No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Maximum Likelihood Estimation and Inference On Cointegration—with Applications to the Demand for Money
Oxford Bulletin of Economics and Statistics
Abstract
This paper gives a systematic application of maximum likelihood inference concerning cointegration vectors in non-stationary vector valued autoregressive time series models with Gaussian errors, where the model includes a constant term and seasonal dummies. The hypothesis of cointegration is given a simple parametric form in terms of cointegration vectors and their weights. The relation between the constant term and a linear trend in the non-stationary part of the process is discussed and related to the weights. Tests for the presence of cointegration vectors, both with and without a linear trend in the non-stationary part of the process are derived. Then estimates and tests under linear restrictions on the cointegration vectors and their weights are given. The methods are illustrated by data from the Danish and the Finnish economy on the demand for money. Copyright 1990 by Blackwell Publishing Ltd
... In the second stage a multivariate VAR system is constructed, with its corresponding VECM . Then in order to determine the number of cointegrating vectors, maximum likelihood tests of [24] Johansen and Juselius (1990) is used. ...
... introduced by[24] is utilized. Johansen method employs Trace test and Eigen value so as to find out the number of cointegrating relationships that may exist between the variables. ...
The study aims to present the linkages or relationship among South African stock market and five other major stock markets in Nigeria, Morocco, Mauritius, Botswana and Kenya using various econometric techniques. The analysis relies on standard and well accepted techniques of ADF Test, Johansen cointegration test and Granger causality to uncover the long-run relationship among the variables using monthly data of six variables for a period of 11 years and 3 months. The responses of a variable to innovations in other variables are traced by simulating Impulse Response Function. This study reveals absence of cointegration between the selected markets. But a uni-directional causality is indicated from LM ASI to LJSE, LJSE to LSEM DEX and LJSE to LBSE. Impulse Response Function shows that that a shock on LJSE solicits an increase in LBSE which is consistent with the Granger Causality.
... There are many methods to examine the cointegration of the variables, like Engle-Granger's two-step method, and the studies mostly use Johansen. In this regard, when variables are integrated at I (1) or I (0), then two-period residual Engle-Granger and the maximum likelihood of Johansen may provide the biased outcome of the long-run relationship of the variables (Johansen, 1990). Regarding this issue, Pesaran and Shin (1999) suggested the ARDL-Autoregressive Distributed Lag method for enabling unbiased results regardless of whether the variables are integrated at I (1) or I (0) in the model. ...
... As discussed, ARDL methods provide the allowance of I(1) and I(0); besides this, the ARDL method provides other benefits compared to other methods. ARDL can also provide statistically significant results with a small sample size, while the Johansen (1990) method only provides significant results with a large sample size. Another benefit of ARDL is that it allows various lag orders, while other cointegration tests use the same lag orders of variables. ...
This study examines the impacts of macroeconomic indicators, such as exchange rate, interest rate, money supply, and inflation, on the stock index of Pakistan (PSX), India (BSE), and China (SSE). The researchers have taken monthly data from Jul 2001 to March 2023 and employed a Nonlinear Autoregressive Distributed Lag (NARDL) approach to investigate the asymmetric effects of the variables. The Bound test result for the cointegration relationship demonstrated a long-run relationship (or cointegration) between LPSX, LSSE, and macroeconomic variables. However, no long-run relationship or Cointegration of LBSE and macroeconomic determinants exists. The findings of Asymmetric ARDL (NARDL) exhibited that the overall goodness of fit of LPSX, LBSE, and LSSE as the Adjusted R 2 is 99.51%, 99.3%, and 94.3%, respectively, which means the exchange rate, interest rate, money supply, and inflation variables determine the changes in LPSX, LBSE, and LSSE. The findings of CUSUM and CUSUMSQ tests suggested that the overall model is stable for LPSX, LBSE, and LSSE. The findings of the asymmetric short and long coefficients of the NARDL model demonstrated a long and short-run relationship between LPSX and LSSE and macroeconomic indicators. However, in the case of LBSE, there is only a short-run relationship between LBSE and macroeconomic indicators. The findings provide essential implications for policymakers in Pakistan, India, and China to manage and sustainably develop the stock markets successfully.
... Notably, two tests are fulfilled to determine the entire quantity of cointegrating vectors, which is developed by Johansen, 80 Johansen, 81 and Johansen and Juselius. 82 Majority of model include Matrix II approximations. In addition, the initial model is relying on eigenvalues whereby a hypothesis of no effect of cointegration existence in the certain data till n cointegration linkages. ...
... According to findings of Johansen cointegration test, there are various cointegrated factors at 95% confidence interval, which confirm the declining of null hypotheses against alternative hypotheses at Table 5. Besides, it should also be noted that components of max-eigenvalue provide the only one cointegration vector at 5% interval importance level which is also significant to express that when there is an inconsistency in selecting the cointegration among max eigenvalue and trace test in the analysis, the convenient test is the trace statistics to set the cointegration factors. 82 It is deduced that both endogenous and exogenous series are cointegrated with each other, establishing the long-term linkage among dependent variable which is EF and independent variables including trade policy and EU. ...
