Indicating the importance for inclusion of
spatial dependence for net capital flows
Jelle Pol*
June 13, 2016
Master’s Thesis
Thesis supervisor:
Prof. dr. J.P. Elhorst
2
AbstractThis paper investigates whether capital flows initiate spillover effects to neighboring states in the United States. With the incorporation of spatial econometrics for net capital flows, significant spillover effects are estimated. This provides evidence of established financial laws and the importance of the inclusion of spatial dependence in finance. This paper should encourage scholars to estimate financial models with spatial econometrics and should serve as a first step to higher engagements for broader research. More extensive, sophisticated models should be implemented to replicate and improve these results.
JEL Classification: C58, G21, H70, N22
3
1. Introduction
Far before the Federal Reserve system was introduced in 1913, every state within the United States of America could be identified as its own country (Broz, 1997). The legal and financial system was far from integrated and each state had its own specific system of regulation. Evidence of this period is still present in the roaring nineties, although integration has made giant leaps. The Federal Reserve system accompanied a monetary system that was nationally implemented, and to a specific degree, the differences in legal status began to transform into similarities (Krause, 1968; Campbell and Hamao, 1992). As a result of its history, the United States’ financial system proves to be one of the most researched systems in the world (Mayer, 1990; Leyshon and Thrift, 1995; Vitols, 2001). It can be enlightening to examine whether this transformation into a more integrated system had effects statewide on different financial variables. The availability of this data for each state, as well as regional orientation of the states, which leads the United States to be the perfect study for spatial econometrics. Anselin (2013) defines spatial econometrics as a field that deals with spatial dependence and spatial heterogeneity, the relevance of these characteristics are concerned because the spatial aspect affects the model’s specification, estimation and other inferences. Due to the aforementioned characteristics, the standard econometric techniques have become inappropriate. Through the incorporation of spatial effects, so-called spillover effects are measurable. Spatial spillover effects exist from the idea that cross-sectional units interact with others, and therefore, may be influenced from those units. For example, Baltagi and Li (2004) examine the cigarette demand in the United States and found evidence of significant and negative spatial spillovers that indicate the importance of the inclusion of spatial dependence. The econometrics section provides a broader explanation of spatial econometrics.
The United States has 50 official states (51 if District of Colombia is counted as an official state) and five states that are more legally independent and still registered as official states in a rather close proximity to one another (see appendix 1 for an regional map of the United States). This paper therefore incorporates spatial econometrics with financial variables to study spillover effects into other neighboring states. By introducing spatial econometrics to a capital flow model, various financial variables provide insights into consequences for neighboring states on the net capital flows. For example, the differences in regional interest rates, the total amount assets of commercial banks or the total outstanding loans and leases are of particular interest. Since differences in regional interest rates have slowly disappeared over time, a proxy is used to establish regional interest rates (Bodenhorn and Rockoff, 1992; Rockoff, 2004). This proxy serves as a starting point for further research which can elaborate and broaden this research to European or worldwide studies. The net capital flows are based on the output divided by the income ratio per state, which thus reveals the relative magnitude of net interstate capital income flows. This method is sourced from Kalemli-Ozcan et al. (2005), as no detailed information exists about the exact capital flows between states.
4
economic activity. This effect naturally also has the opposite effect; regions that have unfavorable economic conditions become less attractive for investors, and thus, create a vicious circle for the whole region. The effect that the total assets of commercial banks per state has on the capital flows and its influence on neighboring states is also of noteworthy interest. This phenomenon, in combination with the significance of spillover effects of total loans and leases per state and its negative effect on capital flows in surrounding states, indicates the importance of spatial econometrics in financial models. The usual regressions lack the incorporation of the spatial dependence factor, which this paper proves to be of highly significant importance concerning spillover effects (Anselin and Griffith, 1988; Pace and LeSage, 2009). Spatial econometric modelling should therefore be more often implemented for financial issues. This paper thereby attempts to emphasize this necessity. The literature review cites several papers that have already implemented the spatial dependence to, for instance, the CDS spread or state banking regulation (Garrett, Wanger and Wheelock, 2005; Eder and Keiler, 2015). A rather large part of the literature review is also dedicated to the explanation of spatial econometrics, as financial readers might not have the appropriate knowledge of this particular field of econometrics.
This paper is a contribution to both the existing literature in economics and finance, as it incorporates both fields. On the one hand, it contributes to the lacking field of spatial econometrics by integrating a capital flow model and the influence of spillover effects that foster economic growth. On the other hand, it contributes to the literature of finance, as it investigates a matter that has never been investigated, through its inclusion of spatial dependence. It thus combines the research tool of spatial econometrics to explain financial movements. This paper’s most idealistic contribution is that it serves as a building block for scholars to investigate broader international issues of interest rates (and other financial variables) that concern spillover effects.
An extensive description of the literature and methodology of spatial econometrics is also included, as the derivations of all models are understood and the different effects per spatial model become apparent. A fair share of the model comparison is part of the methodology and is of importance to interpret the results and its conclusions. For the capital flows, the inclusion of spatial dependence is of critical influence, since the spillover effects for the both the assets of the commercial banks and the total loans and leases are significant. The assets of commercial banks spill positive effects towards surrounding states and the total loans and leases have a negative influence on the state’s region. The spillover effects for the assets of commercial banks are a result of the fact that the extent of interstate economic activity between states is high, which indicates that an increase in capital in one state causes a leak of capital in the neighboring states. There is a different explanation for the increase in loans and leases, as a higher proportion of the loans the state examined experiences debt accumulation, and as a consequence, higher probabilities of default. Due to this element’s role as a predictor of financial crisis, it leads companies to be reluctant to invest in those states centered around the “predicator of financial crisis”. These results once again highlight the importance of including spatial dependence in predicting and explaining financial models.
5
expected effects. Section five presents all the results and tests whether the extension is significant, it also provides a comparison of the spatial weight matrix. Finally, section six concludes the paper.
2. Literature review
One of the most investigated issues in existing literature is the level of economic activity and its effects on financial variables. Whether it is the influence of oil prices on economic activity (Lescaroux and Mignon, 2008) or the explanation of growth by means of the financial development literature (Hulme and Mosley, 1996; Murdoch and Armendariz, 2005). An undeniable relationship between economic and financial
variables holds a significant position. Among this, one of the most interesting phenomenon where economic and financial variables influence each other, are the capital. Capital flows are flows between countries that are the international equivalent of current account deficits or surpluses (Kalemli-Ozcan et al., 2005; Harvey, 2009). According to Bekaert and Harvey (1998), capital flows are positively related to key macroeconomic indicators, including growth and inflation. Other literature indicates that capital inflows influence the exchange rate, interest rates, consumption and investment (Corbo and Hernandez 1994; Khan and Reinhart 1995; Antzoulatos 1996; Kamin and Wood 1997).
In 1990, Nobel prize winner Robert Lucas Jr. attributed his paper to international capital flows and asked why capital did not flow from rich to poor countries (Lucas, 1990). With his paper, Lucas (1990) implicitly assumed that marginal return on capital was greater in less developed countries than in developed countries. Ohanian and Wright (2007) tested this proposition by measuring rate of returns and found that the opposite was true; capital flowed towards developed countries with relatively low returns. In an extension of their paper, Ohanian and Wright (2010) found that in the golden era, capital flows were consistent with standard theory. From the interwar period onwards, however, capital flows behaved in contradiction to the theory (Ohanian and Wright, 2010). These results suggest important domestic factors that drive a sizeable wedge between the marginal product of capital and returns (Ohanian and Wright, 2010).
