Gravity Equation Research Articles

Russian exports amid geopolitical instability: The case of physical and transitional climate risks

The paper examines the impact of physical and transitional climate risks, which to some extend shape the geopolitical situation in the world, on Russian exports. The gravity model of international trade was employed to model the existing relationship. Estimation of the gravity equation by means of the Poisson Pseudo Maximum Likelihood (PPML) method using data on Russian export flows to 72 countries over the period 2010—2021 revealed that climate change and the ambitions of trading partner states towards low-carbon development determine the dynamics of Russian exports. In particular, national physical climate risks have a detrimental impact on Russia’s exports due to the destruction of infrastructure, loss of capital, reduced quality and availability of natural resources, and increased social tensions. Extreme climatic events and climate change measures in trading partner countries spur the development of Russian exports. Namely, physical climate risks of importing countries may increase the demand for key Russian goods for economic recovery purposes. Changes during the transition to a low-carbon economy in trading partner countries also generate opportunities for Russian export growth due to the country’s role as a major supplier of energy and mineral products, as well as technologies for the alternative energy production and electrification of transport

Determining the Predictive Power of the Gravity Model: A Case for Zambia

Purpose: The purpose of this study was to determine the predictive power of the gravity model in explaining trade flows in Zambia. Materials and Methods: The study utilized panel data for the period 1990-2020 for the Zambian economy and its 15 top trading partners based on 2018 trade volumes. The data was collected from the Centre for Prospective Studies and International Studies for International Information (CEPII) Gravity Database. The study employed the gravity equation to predict trade flows in Zambia. Findings: The empirical results show that the gravity model accurately predicts Zambia's trade flows, with GDP positively and distance negatively correlated with exports. The results also show that sharing a common border enhances Zambia’s exports. Surprisingly, trade agreements exhibit a negative relationship with exports. Implications to Theory, Practice and Policy: The significant negative impact of distance on trade highlights the need for improved infrastructure and logistics to reduce transportation costs, thus, facilitating Zambia’s trade flows. Further, the findings suggest that Zambia should focus on strengthening trade with neighboring countries. Additionally, Zambia should diversify export bases away from heavy reliance on the mining sector. Besides, there is a need for active participation in regional integration initiatives to address implementation challenges of trade agreements.

Using generalized estimating equations to estimate nonlinear models with spatial data

. We study the estimation of nonlinear models with cross-sectional data using two-step generalized estimating equations within the quasi-maximum likelihood estimation framework. To improve efficiency, we propose a grouped estimator that accounts for potential spatial correlation in the underlying innovations of nonlinear models. Under mild weak dependence assumptions, we provide results on estimation consistency and asymptotic normality. Monte Carlo simulations demonstrate the efficiency gain of our approach compared to various estimation methods. Finally, we apply the proposed approach to examine the role of cultural distance in an extended gravity equation using international trade data from China. Compared to existing methods, our approach yields estimates with smaller standard errors and reinforces the hypothesis that both cultural and geographical distances significantly negatively influence international trade.

Novel structures and collapse of solitons in nonminimally gravitating dark matter halos

Ultralight dark matter simulations predict condensates with short-range correlation, known as solitons or boson stars, at the centers of dark matter halos. This paper investigates the formation and collapse of dark matter solitons influenced by nonminimal gravitational effects, characterized by gradient-dependent self-interactions of dark matter and an additional source in Poisson's equation for gravity. Our simulations suggest that the initial evolution of dark matter resembles that without nonminimal gravitational effects. However, regions with negative potential curvature may develop, and solitons will collapse when their densities reach certain critical values for both positive and negative coupling constants. With strong nonminimal gravitational effects, we verify that linear density perturbations could grow on both large and small scales, potentially enhancing structure formation.

Foreseeing Potential Trade Effects of Additive Manufacturing: Evidence from Trade in Sound Recordings

Additive manufacturing (AM), known as three-dimensional printing, has the potential to drastically change the mode of production and trade in goods. However, it is challenging to investigate the effects of AM on trade because existing AM production patterns are still immature. As an analogy for the impacts of AM, this study investigates the effects of internet distribution on trade in sound recordings, which has changed after the emergence of online shops or streaming services. Specifically, we estimate the gravity equation in the bilateral trade in sound recordings among 197 countries in 2003–2017 and demonstrate that internet penetration significantly decreases trade in sound recordings. Furthermore, the strong protection of intellectual property rights in importing countries weakens the trade-reducing effect, whereas that in exporting countries magnifies such an effect.