This manuscript investigates the interplay between energy dynamics, economic growth, and environmental sustainability, offering a comprehensive analysis of Türkiye's long-term ecological and economic trends. In this sense, the research elaborates the long-run linkage among natural gas import, energy usage, economic growth, trade openness, urbanization and ecological footprint (EF) by implementing the Johansen cointegration test, fully modified ordinary least squares (FMOLS) analysis, nonlinear distributed lag autoregressive model (NARDL) model, and wavelet analyses from 1980 to 2022 for Türkiye. Furthermore, when the contributions and novelties of this paper to the existing academic literature are considered, time series models comprehending the Johansen cointegration test, FMOLS analysis, and NARDL model point out the long-run relationship between natural gas import, economic growth, and EF, which is confirming the Environmental Kuznets Curve hypothesis for Türkiye in short term. Considering the coefficients of the FMOLS model, 1% increases in gross domestic product increases EF by 0.1972% and a 1% increase in natural gas import increases EF by 0.0369% as negatively. In addition, according to FMOLS test, it should be stated that a 1% increase in energy use increases EF by 0.7600%. When all remaining independent variables are examined deeply and thoroughly, there is a long-term positive effect between them. Empirical findings reveal that natural gas imports ( p = .0428) and energy consumption ( p < .0001) are major contributors to ecological degradation. Conversely, urbanization ( p = .3999) demonstrates potential for mitigating environmental pressure in the long term. The study highlights the need for transitioning to renewable energy, enhancing energy efficiency, and adopting sustainable urban development practices. These findings emphasize the importance of aligning economic growth with ecological sustainability through targeted policy interventions. Unlike previous studies that predominantly concentrate on renewable energy with CO 2 emissions, this paper dissimilarly highlights the overlooked environmental effects of natural gas imports. These insights not only expand the understanding of Türkiye's energy and environmental dynamics but also challenge the common perception of natural gas as an eco-friendly energy source. To sum up, the research includes empirical results which patronizes the necessity for a transition to renewable resources and cleaner technologies to mitigate environmental costs.
... Prior research tested the co-integration relationship between the studied variables employing Engle and Granger [46], Phillips and Hansen [47], and Johansen and Juselius [48] cointegration tests, which have some drawbacks of estimation about the series of integration. Pesaran et al. [49] introduce the ARDL bound test to investigate the long-run co-integration association, which is superior in comparison with the co-integration tests introduced by Engle and Granger [46], Phillips and Hansen [47], and Johansen and Juselius [48]. ...
... Prior research tested the co-integration relationship between the studied variables employing Engle and Granger [46], Phillips and Hansen [47], and Johansen and Juselius [48] cointegration tests, which have some drawbacks of estimation about the series of integration. Pesaran et al. [49] introduce the ARDL bound test to investigate the long-run co-integration association, which is superior in comparison with the co-integration tests introduced by Engle and Granger [46], Phillips and Hansen [47], and Johansen and Juselius [48]. First, the ARDL bound test investigates the long-run association among variables, whether the underlying repressors are integrated of order I(0), I(1), or marginally integrated. ...
This study explores the nexus among clean energy, economic growth, urbanization, trade openness, and carbon dioxide (CO2) emissions nexus in an emerging economy, Sri Lanka. An autoregressive distributed lag (ARDL) econometric technique and different diagnostic tests are used to investigate the linkages. The pairwise Graner causality approach is applied to investigate the causality direction. The estimated results have confirmed that clean energy and urbanization reduce carbon emissions, whereas trade openness induces carbon emissions in the long run in Sri Lanka. The findings revealed the non-existence of the environmental Kuznets curve (EKC) hypothesis in Sri Lanka. In contrast, the pollution haven hypothesis (PHH) exists between trade openness and carbon dioxide emissions in Sri Lanka. Regarding causal relationships, there is bi-directional causality between clean energy and urbanization. This study reports a unidirectional causality from clean energy to CO2 emissions, economic development to carbon emissions, urbanization and trade and CO2 emissions to urbanization and trade. Based on the above findings, this study recommends some policy recommendations.
... This technique becomes popular due to its several advantages like it is a single equation cointegration procedure. Other cointegration procedures like suitable only for two variables and Johansen and Juselius (1990) can only be applied on the series also which are integrated for the same order but more than two variables and correct for large sample dataset. ARDL method is appropriate irrespective of the independent variables that are integrated at the same order or not (Hamuda, 2013). ...
This study identifies the major determinants of gold price forecasting and checks the short-run and long-run relationship along with US-Dollar prices in Pakistan. The data set covers daily observations over the period 2007 to 2018. To examine the relationship between gold price and US-Dollar price, ARIMA, ARDL and ADF model has been used. The Gold price is the variable of interest, whereas the explanatory variable is US-Dollar. The finding of the study indicates that the value of the gold price co-integrated at zero order of interaction, which means that the gold price is stationary at the level and the value of the US-Dollar is not co-integrated there for it is non-stationary at the level, but it become stationary by taking 1st difference. The result also postulated that ADF is more precise to check the short run and long run relationship between gold price and US-Dollar price. There exists long run and short run relationship between gold price and US-Dollar and also ARIMA model is used for the forecasting purpose. ARIMA model is one of the best techniques for the selection of good model. Study shows that ARIMA (3, 0, 1, 1) is a good model.
... The Johansen-Juselius (Johansen, & Juselius, 1990) cointegration approach is employed to examine long-run relationships among variables. The Johansen-Juselius cointegration technique is constructed on λtrace and λmax statistics. ...