Portes and Rey’s (2000) results indicate a strong negative relationship between distance and capital flows. Portes et al. (2001) confirm these results with a completely different data set. For Portes et al. (2001), capital flows are the global international capital markets. The distance between those flows is larger than between states within the United States. Nevertheless, this finding is of particular interest to the construction of the spatial weight matrix, as it becomes interesting to specify different matrices to confirm this finding. The spatial weight matrix is an N X N matrix that describes the spatial arrangement of the units in a considered sample. The methodology section provides an extensive explanation of the weight matrix.
6
contrary, Warnock and Warnock (2006) found that capital flows have a statistically and economically large significant impact on interest rates in the United States. Other research indicated that a one percent decrease in the interest rates would increase capital flows, as the studied relationship suggests (Calvo and Reinhart, 1996).
Since the topic of this paper is the capital spillover effects between capital flows and the interest rate among other financial variables, the following paragraphs consider the existing literature. In addition to the literature between capital flows and the interest rate, an extensive description of literature about the field of spatial econometrics is required, as researchers do not often delve into this topic. In their influential paper, Anselin and Griffith (1988) described spatial econometrics as “the collection of techniques that deal with the peculiarities caused by space in the statistical analysis of regional science models” (Anselin and Griffith, 1988a, p.7). Since 1988, the spatial econometrics field had substantially increased in popularity, which led to LeSage’s paper (2008), which included a broad overview of all spatial econometrics methods (Anselin and Hudak, 1992). Since Anselin’s book (1988) and LeSage’s contributions, researchers have developed more interest in spatial econometrics, and as a consequence, more papers in this field have been published.
Elhorst (2014) provides a historical overview of spatial econometric models implemented over time. The first generation models are based on cross-sectional data, as well as the studies from Anselin (1998) and LeSage (2008), which were mentioned previously. The second generation comprises of non-dynamic models with spatial panel data, which include time-periods to the variables and the error terms of the model. The last generation of spatial econometric modelling is comprised of dynamic spatial panel data models. Due to tremendous improvements in estimation, the third generation modeling has generated more interest, although many issues with estimation still remain (Anselin 1988; Enders, 1995; Hendry 1995; Hsaio, 2003; Baltalgi, 2005; Pace and LeSage, 2009). This paper’s focus is on non-dynamic models with spatial panel data.
7
whole era of textbooks dedicated to spatial econometrics have since appeared. The last characteristic of this stage is the expansion of software availability, and with the ease of obtaining the software expansions, researchers commit earlier to conduct spatial econometric analysis. Among others, Rey and Anseling (2006, 2010), Bivand (2006), Bivand et al. (2008), Rey (2009) and Elhorst (2014) have contributed to this software availability.
The upcoming literature combines spatial econometrics of the last maturity stage with economic and financial subjects. Rey and Montouri (1999) investigate regional income convergence in the United States over the period 1929 – 1994. The results of this investigation provide strong evidence of spatial autocorrelation in the levels of state per capita incomes (Rey and Montouri, 1999). Spatial autocorrelation was also examined among state income growth rates, which leads to the suggestion that regional neighbors display similar growth patterns. This paper indicates that previous literature for regional convergence used wrongly estimated models. Moreover, the specification in this paper suggests a misspecification took place in past studies, as a result of ignored spatial error dependence. Due to the ignorance of the spatial error dependence, the transitional dynamics of the convergence process are not efficient (Rey and Montouri, 1999). This work therefore confirms the third generation model of Elhorst (2014). The more freely available software greatly contributes to the field of spatial econometrics.
The paper by Paas and Schlitte (2006), who offers empirical insights into the regional income disparities and income growth and convergence in the European Union (Paas and Schlitte, 2006), provides more distinct information on regional income disparities and convergence in the European Union during the period between 1995 and 2003 (Paas and Schlitte, 2006). From an examination of regional income levels, the European Union reveals significant regional disparities and the general convergence level is determined by country specific effects. One further result is that spatial growth spillover effects are contained within certain borders. Consequently, the study indicates that the economic integration in the European Union is not effectively implemented (Paas and Schlitte, 2006).
Garrett, Wagner and Wheelock (2005) combined spatial econometrics with state banking regulation. In this paper, the spatial dependence on bank regulatory decisions is tested by adding spatial effects into the model. Subsequently, a probit model is estimated from the choices between permitting intrastate branching or not and through permitting intrastate banking or not (Garrett, Wanger and Wheelock, 2005). This estimation yielded the following result: a state’s choice of regulatory regime is influenced by decisions in other states. The extent of this influence, however, is varied across regions. Another finding is that all estimated models indicated that the larger the share of a state’s banking is held by insurance companies, then the lower the probability of a liberal branching regime (Garrett, Wanger and Wheelock, 2005). In the investigation of the determinants of other state economic policies by means of a spatial econometrics model, effects such as spatial effects should be included within the analysis. Early research in the field of spatial econometrics might ignore valuable characteristics (Anseling, 2009; Elhorst, 2014).
8
autoregressive parameter. The presence of indirect effects indicates new insights in the credit spread puzzle. A further finding is that the spread not only depends on volatility and a firm’s leverage, but in addition, also on market conditions and characteristics. This last finding serves as a suggestion that national and regional authorities need to realign their regulation purposes towards a more macro environment (Eder and Keiler, 2015). The described models and their results would have never been found if the field of spatial econometrics had not been improved as it has over the past decades. This fact indicates the importance of research in this field, and should therefore encourage scholars and established researches to write more papers in this field.
The previously examined articles have one important similar detail; they all combine spatial econometrics with financial models to test for relationships that before could never have been
investigated. This paper tries to establish the relationship between capital flows and the interest rate from a regional perspective. It furthermore attempts to determine whether this relationship induces spill-over effects. Based on the theory of Lucas, one would expect that the states with high interest rates, most likely less developed countries, would indeed have capital inflows. The accompaniment with inflows inherently induces capital spill-over effects, which thus entails that neighboring states benefit from the state with the high-interest rate.
This paper serves as an addition to the existing literature as it combines the research tool of spatial econometrics in order to explain financial movements. As mentioned in the introduction, it incorporates both fields with newly established models and therefore contributes to both fields. In this paper, financial movements indicate how neighboring states are affected by particular movements of financial variables as well as whether this movement encourages capital to spill-over, as research suggests. Hopefully, this paper is to lead more scholars to dedicate their time to analyzing spatial econometrics for broader datasets and more complicated issues.
3. Methodology
3.1. Capital flows
9
3.2. Interest rate
Fischer described the rate of interest as the link between capital and income in his early and influential paper in 1930. According to Fischer (1930), an interest rate can be viewed as the price of money. The interest rate is the difference between the market, which reflects money in the present, and future money, which includes a premium. This premium equals the rate of interest. The interest rate thus represents the value added to the original value as compensation to hold it into deposit. It is often known as required rate of return on riskless assets in financial models (Merton, 1974).The latter is correct for savings accounts, as an interest rate for borrowing also exists. The term structure of interest rates should therefore be
carefully identified, as it is commonly interchanged. Within this model, the focus is purely on the interest rate that commercial banks offer to consumers.
This model employs an adaption of the regional interest rate computation by Bodenhorn and Rockoff (1992) and Landon-Lane and Rockoff (2004). Since the introduction of the Federal Reserve System in 1913, interest rates have gradually converged over time across the states of the United States (McCully, 2012). The interest rates across states still marginally differ due to the existence of different state law regulation. Ribstein and Kobayashi (1996) economically analyzed the state laws and found that the different regulations indeed influence the difference in interest rates, which therefore leads to different cost-benefit analyses in each state. The regional interest rates are completely computed from balance sheet variables of commercial banks for each state. By following Landon-Lane and Rockoff (2004), the regional interest rate is the ratio of “Total Interest Income on Loans and Leases” to “Net Loans and Leases”.
