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Spurious Regressions in Economics

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There occurs on some occasions a difficulty in deciding the direction of causality between two related variables and also whether or not feedback is occurring. Testable definitions of causality and feedback are proposed and illustrated by use of simple ...

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... If the spatial series are first-order non-stationary, a correlation between the global spatial trends of many variables would tend to produce similar regression results. This problem is similar to that of a spurious regression in time series (Granger & Newbold, 1974). It also affects instrumental variables estimation. ...
... For time series, Granger and Newbold (1974) showed that regressions on variables with time trends tend to produce spurious results with high fit indicators, unreliable t-ratios and locally autocorrelated residuals. As in time series, spatial non-stationarity is associated with the presence of unit roots in the data and unreliable statistical tests designed for stationary variables. ...
... 13 3.2. Spatial trends and other spatial estimation issues Granger and Newbold (1974) demonstrated that the presence of time trends in the data was related to the presence of autocorrelated regression residuals. The same happens in a spatial setting. ...
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Previous literature on European regions has shown that structural estimation of New Economic Geography (NEG) wage-type equations obtains results similar to those obtained using old regional economics techniques. I show that this similarity is due to the presence of global spatial trends in the variables (first-order non-stationarity), which produce spurious regressions. Formal tests and graphical models confirm that any variable displaying a core–periphery spatial pattern produces similar predictions for European regional per capita income. Empirical tests of spatial theories should thus pay attention to the geographical features of the administrative units and the global spatial trends of the variables analysed. Access to preprint: https://www.tandfonline.com/eprint/IIU5GEKTEI6ZUFAR3UVQ/full?target=10.1080/17421772.2024.2325517
... Since the crossing trend is highly non-stationary, a naïve regression can misidentify the model due to the problem of spurious regressions [71]. To address this concern, we adopt a timeseries error correction model to analyze the long-and short-term effects of rescue probability on the number of crossings [72]. ...
... In this section we provide a brief overview of the ECM, following the exposition in [72,Section 6]. The development of the ECM was motivated by the observation that when running Ordinary Least Squares (OLS) regressions using non-stationary dependent and independent variables (in our case, N t,cross and P t,rescue , respectively), there is an elevated risk of finding a significant relationship between the two even when none exists (i.e., a spurious regression [71]). One solution in this case is to take first differences in order to obtain stationary variables, and then to fit a regression on the first differences. ...
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The sea crossing from Libya to Italy is one of the world’s most dangerous and politically contentious migration routes, and yet over half a million people have attempted the crossing since 2014. Leveraging data on aggregate migration flows and individual migration incidents, we estimate how migrants and smugglers have reacted to changes in the border enforcement regime, namely the rise in interceptions by the Libyan Coast Guard starting in 2017 and the corresponding decrease in the probability of rescue to Europe. We find support for a deterrence effect in which attempted crossings along the Central Mediterranean route declined, and a diversion effect in which some migrants substituted to the Western Mediterranean route. At the same time, smugglers adapted their tactics. Using a strategic model of the smuggler’s choice of boat size, we estimate how smugglers trade off between the short-run payoffs to launching overcrowded boats and the long-run costs of making less successful crossing attempts under different levels of enforcement. Taken together, these analyses shed light on how the integration of incident- and flow-level datasets can inform ongoing migration policy debates and identify potential consequences of changing enforcement regimes.
... Although RCTs have gained preference over other methodologies, this is not the first time that such a preference for methodological sophistication is witnessed in economics. Similar developments took place in Macroeconomics in the 1970s and 1980s with the emergence of non-stationarity and VAR (Granger & Newbold, 1974;Sims, 1980). Macroeconometric structural modelling originated in the work of the Cowles Commission at the University of Chicago (Pandit, 2001). ...
... The predictive ability of SEM was first called into question by the Box-Jenkins ARIMA modelling (Naylor et al., 1972;Nelson, 1972). The important critiques of SEM are that the regression equations involving nonstationary time series would yield 'spurious' results and that the usual diagnostics are not valid (Granger, 1969;Granger & Newbold, 1974). Although it was shown that any univariate ARMA model can be integrated within the final form of SEM if the latter has enough dynamic structure (Zellner, 1979;Zellner & Palm, 1974), it was not always possible due to the constraints imposed by economic theory. ...