The primary objective of this study was to investigate the dynamic relationship between oil temperature and the Bearing Gearbox Condition Indicator (BGCI) values of the Bell 407 helicopter. The study aims to simplify the fault diagnosis process by proposing a method that utilizes only one vibration sensor and one temperature sensor per bearing. To achieve this goal, we employ robust econometric tools, such as unit root tests, cointegration tests, and Autoregressive Distributed Lag (ARDL) models, for both long-run and short-run estimates. Our findings indicate that the variable temperature tends to converge to its long-run equilibrium path in response to changes in other variables. The results of the ARDL analysis confirmed that spectral kurtosis, inner race, cage, and ball energy significantly contributed to the increase in temperature. Furthermore, we utilized the Impulse Response Function (IRF) to trace the dynamic response paths of the shocks to the system. The identification of a cointegrating relationship between oil temperature and BGCI values suggests a practical and significant connection that can potentially be used to predict hazardous changes in oil temperature using BGCI values, which is an important implication for enhancing the safety and reliability of helicopter operations. The study presents a promising direction for condition monitoring (CM) in rotating machinery, emphasizing the potential of integrating temperature data to simplify the diagnostic process while still achieving reliable results.
... ARDL bounds testing approach as developed by [57] and extended by [58] provides advantages in ascertaining long-run relationship among variables as compared to techniques suggested by Engle and Granger, [18], Johansen and Juselius, [35] and Johansen, [34]. Some of these advantages offered by ARDL bounds testing include that, first, it does not impose restrictions that the variables under consideration have to be of the same order of integration. ...
This study aimed to establish the influence of economic growth (measured by GDP), industrialization (IND), mineral rents (MR) and population growth (PG) on CO2 emissions (CO2) in the context of one of the fastest growing economies in the world, i.e., India. The study employs the ARDL bounds test to analyze the information obtained from the World Bank records for the years 1990–2023. The outcomes of the empirical analysis revealed that GDP and PG clearly affect CO2 in the long run. Similarly, CO2 is negatively affected by its lagged value, whereas FDI is found to positively contribute to CO2 emissions in the short run. Our results also establish that IND negatively affects CO2, establishing the EKC hypothesis in the context of India. Finally, the short-term results indicate a negative impact of MR on CO2. The study produced relevant findings that make noteworthy input to the current knowledge in the area of emerging economies. Policy- and governance-related implications emerging from the analysis are provided by the study.
... To examine the presence of cointegration, we applied the asymmetric NARDL model, as the variables were found to be either stationary at I(0) or I(1). This model offers a significant advantage over traditional cointegration methods such as Johansen and Juselius (1990), Engle and Granger (1987) and Phillips and Hansen (1990), which require all variables to have the same order of integration. The unit root test results, presented in Table 2, confirm that the variables exhibit different integration orders, making the asymmetric ARDL model the most appropriate choice. ...
Purpose-As one of the world's fastest-growing economies, India's energy demand is predominantly met by fossil fuels, which significantly contribute to greenhouse gas emissions. The purpose of this study is to investigate the asymmetric relationship between fossil fuel consumption (disaggregated into coal, oil and natural gas) and carbon emissions in India. Design/methodology/approach-This study uses the nonlinear autoregressive distributed lag (NARDL) methodology, as proposed by Shin et al. (2014), to capture the asymmetric impacts of positive and negative shocks in fossil fuel consumption on carbon emissions. This advanced econometric approach allows for the exploration of non-linearities in the energy-emissions nexus. Findings-The results reveal a significant asymmetric impact of fossil fuel consumption on carbon emissions. Negative shocks (reductions in fossil fuel use) have a more pronounced effect on emissions mitigation than positive shocks (increases in usage). Among the energy sources, oil consumption exhibits the highest emission intensity during negative shocks, underscoring its critical role in emissions dynamics. Practical implications-The findings suggest the urgent need for policymakers and industry leaders to prioritise reductions in fossil fuel consumption, particularly oil, to achieve meaningful emissions mitigation. Investments in cleaner energy alternatives and the adoption of mitigation-oriented energy portfolios are essential to align with India's net-zero emissions goal by 2070. Originality/value-This study contributes to the existing literature by examining the non-linear and asymmetric relationship between fossil fuel consumption and carbon emissions in India, a perspective that has Ethical approval: All authors agree to ethical approval and understand its related rules and content.
... It can be noted, however, that in this context the null hypothesis tested is that of non-stationarity and therefore of non-convergence. In the more interesting multivariate case, we test whether the GDP per capita of the N regions of the sample have a common trend using for example the methodology of Johansen and Juselius [20]. The convergence test therefore amounts, in this context, to testing the presence of N -1 co-integration relationships. ...
The goal of this paper is to explore spatial dependency in the phase of integration of European countries. On the one hand, the recently evolved techniques of an observational study of spatial data are used to improve the definition of the regional complexities of the development of Western countries. This helps us to shed more light on the standard β-convergence metric that hides specific geographical trends that fluctuate across period. On the other side, in Integration systems, they have the existence of spatial self-creation utilizing spatial econometric techniques. It helps us to evaluate the data gathered pre and post considering spatial correlation coefficients in order to highlight the importance of spilling over impacts on geographic development anomalies.
... Johansen's co-integration test was employed to examine the long-run relationship between wholesale and retail sugar prices (Johansen 1988;Johansen and Juselius 1990). The null hypothesis ( H 0 ) of utmost 'r' co-integrating vectorsi.e., rank of error-correction coefficient matrix-against a general alternative hypothesis ( H 1 ) of 'r + 1' co-integrating vectors was tested by trace and maximum eigenvalue statistics (Quandt 1958). ...
