The Impact of Socioeconomic and Environmental Indicators on Economic Development: An Interdisciplinary Empirical Study

Abstract

This paper aims to investigate the effects of environmental sources and health statistics on economic growth and other development indicators of interest. With population growth, urbanization, and industrialization of economies, the built environment for human health has emerged as an important and growing driver in interdisciplinary research and evidence-based policy development, improving a country’s growth prospects and the standard of living. A compressed structural Panel Vector Autoregression is used to address these issues. Methodologically, a hierarchical semiparametric Bayesian approach is involved to reduce the dimensionality, overtake variable selection problems, and model stochastic volatility. Policy-relevant strategies are also addressed to investigate causal relationships between sustainability indicators and economic growth.

1. Introduction

Interdisciplinary research refers to a significant transformation of knowledge through the integration of ideas and tools addressed by two or more research projects. In this study, methodological findings achieved in compressed regression models are combined for undertaking research on development and environment, and cross-country effects that this involves (see, e.g., Lawrence 2004; Handy et al. 2008; Briassoulis 1997; Max-Neef 1995; Reed et al. 2006; Turcu 2013; McNeill 1999, and Oreskes et al. 1994). The empirical application evaluated by means of more than hundreds of macroeconomic–financial and socioeconomic variables in a pool of advanced and developing countries describes the estimating procedure. It approaches three main macroeconomic issues: (i) the existence of (potential) causal relationships between health and environment indicators among developed and developing countries; (ii) the presence of unobserved cross-country interlinkages and dynamic feedback over time; and (iii) the role of economic–financial factors and policy issues when studying multicountry economic dynamics in panel setups.

Let the evidence on the role of the built environment in promoting human health, infrastructure, and manufacturing services be known, while the study of causal relationships between healthy built environments and other economic–financial variables of interest is also compelling. Indeed, in recent decades, much progress has been achieved in connecting the people of the world to reliable improvements in health, highlighting an existing causal effect on economic growth, poverty, and other development indicators of interest (see, e.g., McLeroy et al. 1988; Stokols 1996; Sallis et al. 2006; Pilkington et al. 2008 and Vecchiarelli et al. 2005). However, empirical evidence of the causal effect of health and the built environment on economic growth is weak and most existing studies found contrasting and inconclusive results because of inappropriate methodological approaches, shorter time series to investigate potential causal effects, and high attention toward developed countries (see, among many others, Granger 1969; Lütkepohl 1982; D’Acci 2011; and Diener and Suh 1997). Even if it would be simpler to find evidence for causal effects using disaggregated micro-level data because some variables can more easily be considered exogenous and other field experiments are possible, growth is an economy-wide, dynamic, and long-term process with effects that are unlikely to be captured in micro setups (see, among many others, Borenstein 2015; Dobbie and Dail 2012; Freebairn and King 2003; and Niemeijer and Groot 2008). Thus, cross-country macroeconomic–financial linkages and interactions need to be dealt with (see, for instance, Barro 2003; Canova and Ciccarelli 2009, 2016; Canova and Forero 2015; Pacifico 2019, 2020a, 2021).

Most empirical analysis has been conducted on the economic implications of healthy built environments in developed countries by considering health as an important driver of economic growth when they have been at lower income levels (see, for instance, Gahin et al. 2003; Jesinghaus 2012 and Singh et al. 2009). Over time, growing evidence has shown that the two seemingly disparate professions can work together, continuing to improve their collaborative endeavors and support the ongoing development of the interdisciplinary practice of healthy planning (see, for instance, McLeroy et al. 1992; Macintyre et al. 2002; Thompson 2000; Wooten 2010 and Krajnc and Glavič 2005). Nevertheless, some shortcomings of these studies are that they ignore possible endogeneity and spatial interdependence between the built environment and health problems (such as hypertension, depression, obesity), negatively affecting economic development and labor market performance (see, e.g., Feng et al. 2010; Brownson et al. 2006; Dodson et al. 2009; Black and Macinko 2008 and Coveney and O’Dwyer 2009). Recent studies highlighted the strict relationship between physical appearance and economic growth, affecting—in turn—the individual’s capacity to work (see, e.g., Böckerman et al. 2019; Cawley 2015; Puhl and Brownell 2001 and Angrisani et al. 2018). Indeed, obese workers could be related to non-desirable personality traits potentially, resulting in worse labor market outcomes (see, e.g., Hamermesh and Biddle 1994; Baum and Ford 2004; Rooth 2009 and Sobal 2004).

The computational approach proposed in this paper focuses on the aforementioned issues and aims to deepen the topic of the causal relationship between socioeconomic indicators, economic development, and macroeconomic variables of interest. It is evaluated building on Pacifico (2022b)’s analysis, which estimated a Structural Bayesian Compressed Panel Vector Autoregressive (SBCPVAR) model with time-varying parameters and multivariate stochastic volatilities. Conversely to the standard Bayesian compressed regression and VAR models, it involves a shrinking open robust Bayesian Model Averaging (BMA) procedure. Here, open refers to the use of Markov Chain Monte Carlo (MCMC) algorithms rather than recursive discriminant analysis, and robust stands for the construction of multivariate conjugate informative priors rather than single priors. In this way, a large panel of data accounting for different areas of research can be included in the system and jointly evaluated minimizing some high-dimensional problems such as endogeneity and model misspecification.

The contributions of this paper are threefold. First, semiparametric prior specification strategy is developed using multivariate Conjugate Informative Proper Mixture (mvCIPM) priors to select the best1 model solution (or combination of predictors) fitting the data (see, for instance, Pacifico 2020b). Second, MCMC algorithms based on Posterior Model Probabilities2 (PMPs) are used to construct posterior distributions and shrink jointly parameter and model space to perform business strategies and policy issues. Third, a generalized version of the Granger (Non-)Causality test is conducted in the reduced subset of predictors to verify whether strong causal relationships matter for a subgroup of units (see, e.g., Dumitrescu and Hurlin 2012 concerning dynamic panel data).