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Randomized control trials (RCTs) are recognized as the preferred tool of analysis in modern development economics literature/research and policy evaluation. This may lead to methodologies, including case studies, tabular analysis, simple regressions, taking a back seat. This survey explores the implications of such a methodological hierarchy and the implications of preoccupation with a particular evidence/ methodology for research and policy. Similar developments in macroeconomic modelling are also discussed. Major advantages and limitations of RCTs and the attempts to address them are highlighted. The article argues that preoccupation with a methodology can sometimes lead to important inquiries for research and policy getting side-lined on methodological considerations. This leads to inferences favouring a particular technique/methodology or issue. Focusing solely on methodologies that emphasize quantifying the ‘effect’ may not be appropriate to address all questions relevant to development. As policies involve multiple and conflicting social concerns, methodological pluralism may be preferable.
... The Granger causality test (Granger & Newbold, 1974) was used in both versions of the time series data range before and until the COVID-19 pandemic to see if there was a significant difference between the two time series data ranges. ...
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The COVID-19 pandemic outbreak has caused disruptions in various aspects of life and the economy, including the movement of stock indexes. The objective of this study is to examine the influence of macroeconomic factors on the volatility of the Jakarta Composite Index both before and after the COVID-19 pandemic. Monthly secondary data from June 2007 to December 2019 were analyzed to identify pre-COVID trends, while data from June 2007 to December 2021 were used to identify post-COVID-19 patterns. The analysis incorporated the Granger causality test, Cointegration test, Vector Error Correction Model, and Augmented Dickey-Fuller. The results of the causality analysis revealed variations in the impact of interest rates, global oil prices, inflation, and exchange rates on the Jakarta Composite Index before and following the COVID-19 pandemic. These findings hold significance for investors as they enable the identification of potential risks associated with investments during global crises.
... To test for endogeneity, we utilized the Durbin-Wu-Hausman test which helps in identifying the correlation between endogenous regressors and the error terms, indicating that estimates from Ordinary Least Squares (OLS) may be inconsistent. Upon confirming endogeneity with this test, we used lagged variables (X t−1 ) based on recommendations in the literature [16,53,59]. This approach enhances the robustness of our causal inference by assuming that past values of the predictors are less likely to be correlated with the current error term. ...
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This study investigates the impact of the Energy-related Uncertainty Index (EUI) on corporate investment among Chinese non-financial listed companies, focusing on two aspects: the effect of EUI fluctuations on investment behavior, and its differential impact on energy versus non-energy sectors. Utilizing a dataset of 2487 firms from 2007 to 2022, encompassing 22,346 firm-year observations, our analysis reveals that a 1% increase in the EUI leads to a 0.045% decrease in overall corporate investment. Notably, this effect is more pronounced in energy-related firms, where a 1% increase in EUI leads to a 0.057% reduction in investment. In comparison, non-energy-related firms exhibit a milder response, with a 1% increase in EUI resulting in a 0.026% decrease in investment. Given the average annual change in EUI over the sample period [2007–2022] of 27.710%, a 0.045% decrease in investment implies a substantial 1.246% per annum change in investment. This highlights the economically significant impact of EUI fluctuations on corporate investment decisions, particularly during periods of heightened uncertainty. These findings, validated through alternative EUI measures and investment metrics, provide crucial insights for understanding investment behavior under energy uncertainty. Conclusively, our study contributes to the literature by highlighting how energy uncertainty uniquely impacts corporate investment, taking into account the specific financial and operational conditions within different sectors. The findings highlight the importance of incorporating energy policy considerations into corporate strategic planning, particularly for energy-intensive industries within transitional economies like China.
... When two-time series data are non-stationary, the regression between these two time-series data may give a high R-Squared even if these time-series data are entirely unrelated. The regression between the unrelated time series is called spurious regression (Granger and Newbold 1974). So, checking whether each financial time-series are stationary or contain a unit root (non-stationary) is required before regression between two financial time series data is undertaken. ...