This paper examined the price dynamics and market integration in wholesale and retail sugar markets of India using monthly data from the Food and Agriculture Organization for four major markets from 2014-2015 to 2023-2024. Understanding these dynamics across spatially separated markets is crucial for developing policies that enhance market efficiency and promote sustainable growth. Various analytical tools were employed viz. compound annual growth rate, instability index, seasonal price index, correlation analysis, Johansen's co-integration test, and Granger causality test and impulse response function. The analysis demonstrated that the selected sugar markets exhibit suboptimal integration due to limited market intelligence, slow information flow and inadequate infrastructure. An upward trend was observed in sugar prices in all the markets over the study period. Seasonal price fluctuations were observed, linked to the crushing season and higher demand during summer months. Co-integration analysis confirmed a long-run equilibrium, Granger causality test revealed unidirectional, bidi-rectional and no causality price influence between the markets. Moreover, impulse response analysis concluded relatively well interconnected markets with potential inefficiencies, particularly in Patna market. This study uniquely highlights the interplay between market efficiency and seasonal fluctuations in the Indian sugar sector, providing a nuanced understanding of spatial integration and its policy implications. To enhance market integration and price convergence, policy recommendations include modernizing marketing systems, fostering public-private partnerships, improving infrastructure, strengthening supply chains and facilitating external trade.
... The ARDL model developed by Pesaran et al. (2001) is well suited to estimate the cointegration relationship between the variables included in equations 1 and 2. This approach addresses the problem of non-stationarity that commonly plagues time series data and handles the issue of endogeneity by permitting the incorporation of lagged variables in the models (Pesaran Shin, 1998). In addition, this approach does not cause any econometric issues with small sample sizes and thus produces unbiased and 14 consistent coefficients (Johansen, 1990;Pesaran Shin, 1998). Furthermore, the ARDL offers a unique advantage in cointegration by assessing both the short-and long-run effects of independent variables on the dependent variable simultaneously. ...
This study examines the role of foreign direct investment (FDI) in advancing peacebuilding in Sudan via promoting youth employability using the autoregressive distributed lag (ARDL) model and time series data from 1992 to 2023. The findings indicate that both FDI and financial development substantially decrease youth unemployment rates over the long run. Conversely, the findings reveal that elevated inflation rates lead to higher youth unemployment over time. Furthermore, we find that the prevalent rates of youth unemployment considerably hamper peacebuilding efforts both in the short and long run. The primary conclusion is that augmenting FDI inflows can facilitate peacebuilding initiatives within the Sudanese setting by broadening employment prospects for unemployed youth. Accordingly, by harnessing FDI inflows strategically, Sudan can create a more inclusive labor market that not only provides employment opportunities but also fosters stability and peace.
... Among the other available models, AERC (1993) focuses on public finance while Hanif et al (2011) analyzes the impact of monetary policy. Fatima and Waheed (2014) Johansen and Juselius (1990) where cointegration is tested through trace statistics and maximum Eigen value statistics. ...
The study analyses human capital and economic growth relationship through developing a medium-sized macroeconomic model for PakistanThis study analysed the macroeconomic outcomes of three policies related to government spending on education within a general cut-down policy adopted by the government of Pakistan. The policy of spending 5 percent of G.D.P on education throughout the forecasting period is found to be most effective in improving the sector wise production, employment and income at the earliest possible time. The study found strong linkage between government spending on education and the production of agricultural and industrial sector which implies that the policy would be helpful to increase the production and employment of these sectors. The study found education spending as a tool to address major macroeconomic issues such as trade deficit, fiscal deficit and inflation. This policy would also help in reducing trade deficit through increasing exports especially from the manufacturing sector. The production and employment of services sector is found to be least affected by government spending on education which reflects lack of synchronizing between the types of skills demanded by and supplied to the services sector. In light of the above, the policy of spending 5 percent of GDP on education sector while aligning the skills in accordance to the demand of services sector is an appropriate option to deal with current macroeconomic challenges faced by government.
... To examine the long-term relationship between variables, this study adopts the autoregressive distributed lag (ARDL) bounds testing approach developed by Pesaran, Shin, and Smith (2001), diverging from the traditional co-integration methods of Engle and Granger (1987) and Johansen and Juselius (1990). The ARDL method has gained prominence due to its flexibility in handling variables with mixed integration orders whether purely I(0), purely I(1), or a combination of both unlike earlier techniques that required uniform integration levels. ...
This study examines the impact of inflation on Nigeria’s economic growth from 1990 to 2023. Using time-series econometric
techniques, the study analyzes the short-term and long-term relationships between inflation, unemployment, poverty, national
terrorism index, and economic growth. the findings suggest that inflation has a significant negative impact on economic growth, both
directly and indirectly through its influence on unemployment and poverty. Additionally, we find a strong positive correlation
between national terrorism index and inflation, further exacerbating the negative effects on economic growth. The study concludes
with policy implications, emphasizing the need for macroeconomic stability, effective security measures, and targeted social policies
to mitigate the adverse effects of inflation and insecurity on Nigeria’s economic development.
... Recently, however, a series of studies by Pesaran et al. (2001), Pesaran and Shin (1999), and Nayaran (2004), who introduced an alternative co-integration technique known as the 'Autoregressive Distributed Lag (ARDL)' bound test. There are numbers of advantages of using ARDL model also called 'Bound Testing Approach' over conventional Engle-Granger two-step procedure, Maximum likelihood methods of cointegration (Johansen and Jtiselius, 1990). The advantage of using ARDL approach over other methods is three-fold. ...