An interdisciplinary empirical study is conducted involving large panel sets of macroeconomic, environmental, and socioeconomic variables in a pool of advanced and developing countries. The main thrust is to combine some open research issues in accordance with the impact of environment source, health statistics, and other development indicators of interest in economic growth. Potential causal relationships and policy issues between the most suitable subset of predictors can also be investigated. The empirical strategy covers the period 1995–2020, where natural conjugate priors are involved in dealing with potential (unobserved) structural breaks: 2007, due to the global financial crisis; 2011–2014, due to fiscal recovery programs; and 2019 due to the COVID-19 pandemic. Forecasting is then conducted over a time frame of nine quarters (two years and a quarter) to absorb spillover effects affecting cross-country economic dynamics due to the economic and social disruption caused by the pandemic and Russia-Ukraine war.

The outline of this paper is as follows. Section 2 discusses the econometric methodology and the Bayesian strategy, clarifying prior assumptions and posterior distributions involved in the dynamic analysis. Section 3 illustrates the cross-country empirical analysis, emphasizing the role of the built environment in promoting human health sources, and how possible causal links between socioeconomic indicators and economic development matter. Section 4 contains some concluding remarks.

2. Econometric Methodology

2.1. Estimation Procedure

The multicountry SPBVAR model used in this study has the form:

$$Y_{im,t}=\sum _{\lambda =1}^l\left[A_{im,j\tilde{m}}(L)Y_{im,t-\lambda }+B_{i\xi ,j\tilde{\xi }}(L)Z_{i\xi ,t-\lambda }\right]+{\epsilon }_{im,t},$$

(1)

where the subscripts $(i,j)=1,2,\dots ,N$ and $t=1,2,\dots ,T$ are country indices and time periods, respectively, $m=1,2,\dots ,M$ and $\xi =1,2,\dots ,\Xi$ refer to the variables included in the system for i, with $\tilde{m}=1,2,\dots ,\tilde{M}$ and $\tilde{\xi }=1,2,\dots ,\tilde{\Xi }$ denoting the indices observed for j independent of i, $\lambda =1,2,\dots ,l$ denotes lagged periods, $Y_{im,t}$ is a $NM·1$ vector of observed outcomes to be predicted for each i, $Y_{im,t-\lambda }$ and $Z_{i\xi ,t-\lambda }$ are $NM·1$ and $N\Xi ·1$ vectors of observed lagged variables and additional lagged factors for each i for a given m and $\xi$, respectively, $A_{im,j\tilde{m}}$ and $B_{i\xi ,j\tilde{\xi }}$ are $NM·NM$ and $N\Xi ·N\Xi$ matrixes of time-varying coefficients for each pair of countries $(i,j)$ for a given m and $\xi$, respectively, and ${\epsilon }_{im,t}\sim i.i.d.N(0,{\mathsf{\Omega }}_t)$ is a $NM·1$ vector of heteroschedastic unobservable shocks with variance-covariance matrix ${\mathsf{\Omega }}_t$.

To investigate the effects of health and environment indicators on economic growth and potential relationships with other development factors, we decompose the variables in a conditioning set $c_{it,j}$: $Y_{im,t-\lambda }={\left[Y_{im,t-\lambda }^{o^{\prime }},Y_{im,t-\lambda }^{c^{\prime }}\right]}^{{}^{\prime }}$, with $Y_{im,t-\lambda }^{o^{\prime }}$ denoting lagged outcomes such as economic growth and $Y_{im,t-\lambda }^{c^{\prime }}$ including lagged control variables such as economic development indicators; and $Z_{i\xi ,t-\lambda }={\left[Z_{i\xi ,t-\lambda }^{s^{\prime }},Z_{i\xi ,t-\lambda }^{h^{\prime }}\right]}^{{}^{\prime }}$, referring to additional factors such as socioeconomic conditions ($Z_{i\xi ,t-\lambda }^{s^{\prime }}$) and health issues ($Z_{i\xi ,t-\lambda }^{h^{\prime }}$). Then, let $k=[M+\Xi ]·l$ correspond to the number of all matrix coefficients in each equation of model (1), with $k=1,2,\dots ,\overline{k}$, I group all covariates into a $1·Nk$ vector $X_t={(Y_{im,t-1}^{{}^{\prime }},Y_{im,t-2}^{{}^{\prime }},\dots ,Y_{im,t-l}^{{}^{\prime }},Z_{i\xi ,t-1}^{{}^{\prime }},Z_{i\xi ,t-2}^{{}^{\prime }},\dots ,Z_{i\xi ,t-l}^{{}^{\prime }})}^{{}^{\prime }}$ and all time-varying parameters into a $NM·Nk$ matrix ${\mathsf{\Theta }}_t=(A_{im,j1},A_{im,j2},\dots ,A_{im,j\tilde{M}},B_{i\xi ,j1},B_{i\xi ,j2},\dots ,B_{i\xi ,j\tilde{\Xi }})$.