3.3. Econometric section
As already described in the literature review, spatial econometrics has evolved over time. This section details the econometrics behind the model and explains why spatial extensions are necessary. Collected observations with references to regions are often termed spatially-referenced data (Pace and LeSage, 2009). Spatially-referenced data is the first stepping stone in the concept of spatial dependence. In order to demonstrate how spatial dependence is incorporated within this field of econometrics, the Ordinary Least Squares (OLS) model serves as the starting point.
𝑦𝑖 = 𝑋𝑖𝛽 + 𝜀𝑖 (1)
Where 𝑦𝑖 is the dependent variable with 𝑖 = 1, … , 𝑛 observations. 𝑋𝑖 represents a 1 x K vector of
explanatory variables, with β as the accompanied parameters in a K x 1 vector. The error term denotes the usual univariate normal distribution.
𝜀𝑖~ 𝑁(0, 𝜎2) 𝑖 = 1, … , 𝑛
10
(Pace and LeSage, 2009). The spatial model becomes more extensive by providing a separate equation for every region with some observations that depend on the values of neighboring observations. By adding equation for every region, simply as equation (1), a simultaneous equation model can be estimated that includes spatial dependence across the regions. An is presented below example regarding two regions.
𝑦1 = 𝜌𝑦2+ 𝑋1𝛽 + 𝜀1 (2)
𝑦2 = 𝜌𝑦1 + 𝑋2𝛽 + 𝜀2 (3)
This example assumes that both regions depend on each other, as it is clear from the values of 𝑦1 and 𝑦2
that they respectively depend on 𝑦2 and 𝑦1. This example assumes the same univariate normal
distribution as in equation (1). Since the United States consists of 50 regions, this method becomes a rather inconvenient way to present the model. By parsimoniously parameterizing all equations, based on Ord (1975), a practical model emerges. This method is known as a spatial autoregressive process.
𝑦𝑖 = 𝜌 ∑𝑛𝑖=1𝑤𝑖𝑖𝑦𝑖 + 𝑋𝑖𝛽 + 𝜀𝑖 𝑖 = 1, 2 (4)
The vector of observations on 𝑦𝑖 are deviations from its mean and the term ∑𝑛𝑖=1𝑤𝑖𝑖𝑦𝑖 represents a
combination of values of 𝑦𝑖 that are constructed from neighboring observations. All separate equations
are thus summarized in an n x n weight matrix W, where n is the number of states and rho is a parameter. As a whole, the term is referred to as the spatial lag. Rho indicates the spatial interdependence of states. The next section explains how the spatial weight matrix W is identified. The error term denotes the usual distribution.
Through rewriting the equation (4) into a matrix notation, further calculations can be simplified by allowing a zero mean disturbance process, with a constant variance and zero covariance between observations. When 𝑁(0, 𝜎2𝐼
𝑛) is used as in this process, a diagonal variance-covariance matrix 𝜎2𝐼𝑛
comes to existence. 𝐼𝑛 is an n-dimensional identity matrix. Through the application of this process and
rewriting equation (4), the following equation is obtained.
𝑌 = 𝜌𝜌𝑌 + 𝑋𝛽 + 𝜀 (5)
The distribution process can now be identified as 𝜀 ~ 𝑁(0, 𝜎2𝐼 𝑛).
Equation 5 thus represents matrices and for this particular model, W is an n x n matrix, 𝑌 is a n x 1 vector, β is an K x 1 vector and 𝜌 is a parameter. The three estimation models are explained and derived from the starting point of this matrix notation. For convenience, we begin with the OLS matrix notation.
𝑌 = 𝛼1𝑁+ 𝑋𝛽𝑘 + 𝜀 𝑘 = 1, … , 𝐾 (6)
No further derivations are needed for this specification. The only obtainable effects from this model are the direct effects that are represented by 𝛽𝜅. It is particularly interesting to add extensions to this model in
11
effect, which means the dependent variable of a particular unit depends on independent explanatory variables of other units (Elhorst, 2014). Elhorst (2010) provides an example with respect to the savings rate. For a single country, the savings rate must equal the investment rate. For regions, however this finding does not necessarily have to be true, which leads savings to flow to other regions and vice versa. Through the addition of this term, the model becomes the SLX model. This model was recently introduced by Halleck Vega and Elhorst (2015). It is not commonly included in the spatial econometrics toolbox, and therefore, it lacks theoretical and empirical knowledge. Since this model produces local spillover effects, this paper tries to estimate the SLX model with a somewhat unfamiliar method. The SLX model is thus an extension of the OLS through the addition of the exogenous interaction effect term.
𝑌 = 𝛼1𝑁+ 𝑋𝛽 + 𝜌𝑋𝑊 + 𝜀 (7)
The own and spillover effects of this model are easily readable in the model. The direct effects are presented by the coefficient βκ and the spillover effects by the coefficient θκ. These spillover effects
denote local spillover effects, Anselin (2003) describes local spillovers as spillovers that occur at locations that are connected by the spatial weight matrix. These are the spillover effects that are of interest for this paper, as these are spillover effects on neighboring states. In order for this extension to be statistically meaningful, a comparison with the OLS model is required to test whether (θ=0) is significant.
Global spillover effects are the counterpart of local spillover effects. Global spillover effects are effects that might induce a change in one state, whereas that state is not even connected to the state where the change originally started. Intuitively, the definition of the spillover effect would indicate something else. The Spatial Autoregressive Model (SAR) model is a model that includes global spillover effects. The direct and spillover effects are also more difficult to identify, as there is an endogenous interaction effect and the partial derivatives of the expectation of Y need to be obtained. We therefore firstly need to compute the reduced form.
𝑌 = 𝜌𝜌𝑌 + 𝛼1𝑁+ 𝑋𝛽 + 𝜀 (8)
𝑌 = (𝐼 − 𝜌𝜌)−1 𝛼1
𝑁+ (𝐼 − 𝜌𝜌)−1𝑋𝛽 + (𝐼 − 𝜌𝜌)−1𝜀 (9)
By taking the partial derivatives of X, the global indirect effects become apparent. Even the spatial weight matrix contains zero elements, and the spillover effect still affects those observations. These effects are due to the term (𝐼 − 𝜌𝜌)−1. This matrix does not contain zero elements.
⎝ ⎛ 𝑑𝑑(𝑦1) 𝑑𝑑1𝑘 ⋯ 𝑑𝑑(𝑦1) 𝑑𝑑𝑛𝑘 ⋮ ⋱ ⋮ 𝑑𝑑(𝑦𝑛) 𝑑𝑑1𝑘 ⋯ 𝑑𝑑(𝑦𝑛) 𝑑𝑑𝑛𝑘 ⎠ ⎞ = (𝐼 − 𝜌𝜌)−1𝛽 𝜅 (10)
The direct effects are the diagonal elements of (𝐼 − 𝜌𝜌)−1𝛽
𝜅 and the indirect effects are the off-diagonal
12
and indirect effects are the same for every explanatory variable. For the direct effect, the mean diagonal element acts as the summary indicator, and for the indirect effects, the mean row sum of the off-diagonal elements acts as the summary indicator. (Elhorst, 2014). Due to this restriction, the spatial spillover effects are limited in their flexibility. Through testing whether (ρ=0), it is possible to test whether this extension is statistically significant.
In the previous two extensions, exogenous and endogenous interaction effects were added. The last effect is an interaction effect among error terms. This interaction term, 𝜆𝜌𝜆, assumes that the error terms between different observations influence one another. By adding this term to the OLS equation, the Spatial Error Model (SEM) can be obtained.