This paper investigates linkage between financial development and economic growth in Ethiopia during the period from 1975 to 2016 using Autoregressive Distributed Lag (ARDL) approach. The paper also schedules Vector Error Correction Model (VECM) in order to observe how fast the cointegrated variables convergence in long-run. Accordingly, the results of bound test confirm existence of the long-run relationship between explanatory variables and economic growth. The empirical results show evidence of long-and short-run positive impacts of financial development on economic growth in Ethiopia which implies that progesses in financial sector contribute to economic growth in both short-and long-run. In consideration of few control variables, the study finds all indicators, except inflation and government expenditure, significantly influence economic growth in the long-run. However, it also reveals that government expenditure, trade openness, human capital, and gross investment are pioneering determinants of the economic growth in Ethiopia in short-run. Moreover, the study employs Granger causality tests in order to show direction of impact is running from financial development to economic growth both in short-and long-run. As a result, it finds that the 'supply-leading' hypothesis holds in Ethiopia.
... This method allows the estimation and testing of cointegrated vectors as well as testing some restrictions on the parameters. Johansen and Juselius (1990) further extended the limitations of the method by adding a constant number and trend to the Vector Autoregressive Model (VAR) and even shadow (dummy) variables expressing seasonality, if any, to the model. In the Johansen method, calculations are based on eigenvalues and eigenvectors. ...
Banks are among the most important actors in the economy due to their role as market makers. The banking sector stands out as one of the sectors with the highest liquidity. Borsa Istanbul (BIST) Bank Index represents the index of banks whose shares are traded on the stock exchange in Turkey. Money supply and policy interest rates are among the main monetary policy instruments most frequently used by the Central Bank (CB) to control liquidity. In this respect, analysing the effects of monetary policy instruments on bank index returns is deemed worthy of research. For this purpose, time series consisting of 225 monthly observations from 01/12/2005 to 01/08/2024, which is the earliest available date, are constructed for BIST Bank index, policy interest rate and M2 money supply. These three time series were subjected to Johansen Co-integration analysis and then the error correction model and the long-run equation of the variables were obtained. As a result of the analyses, it is decided that all three variables are cointegrated in the long run between 2005 and 2024, and it is observed that in case of a possible imbalance between the three variables, the variables converge to each other again in 52.4109 periods and move to a new equilibrium position. In addition, it is determined that a 1% increase in money supply in the long run causes a 0.9% increase in the bank index and a 1% increase in the interest rate causes a 0.7% increase in the bank index.
... According to Pesaran, Shin and Smith (2001), different econometric analyses are utilized in determining economic relationships, and in particular, different Co-integration analyses like Engle & Granger (1987), Johansen (1988) and Johansen and Juselius (1990). This method allows us to investigate how variables interact with each other over both extended and shorter time periods. ...
Defense expenditures are an item that exists cyclically throughout the world in every period and covers most of the public expenditures of countries. The effect of defense expenditures on inflation, employment, balance of trade balance, gross domestic product, geopolitical risk index, and political stability index within the scope of Türkiye has been examined. The findings, while the causality relationship from defense spending to balance of trade, geopolitical risk index, and political stability index is determined and there is a positive relationship from defense spending to foreign trade balance and a negative relationship to geopolitical risk index, there is a cointegration towards gross domestic product. Empirical findings support the military Keynesian approach in the long and short term, indicating that the increase in defense expenditures in Türkiye increases exports and the balance of trade. Increasing R&D activities and implementing policies that encourage investment in higher-density defense industry products will increase positive externalities in the balance of trade. Long-term, the rise in defense spending allows one to draw the conclusion that the country tends to lower geopolitical risks by boosting confidence in its political, economic, and security realities and lowering the threat of terrorism.
... To examine the long-term relationship between variables, this study utilizes the autoregressive distributed lag (ARDL) bounds testing approach developed by Pesaran, Shin, and Smith (2001), diverging from the traditional co-integration methods of Engle and Granger (1987) and Johansen and Juselius (1990). This method has gained popularity due to its effectiveness when variables are of mixed integration orderseither I(0), I(1), or both-which earlier approaches could not handle. ...
This study examines the impact of unemployment on economic growth in Nigeria from 1990 to 2023. Using econometric techniques, the study analyzes the relationship between unemployment rates, measured as a percentage of the labor force, and real GDP growth. The findings suggest a negative correlation between unemployment and economic growth, aligning with Okun's Law. Higher unemployment rates are associated with lower economic output, potentially due to reduced consumer spending, decreased labor force participation, and diminished investment. The study also considers the impact of other factors such as poverty, inflation, and security on economic growth and unemployment. The results highlight the importance of addressing unemployment as a key strategy for promoting sustainable economic development in Nigeria.
... Γ k -matrix for each differential delay. The Johansen test examines the null hypothesis of no cointegration, which occurs when the matrix A = 0 [90]. The testing of the number of cointegrating relationships utilizes two statistics: the Trace test, which examines how many cointegrating vectors exist, and the Max-Eigenvalue test, which assesses whether the number of cointegrating vectors is exactly equal to a specified value [91,92]. ...
The observed increase in demand for transport leads to higher energy consumption, which still predominantly originates from fossil fuels. As a result, the transport sector remains one of the main sources of GHG emissions. At the same time, transport activities bring economic benefits by generating public income and contributing to GDP. This article analyzes the relationship between total final energy consumption in transport, CO2 emissions from transport, and government revenues, using Poland as a case study. The study applies Johansen’s cointegration method to identify long-term relationships between time series. Unlike many cross-country studies, this research addresses a gap by focusing specifically on Poland—a post-transition economy where the transport sector holds both fiscal and environmental significance. After cointegration test, the Impulse Response Function was used to examine dynamics and identify system shocks. Results indicate that energy consumption in transport significantly affects both CO2 emissions and government revenues. A rise in energy use leads to higher emissions and also correlates with increased public income. The study contributes to the understanding of how transport-related energy use impacts both fiscal outcomes and emissions in a national context. These findings offer a foundation for shaping future policies that promote economic growth and stable revenue while encouraging more efficient energy use and lower emissions.