Four important features matter. First, the use of a hierarchical framework and variable selection procedure to make the model (1) feasible and reliable because of (possible) different dimensions between matrixes ($A_{i,j},B_{i,j}$). Second, the use of random walk processes ensures that multiple change points are evaluated when modeling time-varying coefficients and shrinking a large set of indicators in a lower-dimensional space. Third, even if the block diagonality of ${\mathsf{\Sigma }}_{\delta }$ guarantees the identifiability of the ${\delta }_t$’s, Bayesian inference is involved to also identify excessive volatility changes and replace them by coefficient changes, where excessive stands for a sudden high time-varying volatility. The latter is evaluated using the excess kurtosis index according to the information over the past. Fourth, the heteroscedasticity imposed in the variance-covariance matrix of ${\epsilon }_{i,t}$ is able to capture potential unobserved shocks (impulse) among variables and countries affecting outcomes (response). Indeed, when studying macroeconomic–financial linkages and other related socioeconomic–development indicators, the model (1) would involve multiple and multivariate structural breaks. Thus, the error terms in (1) are rewritten as

$${\epsilon }_{i,t}={\Delta }_t·{\omega }_{i,t}\mathrm{with}{\mathsf{\Omega }}_t={\Delta }_t{\Delta }_t^{{}^{\prime }},$$

(2)

where ${\Delta }_t$ is an $NM·Nk$ matrix with elements equal to (absence of volatility changes) or different from (presence of volatility changes) zero, and ${\omega }_{i,t}\sim N(0,I_{Nk})$ is a $Nk·1$ vector for each set of variables $(m,\xi )$. Let ${\delta }_{i,t}=vec({\Delta }_t)=vec{(d_{im,j1}^{{}^{\prime }},d_{im,j2}^{{}^{\prime }},\dots ,d_{im,j\overline{k}}^{{}^{\prime }})}^{{}^{\prime }}$ be a $NMK·1$ vector, with $K=Nk$, containing the elements of the matrix ${\Delta }_{i,t}$ stacked by columns, the parameter ${\delta }_{i,t}$ is modeled as a random walk process:

$${\delta }_t={\delta }_{t-1}+v_t\mathtt{where}{v}_t\sim N(0,{\mathsf{\Sigma }}_{\delta }),$$

(3)

where ${\mathsf{\Sigma }}_{\delta }=diag({\sigma }_{d_{im,j1}}^2,{\sigma }_{d_{im,j2}}^2,\dots ,{\sigma }_{d_{im,j\overline{k}}}^2)$ is a block diagonal covariance matrix of size $NM·K$, and ${\delta }_0$ denotes the initial conditions to be estimated.

With these specifications, model (1) can be expressed in a simultaneous-equation form:

$$Y_t={\mathsf{\Theta }}_t{X}_t^{{}^{\prime }}+{\Delta }_t{\omega }_{i,t},$$

(4)

where $Y_t={(Y_{1m,t}^{{}^{\prime }},\dots ,Y_{Nm,t}^{{}^{\prime }})}^{{}^{\prime }}$ and $X_t^{{}^{\prime }}$ is a $NM·1$ vector containing the observable variables of interest. Let ${\gamma }_t=vec({\mathsf{\Gamma }}_t)$ be a $NMK·1$ vector containing the time-varying parameters and volatilities stacked into a vector, where ${\mathsf{\Gamma }}_t=({\mathsf{\Theta }}_t,{\Delta }_t)=(A_{im,j1},{\Delta }_t,A_{im,j2},{\Delta }_t,\dots ,$$A_{im,j\tilde{M}},{\Delta }_t,B_{i\xi ,j1},{\Delta }_t,B_{i\xi ,j2},{\Delta }_t,\dots ,B_{i\xi ,j\tilde{\Xi }},{\Delta }_t)$ is an auxiliary $NM·Nk$ matrix built to combine the coefficient vectors of ($A_{i,t},B_{i,j}$) with the elements of ${\Delta }_t$. The reduced form in (4) can be rewritten in a compressed regression form:

$$Y_t={\mathsf{\Gamma }}_t\left(X_t^{{}^{\prime }}+{\omega }_{i,t}\right).$$

(5)

The variable selection procedure entails when some unknown subset of $X_t$—grouped in ${\gamma }_t$—is so small that it would be preferable to discard it (${\gamma }_t=0$). In this framework, two auxiliary indicator variables are used: $N\phi ·1$ vector ${\varphi }_t$ containing the compressed ${\gamma }_t$’s parameters (${\gamma }_t^c$) and a $NMK·1$ vector ${\beta }_t$ containing all $2^K$ possible model solutions, with $\phi \ll K$ denoting the compressed regression coefficients. Furthermore, the ${\gamma }_t^c$’s parameters are assumed to follow the below factor structure:

$${\gamma }_t^c={\mathsf{\Phi }}_t·{\varphi }_t+u_t,$$

(6)

where $dim({\varphi }_t)\ll dim({\gamma }_t)$ by construction, $N\varphi \ll NMK$ denotes the length of the lower-dimensional parameter space obtained through the shrinking process, ${\mathsf{\Phi }}_t$ is a $NMK·N\phi$ conformable matrix with elements equal to zero (absence of K-th covariate in the model) and one (presence of K-th covariate in the model), and $u_t$ is a $NMK·1$ vector of disturbances. Both the auxiliary variable ${\varphi }_t$ and the error term $u_t$ are supposed to be distributed as further random walk processes:

$${\varphi }_t={\varphi }_{t-1}+{\eta }_t\mathrm{with}{\eta }_t\sim N(0,{\mathsf{{\rm Y}}}_t);$$

(7)

$$u_t=u_{t-1}+{\varsigma }_t\mathrm{with}{\varsigma }_t\sim N(0,{\mathsf{\Sigma }}_u).$$

(8)

Here, ${\mathsf{\Sigma }}_u=V·{\sigma }_t$, with $V={\sigma }^2·I_{NMK}$ as in Kadiyala and Karlsson (1997) and ${\sigma }_t\cong {\mathsf{\Omega }}_t\otimes (X_t^{{}^{\prime }}{X}_t)$ denoting (potential) volatility changes, ${\mathsf{{\rm Y}}}_t=diag({\mathsf{{\rm Y}}}_{mt,1},{\mathsf{{\rm Y}}}_{mt,2},\dots ,{\mathsf{{\rm Y}}}_{mt,\overline{k}})$ is a block diagonal matrix, with ${\mathsf{{\rm Y}}}_{mt,k}=({\upsilon }_{mt,k}·I_{NMK})$ and ${\upsilon }_{mt,k}$ controlling the stringent conditions of the shrinking process to make the time-varying ${\gamma }_t^c$’s regression coefficients estimable. The error terms $u_t$ and ${\upsilon }_t$ are correlated between them by construction, but ${\eta }_t$ and ${\upsilon }_t$ can be uncorrelated.