𝑌 = 𝛼1𝑁+ 𝑋𝛽 + 𝜆 with 𝜆 = 𝜆𝜌𝜆 + 𝜀 (11)
Since this interaction effect causes effects among the error terms, no spillover effects exist. The spatial interaction effects are set to zero by construction. This is a limitation since because spatial spillover effects are one of the main reasons that a spatial econometric model is implemented. In order to test whether this extension is statistically significant, (λ=0) should be statistically different from zero.
The Spatial Durbin Model (SDM) is a particularly strong model. This model is an extension of either the SAR, SLX or SEM, appendix 2 presents an overview of all models and the possible extensions. This model’s strength is that it imposes no prior restriction on the magnitude of the indirect effects, and thus, does not produce biased parameters.
𝑌 = 𝜌𝜌𝑌 + 𝛼1𝑁+ 𝑋𝛽 + 𝜌𝑋𝑊 + 𝜀 (12)
Since the SDM model has the endogenous interaction term, the interaction terms are more difficult to identify. As with the SAR model, the starting point is the reduced model.
𝑌 = (𝐼 − 𝜌𝜌)−1 𝛼1
𝑁+ (𝐼 − 𝜌𝜌)−1(𝑋𝛽 + 𝜌𝑋𝑊) + (𝐼 − 𝜌𝜌)−1𝜀 (13)
By taking the partial derivative of X, the effects of the explanatory variables become evident.
⎝ ⎛ 𝑑𝑑(𝑦1) 𝑑𝑑1𝑘 ⋯ 𝑑𝑑(𝑦1) 𝑑𝑑𝑛𝑘 ⋮ ⋱ ⋮ 𝑑𝑑(𝑦𝑛) 𝑑𝑑1𝑘 ⋯ 𝑑𝑑(𝑦𝑛) 𝑑𝑑𝑛𝑘 ⎠ ⎞ = (𝐼 − 𝜌𝜌)−1(𝛽 𝜅+ 𝜌𝑊𝑘) (14)
The diagonal elements of (𝐼 − 𝜌𝜌)−1(𝛽
𝜅+ 𝑊𝑘) act as the direct effects and the off-diagonal elements
serve as the spillover effects. The spillover effects in the SDM are global because the exogenous variables are multiplied by the spatial weight matrix. This effect therefore does not consider whether the spatial identities share borders.
13
among error terms. In the case that the SDM is the most appropriate model, this model may be an alternative. Since the SEM model does not provide spatial spillover effects, this model may be attractive. The coefficients between the models are almost identical with the great benefit of spatial spillover effects for the SDEM model.
𝑌 = 𝛼1𝑁+ 𝑋𝛽 + 𝜌𝑋𝑊 + 𝜆 with 𝜆 = 𝜆𝜌𝜆 + 𝜀 (15)
No further calculations are necessary to obtain the coefficient estimates for the direct and spillover effects. The direct effects are equal to 𝛽𝜅 and the spillover effect is equal to 𝑊𝑘. Both these effects may be different
among explanatory variables.
All the six described models are tested and conclusions are based on the most appropriate model. The most appropriate model is chosen according to whether the extension is statistically significant. The benefits and limitations of the different models are also considered. Appendix two provides an overview of all model specifications and indicates how the extensions are tested and constructed. The next section describes the construction of the spatial weight matrix and section 4 identifies the actual model.
3.4. Construction of the weighting matrix
A spatial weight matrix must be identified for the spatial econometric application. The spatial weight matrix W represents a linear combination of values, depending on the quantification of the matrix, which is taken by neighboring observations in time (Pace and LeSage, 2009). The matrix W is an n x n spatial matrix that places elements, either a 0 for no connection or a 1 for sharing a common side of interest (Lesage, 2008). The spatial contiguity is quantified as the rook contiguity matrix; the rook contiguity matrix defines 𝜌𝑖𝑖 = 1 for entities that share a common border. This is commonly known as the
first-order neighbor matrix, as the only regions of interest are the regions that share a common bfirst-order. This contiguity matrix is symmetrical by its nature. Besides the binary contiguity matrix, the inverse distance matrix is created in order to test whether which matrix most appropriately suits the data.
The zero mean disturbance process exhibits constant variance 𝜎2 and zero covariance between
observations, 𝜀 ~ 𝑁(0, 𝜎2𝐼
𝑛). Due to this process, the diagonal variance-covariance matrix is 𝜎2𝐼𝑛. The last
term of this equation, 𝐼𝑛, is the identity matrix (LeSage, 2008). The identity matrix is the n-dimensional
matrix, which contains ones on the main diagonal and zeros elsewhere (Hoy et al., 2011). The spatial weight matrix must follow two conditions: (1.) The row and sums of the matrix W before W that are row-normalized should not uniformly bounded in absolute value, as N approaches infinity and (2.) This summation should not diverge to infinity at a rate equal or faster than the rate of the sample size (Elhorst, 2014). Fortunately, since this is a first-order matrix, both these conditions are automatically satisfied.
This spatial matrix is 49 by 49, since Hawaii and Alaska do not share borders with other states. These states are therefore excluded from the total sample. The District of Colombia is added to the matrix, despite the fact that it is not an official state. The matrix is constructed as a first-order neighbor matrix with the states in alphabetical order, which thus begins in column 𝑎1,1with Alabama and 𝑎1,49 with
14
implementing 𝜌𝑖𝑖 = 1 for shared borders among states, the binary contiguity matrix is constructed. See
appendix 1 for an overview of all states as well as which states share borders. This matrix is constructed in excel and implemented in Stata for row-normalization.
We have now specified the spatial weight matrix. For the ease of interpretation, W is normalized such that all elements of each row sum to unity. Since W is always positive, the matrix W weighs each neighboring observation equally and thus can be interpreted as an average of the values of neighboring values (Pace and LeSage, 2009; Elhorst, 2014).
Besides the binary contiguity matrix, the inverse distance matrix is also constructed. Through its focus on the capital per state and the accompanying latitude and longitude, the inverse distance matrix can be constructed in MATLAB. By dividing the square of the difference between the latitude and
longitude per spatial entity, and squaring that value, the inverse distance matrix can be obtained. Instead of row-normalization, the inverse distance matrix is labeled as matrix normalization. In this approach, the elements of W are divided by its largest characteristic root. This calculation is completed because if the inverse distance matrix is row-normalized, the weights sum would cause the matrix to lose its economic interpretation for this decay. This matrix also needs to satisfy both conditions. Condition (2.) is
automatically satisfied since the ratio divided by the sample approaches zero as the sample approaches infinity. For condition (1.) this condition may not be satisfied if an infinite number of spatial units are linearly arranged. Since the distance of its first left- and right-hand neighbor is d; to its second left- and right-hand neighbor, this is 2d. This process continues to infinity and therefore each row sum represents a series that is not finite. Fortunately, since this matrix does not consist of an infinite number of spatial units and is not linearly arranged, there is no need for a cut-off point and condition (1.) is therefore also
satisfied.
The spatial autoregressive model controls the interaction of the interest rates in neighboring states (Bodenhorn and Rockoff, 1992). The spatial weight matrix also determines the economic links that it has with states. This value is also a measurement of financial market integration over the years.
4. Data
4.1 Data description
15
In addition to the FDIC, the data for State GDP and for personal income per state is provided by the Bureau of Economic Analysis (BEA). The BEA has a special department for regional United States data. The variables obtained from the BEA form the approximation for the capital flows and are covered below. Personal income expenditures, State GDP, disposable income and personal income are the variables that are of particular interest for this paper.
4.2 Model
Following the explanation of the econometrics of the model and the model differences, this section presents the model itself. The model explains the capital flows between states and examines whether the interest rate differences between states cause spill-over effects. The next sections explains all the variables in the model. The whole model is in vector form and equations (6), (7), (8), (11), (12), (15) are estimated. Firstly, a regression takes place of the OLS equation and thereafter the interaction terms are added one by one. After an estimation of the SDEM model, all the extensions are tested for significance and the most appropriate model is then selected.