... represents the reduced form coefficients, which are equal to Π = −B −1 Γ, and v t = g.1 represents the reduced form, which is equal to v t = B −1 u t . When Equation (2) is transposed, we get [56,57]: ...
This study aimed to develop a strategic management model for the agricultural sector to effectively reduce greenhouse gas emissions in the future, primarily focusing on increasing agricultural waste. This study was built upon a model known as the Path Analysis with Simultaneous Equation System based on Full Information Maximum-Likelihood (Path-SFIML) Model, which has been thoroughly validated for its validity, measurement of model fit, and absence of spurious results. The findings revealed that the environmental sector is with the has low capacity to readjust to equilibrium, requiring thousands of years to recover. Therefore, this study proposes a new policy scenario for urgent national management through scenario planning. Based on the research results, the key indicators identified for scenario planning include clean technology, waste biomass, organic waste treatments, and renewable energy. These indicators must be prioritized to effectively manage the increase in agricultural waste. This study demonstrates that implementing these measures would reduce the growth rate of agricultural waste to 30.38% (2037/2018) and decrease the growth rate of greenhouse gas emissions to 36.20% (2037/2018). These rates remain within the national safety threshold, which is set at 1302 Gg CO2e. This study also derived strategic guidelines from stakeholders to enhance the dissemination of research findings and address gaps in quantitative research, enabling more appropriate strategy formulation. It was found that the key approach to defining the new scenario policy in this research is suitable but requires improvements in criminal law, administrative law, and environmental law to ensure they are relevant and enforceable in the present context. Hence, the 20 Year National Strategy must urgently adopt this critical tool for decision-making to achieve sustainable green environmental goals.
... The objective function incorporating economic factors could be represented as in equation (3) ( , , ) = ⋅ ( ) + ⋅ ( ) (3) In equation (3) and are weights that balance the trade-offs between cost and benefit, ensuring that resource allocation leads to both economic and environmental sustainability. The final optimization problem combines DRL and economic models to achieve optimal resource allocation represented in equation (4) = arg [ ( , , )] + [∑ = ] (4) The IDL method combines the advanced capabilities of economic modeling with the dynamic, adaptive learning power of DRL to address the complexities of resource allocation in smart cities. By integrating these models, the system not only maximizes resource efficiency but also ensures that decisions are sustainable, cost-effective, and beneficial for long-term urban development. ...
By improving resource management, lowering environmental impact, and improving resident quality of living, smart cities using IoT, artificial intelligence, and big data are becoming more significant part of sustainable urban development. Particularly in energy usage, trash management, and water use, optimal resource allocation is a major obstacle these communities are confronting. This study presents a fresh strategy aiming at optimizing the resource allocation in the smart city by means of the synergy between the advanced economic models and DRL. Six statistical tools comprising Granger Causality, Co-integration Analysis, Dynamic Time Warping (DTW), Vector Autoregressive Models (VAR), Structural Equation Modelling (SEM), and Bayesian Networks have been applied to identify and examine the intricate interactions among several smart city components. The findings will provide a thorough awareness of how these instruments may enhance decision-making procedures so that municipal resources might be managed more ecologically and efficiently.
... After estimating the VAR model, we tested the hypothesis of cointegrating vectors within the system of real GDP growth, exports, and imports using the procedures of Johansen (1988) and Johansen and Juselius (1990). The trace test was applied to assess the number of cointegrating relationships. ...
This paper develops a unified framework to analyze the environmental, social, and economic dimensions of sustainable development within the context of a center-periphery international system. It introduces a three-gap model to address the challenges posed by the discrepancies among three key growth rates: the maximum growth rate compatible with external equilibrium, the minimum growth rate required for social inclusion, and the maximum growth rate consistent with environmental sustainability. Using updated theoretical and empirical insights, the paper applies the model to Latin American economies, highlighting the structural constraints and opportunities for achieving sustainable development in peripheral regions. By quantifying the interactions between technological capabilities, green investments, and social inclusion policies, the study offers policy recommendations to foster balanced and inclusive growth paths aligned with global sustainability commitments.
... This model helped capture the linear interdependencies among ICT adoption and GDP, enabling an evaluation of their collective impact on Oman's economic growth.To accurately apply the VECM model, the optimal lag length was identified using four criteria: the Akaike information criterion (AIC), Schwarz Bayesian information criterion (SBIC), Hannan-Quinn criterion (HQC), and final prediction error (FPE). Furthermore, Johansen and Juselius' (1990) cointegration tests (the maximum eigenvalue and trace tests) were used to determine the number of cointegration vectors to understand the long-term relationship among variables. If the cointegration results indicated long-term relationships among ICT adoption, economic growth, this allowed for further modeling with the VECM to capture short-term dynamics and long-term equilibrium adjustments. ...
International tourism is significantly impacted by global political, financial, and environmental events. In Thailand, where tourism is a key economic driver, visa regulations play a crucial role in shaping travel demand. This study examines the financial impact of Thailand’s visa policies on Chinese visitors, focusing on the effects of the Beijing 2008 Olympic Games and the COVID-19 pandemic. Using a combination of econometric modeling and Computable General Equilibrium (CGE) analysis, the study evaluates changes in tourism revenue, visitor arrivals, and economic welfare. Findings indicate that visa restrictions during both events contributed to substantial financial losses, outweighing the potential economic benefits. Policymakers must balance security concerns with the economic consequences of restrictive visa policies. The study provides insights into how major events influence travel behavior and offers recommendations for sustainable tourism policies that minimize financial disruptions while ensuring long-term growth.