Finally, according to the factorization in (6) and let ${\tilde{X}}_t=I_{NM}\otimes (X_t+{\omega }_{i,t}^{{}^{\prime }})$ be an $NM·NMK$ matrix containing all (lagged) time-varying variables and volatilities stacked in $X_t$ and ${\omega }_{i,t}$, respectively, the compressed regression model in (5) can be better displayed in the form of a Compressed Seemingly Unrelated Regression (CSUR) model:

$$Y_t={\tilde{X}}_t\left[\left({\mathsf{\Phi }}_t·{\varphi }_t\right)+u_t\right]\equiv {\chi }_t^c{\varphi }_t+E_t^c,$$

(9)

where ${\chi }_t^c\equiv ({\tilde{X}}_t·{\mathsf{\Phi }}_t)$ are $NM·N\phi$ matrixes stacking all coefficients and their possible interactions evaluated in (1), and $E_t^c\equiv {\tilde{X}}_t·u_t$ is an $NM·1$ vector disturbance terms.

2.2. Shrinking Procedure

The main thrust of the variable selection procedure is to discard the ${\gamma }_t$’s predictors from the procedure when sufficiently small, and then obtain a lower-dimensional parameter space of size $N\varphi \ll NMK$.

Let $M_K=(M_{i1},M_{i2},\dots ,M_{i\overline{k}})$ be a countable collection of all (potential) $2^K$ model solutions—evaluated through the auxiliary parameter ${\gamma }_t$—the full model class set is:

$$\mathcal{F}=\left\{M_K:M_K\subset \mathcal{F},M_K\in \mathcal{M},k\in \mathcal{K},{\mathsf{\Theta }}_t{X}_t^{{}^{\prime }}+{\Delta }_t{\omega }_t\right\},$$

(10)

where $\mathcal{M}$ and $\mathcal{K}$ denote the multidimensional natural model and parameter space, respectively. Thus, the related probability of each candidate model in fitting the data (PMPs) are defined as:

$$\pi (M_K|Y_t)=\frac{\pi (Y_t|M_K)·\pi (M_K)}{{\sum }_{M_K\in \mathcal{M}}\pi (Y_t|M_K)·\pi (M_K)},$$

(11)

where $\pi (Y_t|M_K)=\int \pi (Y_t|M_K,{\varphi }_t)·\pi ({\varphi }_t|M_K)d{\varphi }_t$ is the marginal likelihood, and $\pi ({\varphi }_t|M_K)$ is the conditional prior distribution of ${\varphi }_t$ given $M_K$. However, when N is high-dimensional and T sufficiently large, the calculation of the integral $\pi (Y_t|M_K)$ is unfeasible, and then a prior specification strategy and MCMC algorithms have to be involved.

Conversely to Pacifico (2022b), in this study, the final model solution is obtained in a unique step, and causal relationships are then tested on the compressed subset of predictors. Thus, the full set in (6) will be reduced in a lower-dimensional model class:

$$\mathcal{E}=\left\{M_F:M_F\subset \mathcal{E},\mathcal{E}\subset \mathcal{F},\sum _{M_K\in \mathcal{M}}\pi (M_F|Y_t,{\varphi }_t)\ge \tau \right\},$$

(12)

where $M_F$ denotes the subset containing the best model solutions of the CSUR in (9), with $M_F<M_K$, $F\ll K$, $\{1\le \phi <k\}$, and $\tau$ referring to an arbitrary threshold for achieving enough posterior consistency. In this study, $\tau =1\%$, resulting in being (slightly) more restrictive than that used in Pacifico (2022b). More precisely, the choice is because of high-dimensional N, much larger than the observational units used in Pacifico (2022b)’s case study (43 vs. 24), and more time periods T (129 vs. 117). Moreover, the aim of this study consists of addressing an interdisciplinary empirical study when combining more than one assignment (such as environment source, health issues, and development indicators). Thus, problems related to the overestimation of effect sizes (or individual combinations) and dynamic interactions (or cross-term lagged interdependencies) have to also be dealt with.

The shrinking procedure is completed by choosing the best final model solution. It corresponds to one of the submodels $M_F$ with higher log natural Bayes Factor (lBF):

$$lB{F}_{\phi ,k}=log\left\{\frac{\pi (M_F|Y_t)}{\pi (M_K|Y_t)}\right\}.$$

(13)

In this analysis, the lBF is interpreted according to the scale evidence in Pacifico (2022b) but with fewer restrictions to deal with some data-mining concerns such as different kinds of knowledge in databases, presence of noisy or incomplete data, and pattern evaluation:

$$\left\{\begin{array}{cc}0\le lB{F}_{\phi ,k}<1.99\hfill & \mathrm{no}\mathrm{evidence}\mathrm{for}\mathrm{submodel}{M}_F\hfill \\ 3\le lB{F}_{\phi ,k}<4.99\hfill & \mathrm{moderate}\mathrm{evidence}\mathrm{for}\mathrm{submodel}{M}_F\hfill \\ 6\le lB{F}_{\phi ,k}<7.99\hfill & \mathrm{strong}\mathrm{evidence}\mathrm{for}\mathrm{submodel}{M}_F\hfill \\ lB{F}_{\phi ,k}\ge 8.00\hfill & \mathrm{very}\mathrm{strong}\mathrm{evidence}\mathrm{for}\mathrm{submodel}{M}_F\hfill \end{array}\right.$$