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This paper evaluates the stock market cointegration as a result of COVID-19 and the investment implications, among six countries representing four major continents. We use the Gregory and Hansen cointegration test, to avoid any structural change issue within the time series, to test if one stock market cointegrates with another and the multivariate Dynamic Conditional Correlation model to estimate time-varying conditional correlation relationships among these stock markets. Using daily stock market data between January 2011 and December 2022 which we further divided into three sub-samples of pre, during and post COVID-19, the Gregory and Hansen results show a long-run relationship among sixty percent of the stock markets investigated before COVID-19. However, we find that there are no stable long-run relationships among eighty percent of the same stock markets after COVID-19, indicating potential portfolio diversification benefits for investors. Our findings using the Dynamic Conditional Correlation model show that stock market correlations are low before and after COVID-19 but find a © Author(s) Licensed under Creative Common Page 2 dramatic increase in correlation during the COVID-19 period and that the correlation starts to decrease after the crisis. Therefore, active investors should understand how markets cointegrate at normal times, during economic crises and after such crises as well as how they correlate and apply such in the design of investment portfolios to fully leverage on the inherent benefit of international diversifications.
... Yule's claims remained unnoticed until 1974 when computer simulations provided further proof to the observations he had made by drawing playing cards from previously shuffled packs. 6 Since then, the analysis of these correlations has constituted an important topic in econometric and economic modeling, where it receives the names of "spurious regressions" or "spurious correlations". 7,8 Recent research was able to determine the analytical expression for the second moment of the correlation coefficient for a pair of independent variables carrying out long random walks; and even for short walks, a characterization of the expected correlations has been presented. ...
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Nonsense correlations frequently develop between independent random variables that evolve with time. Therefore, it is not surprising that they appear between the components of vectors carrying out multidimensional random walks, such as those describing the trajectories of biomolecules in molecular dynamics simulations. The existence of these correlations does not imply in itself a problem. Still, it can present a problem when the trajectories are analyzed with an algorithm such as the Principal Component Analysis (PCA) because it seeks to maximize correlations without discriminating whether they have physical origin or not. In this Article, we employ random walks occurring on multidimensional harmonic potentials to evaluate the influence of fortuitous correlations in PCA. We demonstrate that, because of them, this algorithm affords misleading results when applied to a single trajectory. The errors do not only affect the directions of the first eigenvectors and their eigenvalues, but the very definition of the molecule’s “essential space” may be wrong. Additionally, the main principal component’s probability distributions present artificial structures which do not correspond with the shape of the potential energy surface. Finally, we show that the PCA of two realistic protein models, human serum albumin and lysozyme, behave similarly to the simple harmonic models. In all cases, the problems can be mitigated and eventually eliminated by doing PCA on concatenated trajectories formed from a large enough number of individual simulations.
... Although two variables may appear to be strongly associated, they may not actually be if a spurious regression error is committed. Granger and Newbold (1974) demonstrated that two random walk series that have no meaningful association can be strongly correlated, generating a regression model with good fit. The problem can be addressed by determining the degree of stationarity for each variable using a unit root test. ...
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Canada’s universities each receive an annual operating grant from their provincial gov- ernment to partially finance operating expenses. This paper estimates the sensitivity of provincial operating grants to the business cycle by disentangling the effects of procyclical income on government revenue and the countercyclical effect on student demand by utilizing an economic regression model composed of three equations. Our panel data include the total real operating grant paid to all universities within a province, total student enrolment, real per capita government revenue, and real per capita gross domestic product for Canada’s ten provinces over the 1992–2019 sample period. The results confirm that real per capita government revenues are procyclical and that full-time equivalent student enrolments are counter-cyclical. The total real operating grant is only weakly associated with cyclical changes in provincial government revenue. Instead, the total real operating grant is mainly determined by counter-cyclical changes in student demand. This partially offsets the potential reduction in funding to universities during an economic downturn. Provincial governments in Canada can smooth the total allocation over the business cycle by adjusting other expenditures and using debt financing. Our results suggest they do this to some extent, but not enough to avoid a net reduction in real operating grants during an economic downturn.