... There are various methods to test cointegration between series. Among these methods, the tests developed by Engle and Granger (1987), Johansen (1988) and Johansen and Juselius (1990) stand out. However, these methods have some limitations. ...
This study analyzes the impacts of economic growth on ecosystem in Türkiye. The study uses annual data for the period 1995-2021 and the ARDL method. The study utilizes the Ecosystem Vitality Index, a sub-dimension of the Environmental Performance Index. In addition, seven models were constructed to assess in detail the impact of economic growth on different dimensions of the ecosystem. The results show that economic growth has a significant impact in all models analyzed. However, the direction of this impact differs across ecosystem components. Economic growth is found to have a positive impact on agriculture and water resources. In these models, a 1% increase in GDP increases the agriculture and water resources indices by 0.074-0.672%. In contrast, economic growth has a negative impact on biodiversity and habitat, ecosystem services, fisheries, acid rain and total ecosystem vitality. In these models, a 1% increase in GDP reduces the indices of biodiversity and habitat, ecosystem services, fisheries, acid rain and total ecosystem vitality by 0.101-2.144%. The results suggest that the environmental costs of economic growth processes need to be considered. Environmentally friendly policies should be combined with sustainable development strategies to reduce the negative impacts of economic growth.
... The ARDL approach is a more suitable model for empirical work if we are uncertain about the unit root features of the data. Similarly, the (Johansen & Juselius, 1990) co-integration approach is not suitable when there is just one co-integrating vector. Therefore, regardless of whether the underlying variables are I(0), I(1), or a combination of both, Pesaran and Shin (1995) presented the Autoregressive Distributed Lag (ARDL) technique for co-integration or the limits procedure for estimating a long-run connection. ...
This empirical study aims to investigate the relationship between financial technology (FinTech) and financial access in Cameroon. With the increasing adoption of financial technology in the financial service sectors, it is essential to determine whether the use of these technologies has a significant impact on financial access. Methodologically, to appraise the link between FinTech and financial access, the study applied the autoregressive distributed lag (ARDL) technique. Data related to financial access were obtained from the Financial Development and Structural Dataset, while bank technological-related data, such as the Depth of Automatic Teller Machines (ATMs), were obtained from the International Monetary Fund (IMF) database. The ARDL Bounds Test results make a substantive contribution to the scholarly discourse by empirically affirming the existence of a long-term cointegration relationship between FinTech and financial access. The outcome shows that in the short run, FinTech has a positive effect on financial access up to the third lag, and the long-run outcome equally confirms a positive and significant effect of FinTech on financial access in Cameroon. In terms of policy recommendations, policymakers should implement programs that incorporate initiatives to promote FinTech, while consumers need to learn about the benefits of FinTech and how to use FinTech services safely.
... I(0) seviye değişkenler için Johnson eşbütünleşme yöntemi kullanılamamaktadır (Işık, Acar & Işık, 2004). Johansen (1988) ve Johansen & Jesulius (1990) tarafından Eangle- Granger (1987) yöntemini iyileştirmek için geliştirilen Johansen eşbütünleşme yöntemi, birinci farklarda durağan hale gelen serilerde, serilerin düzey değerde analiz edilebilmesine imkân tanımaktadır (Işık, Acar & Işık, 2004). Johansen eşbütünleşme testi için ilk olarak VAR modeli kurularak Hall'ın (1991) önerdiği uygun gecikme uzunluğu saptanmalıdır. ...
Bu çalışmanın amacı, Borsa İstanbul (BİST) sektörel
endeksleri ile CDS primleri arasındaki ilişkiyi araştırmaktır. Yapılan
literatür taramasında ülkelerin CDS primleri ile borsa endeksleri
arasındaki ilişkiye yönelik birçok çalışmanın yapıldığı gözlenmiştir.
Ancak bu çalışmaların büyük bir kısmında borsa endeksi olarak ülke
ya da ülkelerin tek bir endeksi ele alınarak araştırılmıştır. Bu
çalışmada ise BİST’te yer alan sektörel endekslerin tamamı ele
alınarak CDS primleri ile borsa endeksleri arasında sektörel bir
farklılaşmanın varlığı araştırılmıştır. Buradaki temel motivasyon,
CDS ile borsa endeksi arasındaki beklenen negatif ilişkinin, tüm
sektörler için geçerli olup olmadığıdır. Beklenen negatif ilişkinin
dışında sektörel bir farklılaşmanın varlığı, yatırımcılar ve portföy
yöneticileri açısından oldukça önemlidir.
... d(A i ) = minV(s i ≥ s k ) for k = 1, 2, 3, . . . , n; k ̸ = i, the weight value can be determined as follows [58,60,61]: ...