(14)

2.3. Dynamic Investigation

The variable selection procedure entails estimating the parameters (${\mathsf{\Sigma }}_{\delta },{\delta }_t,{\varphi }_t,{\beta }_t,{\upsilon }_t$) as posterior means3. Then, mvCIPM priors are used to hierarchically model them:

$$\pi \left({\mathsf{\Sigma }}_{\delta }^{-1},{\delta }_0,\varphi ,{\upsilon }_0\right)=\pi \left({\mathsf{\Sigma }}_{\delta }^{-1}\right)·\prod _F\pi ({\delta }_0)·\pi (\varphi )·\prod _F\pi ({\upsilon }_0),$$

(15)

where

$$\pi \left({\mathsf{\Sigma }}_{\delta }|Y_t\right)=IIG\left(\frac{\overline{\omega }}{2},\frac{\overline{D}}{2}\right),$$

(16)

$$\pi ({\delta }_0|{\mathcal{F}}_{t-1})=N(0,\varkappa ),$$

(17)

$$\pi ({\varphi }_t|{\mathsf{\Sigma }}_{\delta },Y_t)=N\left({\overline{\varphi }}_{t-1|t-1},{\overline{R}}_{t-1|t-1}\right),$$

(18)

$$\pi ({\upsilon }_0|{\mathcal{F}}_{t-1})=IG\left(\frac{{\vartheta }_0}{2},\frac{S_0}{2}\right).$$

(19)

Here, $N(·)$ and $IG(·)$ stand for Normal- and Inverse-Gamma distribution, respectively, ${\mathfrak{F}}_{t-1}$ refers to the information given up to time $t-1$, ${\mathsf{\Sigma }}_{\delta }$ in (16) is modeled through an Independent Inverse Gamma (IIG) distribution to disentangle the dependency between ${\varphi }_t$ and ${\mathsf{\Sigma }}_{\delta }$, with ${\overline{\omega }}_0$ and ${\overline{D}}_0$ denoting the initial conditions to be estimated, and $\varkappa$ in (17) denotes the decay factor. This latter usually varies in the range [0.9–1.0] and controls the process of reducing past data by a constant rate over a time period. Finally, let the data run ($t=0$) to ($t=T$) with training sample $\{t-1,0\}$, and the hyperparameters in identifying $\varphi$ in (18) are further modeled via a variant of the Gibbs sampler approach (Kalman-filter technique):

$$\pi ({\varphi }_t|{\varphi }_{t-1},Y_t)=N\left({\overline{\varphi }}_{t|t},{\overline{R}}_{t|t}\right),$$

(20)

where ${\overline{\varphi }}_{t|t}$ and ${\overline{R}}_{t|t}$ denote the conditional distribution of ${\varphi }_t$ and its variance-covariance matrix at time t given the information over the sample $\{t-1,0\}$, respectively. All the hyperparameters involved in the mvCIPM priors are known and collected into a vector $\varrho =({\omega }_0,D_0,{\vartheta }_0,S_0)$4.

The conditional posterior distribution of (${\varphi }_1,\dots ,{\varphi }_T|Y_T$) is obtained from forward recursions for posterior means (${\overline{\varphi }}_{t|t+1}$) and covariance matrix (${\overline{R}}_{t|t+1}$):

$$\pi ({\varphi }_t|{\varphi }_{t-1},Y_T)=N\left({\overline{\varphi }}_{t|t+1},{\overline{R}}_{t|t+1}\right).$$

(21)

According to Pacifico (2022b), the other posterior distributions are defined as:

$$\pi \left({\mathsf{\Sigma }}_{\delta }|Y_T\right)=IIG\left(\frac{\widehat{\omega }}{2},\frac{\widehat{D}}{2}\right),$$

(22)

$$\pi (\delta |Y_T)=N(0,\widehat{\varkappa }),$$

(23)

$$\pi (\upsilon |Y_T)=IIG\left(\frac{\overline{\vartheta }}{2},\frac{\overline{S}}{2}\right).$$

(24)

Evaluating an interdisciplinary empirical study over a large set of different indicators, some restrictions on the estimated hyperparameters are accounted for. In Equation (22), $\widehat{\omega }=\overline{{\omega }_0}·\overline{\omega }$ and $\widehat{D}={\overline{D}}_0·\overline{D}$, with $\overline{{\omega }_0}\cong 0.001$, ${\overline{D}}_0\cong 0.90$, and $\varkappa =0.90$. In this study, initial conditions of ${\overline{D}}_0$ and the decay factor coincide to ensure identification. In Equation (23), $\widehat{\varkappa }=\varkappa ·exp\{0.3·\kappa \}$. The time of constant volatility ($\kappa =0$), $\widehat{\varkappa }$ will be close to the decay factor ($0.90$); conversely, in case of very large volatility changes (e.g., $\kappa \cong 1.0$), $\widehat{\varkappa }$ will assume higher values. In Equation (24), $\overline{\vartheta }={\vartheta }_0·\varpi$ and $\overline{S}=S_0+\widehat{\varkappa }$, with ${\vartheta }_0=0.001$ and $S_0=0.1$.

