** at 5%, and * at 10% levels of significance.

.

The results reveal robust two-way relationships between the unemployment rate, the producer price indices, and trade in goods at a 1% significant level. Similarly, a significant correlation exists between the consumer confidence indicator and the business confidence indicator. Notably, a causal relationship emerges between trade in goods, the unemployment rate, and the composite leading indicator at a 5% significance level.

A concise summary of the empirical findings regarding the indicators’ effects on the FAVAR model is presented below. For detailed results, refer to

Table 3. FAVAR estimation results for three factors.

Equation	Dim.1	Dim.2	Dim.3	G7_BCI	G7_CCI	G7_CLI	G7_HUR	G7_PPI	G7_TRG
p-value	<2.2 × 10−16	<2.2 × 10−16	<2.2 × 10−16	<2.2 × 10−16	<2.2 × 10−16	<2.2 × 10−16	<2.2 × 10−16	<2.2 × 10−16	<2.2 × 10−16
R2	0.9922	0.9794	0.9521	0.9958	0.9975	0.9816	0.989	0.9967	0.9409

and

Table 4. FAVAR estimation results for four factors.

Equation	Dim.1	Dim.2	Dim.3	Dim.4	G7_BCI	G7_CCI	G7_CLI	G7_HUR	G7_PPI	G7_TRG
p-value	<2.2 × 10−16	2.37 × 10−13	1.47 × 10−10	5.03 × 10−7	<2.2 × 10−16	<2.2 × 10−16	1.36 × 10−14	<2.2 × 10−16	<2.2 × 10−16	2.22 × 10−9
R2	0.9923	0.9764	0.9527	0.8824	0.9961	0.9982	0.9826	0.9919	0.9978	0.9362

, which summarize the estimation results for three and four factors, respectively. Table 3 and Table 4 present the FAVAR results for three-factor and four-factor models, respectively, allowing for a direct comparison of the two approaches.

Three dimensions explain the variation in BCI, CCI, CLI, HUR, PPI, and TRG with extremely high significance (p-values < 2.2 × 10⁻¹⁶ for all equations). The R² values for all equations are very high, ranging from 0.9409 for TRG to 0.9975 for CCI. This suggests that the three-factor model captures most of the variance in these economic indicators, leading to the conclusion that a three-factor FAVAR model effectively captures the dynamics of the indicators with excellent explanatory power across the board.

Table 4 shows that adding a fourth factor slightly reduces the explanatory power for some variables, particularly for Dimension 4 (R² = 0.8824) and TRG (R² = 0.9362). While the p-values remain highly significant across all factors and indicators, some degradation in fit occurs compared to the three-factor model, showing that the four-factor model leads to marginal improvements in fit for certain indicators (e.g., CCI and BCI), but overall, the three-factor model provides a more effective explanation.

Figure 2 displays the scree plot, illustrating the variation captured by each principal component from the data. The percentages indicate three factors (>10%) for the FAVAR model, while the “elbow” rule suggests four factors.

Figure 3, Figure 4, Figure 5, Figure 6 and Figure 7 provide a visual representation of the impulse response functions (IRFs) and variable responses in the FAVAR model, facilitating a more detailed comparison of the results. Figure 3 depicts the trends of the three and four factors, revealing the adverse effects of the 2020 COVID-19 pandemic and marked by a deep V shape occurring from January to June 2020 in the second factor.

Figure 4 and Figure 5 provide a visual representation of the impulse response functions (IRFs) and variable responses in the FAVAR model. The IRFs show the response of each variable to a one-standard-deviation shock to each of the other variables. For example, Figure 3 shows the IRF of a pair of variables in an off-diagnostic subgraph. A positive shock to the variable BCI leads to a mixed response in the CCI, which peaks after two periods and then declines for 10 periods, even to a negative response at period 8 before increasing again. A positive shock to the variable CCI leads to a positive-response TRG, which peaks after 15 periods. A positive shock to the variable PPI leads to a negative response in the TRG, which keeps a downward trend for the whole period.

