From this and to cover with the outlined goal, the present research work has been divided into different sections. The first section is a descriptive analysis of Ecuadorian foreign trade such as its main exported and imported products, the main destinations and origins of the products it sells. Then, it moves to the methodological part of the work. In this research it has been decided to use different estimations of the **gravity** **model**: Ordinary Least Squares (OLS), country pair fixed effects (CPFE), the Hausman Taylor **model** (HT), and the Pseudo Poisson Maximum Likelihood Estimation (PPML). This section presents a brief description of its main concepts, features and advantages of each estimation **model**.

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19 Lee mas

As shown earlier, distance measured in minutes provides the best fit in the **gravity** **model** compared with the other two measures. However, travel time and road distance between places are not constant over time. Improvements in transportation technol- ogy, new roads and changes in government legislation, such as maximum speed lim- its, do affect travel time and road distance between places. We examine evidence on the effect of changing distances between specific origin-destination pairs over time, using historical and current road travel distance information. During the decades that correspond to the available migration data there have in fact been significant chang- es in some road distances and travel times. For example, the 793 km journey from Whangarei to Wellington which currently takes around 9 hours 23 minutes (based on 2013 information) was an 839 km journey that took 15 hours 5 minutes in 1984. For the 600 origin-destination pairs for which we have comparable data, there was about a 30 percent average decline in travel time between 1984 and 2013. It is important to see whether such improvements actually matter for migration. Pooling the 1986- 1991 and 2008-2013 migration flows data, as well as the roughly corresponding 1984 and 2013 distance data, we have 1200 observations with which we can run the fol- lowing two-wave fixed effects panel **model** regressions (one for distance in time and one for distance in kilometres):

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We employ a similar panel data **gravity** **model** to Bellos and Subasat (2012a and 2012b) as our main purpose is to verify their results in the context of 18 Latin American countries in the period 1985-2004. We develop their **model** by employing governance variables in target and source countries in order to take both push and pull factors into account. We also employ a number of new control variables in our **model**. **Gravity** models are commonly used to investigate FDI flows from source to host economies (Eaton and Tamura, 1994; Brainard, 1997; Blonigen and Davies ,2004; Egger and Pfaf fermayr, 2004; Blonigen et al., 2007; Baltagi et al., 2007; Guerin, 2006). The **model** aims to measure FDI potential between the source and target countries by using two main components: the relative market sizes of the two Figure 3. Change in regulatory quality

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This paper contributes to the existing literature in two ways. First, it explores the empirical performance of the **gravity** **model** to explain trade flows between regions using a spatial approach. To do so, it employs two different methodologies. The first methodology extends the **gravity** **model** controlling for the so-called multilateral resistance (MR) and introducing spatial lags, while the second methodology is based on the spatial econometric flow **model** introduced by LeSage and Pace (2008). Second, following the latest research in spatial econometrics, we control for the role of connectivity at a highly disaggregated territorial level. Specifically, we focus on level NUTS3 1 in Spain (i.e. provinces).

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he objective of this research is to determine the influence of the main factors that affect bilateral trade between Ecuador and Germany through the application of a **gravity** **model**, seeking to answer the ques- tion: how does the bilateral trade flows between Ecuador and Germany af- fect the size of their economies and the costs of trade? To solve it, an analysis of the bilateral trade flows between Ecuador and Germany in relation to the GDP of each country and the trade costs generated will be carried out. The study covers the period 2002 - 2017 and the information was obtained from official data bases of both countries and the United Nations. For the calcu- lations, the linear regression using least squares was used with the software Microsoft Excel. The findings make it possible to show that Ecuador’s GDP is the most influential factor in bilateral trade flows, while Germany’s GDP has an opposite effect to that expected, decreasing trade when the GDP increas- es. Likewise, it is determined that, although total trade flows decrease with increasing trade costs, Ecuadorian imports do not decrease in this increase.

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Reduced **gravity** **model** it is a very used tool to understand many of the oceanic process, and in the elaboration of precise and more complex numerical models. The angular momentum it is a quantity that it should be conserved in isolated systems without external pairs, because the internal interactions should take place, for the third law of Newton, internal pairs that they should be compensated among them. The angular momentum it is an extensive property that must consider in his balance, for isolated systems, the masses that are exchanged and the external pairs. In this study it is only analyzed the vertical component of angular momentum and in the conventional approach of f-plane geometry. Impermeability at the boundaries (i.e. without exchange of mass) the pairs due pressure distribution and shear stresses must be the only involve in angular momentum variation. Using these notions we find a consistent parametrization of lateral diffusion of momentum. This work shows the relevance of this parametrization in relation to angular momentum balance and energy ‘consistency’. Another parametrization that is consistent with energy, it persists in defect concerning the angular momentum. Using a finite difference **model**, and in Matlab ambient, it is shown some examples that make patent the role of the different pairs imposed by boundary conditions, including an internal sub-domain, with entrances and exits of fluid.