Holographic RG flows in a 3D gauged supergravity at finite temperature

In this paper, we consider finite-temperature holographic renormalization group (RG) flows in D=3 N=(2,0) gauged truncated supergravity coupled to a sigma model with a hyperbolic target space. In the context of the holographic duality, fixed points (CFTs) at finite temperature are described by anti–de Sitter (AdS) black holes. We come from the gravity equations of motion to a 3D autonomous dynamical system, which critical points can be related to fixed points of dual field theories. Near-horizon black hole solutions correspond to infinite points of this system. We use Poincaré transformations to project the system on R3 into the 3D unit cylinder such that the infinite points are mapped onto the boundary of the cylinder. We explore numerically the space of solutions. We show that the exact RG flow at zero temperature is the separatrix for asymptotically AdS black hole solutions if the potential has one extremum, while for the potential with three extrema the separatrices are RG flows between AdS fixed points. We find near-horizon analytical solutions for asymptotically AdS black holes using the dynamical equations. We also present a method for constructing full analytical solutions. Published by the American Physical Society 2024

Investigating the weak gravitational lensing in Starobinsky–Bel–Robinson gravity black hole

This paper is motivated to study the weak gravitational lensing of the black hole in the context of Starobinsky–Bel–Robinsion gravity. We deduce the deflection angle of light in the weak field limits. For this purpose, we find the Gaussian curvature and apply the Gauss–Bonnet theorem. We also investigate the deflection angle at which light is deflected by a plasma medium. Furthermore, we analyze the graphical behavior of the deflection angle in the framework of SBR gravity. We also calculate the energy extracted from the black hole in SBR gravity, Einstein ring, and lens equation in the non-plasma and plasma framework. We conclude this study with a discussion of how light beams behave when they approach such a four-dimensional black hole by calculating the deflection angle.

Field equation of thermodynamic gravity and galactic rotational curves

The rotational velocity curve (RC) of galaxy NGC 3198 is modelled in various theoretical frameworks: Thermodynamic Gravity (TG) is compared to Dark Matter (DM) and Modified Newtonian Dynamics (MOND). The nonlinear gravitational field equation of TG is solved using the baryonic mass density as the source of the gravitational field. In this paper, first, a dissipation motivated numerical method is verified with the help of exact solutions. Then, the obtained optimal velocity curve is compared to DC14 model DM and MOND EFE (Modified Newtonian Dynamics-External Field Effect aspect) parametrisations for the RC of the galaxy.

Understanding the natural units and their hidden role in the laws of physics

The natural units of measure lauded by Max Planck more than 100 years ago are underutilized today. Many physical constants, including the Planck constant, the gravitational constant, the speed of light, vacuum permittivity, and vacuum permeability consist of natural units in their unit dimensions. The natural units are present in all formulas containing these constants. The defining characteristic of the natural units is an alignment of unit values at the Planck scale. This alignment gives a computational basis of proportionality from which the correlated properties and dynamics of elementary particles, including wavelength, period, mass, momentum, and energy, manifest in equal or inversely proportional ratios of the Planck scale. These correlations explain many of the defining equations of quantum mechanics, classical gravity, and electromagnetism.

Gravity for cross‐border licensing and the impact of deep trade agreements: Theory and evidence

AbstractWe examine whether deep regional trade agreements facilitate cross‐border licensing. A micro‐founded gravity equation for each supply mode is derived from a model in which heterogeneous firms choose to supply their goods to foreign markets through export, foreign direct investment or licensing. We present several comparative statics results regarding the effects of changes in the fixed costs of serving the destination country, the freeness of trade, and the strength of intellectual property rights protection on bilateral flows of licensing revenues. We then empirically test our theoretical predictions using data on the cross‐border flows of royalties and licence fees for 49 countries in the period 1995–2012. In addition to variables that capture the impact of shallow and deep regional trade agreements, we construct dummy variables that represent subcategories of IP rights‐related provisions. Consistent with our theoretical predictions, we find that improved access to the destination market through a deep regional trade agreement and stronger IP rights protection through a regional trade agreement with legally enforceable IP rights and technology‐related provisions increase bilateral flows of licensing revenues. Among IP rights‐related provisions, the accession to or ratification of existing international IP agreements and the protection of trademarks, patents, or industrial designs are important for facilitating cross‐border licensing.