... Within a VAR model, the Granger causality concept is based on the idea that if past values of one variable aid in the prediction of another variable, then the first variable is deemed "Granger's cause" for the second variable. See the authors' papers, Granger (1969) and Granger and Newbold (1974) for a deeper understanding. Figure 1 shows the evolution, in returns, of the Brent Crude Spot, Euro Stoxx Oil & Gas, Nasdaq Clean Edge Green Energy, WilderHill Clean Energy, and Clean Energy Fuels stock indexes from May 3, 2018, to May 2, 2023. ...
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The recent worldwide pandemic of 2020 and Russia's invasion of Ukraine in 2022 have sparked interest in understanding the links between clean and dirty energy markets. This research investigates the co-movements of clean energy and dirty energy stock indexes before and during the 2020 and 2022 events. The study focuses on the Brent Crude Spot, Euro Stoxx Oil & Gas, NASDAQ Clean Edge Green Energy, WilderHill Clean Energy, and Clean Energy Fuels stock indexes from May 3, 2018, to May 2, 2023. The goal is to determine if the events of 2020 and 2022 have increased co-movements between clean and dirty energy stock indexes, potentially challenging portfolio diversification. The results show that co-movements have increased, but portfolio diversification was no longer efficient during the tranquil period in international markets. These findings hold relevance for investors, policymakers, and other players in the energy financial market.
... For example, Auto regressive distributed lag is more flexible than Vector Auto regressive or Vector error correction Model (VecM) in terms of stationarity for i(0) and i (1). however, stationarity is a necessary condition for estimating cointegration and error correction methods and is important for checking the accuracy and adequacy of the data. in addition, the regression of non-stationary variables often leads to problems with spurious regressions, and variables only have contemporaneous relationships rather than full causality (Granger & Newbold, 1974;harris & Sollis, 2003). therefore, taking stationarity with the Ardl model does not guarantee data quality and assurance, so this flexibility leads to incorrect inferences and wrong conclusions, and undermine the overall robustness of the findings. ...
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Most of the previous economic theories and empirical studies revealed that the relationship between population and economic growth is controversial and inconclusive in different parts of the world. However, previous studies have attempted to examine the relationship between population and economic growth, but their results have been vague or not even sufficiently realistic to address the issue practically. Thus, cognizant of this fact, this study investigates the dynamic effect of population and economic growth in Ethiopia. This study used a Vector Error Correction Model (VECM) and estimated using annual data for the period 1991-2022. The study found that, in the short run, high population growth was associated with increases in real gross domestic product. However, in the long run, population expansion hurts economic growth. Furthermore, the analysis shows that there is no causal relationship between population growth and economic growth by using block exogenity test. In conclusion, population growth has a greater short term positive impact on economic growth than it does in the long term. This study suggests that the government should adopt a pro-natal strategy that uses incentives for agricultural output in the short term to encourage individuals to have more families; the government should promote anti-natal policies to sustain economic growth that encourages individuals to have fewer children in the long run. Additionally, instead of solely focusing on population growth, the study suggests that the government prioritize and sustain economic growth by centralizing and improving the real money supply.
... Finally, the VAR Residual Serial Correlation LM test is used to determine whether the residuals are temporally autocorrelated. For more in-depth knowledge, reading the articles by Granger (1969) and Granger and Newbold (1974) is suggested. the volatility these markets were exposed to, especially in the first few months of 2022, coinciding with the Russian invasion of Ukraine. Figure 2 shows the mean returns of the Clean Energy Fuels, Nasdaq Clean Edge Green Energy, S&P Global Clean Energy, WilderHill Clean Energy stock indices and the precious metals Gold, Handy & Harman, Silver, Handy & Harman, and London Platinum over the period from January 1, 2021 to November 23, 2023. ...
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This study contributes to the literature by examining the links between clean energy stocks and commodities such as gold, silver, and platinum. The purpose was to examine the clean energy stock indices, namely Clean Energy Fuels, Nasdaq Clean Edge Green Energy, S&P Global Clean Energy, WilderHill Clean Energy, and the precious metals Gold, Handy & Harman; Silver, Handy & Harman; and London Platinum over the period from January 1, 2021 to November 23, 2023. The results revealed significant changes in hedging asset characteristics related to the sustainable energy and precious metals indices. The movements that impact price formation increased from 11 to 18 in the conflict sub-period, indicating greater complexity and interdependence between the assets analyzed. These results have important implications in the context of enormous growth in investments in clean energy stocks and the repeated occurrence of periods of uncertainty.