𝑌 = 𝛼1𝑁+ 𝜌𝜌𝑌 (𝑜𝑜𝑜𝑖𝑜𝑛𝑎𝑜) + 𝑋𝛽 + 𝜌𝑋𝑊 (𝑜𝑜𝑜𝑖𝑜𝑛𝑎𝑜) + 𝜆
with 𝜆 = 𝜆𝜌𝜆 (𝑜𝑜𝑜𝑖𝑜𝑛𝑎𝑜) + 𝜀
Whereas all variables expect the parameters 𝜌, 𝜌, 𝑊 and 𝛽 are matrices of the form 49 x 1 with the information for each state (i = 1,…,49) and time period (t = 1,…,49). Y represents the net capital flows. 𝜌𝜌𝑌 is the spatial lag of the net capital flows and is only included in the SAR and SDM models. 𝑋𝛽 represents the explanatory variables, which are the regional interest rate, taxes, total assets of the
commercial banks, the number of institutions, net income, number of employee, total loans and leases and dividends. 𝜌𝑋𝑊 measures any potential difference in the exogenous level of the explanatory variables across states and over time. These terms are only included in the SLX, SDM and SDEM model. 𝜆𝜌𝜆 measures the differences among error terms across states. This term is only applicable to the SEM and SDEM model. The results section determines and statistically tests which extension would be the most suitable for this paper.
The relationship between capital flows and the exchange rate is normally included. This paper, however, only examines the states of the United States, and since all states have the dollar as their currency, the exchange rate can be excluded (Kouri and Porter, 1974; Calvo et al., 1993; Hau and Rey, 2006).
4.3 Variables
Dependent variable:
Net capital flows: As already mentioned in the methodology section, capital flows are flows of
16
accessible by the BEA as part of the U.S. state-level National Accounts. The GSP is the equivalent of the GDP, but is noted per state. The approximation of GNI is the income measure of states, and since no GNI exists at the state level, this measure is Personal Income at the State level. This variable is also obtained from the BEA. Combined together, these two variables prove a good approximation for net capital interstate flows. Kalemli-Ozcan et al. (2005) test this approximation at the national level and found that the approximation only slightly deviated from the original capital flow.
Independent variables:
Regional interest rate: Interest rates in the United States used to be very different among states
(Bodenhorn and Rockoff, 1992). Over the past decade, interest rates gradually converged. Due to different state regulations, however, the interest rate across states has still not completely converged (Landon-Lane and Rockoff, 2004). As the literature and methodology sections explain, in theory, a higher rate of interest would increase capital flows since the cost of money is higher when the interest rate is higher (Fischer, 1930). The regional interest rate is based on Landon-Lane and Rockoff (2004) as previously explained. Since both components of the regional interest rate are obtained from the commercial bank balance sheet, this method is plausible. The regional interest rate is the ratio of “Total Interest Income on Loans and Leases” to “Net Loans and Leases” (Bodenhorn and Rockoff, 1992; Landon-Lane and Rockoff, 2004).
Taxes: Taxes influence the incentives of all firms in areas of economic activity, and thus, also
affect capital flows (Di Giovanni, 2005). Hines Jr. (1996) extensively summarizes the literature through empirical research of the impact of different forms of taxation on U.S. in and out flows (Hines Jr, 1996). This finding, however, is based at national level data rather than state level data, on which this paper focuses. The taxes still differ among states and these variables are therefore included in the model. The tax variable is obtained from the balance sheet as Applicable Income Taxes, and therefore, is considered a suitable proxy for taxes.
Total assets Commercial Banks: The total value of the assets of commercial banks is a control
variable since large increases in this total asset value may indicate high capital inflows (Vargas and Varela, 2008). Similar reasoning applies for large decreases in total asset value. Large decreases may be an example of significant high capital outflows to other surrounding states (Vargas and Varela, 2008). For all commercial banks for each state, the total asset is taken from the accompanying balance sheet.
Number of Institutions (commercial banks): The number of commercial banks in a state is
important for the capital flows, since overall, the number of commercial banks is an indicator for the level of economic activity. The more banks that operate in a state, the higher the change of capital flows, simply because the economic activity may be higher. According to Stiglitz (2000), as learned from the global crisis in 2008, the financial institutions needed a strong establishment and thus a strong revolution. Since all states most likely reacted differently to the crisis, institutions are an important state-specific
17
Net income: Net income is used as a control variable, as it is important in equalizing capital flows
between accounts. In the identification of national income, it is evident that the net inflow of investments is equal to the current account deficit (Feldstein and Horioka, 1980). Feldstein and Horiaka (1980) state that capital flows have a close link with savings and investments, and thus a high domestic marginal product of capital, referred to as net income in this paper, has higher levels of capital inflows. The value for net income is obtained from the income statement of the commercial banks for each state.
Number of employee: The level of employment activity for the commercial bank sector per state
is another indicator of economic activity, and thus acts as a control variable for the differences between states. This variable is the total number of employees that work at commercial banks per state. Therefore, only employees employed in the specific years are counted in the total. Lay-offs are not included in the total number unless an employee has worked for more than six months of that year.
Total Loans and leases: The total of debt accumulation is expected to have a negative effect on
capital flows, as banks with high debt accumulation levels have higher changes of default (Harris and Raviv, 1990; Leland 1998; Aguair and Gopinath, 2006). Higher debt levels can be predictors for financial crisis. The crisis of 2008 is an excellent example of this phenomenon, and as a consequence, has reverse capital flows (Rodrik and Velasco, 1999). Total loans are the total loans and leases reported on the balance sheet per state.
Dividends: The divided yield is directly related to the cost of capital (Bekaert and Harvey, 1998).
This dividend yield is assumed to sharply decrease after capital inflows (Beakaert and Harvey, 1998). The level of dividends for the commercial banks per state is thus a control variable for the net capital
interstate flows. This variable is expected to converge over the time, as the United States market has since greatly integrated (Campbell and Hamao, 1992; Bekaert and Harvey, 1995; Huang and Yang, 2000).
5. Results
5.1 Model comparison
This section estimates the various spatial models, all the models described in section 3, as well as the significance of their extension. Before the results are presented, one critical note of the R-squared requires an explanation. Since all the data, with the exception of the inverse distance matrix calculated in MATLAB, is processed in Stata, the R-squared of the fixed effects model is not of the appropriate proportion that the model requires. The R-squared variable is the variable that shows the extent to which the model is correctly estimated, and thus an R-squared of 0.9 indicates that the model is predicated ninety percent correct. Therefore, the higher the R-squared, the more correctly the model explains the dependent variable. In the case of a fixed effects model, the R-squared presented by Stata assigns no explanatory power to the individual intercepts, and thus, does not consider the variation that is present in regression fixed effects models.
18
is safe to assume that the data fits all models, and thus, that all the models are appropriate to draw conclusions. The Log Likelihood estimator compares the SDM and SDEM since there is no extension to test between these models. The first section covers all the estimated extensions and concludes which model most appropriately fits. All the extensions are combined with both spatial weight matrices, and a conclusion follows at the end of the section which determines the chosen spatial weight matrix.
The tables below consider the extensions based on the spatial model scheme presented by Elhorst in his paper “Applied spatial econometrics: raising the bar” from 2010. The first table considers the extensions from OLS for both spatial weight matrices. The extensions should be statistically different from zero. The distribution of the extensions tests is the chi-square distribution. This value and the accompanying p-value are presented in table 1. Rho, theta and lambda are the extensions to SAR, SLX and SEM, respectively. As clear from the table, all the extensions are significant, and are therefore applicable and preferred over OLS.