Impact of particle creation in Rastall gravity

In this paper, we investigate the Friedmann–Lemaitre–Robertson–Walker cosmological models within the framework of Rastall gravity incorporating particle creation. The modified field equations for Rastall gravity are derived and exact solutions are obtained under various assumptions of the scale factor. The qualitative behavior of our solutions depends on the Rastall coupling parameter [Formula: see text]. Following Akarsu et al. [Ö. Akarsu et al., Rastall gravity extension of the standard [Formula: see text] CDM model: Theoretical features and observational constraints, Eur. Phys. J. C 80 (2020) 1050], we have restricted the Rastall coupling parameter [Formula: see text] to the range [Formula: see text] at 68% CL from CMB+BAO data. Further, we have discussed the distinct physical behavior of the derived models in detail.

Multilevel Modelling in Economics: A Way to Test the Natural-Partner Hypothesis

This study applies multilevel modelling to the analysis of trade flows. This methodology can complement the use of the standard gravity equation in addressing the influence of geographical distance on the impact of trade agreements on bilateral trade (the natural-partner hypothesis). The analysis suggests that the simplest, most obvious, and best way to nest country pairs with international trade data is by distance. To this end, a sample of 69 countries with data on domestic flows over the period 1986–2016 was used. This sample accounts for around 85% of world trade data. The estimations suggest that the pro-trade effects of preferential trade agreements decrease with distance to trade partners, while this does not occur with the multilateral trading system. What is more interesting is that the former result only holds for the preferential trade agreements involving goods, which supports the natural-trading partner hypothesis, but not for those that include services. In the latter case, the impact increases with distance. This suggests that deeper preferential trade agreements reduce the cost of distance as a barrier to trade, which probably reflects cultural (regulation) distance.

Does Climate Variability Influence Internal Migration Flows in Senegal? An Empirical Analysis

This paper aims to estimate the total effect of climate variability on interregional migration flows in Senegal. We match regional climate data at origin, represented by normalised rainfall and normalised temperatures (maximum and minimum), with regional migration flow data from Senegal’s Agence Nationale de la Statistique et de la Démographie (ANSD) censuses to construct a panel database covering the five-yearly internal migration waves of 1976, 1988, 2001 and 2013. Using a gravity equation model where migration flows are explained by measures of climatic variability at origin, controlled for geographical, socioeconomic and demographic factors traditionally identified in the literature. Our results show that only negative precipitation anomalies at the origin area act as a push factor and accelerate emigration. In the predominantly agricultural regions, rainfall deficits appear, alongside traditional socioeconomic variables, as an additional significant factor shaping mobility across the country.

Trade, Gravity, and Aggregation

Abstract Gravity equations are an important tool in empirical international trade research. We study to what extent sector-level parameters can be recovered from aggregate gravity equations estimated via Poisson pseudo maximum likelihood. We show that in the leading case where trade cost regressors do not vary at the sector level, estimates obtained with aggregate data have a clear interpretation as a weighted average of sectoral elasticities. Otherwise the estimates are biased, but researchers may possibly infer the direction of the bias. We illustrate our results by revisiting Baier and Bergstrand’s (2007) influential study of the effects of free trade agreements.

Economic Community of West African States (ECOWAS): A Regional Integration Analysis

In 1975, the 15 countries that comprise the Economic Community of West Africa States (ECOWAS) formalized a trade agreement to integrate their economies to make it easier for them to trade with each other and thus promote economic growth and development. Since then, the evidence suggests that intra-regional trade has not changed much. In this paper, we examine the factors hindering trade using data from 2000, 2010, and 2020 and a modified version of the gravity equation. The results of our study suggest that economic factors are primarily responsible for intra-ECOWAS trade and that policies designed to improve transportation infrastructure and reduce administrative barriers could significantly improve intra-ECOWAS trade.

Reilly’s gravity law adapted to finance

The present paper proposes new indicators that explain the pricing of the unitary pure interest rates and interests by adapting previous Reilly’s Law (RL) models of urban economics and regional economics and Financial Gravity (FG) models for financial services. A panel dataset of 114 countries for 1967-2021 is handled, applying the OLS methodology. The results show the higher explanatory power of the adaptation of the FG models rather than the proposed adaptation of the RL ones. Purpose: This paper tries to adapt previous Gravity Equations from Urban Economics to Finance and empirically checks whether they behave better than the recently found Financial Gravity (FG) models. For that, new indicators are provided jointly with their adaptations to Ordinary Least Square (OLS) methods. Additionally, an economic perspective of the bid-asks of financial products is provided. Design/methodology/approach: OLS methods are used to check the desirability and accuracy of the new indicators. A panel dataset of 114 countries for 1967-2021 is handled, applying the OLS methodology. Findings: The most adequate are the FG models after the empirical check, providing the desirable properties of those models. The results show the higher explanatory power of the adaptation of the FG models rather than the proposed adaptation of the RL ones. Originality: This is the first paper, to the author’s knowledge, on providing an adaptation of Reilly’s Law from urban economics models to finance, also providing empirical evidence after adapting these models to linear expressions for applying OLS methods. We also provide evidence on the statistical equality between the unitary pure interest of loan and deposit interests, confirming the good properties of the FG models.