... Granger and Newbold (1974) [63] proposed that conducting a regression analysis with non-stationary parameters could result in misleading regression. As a result, it became vital for a time series regression that the variables be stationarized. ...
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... Previous studies have shown that spurious regression can occur between stationary and nonstationary time series [21,22]. For example, Kim et al. [23] found that when the sample size approaches infinity, the ordinary least square (OLS) estimator of regression coefficient for two series with trends convergence in probability to the ratio of the corresponding trend component, rather than the true correlation coefficient value between two series. ...
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... To examine the relationship between variables using F-statistics, the value must fall between the ranges of 0.01 to 0.05. According to Granger and Newbold (1974), the Durbin-Watson test value must be between the ranges of 1.5 to 2.5 in order to be recognized as acceptable. As showed in Table 3, the model utilizing DPA_avg and PTM_Avg as predictors accounts for approximately 31.4% of the variability observed in APS_avg.The variables DPA_avg and PTM_Avg have a moderate association (0.560) with the variable APS_avg. ...
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The study examined the relationship between teachers' teaching methods and the academic performance of 150 undergraduate and Master's students from various fields of study. It contains a structural sample strategy to ensure the inclusion of individuals from various fields. A quantitative research methodology was used to administer a structured survey questionnaire, which was designed through a systematic literature review, in order to analyze students' diverse perspectives on teaching methods, academic performance, and demographic information. The independent variables consisted of perceptions of Teaching Methodologies and different pedagogical approaches, whereas the academic performance of students was the dependent variable. The statistical studies performed using SPSS software encompassed descriptive, regression, and factor analyses, revealing the connections between teaching approaches and academic success. The results emphasized the crucial significance of interactive, learner-focused instructional approaches in promoting enhanced academic performance. The active participation of students and the use of diverse teaching methods had a substantial impact on student achievement, emphasizing the importance of flexible instructional strategies. Nevertheless, traditional teacher-centered approaches demonstrated restricted influence. Although this study has limitations in terms of sample size and reliance on self-reported data, it highlights the need for an adaptable educational approach that incorporates evolving teaching methods to improve student outcomes. The research provides useful insights into effective pedagogical methods, advocating for a versatile and learner-centered educational environment. The study highlights the need for a better understanding of teaching methods' impact on academic performance to improve educational outcomes, resource allocation, curriculum development, and policy formulation.
... Time series are exposed to impacts that can create regular fluctuations, leading to biases. Granger and Newbold [48] claimed that a non-stationary time series could yield an incorrect outcome. Therefore, a series is said to be stationary if its second and first moments are constant and its relationship between its periods is constant regardless of the passing of time or the distance separating them. ...
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... The assumption of the classical regression model necessitates that both the dependent and independent variables be stationary and the errors have a zero mean and finite variance. According to Granger and Newbold (1974), the effects of non-stationarity include spurious regression, high R 2 and low Durbin-Watson (DW) statistic. Below are basic reasons why data must be tested for non-stationarity. ...
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... The concept of Granger causality within a SVAR model is based on the idea that if the past values of one variable help to improve the prediction of another variable, then the first variable is considered a "Granger cause" of the second variable. For a better understanding of the model, the papers by Granger (1969) and Granger and Newbold (1974) are helpful. Based on the results, it was found that all the indices had positive mean returns, with the exception being the MASI (-2.074e-05) and the Platinum market (-2.10e-05), while concerning the index with the greatest risk, it was found that the MOEX (0.0175) had the most significant deviation from the mean. ...