3. Empirical Application

3.1. Data Description and Results

The model is estimated for 43 country-specific models, referring to 22 developed economies and 21 developing countries. The estimation sample covers the period from March 1990 (1990:q1) to December 2020 (2020:q4). Only one lag has been chosen to ensure stationarity among all series. The dataset contains 153 observable variables split into three groups: (i) Macroeconomic–financial Indicators, including 61 variables combining information on economic development, financial markets, and labor force; (ii) Socioeconomic–health Status, addressing 47 factors concerning information on health determinants and population growth; and (iii) Environmental Source, referring to 45 covariates dealing with environment, high-technology, and energy use.

By running the shrinkage procedure, 26 predictors better fit the data and then there are $2^{Nf}=2^{1118}$ compressed model solutions ($M_F\subset \mathcal{E}$). The final best model solution performing the data consists of 12 covariates with Posterior Inclusion Probability (PIP) $\ge \tau$ and higher log Bayes Factor equals to $11.53$ (

Table 1. Final Best Predictors.

Idx.	Predictor	Label	PIP (%)	CPS
Macroeconomic–financial Indicators
1	Weighted income per capita	weig	62.12	$0.95$
2	Expenditure on R&D	rdexp	$0.34$	$0.64$
3	Final consumption expenditure	fexp	53.83	$0.96$
4	GDP per capita growth	gdpg	79.23	$1.00$
5	GDP per capita, PPP	gdp	$0.29$	$1.00$
6	Labour force	labtot	47.58	$0.95$
7	Poorly paid job	ppjob	$0.41$	$0.28$
8	Gross fixed capital formation	gfcf	67.52	$0.98$
9	Consumer price index	infl	38.76	$0.33$
Socioeconomic and Health Status
10	Overweight	obe	45.93	$0.27$
11	Cultural interests	cult	$0.25$	$0.44$
12	Social participation	socio	$0.27$	$0.68$
13	Risk of poverty	pover	$0.18$	$0.19$
14	Current health expenditure	hexp	75.13	$0.96$
15	Total population age (15-above)	pop	$0.38$	$0.52$
16	Population Growth	popg	55.21	$0.98$
17	Rural population	rpop	$0.15$	$0.62$
18	Urban population	upop	$0.17$	$0.65$
19	Employment to population ratio	epop	$0.31$	$0.99$
Environmental Source
20	Exports of goods and services	exp	$0.37$	$0.86$
21	Imports of goods and services	imp	$0.44$	$0.91$
22	Energy use	use	68.35	$0.95$
23	Energy net imports	import	$0.36$	$0.53$
24	Individuals using Internet	int	58.74	$0.82$
25	High-technology exports	hexports	65.72	$0.98$
26	Trade	trade	$0.24$	$0.92$
-	productivity	prod	-	-

The table is so split: the first column denotes the predictor number; the second and the third column display the predictors and their labels, respectively; and the last two columns display the PIPs (in %) and the CPS, respectively. The last row refers to the outcomes of interest at time t corresponding to the productivity level in a given country, which refers to the real GDP per capita in logarithmic form. All data refer to OECD and Eurostat databases.

in bold). The PIP corresponds to the sum of the PMPs in (11) computed for every model solution for all $M_K$ models wherein a covariate $X_t$ has been included with the auxiliary variable ${\gamma }_t$.

All of their lags are put as external instruments in the estimation model to capture some exogenous variations because of endogeneity issues, functional forms of misspecification, and dynamic causal effects. External instruments refer to variables correlated with a shock of interest, but not with other shocks.

In Table 1, the Conditional Posterior Sign (CPS) denotes the sign certainty assuming values close to 1 or 0 whether a covariate has a positive or negative effect on the outcomes of interest, respectively. It is better emphasized displaying the CSUR estimates (

Table 2. Compressed SUR Results.

Idx.	Variables	CSUR Model
Macroeconomic–financial Indicators
1	weig	3.84 ***
		(0.23)
3	fexp	9.32 ***
		(2.52)
4	gdpg	8.58 ***
		(3.23)
6	labtot	5.33 **
		(3.16)
8	gfcf	1.91 ***
		(0.30)
9	infl	−1.71 ***
		(0.65)
Socioeconomic and Health Status
10	obe	−1.91 **
		(0.80)
14	hexp	8.76 ***
		(2.26)
16	popg	−1.95 ***
		(0.32)
Environmental Source
22	use	1.89 ***
		(0.47)
24	int	−2.43 ***
		(0.34)
25	hexports	2.68 ***
		(0.44)
Exogenous Factors
-	$X_{1t}^{*}$	−3.27 ***
		(0.17)
-	$X_{2t}^{*}$	2.76 ***
		(0.21)

The first two columns denote the predictor number and labels, and the last column displays the estimates and the standard errors (in parenthesis). The significant codes are: *** significance at 1%; ** significance at 5%.

).

Let the final subset consist of 12 final best covariates; a total of 10,000 draws for every model solution has been used to conduct posterior inference at each t. Conditional density forecasts are then obtained according to a time frame of nine quarters (two years and a quarter) in order to assess interdisciplinary research on how a set of different indicators and their interactions affect cross-country economic dynamics.

Some preliminary empirical results are addressed. (i) Socioeconomic–health indicators and general economic conditions hold a relevant position when studying dynamic feedback such as cross-country spillover effects. (ii) Macroeconomic–financial linkages have to be accounted for, representing the most relevant indicators to evaluate economic dynamics. (iii) Heterogeneity, interdependence, and co-movements are also addressed; let the framework be hierarchical. (iv) A multidimensional panel setup is useful to also address causal relationships when dealing with a large set of different variables. (v) Multicollinearity problems are dealt with using lagged variables as external instruments.