The curves above the red line in Figure 3 indicate a positive relationship, while the curves below the red line show a negative one.

Table 5. Pairwise relationships of three-factor IRFs.

	BCI	CCI	CLI	HUR	PPI	TRG
BCI		Mixed	Mixed	Mixed	Positive	Mixed
CCI			Mixed	Mixed	Negative	Positive
CLI				Mixed	Mixed	Mixed
HUR					Mixed	Mixed
PPI						Negative
TRG

For instance, TRG and CCI, as well as PPI and BCI, show a positive relationship, while CCI and PPI show a negative relationship. Some relationships are mixed in different periods.

summarizes the pairwise relationships between the variables.

Figure 6 and Figure 7 present IRFs and response figures for four factors from the FAVAR model, respectively. Figure 6 suggests the presence of a singular dynamic factor that translates into three distinct static factors. These factors respond to various structural shocks, and their reactions to these shocks differ significantly. This structural instability might result in the generation of excessively numerous static factors, potentially leading to misleading conclusions or interpretations in the analysis.

Table 6. Pairwise relationships of four-factor IRFs.

	BCI	CCI	CLI	HUR	PPI	TRG
BCI		Negative	Mixed	Negative	Positive	Mixed
CCI			Mixed	Negative	Negative	Positive
CLI				Mixed	Mixed	Mixed
HUR					Mixed	Mixed
PPI						Negative
TRG

summarizes the pairwise relationships of four-factor IRFS between the variables.

As it can be observed, the relationship between variables is not changed greatly between three- and four-factor IRFs with only minor changes in magnitude, which accurately depicts the dynamic relationships that exist [18]. For instance, a significant increase in PPI can signal rising manufacturing costs, which in turn, can lead to higher prices, potentially influencing demand. Meanwhile, a high BCI can sometimes result in increased production, which can increase demand for raw materials, potentially increasing producer prices and impacting the PPI.

4. Discussion and Conclusions

The contribution of the proposed model is its ability to consider the interdependencies among the varied factors affecting supply chains. Additionally, the paper incorporates an econometric analysis to study the relationships between the model components. By developing a comprehensive approach, this research contributes to the understanding of supply chain vulnerabilities and resilience strategies in the face of disruptions. The advantage of the FAVAR method is that it addresses the omitted variable problem and enables the estimation of internally consistent structural impulse response functions for a wide range of variables. Observable and unobservable factors follow a vector autoregressive process, driving the co-movement of numerous observable variables.

The results show that past values of economic indicators, especially BCI, CCI, HUR, and PPI, play crucial roles in predicting future movements. The three-factor FAVAR model offers a highly effective explanation of the dynamics of these indicators, with near-perfect fit (R² values exceeding 0.95 for most indicators). Adding a fourth factor adds complexity without significant improvement. This analysis suggests that economic confidence, unemployment rates, and price indices are tightly interconnected, and understanding their historical data helps forecast future trends effectively.

This study introduces a comprehensive model that incorporates supply chain disruption indicators and response capabilities, including those of governments. Faced with the challenges of high-dimensional data in supply chain modeling and the limitations of conventional economic theory models, we employ a Granger causality test and a FAVAR model for empirical analysis, enhancing the traditional state-space model VAR. Utilizing a dataset spanning from 2010 to 2022 with eight variables for the G-7 countries, the FAVAR model explores relationships amid external shocks, bridging data-driven empirical models with theoretical frameworks and advancing our understanding of economic dynamics.

The proposed supply chain risk management model, grounded in economic and management theories, is validated through Granger tests and the FAVAR model. While the empirical results affirm the model’s viability, further research avenues are identified. Future studies may expand the model by incorporating additional indicators related to risk management policies, external factors, infrastructure, economic environment, government response, and supply chain resilience. Additionally, extending the research scope to include diverse global regions would allow for testing the model on countries with varying economic, political, and environmental characteristics.