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In the context of the global pandemic of 2020 and the Russian invasion of Ukraine in 2022, a newfound interest is emerging in understanding the interconnections between the Dow Jones (United States), Amman SE General (Jordan), BLSI (Lebanon), EGX 30 (Egypt), ISRAEL TA 125 (Israel), MASI (Morocco), and MOEX (Russia) indices and the precious metals markets Gold Bullion LBM, Silver, Handy & Harman, London Platinum, from January 1, 2018 to November 23, 2023. The study aimed to determine whether precious metals such as Gold, Silver, and Platinum can be considered hedging assets to the stock markets of the Middle East and North Africa (MENA) countries, i.e., whether investors operating in these regional markets can rebalance their portfolios with these precious metals. The structural vector autoregressive (SVAR) methodology allowed assessing the influence of the analyzed markets on each other regarding price formation. The results show that the markets interacted very significantly during the stress period. Platinum was the market that most influenced its peers (1 to 8 comove-ments), the MOEX, 1 to 7, MASI, 2 to 6, the Dow Jones went from 4 to 7 comove-ments, the Amman SE General and EGX 30 markets went from 1 to 4, the Israeli market (ISRAEL TA 125) and Silver went from 2 to 4 comovements, and finally the Gold Bullion LBM from 3 to 4.
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A condição de não estaticidade dos seguros em geral se dá por se tratar de uma ciência que depende de fatores sociais e econômicos para se sustentar. O Seguro de Vida, em especial, é impactado por diversos agentes, desde políticas econômicas e culturais, até o desempenho das seguradoras quanto a oferta e demanda do seu produto e aspectos sociodemográficos que influenciam no comportamento do próprio segurado. O conhecimento sobre o risco identificado é fundamental para que a avaliação seja realista e precisa. Para garantir a solvência dessas empresas e assegurar os compromissos futuros, diversas premissas atuariais estão envolvidas no gerenciamento e precificação de riscos, como análise de frequência de sinistros, severidade, risco biométrico, análises de sensibilidade e subscrição, acompanhamento de sinistralidade, entre outras, cabendo ao atuário responsável adequar tais medidas a realidade da instituição de risco. Portanto, este trabalho tem como objetivo avaliar modelos de previsão para uma das premissas atuariais mencionadas, a saber, a sinistralidade, por meio de métodos de regressão e Box-Jenkins. Foram analisados os dados mensais disponíveis no Sistema de Estatísticas (SES) da Superintendência de Seguros Privados (SUSEP), entre os anos de 2011 e 2021, das oito seguradoras com maior volume de prêmio. A capacidade de previsão dos modelos foi avaliada comparando os valores previstos com os dados reais do 1° semestre de 2022. O modelo de regressão foi o mais adequado para a previsão da sinistralidade, embora ambos os métodos tenham apresentado desempenho satisfatório.
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Ekonomik büyümeyi artıran nedenlerin başında beşeri sermaye stoğuna yapılan yatırımlar gelmektedir. Bu yatırımlardan biri de sağlık harcamalarıdır. Bir ülkedeki sağlık harcamalarının artması, eğitimin etkisiyle bilinçli toplumun sağlık hizmetlerinden daha verimli yararlanmasına ve dolayısıyla o toplumun gelişmesine ve refah seviyesinin artmasına pozitif katkı sağlayacaktır. Çalışmada Türkiye’de 2000-2018 dönemlerine ait ekonomik büyüme ve sağlık harcamaları değişkenleri arasındaki uzun dönem ilişki Auto Regressive Distributed Lag, (ARDL, Gecikmesi Dağıtılmış Otoregresif Model) testi ile incelenmiştir. Yapılan analizler sonucunda ekonomik büyüme ile sağlık harcamaları arasında pozitif ve anlamlı uzun dönemli bir ilişki olduğu gözlemlenmiştir.
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The paper examines the causality between the German current account and financial account. It contrasts with past research which assumes the current account and financial account to be jointly determined by a saving-investment imbalance. Our analysis decomposes the current account into exports and imports (real resource flows) and the financial account into domestic capital outflows and foreign capital inflows (gross capital flows). Evidence from the Toda-Yamamoto causality test shows that for Germany from Q1.1980 to Q2.2023, the causality runs from the financial account to the current account. It is not real resource flows but gross capital flows which exert significant impacts on the German real exchange rate. The finding implies that over the long run, strong German capital outflows and weak foreign capital inflows contributed to weak wage growth and stagnant investment in Germany, sustaining the persistent German current account surpluses. A reduction of the German current account surpluses requires a policy mix of fiscal expansion and monetary tightening which would expand the absorption of German and foreign capital in the German economy.
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