Table 1: Model extensions from OLS for both spatial weight matrices
Binary Weight matrix Inverse Distance weight matrix
ρ=0 θ=0 λ=0 ρ=0 θ=0 λ=0 Chi² 163.43 154.80 32.67 6.71 7.79 31.93 P-value 0.0000 0.0000 0.0000 0.0096 0.0052 0.0000 Degrees of freedom 2392 k392 2392 2392 2392 2392
Since all extensions are statistically significant, it is still possible that the SDM model exists. For this reason, all three models can be extended that the model becomes the SDM model. Therefore, the next extensions test whether the SDM model is preferred over the other three models. If all extensions prove to be significant, then the SDM model is the model that most appropriately suits the data. To deem which model is appropriate, the null hypotheses are that theta equals to zero, rho equals zero and theta plus rho times beta equals zero. These hypotheses are tested for the SAR, SLX and SEM models, respectively. Table 2: Model comparison between SDM and the models SAR, SLX and SEM
Binary Weight matrix Inverse Distance weight matrix
19
For the binary weight matrix, the extension of SDM is preferred over SAR, SEM and SLX. For the inverse distance weight matrix, the SDM is preferred over SAR and SEM. In comparison with SLX, however, the extension is not statistically significant, with an p-value of 0,3120. SLX is thus preferred over SDM, which means that the only extension that is possibly more suited for the data is the SDEM. This model is compared with the SLX along the Log Likelihood ratio test, and thus, this extension is tested for the inverse distance weight matrix. By testing lambda is equal to zero, the chi-squared test results in 152,10 with an accompanying p-value of 0.00001. This result rejects the null hypothesis and provides evidence
that prefers the SDEM model over the SLX model. With all extensions examined and tested, the SDM model and SDEM model prove to appropriately fit the dataset for the binary contiguity matrix and inverse distance matrix, respectively. In the direct and spillover section, both models are compared by means of the Log Likelihood ratio test.
5.2. Main results
As the SDM model and SDEM model are deemed the most appropriate models for the implemented dataset, this section now presents and discusses these models. The output of the OLS model is added to indicate the differentiations between the models. Table 3 presents the results of these models. The effect that regional interest rates have net capital flows is significant and positive, which therefore explains that the increase in one additional percent of the interest rate per state increases the net capital flows by approximately 0.1 for every model. The coefficient estimates of the different models cannot be compared directly, since the nature of the specifications is different between models; the SDM model contains global specifications and the SDEM contains local specifications. The positive coefficient, nevertheless, is a reasonable and expected effect, as the higher the interest rates are, the larger the reward on capital becomes, which thus creates additional capital flows, because the interest rate offers investors a higher reward. Lambda is also statistically significant, as confirmed by the model comparison section. This same reasoning applies to rho, although in the inverse distance matrix, rho becomes insignificant. The model comparison also confirmed this finding. The variables taxes and number of employees are also significant in all the presented models. Despite its significance, the extremely low coefficient leads the interpretation of these variables to be useless.
Through the multiplication of all the variables with the spatial weight matrix, the number of institutions is the only variable, which is significant in all models. For the inverse distance matrix, the log total assets of commercial banks multiplied by the matrix itself provides an interesting variable in this estimation, due to the significance and the coefficients of 0.9449 and 0.8686 for the SDM model and SDEM model, respectively. Of greater interest is the observation that the coefficient of the main variable is negative, which indicates that by multiplying with the inverse distance matrix, this variable becomes highly significant and switches to a positive coefficient. The total effect that the total assets of commercial banks have on net capital flows is as follows: for every asset increase, the capital flows decrease with 0.039 and 0.0013 for SDM and SDEM, which accounts for the inverse distance matrix. One possible explanation of this relationship is that the increase in the assets of the banks leads to more investment in
20
the state itself. Since the proxy of the implemented net capital flows are the capital interstate flows, a negative coefficient is a confirmation of more assets being retained in the state. The next section describes the spillover effects more extensively.
Table 3: Model comparison of the OLS, SDM and SDEM model with both weight matrices.
The inverse distance matrix multiplied by the variable log loans and leases also becomes highly significant. The coefficient further decreases in comparison to the main coefficient, which leads the spillover effects to be significant and its effect to be large. One common financial explanation for these results is that when loans and leases increase, capital flows becomes smaller due to the higher risk
Variable (1) No spatial effects (2) Binary weights matrix (3) Inverse distance matrix
Fixed OLS SDM SDEM SDM SDEM
Regional Interest Rates 0.0933
(3.42) 0.1000 (3.23) 0.0984 (3.05) 0.0943 (2.92) 0.1001 (3.26)
Taxes
(*10^7) 0.158 (3.42) 0.157 (3.63) 0.168 (3.90) 0.157 (3.49) 0.172 (4.27)
Log Total Assets of Commercial
Banks -01.02 (2.80) -.0199 (-1.28) -0.1413 (-0.86) -0.039 (-0.25) -0.0013 (-0.09)
Number of Institutions 0.0000
(5.31) 0.0000 (1.18) 0.0000 (2.54) 0.0000 (5.73) 0.0000 (2.39)
Log Total Loans and Leases 0.0042
(0.27) 0.0159 (1.18) 0.0092 (0.60) -0.0023 (-0.16) -0.0023 (-0.16) Net Income (*10^8) -0.297 (-1.42) -0.307 (-1.58) -0.313 (-1.55) -0.267 (-1.32) -0.253 (1.34) Number of Employees (*10^6) -0.181 (-2.68) -0.127 (-2.01) -0.121 (-1.98) -0.183 (-2.78) -0.123 (-2.14) Dividend (*10^8) 0.211 (1.10) 0.140 (0.78) 0.143 (0.65) 0.276 (1.48) 0.166 (0.94)
W x Regional Interest Rates -0.0691
(-1.04) -0.0146 (-0.20) 0.0581 (0.23) 0.0158 (0.07)
W x Taxes
(*10^7) -0.0396 (-0.45) 0.0395 (0.41) 0.111 (0.49) -0.00284 (-0.01)
W x Log Total Assets of Commercial
Banks 0.1271 (0.47) 0.0232 (0.78) 0.9449 (4.85) 0.8686 (4.67)
W x Number of Institutions 0.0002
(5.97) 0.0001 (4.28) -0.0014 (-3.46) -0.0014 (-3.58)
W x Log Total Loans and Leases -0.2019
(-0.88) -0.0362 (-1.37) -0.9210 (-4.96) -0.8605 (-4.86) W x Net Income (*10^8) 0.695 (-0.17) -0.244 (-0.54) -0.419 (-0.35) 0.201 (-0.81) W x Number of Employees (*10^6) 0.00068 (0.06) 0.00228 (0.18) -0.0304 (-1.27) -0.0182 (-0.81) W x Dividend (*10^8) 0.446 (1.43) 0.443 (1.38) 0.462 (0.80) 0.357 (0.65) ρ 0.3313 (12.02) -0.0724 (-1.01) λ 0.3424 (12.20) 0.3441 (12.26) N 2,401 2,401 2,401 2,401 2,401 Log-Likelihood 3113.39 3206.29 3192.43 3135.61 3200.83
21
involved when more loans are outstanding. Banks, and almost all economic players become more
reluctant since the proportion of loans and leases in the state has increased, which causes capital flows to stagnate. The other variables are near 0 and insignificant, which the discussion part of the results section explains.
5.3 Direct and spillover effects
Table 4: Model comparison of the estimated direct and spillover effects for the OLS, SDM and SDEM with both weight matrices.