Does Trade Openness Influence Democracy? Evidence from Ex-communist Countries

Abstract This paper analyses the influence of trade on democracy, aiming to understand whether becoming more open to trade also makes a country more democratic. So far, the scientific literature that investigate this topic is scarce, and has not reached any solid consensus: while some papers find a positive effect of trade openness on democracy levels, others find a negative effect, or no effect at all. Moreover, the empirical literature on this topic is also very prone to technical problems of the research design, such as endogeneity, which increases the risk of obtaining biased estimates. This paper uses an instrumental variable approach, this way avoiding any omitted variable bias and reverse causality problems. More precisely, we instrument trade openness with its natural, geography-determined rate, based on the gravity equation of trade; we then use the predicted rate of trade openness to capture its effect on democracy, employing an OLS regression on a panel sample of 27 post-communist countries across a period of 24 years. Democracy is measured using the polity index (from Polity V dataset), and also five other variables that capture different facets of democracy – electoral, liberal, participatory, deliberative and egalitarian dimension (from V-Dem dataset). Empirical results suggest that trade openness has a significant, positive effect on democracy. The effect is only marginally higher for the liberal dimension of democracy, and rather similar in magnitude for the rest of four dimensions.

Indirect channel of trade agreements in deepening global value chains

AbstractPreferential trade agreements (PTAs) between trading partners are known to have positive impact on the expanding and deepening of global value chain integration due to lower trade and investment barriers. Less is known, however, is if other PTAs of PTA partners have any impact on the value‐added trade linkages of the direct PTA partners concerned. Based on compositive indicators measuring the breadth and depth of PTAs from 2007 to 2018 and using Multiregional Input–Output Table database covering 62 countries and 35 sectors and the Content of Deep Trade Agreements database, this paper estimates the multiplicative form of the constant‐elasticity augmented gravity equation model by a Poisson Pseudo Maximum Likelihood (PPML) estimator. This study shows that indirect impact of the deepening of trade agreements of a country's PTA partner exerts positive, significant impact on value‐added exports of a country. Both backward and forward linkages of a country measured by various decomposition of valued added exports indicate this indirect channel of value chain deepening effect even outweighs the direct impact from the deepening of PTAs between direct trading partners with significant policy implications in formulating PTA strategies.

The gravity equation in international trade: an overview of the introduction of gravity to the study of economics and its systematic barriers

This article explores the evolution of the gravity model in international trade studies, emphasising systematic barriers to its acceptance. Employing a chronological and argumentative approach, it examines the emergence of the gravity concept, comparing Isard’s original contribution with Tinbergen’s econometric approach. It discusses how the heuristic nature of economics and a perceived lack of theoretical foundation initially hindered the gravity equation’s use. The works of Tinbergen’s contemporaries, including Linnemann and Anderson, are introduced. Lastly, recent findings in research will be reviewed, such as Krugman’s New Economic Geography, which seeks to encompass Isard’s intention to combine international trade with localisation theories.

Factory Asia Meets Factory North America: How Far Does Latin America Get Involved in Machinery Production Networks?

International production networks in machinery industry have formed three large clusters, each of which is in East Asia, North America, and Europe. This paper investigates the recent evolvement of the connection between Factory Asia and Factory North America with highlighting the role of Latin American countries as a mediator. For this purpose, we utilized trade matrices and gravity equations to measure each country’s level of commitment to each bilateral machinery trade after controlling the size of the economies, distance, and others. Our major findings are threefold: first, Mexico is the only Latin American country that plays a connecting role between two Factories. Second, in 2010–2019, the linkage of exports to Mexico from not only China but also other East Asian countries is strengthened particularly in machinery parts and components. Third, export linkage of China with Mexico is further intensified in 2019–2021 particularly in machinery parts and components due to the US-China confrontation, the USMCA, and other factors.