The CSUR estimates are displayed in Table 2. From a modeling perspective, economic and financial indicators strongly positively affect productivity levels, except for the inflation rate. Indeed, according to the CPS in Table 1, the predictor 9 has to be evaluated with care, displaying mixed effects. More precisely, the results of the empirical evidence on the inflation-productivity relationship are mixed because of sensitivity to the inclusion of additional variables as determinants of productivity growth. Indeed, many studies suggest a link between inflation and economic conditions across countries (long-run effect), highlighting that high rates of inflation would create distortions leading to inefficient resource allocation and then lower productivity levels (see, among many others, Levine and Renelt 1992; Stock and Watson 1988; Watson 1994 and Blanchard and Quah 1989). Conversely, related works argue the existence of a causal interpretation and policy implication (cyclical comovements), emphasizing that lower inflation would increase productivity (see, among many others, Fischer 1993; Feldstein 1982; Canova et al. 2012 and King and Watson 1992). Health status, social factors, and environmental indicators significantly affect outcomes and—for the most part—negatively so. Positive effects are highlighted according to predictors 14, improving (general) health statistics, and 25, increasing the economic conditions. Predictor 10, such as predictor 9, has a negative impact on productivity levels displaying a not sufficiently high CPS. Finally, even if the use of the Internet would positively affect the outcomes of interest, it should be analyzed with care because of a CPS large but not quite close to 1. Indeed, productivity growth effects from the Internet have been positive and strictly significant over time, but with a significant decrease in the last decade (see, for instance, Gordon 2002; Maurseth 2018; Choi and Yi 2009 and Sichel 1999).

Finally, potential (unobserved) structural breaks and spillover effects affecting estimates and forecast results are absorbed within the system because of the use of conjugate informative priors. They correspond to strictly exogenous factors added in the final subset as permanent shifts, and evaluated through the Chow test. More precisely, two dummies were involved within the system: $X_{1t}^{*}$, time-fixed effects due to triggering events (such as global financial crisis, pandemic disease, inflation in the aftermath of wars and pandemics)5; and $X_{2t}^{*}$ time-fixed effects due to fiscal policy implications (such as European recovery programs). The effects are significant and negatively and positively affected by productivity, respectively, as in Table 2.

Table 3. Diagnostic Tests.

Test Statistic	CSUR Model
Significance, Robustness, & Stationarity
$R_{adj.}^2$	$0.87$
$Q_S$	$138.24(0.00)$
$Q_A$	$1.67(0.13)$
$Q_{LB}$	$0.07(0.71)$
$U_H$	$-2.61(0.06)$

The table refers to the test statistics and the corresponding p-values (in parenthesis) dealing with the significance, robustness, and stationarity of the structural compressed regression. They are $R_{adj.}^2$, Sargan’s test for over-identification ($Q_S$), Arellano’s serial correlation test ($Q_A$), and Multivariate Ljung-Box Tests for serial correlations among residuals over time ($Q_{LB}$). The panel unit root test refers to the Hadri (2000)’s ($U_H$) analysis.

displays the main diagnostic tests accounting for significance, robustness, and stationarity. Here, some considerations are in order. (i) The structural compressed regression in (9) is robust by explaining most of the variability of the outcomes of interest ($R_{adj.}^2\ge 87\%$). (ii) The Sargan–Hansen test of overidentifying restrictions ($Q_S$) highlights the usefulness of a multidimensional (panel) framework to deal with endogeneity issues and model misspecification problems (see, for instance, Bowsher 2002). In addition, the findings also highlight that—through the estimated CSUR model—one is able to address variable selection problems such as model uncertainty and overfitting. Indeed, the CPS of the final best predictors in Table 1 are close to 1 or 0. (iii) The estimates are robust and efficient showing linear dependencies among series and no serial correlations among residuals over time according to Arellano (2003) ($Q_A$) and Ljung-Box test ($Q_{LB}$), respectively. (iv) Let the framework be multidimensional, and panel unit root tests are also assessed through the Hadri (2000)’s test statistic ($U_H$), rejecting the null of nonstationary for all series. (v) The validity of the model also confirms the accuracy of the arbitrary threshold ($\tau$) chosen in the computational approach.

The presence of Granger causality when studying heterogeneous dynamics is displayed in

Table 4. Granger Causality Test.

Idx.	Variables	$\tilde{\mathit{Z}}$ Test Statistic
Macroeconomic–financial Indicators
1	weig	$13.19$ ***
3	fexp	$3.08$ **
4	gdpg	$28.61$ ***
6	labtot	$4.43$ **
8	gfcf	$21.12$ ***
9	infl	$-7.92$ ***
Socioeconomic and Health Status
10	obe	$-8.56$ **
14	hexp	$25.90$ ***
16	popg	$3.45$ **
Environmental Source
22	use	$22.55$ ***
24	int	$5.71$ ***
25	hexports	$15.23$ ***

The first two columns denote the predictor number and labels, and the last column displays the $\tilde{Z}$ test statistics. The significant codes are: *** significance at 1%; ** significance at 5%.

. It is tested through a generalized version of the Granger (Non-)Causality of Dumitrescu and Hurlin (2012) referring to dynamic data in a context of multivariate time series. The test statistic is the $\tilde{Z}$ used in Dumitrescu and Hurlin (2012), where the degrees of freedom at the denominator denote the final subset $\mathcal{E}$. Under the null hypothesis, there is no causal relationship among outcomes and predictors for any observation unit (country), whereas there are causal links for at least a subgroup of countries under the alternative. As is already known, when dealing with time-varying variables, estimates accounting for lagged variables would be biased if tested under the wrong hypothesis (see, for instance, Pesaran and Smith 1995). Moreover, if coefficient homogeneity is imposed, causality test statistics may lead to fallacious inference (or risk of failing to reject the wrong hypothesis). The resulting estimates displayed in Table 4 show that the null of non-causality is rejected for all variables and then dynamic feedback and cross-unit interdependencies matter. These findings would emphasize the computational approach addressed in this study.