The previous section describes the main effects of the variables that have a coefficient different than approximately zero. The results of the direct effects of the SDM model and the estimations presented in table 3 differ as a result of the impact of the effects, which pass through different states for global specifications. These values are equal for OLS and SDEM, since they do not incorporate global
specification, but instead incorporate local specification. Before the description of the direct and spillover effects, the Akaike’s Information Criterion (AIC) is implemented. Since the models are not nested, the Log-Likelihood ratio test is not suitable. The lowest value of the AIC indicates that it is the most suitable model
Variables (1) No spatial effects (2) Binary weights matrix (3) Inverse distance matrix
Fixed OLS SDM SDEM SDM SDEM
Direct effects
Regional Interest Rates 0.0933
(3.42) 0.0985 (2.96) 0.0984 (3.05) 0.0953 (2.87) 0.1001 (3.26)
Taxes
(*10^7) 0.1580 (3.42) 0.1560 (3.55) 0.1680 (3.90) 0.1550 (3.56) 0.1720 (4.27)
Log Total Assets of Commercial
Banks -0.0102 (2.80) -0.0178 (-1.11) -0.1413 (-0.86) -0.0047 (-0.31) -0.0013 (-0.09)
Number of Institutions 0.0000
(5.31) 0.0000 (2.29) 0.0000 (2.54) 0.0001 (5.77) 0.0000 (2.39)
Log Total Loans and Leases 0.0042
(0.27) 0.0132 (0.91) 0.0092 (0.60) -0.0013 (-0.09) -0.0023 (-0.16) Net Income (*10^8) -0.2970 (-1.42) -0.3100 (-1.55) -0.3130 (-1.55) -0.2540 (-1.27) -0.2530 (1.34) Number of Employees (*10^6) -0.1810 (-2.68) -0.1320 (-1.92) -0.1210 (-1.98) -0.1840 (-2.69) -0.1230 (-2.14) Dividend (*10^8) 0.2110 (1.10) 0.1770 (0.99) 0.1430 (0.65) 0.2760 (1.50) 0.1660 (0.94) Spillover effects
Regional Interest Rates -0.0417
(-0.45) -0.0146 (-0.20) 0.0105 (0.30) 0.0158 (0.07)
Taxes
(*10^7) 0.0211 (0.17) 0.0395 (0.41) 0.0015 (0.45) -0.0028 (-0.01)
Log Total Assets of Commercial
Banks 0.0087 (0.22) 0.0232 (0.78) 0.1330 (4.88) 0.8686 (4.67)
Number of Institutions 0.0003
(6.13) 0.0001 (4.28) -0.0002 (-3.17) -0.0014 (-3.58)
Log Total Loans and Leases -0.0218
(-0.66) -0.0362 (-1.37) -0.1296 (-4.96) -0.8605 (-4.86) Net Income (*10^8) -0.2370 (-0.40) -0.2440 (-0.54) -0.0566 (-0.32) 0.2010 (-0.81) Number of Employees (*10^6) -0.0572 (-0.34) 0.0228 (0.18) -0.0432 (-1.33) -0.1820 (-0.81) Dividend (*10^8) 0.6940 (1.53) 0.4430 (1.38) 0.0646 (0.76) 0.3570 (0.65)
22
to fit the data. In our case, therefore, this is the SDM model in combination with the binary contiguity matrix. inverse distance matrix. One would expect the SDM model with the inverse distance matrix to be more suitable than the SDM with the binary weight matrix. Since the SDM model extension is not
statistically significant, however, this AIC is lower. This section’s focus is therefore the direct and spillover effects of the SDM model with the binary contiguity matrix. These spillovers have a global specification, and for this reason, both neighbors who share a border as well as states that are not connected, are taken into consideration. This thus meaning that effects flow through states.
From an economic and geographical point of view, local spillover effects make more sense. Therefore, in addition to explaining the SDM model with the binary weight matrix that suits the overall data most appropriately, a small section is dedicated to explain the outcome of the SDEM model with the inverse distance matrix. It is debatable which matrix is more logical to implement and the SDEM model fits the inverse distance matrix more appropriately.
Table 5: Log-likelihood values for the SDM and SDEM model for both matrixes Log-Likelihood (1) Binary weight matrix (2) Inverse distance matrix
SDM 3206.29 (-6384.577) 3135.61 (-6245.212) SDEM 3192.43 (-6362.293) 3200.83 (-6375.667)
Note: the AIC are presented in parentheses 5.3.1 SDM model with binary contiguity matrix
The direct effect of the regional interest rate on net capital flows is highly significant and its effect is 0.0984. To explain this positive effect, the interest rate influences other states even if they are not connected. The higher the interest rate in one particular state, the more that capital flows towards that state; it is fairly easy to purchase state specific bonds or even assets from state-specific companies without physically visiting that state. In accordance with the cost of capital theory, countries with higher interest rates attract more capital because the reward on capital is higher in those countries. The same reasoning applies for states, as states that have higher interest rates than comparable states attract more capital simply because investors earn more money in those particular states.
Taxes are also highly significant, with a coefficient of 0.1560, despite only marginally affecting capital flows. The variables that are approximately zero are impossible to interpret, and thus the only two remaining variables are the assets of commercial banks and the loans and leases. One variable is negative and is -0.0178 and the other is positive with a value of 0.0132, respectively. Since these values are both insignificant, no further conclusions can be based of both parameters.
The only significant global spillover effects are the number of institutions that affect the capital flows in states, which is only 0.0003. One possible explanation of this positive spillover effect is the existence of higher institutionalized states that leak capital to surrounding states. States with less
23
5.3.2 SDEM model with an inverse distance matrixThe direct effect of the regional interest rate on net capital flows is highly significant and is 0.1001, which thus again confirms the reward on capital theory, as under the first-order neighbor matrix.
Taxes are also highly significant, with a coefficient of 0.1720, despite only marginally affecting capital flows. The variables that are approximately zero are impossible to interpret, and thus the only two remaining interpretable variables are the assets of commercial banks and the loans and leases. Both direct effects are negative, -0.0013 and -0.0023, respectively. Since these are both insignificant, no further conclusions can be based of both parameters.
The spillover effects in this model prove to be an interesting example. Especially the variables assets of commercial banks and loans and leases, which increased (decreased) tremendously, are highly significant. Indicating that neighboring states profit from these variables. The coefficient for assets of commercial banks is 0.8686, and thus spills a part of the variable to neighboring states. The increase in the level of assets might improve the economic situation because interstate economic activity, by increasing the capital of commercial banks in one state, causes commercial banks to invest in neighboring states causes spillovers.
The loans and leases coefficient is -0.8605, which is also highly significant. This relationship between loans and leases and the capital flows is expected. Since higher debt accumulation leads to higher changes of default, debt serves as a predictor for financial crisis. In other words, when a state performs worse and starts lending more, the chance that surrounding regions are also expecting more severe economic conditions is probable. This dynamic leads to negative spillover effects.
5.4 Discussion
24
6. Conclusion
This paper has examined the capital flows and the effect of regional interest rates and other financial variables. Based on statistical software, it selected the most appropriate spatial econometrics model. This subject, in combination with the spatial econometric toolbox, provides evidence for the proposition that the difference in interest rates causes capital flows to deviate. The direct effect that regional interest rates has on net capital flows, in the most suitable spatial model, is highly significant and positive. The positive coefficient was expected, as higher interest rates imply a higher reward on capital, which thus leads more capital to flow into states with higher interest rates. No spillover effects exist as a result of differences in regional interest rates. Increases in assets of commercial banks per state and the level of loans and leases per state induce highly significant results. The explanation of the significant spillover effect for assets per commercial banks lies in the economic interstate activity, as states are more financially bounded to their closest neighbors. An increase in the assets of commercial banks partly splits into neighboring states, and spillover might be, for example, banks’ investments toward companies in neighboring states. Loans and leases indicate a negative spillover effects, which from financial theory is extremely plausible. Loans and capital flows have a negative relationship because a higher level of loans indicates debt accumulation, and as a consequence of debt accumulation, higher change of default. When one particular state has increased loan levels, it leads neighboring states to be less attractive as well, since companies are reluctant to invest in states where the prediction levels of, for example, a financial crisis are higher. Further research on spatial econometric implementation in finance should be conducted, particularly with respect to capital flows models, as many variables in this paper are approximately equal to zero.