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None of the abovementioned studies have investigated the cost of remitting as a factor influencing remittances flows. Hence, the effect of implementing policies in the receiving country to facilitate the transfers and lower the cost remains an empirical question. For this reason, the main aim of this paper is to provide an estimate of the effect of transaction costs on remittances and to evaluate the magnitude of this effect. At the conceptual level, the contribution is also the comparison of the effect of distance with the effect of remittance costs. At the empirical level, this is the first country-study of this kind for the South Asian region. Given that the region accounts for the highest share of world wide remittances, the results could be helpful in better understanding these remittance flows. More specifically, we estimate a **gravity** **model** using panel data for remittances from 23 sending countries 2 to Pakistan over the period from 2001 to 2013. The **model** is augmented with a new proxy for cost of remitting that, to the best of our knowledge, has never been used in previous studies. Moreover, we also include migration networks in the analysis as an important factor explaining the _________________________

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Abstract: This paper investigates to what extent international migration can be explained by climatic variations. A **gravity** **model** of migration augmented with average temperature and precipitation in the country of origin is estimated using a panel data set of 142 sending countries for the period 1995 to 2006. We find two primary results. First, temperature is positively correlated with migration. Second, stronger changes in precipitation are also associated with aligned, but small changes in migration. Both effects are robust to various **model** modifications. Furthermore, we present initial explorations into the channels relating climate changes with migration via agriculture and internal conflict.

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distribution. To construct the index, we first estimate the distribution of income within each country and then we measure to what extent the distributions of two given countries overlap. The underlying assumption is that the overlap between the respective density functions of income within each country can be considered as a good proxy for the similarity in the demand structure between trading partners. This assumption has been made by Fajgelbaum et al. [9], and justified by the fact that demand differences are not caused by exogenous variations in tastes across countries, but rather derive from differences in income distribution. Also empiri- cally, a robust relationship has been found between per capita income and the composition of national consumption [26, 27]. The proposed measure of demand similarity is added as explanatory variable in a **gravity** **model** of trade that is also augmented with within country inequality measures and with per capita income differences. The main advantage of the density functions used in this paper with respect to Choi et al.’s [25] measure is that we are able to obtain full density functions for more than a hundred countries and for different periods, whereas Choi et al. [25] restricted their analysis to 26 countries and constrained their analysis to a single wave of income data.

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The effect is similar to that calculated by Martínez-Zarzoso et al. (2009) and Nowak-Lehmann D. et al. (2013) using total exports. Figure 1 shows the evolution over time of the aid coefficients in the **gravity** **model** by interacting them with specific time dummies. The point estimates (bold line) and the corresponding confidence intervals at the 95 % confidence level are shown. The coefficients on the control variables appear in Table A.4. The income effects show the expected positive sign and are statistically significant, the values are considerably lower than unity, as the theory predicted, but this is generally the case when using sectoral data. The effect of aid from other donors on German exports is not statistically significant, indicating that aid from other donors does not act as a trade-deterrent factor for German aid. The exchange rate variable is also not

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24 Lee mas

However, our key observation is: Vasiliev’s higher-spin gravities are not formulated a priori in terms of Lorentz tensors and tensor-spinors; rather they are formulated in terms of master fields living on products of space-time and fiber manifolds. The latter contain non-commutative twistor or twistor-like spaces whose coordinates generate the higher-spin and internal symmetry algebras. The full specification of a Vasiliev-type higher-spin **gravity** **model** thus requires the choice of a set of fiber functions that form an associative algebra. Hence, the incorporation of fractional-spin fields into the higher-spin framework can be reduced to the technical problem of in which ways Vasiliev’s theory admits non-standard embeddings of the Lorentz connection leading to fractional-spin representations.

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the Universe has lived almost half of its life. Phantom fields also produce a cosmological **model** that has this property [51, 52]. In the δ ˜ **gravity** **model**, we can avoid a Big Rip at later time by a mechanism that gives masses to all massless particles. Some options are quantum effects (which are finite in this **model**) or massive photons due to superconductivity [56] which could happen at very low temperatures, which are natural at the later stages of the expansion of the Universe.

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In accordance with Talamo (2007) who considers the **gravity** **model** to measure the FDI flows, we are going to use the GDP of domestic and foreign countries, the exports and imports as a level of openness, a dummy variable if one specific country is a member of the EU and has important trade agreements representing the economic integration as well as the corruption level, which is considered by previous literature as main inconvenient for FDI inflows in Romania. The choice for these explanatory variables was based on the existing theoretical and empirical literature on the **gravity** **model**. Generally, **gravity** models suggest positive relationship between the size of economies and direct investment flows as stated in (Talamo, 2007) and is negatively related to distance. That is the reason we consider the gross domestic product of both domestic and foreign countries in our **model**. We take into account the direct investments of the main countries or group of countries that invest in other countries. We consider a variable called “id” which is the control variable representing the name of the country or group of countries investing directly in Romania through locating a company there or a plant for production. These are North Africa, Japan, United States, Canada, European Union, Russia and Switzerland. The level of Gross Domestic Product in Romania, to have an idea of the Romanian market size. In addition, the GDP of the foreign considered countries to be able to see their market potential for investing in Romania. In order to see the degree of openness to trade we include in the **model** exports and imports values from Romania with the previously mentioned countries. Furthermore, the dummy variable which indicates the membership to the EU, as well as the corruption level measured by Transparency International in its Corruption Perception Index (CPI). Therefore we can perform an econometric **model** with FDI as dependent variable and the previous mentioned factors as independent variables affecting the Foreign Direct Investment.