3.2. Recommendations and Policy Improvements

The interdisciplinary empirical study has been addressed by first reviewing the literature for practical guidance from the above case study example and then discussing which socioeconomic and financial indicators strongly affect economic growth. According to the estimation results, the findings highlight a defined role for health status and related determinants and that economic conditions in a given country are important drivers (Table 1). However, when is the evidence of relationships between socioeconomic–financial and economic development ’good enough’ to involve policy regime shifts? This study finds that the relationships between countries’ productivity and environment source are driven by macroeconomic–financial interlinkages (e.g., predictors 1, 3, 4, 6, 8, 9), representing the most set of best covariates. Furthermore, socioeconomic and health status also cover an important role in this context emphasizing strong causal relationships with some development indicators (e.g., predictors 10, 14, 16).

According to these results, three key factors to address an interdisciplinary analysis of economic growth can be designed. (i) Current health expenditure (predictor 14), higher labor productivity (predictor 6), and employment opportunity (predictor 10) would implement outcomes of various health- and finance-related planning policies such as healthier and safer workplaces (predictors 1, 3). In this way, a better and more active workforce for individuals with specific risk factors—such as obesity and social participation—can be designed (see, for instance, Pacifico 2022a). (ii) Environment source in terms of energy efforts would positively affect economic growth and other development indicators (e.g., predictors 3, 9, 22, 24, 25). However, they should be handled carefully by displaying a CPS at the center of the range. (iii) Financial indicators are the main drivers of spillover effects across countries and sectors (e.g., predictors 4, 8, 9), and their sudden change—whether through being unobserved or badly managed—would negatively affect economic growth (structural breaks).

Concerning the field of socioeconomic and health sources, it is important and has to be accounted for, mainly when dealing with quality of life and risk factors. Indeed, they face many methodological weaknesses, most of which stem from their insufficiently developed theoretical framework. Most of these studies believe that research on quality of life and individual–specific risk factors should be turned away from composite indicators because of serious methodological inconsistencies or should be constructed a list of clear indicators of well-being and workplace (see, e.g., Diener and Suh 1997; Michalos 1997 and Saltelli 2007). The empirical results addressed in this study find evidence concerning the need to highlight a set of potential covariates affecting a country’s productivity, and then design a monitoring system for the cross-country socioeconomic–environmental report.

The field of macroeconomic–financial variables is being sufficiently developed both in theoretical and applied issues of indicators’ use. More precisely, the use of indicators has been successfully integrated into the theoretical model of business cycles. Thus, most recent studies highlighted a finite set of indicators linked to certain economic phenomena. These relationships were used to explain the observed values of an indicator, and then facilitate the understanding of causal relationships among the indicators’ outcomes and certain economic phenomena (see, for instance, Banbura et al. 2010; Bernanke et al. 2005; Canova and Ciccarelli 2016; Carriero et al. 2015, 2016; Ciccarelli et al. 2018; Clark and Ravazzolo 2015; Dees et al. 2007; Pacifico 2019, 2020a). All of these issues have been successfully involved and assessed in this study.

Last but not least, environmental science–in terms of environmental impact–also manages to translate its main concerns to specific methodological frameworks of indicators’ use. In this context, recent studies have selected a set of indicators in the environmental policy context based on their operational utility, without focusing on their methodological contribution to exploit empirical approaches evaluating business cycles and related economic indicators. In other words, both fields have to be managed by connecting theory with the corresponding indicators’ practice, and formulating the latter for the benefits of an empirical interdisciplinary perspective (see, e.g., Faber 2008; Kroll 2011; Lawn 2003; Neumayer 2000 and Sirgy 2011). Let the hierarchical framework and the open robust shrinking procedure be adddressed in this study, the set of the best selected indicators supports either theoretical or practical statements.

The final suggestion highlighted in this study would be to better define and clarify theory and empirical issues which could be implicit in an interdisciplinary research analysis. It would facilitate more fruitful implementations and contributions for future approaches. Overall, interdisciplinary research in financial econometrics would require not only the claims of an empirical case study, but also the language and concepts embedded within the research process. More precisely, instead of focusing on the construction of composite indicators that cover different areas of knowledge, interdisciplinary empirical issues should be based on the identification of key indicators and their linkages through appropriate computational approaches, dealing with complex mathematical-statistical relationships and high dimensionality.

4. Concluding Remarks

This paper improves statements and findings developing an interdisciplinary empirical research in development economics and financial econometrics. Methodologically, a multicountry time-varying Bayesian compressed regression model is used to select the best subset of predictors affecting economic growth. Causal relationships and linkages are also investigated in the shrinking procedure to better understand empirical results based on business cycles and related economic indicators. Every relationship is evaluated dealing with potential volatility changes affecting macroeconomic and social indicators. A dynamic investigation is addressed through multivariate conjugate informative mixture priors and MCMC algorithms.

An empirical example is developed by accounting for a large set of macroeconomic–financial and socioeconomic–health variables to perform policy issues and implications. The estimation sample accounts for 43 country-specific models covering the period from March 1990 to December 2020. All data come from OECD and Eurostat databases.

From a modeling perspective, socioeconomic–health indicators and macroeconomic–financial factors hold a relevant position when studying dynamic feedback such as cross-country spillover effects. From a policy perspective, macroeconomic–financial, health, and environmental indicators should be performed in the fields of quality of life, workplace safety, and economic sustainability.