References
Aguiar, M., & Gopinath, G. (2006). Defaultable debt, interest rates and the current account. Journal of international Economics, 69(1), 64-83.
Anselin, L. (2009). Spatial regression. The SAGE handbook of spatial analysis, 1, 255-276.
Anselin, L. (2013). Spatial econometrics: methods and models (Vol. 4). Springer Science & Business Media. Anselin, L., & Bera, A. K. (1998). Spatial dependence in linear regression models with an introduction to spatial econometrics. Statistics Textbooks and Monographs, 155, 237-290.
Anselin, L., & Griffith, D. A. (1988). Do spatial effects really matter in regression analysis?. Papers in Regional Science, 65(1), 11-34.
Anselin, L., & Hudak, S. (1992). Spatial econometrics in practice: A review of software options. Regional science and urban economics, 22(3), 509-536.
Antzoulatos, A. A. (1996). Capital flows & current account deficits in the 1990s: why did Latin America & East Asian countries respond differently? Federal Reserve Bank of New York, (9610).
Baltagi, B. H., Bratberg, E., & Holmås, T. H. (2005). A panel data study of physicians' labor supply: the case of Norway. Health Economics, 14(10), 1035-1045.
Baltagi, B. H., & Li, D. (2004). Prediction in the panel data model with spatial correlation. Advances in spatial econometrics, 283-295.
25
Bekaert, G., & Harvey, C. R. (1998). Capital flows and the behavior of emerging market equity returns. National Bureau of Economic Research Working paper, (6669).
Berry, B. J. L., & Marble, D. F. (1968). Spatial analysis. Prentice Hall.
Bivand, R. (2006). Implementing spatial data analysis software tools in R. Geographical Analysis, 38(1), 23-40. Bivand, R. S., Pebesma, E. J., & Gomez-Rubio, V. (2008). Spatial Data Import and Export. Applied Spatial Data Analysis with R, 81-111.
Bodenhorn, H., & Rockoff, H. (1992). Regional interest rates in antebellum America. In Strategic factors in nineteenth century American economic history: A volume to honor Robert W. Fogel, 159-187. University of Chicago Press. Broz, J. L. (1997). The international origins of the Federal Reserve System. Cornell University Press.
Calvo, G. A., Leiderman, L., & Reinhart, C. M. (1993). Capital inflows and real exchange rate appreciation in Latin America: the role of external factors. Staff Papers-International Monetary Fund, 108-151.
Calvo, S. G., & Reinhart, C. M. (1996). Capital flows to Latin America: is there evidence of contagion effects?. World Bank Policy Research Working Paper, (1619).
Campbell, J. Y., & Hamao, Y. (1992). Predictable stock returns in the United States and Japan: A study of long-term capital market integration. The Journal of Finance, 47(1), 43-69.
Can, A. (1992). Specification and estimation of hedonic housing price models. Regional science and Urban Economics, 22(3), 453-474.
Case, A. C. (1991). Spatial patterns in household demand. Econometrica: Journal of the Econometric Society, 953-965. Corbo, V., & Hernandez, L. (1994). Macroeconomic adjustment to capital inflows: Latin American style versus East Asian style. World Bank Publications, (Vol. 1377).
Di Giovanni, J. (2005). What drives capital flows? The case of cross-border M&A activity and financial deepening. Journal of international Economics, 65(1), 127-149.
Eder, A., & Keiler, S. (2015). CDS spreads and contagion amongst systemically important financial institutions–a spatial econometric approach. International Journal of Finance & Economics, 20(4), 291-309.
Elhorst, J. P. (2010). Applied spatial econometrics: raising the bar. Spatial Economic Analysis, 5(1), 9-28.
Elhorst, J. P. (2014). Spatial econometrics: from cross-sectional data to spatial panels. Heidelberg, New York, Dordrecht, London: springer.
Enders, W. (1995). Applied Econometric time series: Wiley series in probability and mathematical statistics. Applied econometric time series: Wiley series in probability and mathematical statistics.
Feldstein, M. (1994). Tax policy and international capital flows. National Bureau of Economic Research Working paper, (4851).
Feldstein, M. S., & Horioka, C. Y. (1979). Domestic savings and international capital flows. The Economic Journal, 90, 314-329.
Fisher, I. (1930). The theory of interest. New York, 43.
26
Garrett, T. A., Wagner, G. A., & Wheelock, D. C. (2005). A spatial analysis of state banking regulation. Papers in Regional Science, 84(4), 575-595.
Getis, A. (1990). Screening for spatial dependence in regression analysis. Papers in Regional Science, 69(1), 69-81. Halleck Vega, S., & Elhorst, J. P. (2015). The SLX model. Journal of Regional Science, 55(3), 339-363.
Harris, M., & Raviv, A. (1990). Capital structure and the informational role of debt. The Journal of Finance, 45(2), 321-349.
Harvey, J. T. (2009). Currencies, capital flows and crises: A post Keynesian analysis of exchange rate determination. Routledge.
Hau, H., & Rey, H. (2006). Exchange rates, equity prices, and capital flows. Review of Financial Studies, 19(1), 273-317. Haynes, S. E. (1988). Identification of interest rates and international capital flows. The Review of Economics and Statistics, 103-111.
Hendry, D. F. (1995). Dynamic econometrics. Oxford University Press on Demand.
Hines Jr, J. R. (1996). Tax policy and the activities of multinational corporations. National Bureau of Economic Research Working paper, (5589).
Hoy, M., Livernois, J., McKenna, C., Rees, R., & Stengos, T. (2011). Mathematics for economics (3th). MIT Press, Cambridge.
Hsiao, C. (2003). Analysis of panel data, 2nd. Cambridge: Cambridge University Press. Kose, MA, ES Prasad and ME Terrones (2003), Financial Integration and Macroeconomic Volatility, IMF Staff Papers, 50, 119-142.
Huang, B. N., Yang, C. W., & Hu, J. W. S. (2000). Causality and cointegration of stock markets among the United States, Japan and the South China Growth Triangle. International Review of Financial Analysis, 9(3), 281-297.
Hulme, D., & Mosley, P. (1996). Finance against poverty (Vol 2.). Psychology Press.
Kalemli-Ozcan, S., Reshef, A., Sørensen, B. E., & Yosha, O. (2005). Net capital flows and productivity: evidence from US states. National Bureau of Economic Research Working paper, (11301).
Kamin, S. B., & Wood, P. R. (1997). Capital inflows, financial intermediation, and aggregate demand: empirical
evidence from Mexico and other Pacific Basin countries. Board of Governors of the Federal Reserve System International Finance Paper, (583).
Khan, M. S., & Reinhart, C. (1995). Capital flows in the APEC region (Vol. 122). International monetary fund. Kouri, P. J., & Porter, M. G. (1974). International capital flows and portfolio equilibrium. The Journal of Political Economy, 443-467.
Krause, L. B. (1968). European economic integration and the United States. European economic integration and the United States.
Landon-Lane, J., & Rockoff, H. (2004). Monetary policy and regional interest rates in the United States, 1880-2002. National Bureau of Economic Research Working paper, (10924).