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Hellvin & Nilsson claim that bilateral trade is determined by “three sets of variables: i) variables indicating total potential demand of the importing country i, ii) variables indicating to- tal potential supply of the exporting country j, and (iii) variables aiding or hindering trade between importing and exporting countries” (2000, p.6). In the first and second sets there are variables related to the size of the economies of the importer and exporter (approxima- ted by GDP or population), respectively; and in the third set there are variables such as transportation costs, culture, trade agreements, among other factors. Tinbergen (1962) pioneered the use of the **gravity** **model**, since it is used to study trade flows among countries; however, the **model** was not widely accepted by the perception that it was more an analogy with physics than an analysis economic. Given its success as an empirical tool, a series of research studies have shown that the **gravity** equation fits different international tra- de models.

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31 Lee mas

which, in particular, tends to the usual mass parameter m in the absence of higher-curvature terms ( α ¼ β ¼ 0 ) or in the absence of a cosmological constant ( Λ ¼ 0 ). In general, there is no need to go beyond linear order in the curvature, as the energy is linear in m. Thus, even if the Lagrangian contains higher powers in the curvature, the conserved charge can be consistently truncated to an expression linear in R if the corresponding background is not degenerate. An exception to this happens at the so-called critical points, which are special points of the space of coupling constants where the massive spin-2 field actually becomes massless and the spin-0 mode becomes strongly coupled. At such a critical point, the black hole solutions of the QCG theory have vanishing energy and vanishing angular momentum, and the fourth-order linearized equations become confluent and develop low-decaying extra modes. This is, for instance, the case of critical **gravity** [6], which is defined by choosing the values α ¼ −3β ¼ 3=ð2ΛÞ in Eq. (1). We have already mentioned that when α ¼ −3β the scalar mode in Eq. (11) is eliminated and h ¼ 0 becomes the only possible solution. Then, Eq. (10) reduces to

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In this paper we have shown that the singularity- avoiding ‘‘loitering’’ behavior observed for > 0 and domination by a perfect fluid is upheld for w > 0 and that this result is not affected by the presence of spatial curvature. This behavior shows remarkable similarities to the behavior in GR with a cosmological constant ¼ 8 1 . Similar behavior is also seen in the case of domina- tion by a scalar field with an exponential potential. The scaling of the density with the scale factor in such uni- verses is reminiscent of that observed in a GR universe with such a scalar field and (initially more slowly scaling) ordinary matter. The similarities to GR in each of these cases deserve further investigation which will shed light on the high density behavior of Eddington **gravity**.

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General Relativity (GR) is a successful theory of **gravity** at a classical level but it lacks of consistency in a quantum regime because it is not renormalizable. On the other hand, in the low energy limit of String Theory, which should be ﬁnite to all orders, there appear contributions that are quadratic in the curvature. As a consequence, higher curvature extensions of Einstein **gravity** are expected to give rise to a **gravity** theory with a better ultraviolet behavior. Early work on the subject has suggested that this class of theories should be renormalizable [1].

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(5) Observe the particular coupling to the matter Lagrangian. We shall not consider a matter lagrangian for each metric, as often done in the literature. We shall argue below that the coupling of normal matter to g µν + σf µν is the mot natural choice. The point is that g µν + σf µν describes a massless graviton (see below) and therefore masses are still attracted by the action of spin 2 massless particle in this theory, just as in ordinary **gravity**.

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Chern-Simon theory and how we are able to perform a themodynamic analysis of the BTZ black hole exclusively in terms of gauge fields and the topology of the manifold, without making any reference to the spacetime metric. Chapter five follows the former approach but now, applied to hairy black holes. We present a procedure to describe these solutions for **gravity** with a conformally coupled scalar field in terms of connections and formulate the action as a Chern-Simons-like action. The Euclidean version of this action is used for analyzing the thermodynamics of the rotating hairy black hole solution in the grand canonical ensemble. Regularity conditions on the holonomy at the horizon fix the integration constants of the solution in terms of the chemical potentials. The mass and angular momentum are computed and they coincide with the global charges obtained from the Hamiltonian approach. The entropy is derived in two ways; the first one from the Gibbs free energy and the second one from a general formula for the entropy in terms of the on-shell holonomies. Both give the same result compared with the modified area law. The final part of this chapter is devoted to explain how this formulation can be also applied to **gravity** with a minimally coupled scalar field.

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