This research aims to develop mitigation and adaptation strategies for greenhouse gas emissions Thailand in accordance with Climate-Smart Agriculture policies. The research employs a mixed-methods approach, integrating both quantitative and qualitative research as a crucial framework for impact analysis and an early warning tool for the government in achieving sustainability. On the quantitative side, an advanced model called the Longitudinal Mediated Moderation Analysis Based on the Fuzzy Autoregressive Hierarchical Process (LMMA-FAHP) model has been developed. This model meets all validity criteria, shows no signs of spuriousness, and outperforms previous models in terms of performance. It is highly suitable for policy formulation and strategic planning to guide the country’s long-term governance toward achieving net-zero emissions by 2065. The findings indicate that the new scenario policy, with an appropriateness rating of over 80%, includes factors such as the clean technology rate, biogas energy, biofertilizers, organic fertilizers, anaerobic digestion rate, biomass energy, biofertilizer rate, renewable energy rate, green material rate, waste biomass, and organic waste treatments. All indicators demonstrate a high sensitivity level. When the new scenario policy is incorporated into future greenhouse gas emissions forecasts (2025–2065), the research reveals a declining growth rate of emissions, reaching 78.51 Mt CO2 Eq., with a growth rate of 11.35%, which remains below the carrying capacity threshold (not exceeding 101.25 Mt CO2 Eq.). Moreover, should the government adopt and integrate these indicators into national governance frameworks, it is projected that greenhouse gas emissions by 2065 could be reduced by as much as 36.65%, significantly exceeding the government’s current reduction target of 20%. This would enable the government to adjust its carbon sequestration strategies more efficiently. Additionally, qualitative research was conducted by engaging stakeholders from the public sector, private sector, and agricultural communities to develop adaptive strategies for future greenhouse gas emissions. If the country follows the research-driven approach outlined in this research, it will lead to effective long-term policy and governance planning, ensuring sustainability for Thailand.
... From the result in table 3, the ADF indicated that INF integrated at level i.e. order zero or 1(0) or (∆ = 0), while the explanatory variables were integrated at first difference i.e. order one or 1(1). Due to the existence of mixed integration, the Autoregressive Distributed Lag (ARDL) bounds test approach to Co-integration was applied (Johansen & Juselius, 1990;Pesaran, Smith, & Shin, 2001). ...
Keynesian fiscal policy framework and multiple regression analysis technique were used to appraise the impact of taxation and public expenditure on economic stability in Nigeria from 1981 to 2022. The results show that petroleum profits tax, capital expenditure and recurrent expenditure significantly influenced inflation in Nigeria, with increase in recurrent expenditure and petroleum profits tax causing inflation to rise. The study recommended that government should cut down recurrent expenditure, subsidise petroleum products and increase expenditure on public goods and services. Tax authorities should diversify tax revenue generation by fine-tuning current tax policies to capture more taxpayers into the tax net.
... World Bank database was employed to obtain the relevant data. The summarized statistical information is given below: Previous cointegration tests (Engle and Granger,1987;Johansen and Juselius, 1990;Phillips and Hansen,1990) require that it is necessary for all series to be stationary at the same level. On the other hand, Pesaran et al. (2001) created a technique called the autoregressive distributed lag model (ARDL), which allows variables to be I(0), I(1), or a combination of the two. ...
This study explores the symmetric and asymmetric effects of inward FDI on unemployment by using data from Türkiye from 1988 to 2020. ARDL (Autoregressive Distributed Lag), NARDL (Nonlinear Autoregressive Distributed Lag) and asymmetric causality test are applied to identify impacts of FDI on unemployment. While ARDL findings show no cointegration relationship, the NARDL findings prove the cointegration relationship between the variables. According to NARDL findings, in the long run, while a rise in FDI decreases unemployment, a reduction in FDI increases unemployment. Also, NARDL findings concur with the asymmetric causality test results. Positive shocks in FDI are seen as the cause of negative shocks in unemployment. Moreover, negative shocks in FDI are seen as the cause of positive shocks in unemployment. As a result, the analysis clearly demonstrates that FDI has a crucial impact on unemployment in Türkiye. Considering that Türkiye ranks 29th in the list of countries attracting foreign direct investment, it is understood that rule-based and incentive policies are necessary in order to attract more amount of FDI.
... Cointegration methods for univariate analysis include the Engle and Granger (1987) and Phillips and Hansen (1990) fully modified ordinary least squares (OLS) approach. With regards to the multivariate cointegration analysis, the well-known method is the maximum likelihood procedure of Johansen (1988), and Johansen and Juselius (1990). ...
Financial markets have been used in developing economies to raise and maintain these economies social stability level, and to facilitate economic development. Economic development is about the upliftment of the living standards and freedom of the citizens by upgrading the quality of human lives. The study strove to realise the objective of determining if different forms of financial markets can influence economic development in selected Southern Africa Development Community (SADC) countries. Panel econometric techniques were utilised and periods examined spanned from 2007 to 2021. Economic development may not be quantified using a single indicator. Economic development as the dependent variable was measured by the Economic Development Index (EDI) which was constructed using indicators such as the Human Development Index, Economic Complexity Index and Gross Domestic Product per capita. The money market, stock market and foreign exchange market were found to negatively influence EDI in the long-run. Financial markets can be stated to influence the development and economic performance of the selected SADC countries. Based on the findings, it is recommended that monetary authorities and regulatory authorities ensure that the monetary, fiscal, and financial policies are well managed, and that these policies are implemented to develop the social and economic level of the country.
To account for nonlinearities in the relationship between financial and technological development on income inequality, this chapter uses a nonlinear panel ARDL model that allows for heterogeneity within countries. The results show that in the long run, financial and technological development significantly impact income inequality in SSA countries. However, the impact of positive technology on income inequality is negative, while both positive and negative financial shocks have a positive impact on income inequality. The study indicates the importance of fiscal and financial policies of developing economies that should be implemented to achieve inclusive growth, improve welfare, and reduce income distribution in the SSA region.
This paper investigates the key factors influencing rice export decisions in Vietnam, one of the world's leading rice exporters. Using a mixed-method approach combining quantitative surveys and in-depth interviews with rice exporters and policymakers, the study identifies variables such as government policy, international market demand, production capacity, logistics infrastructure, and global price fluctuations as critical determinants. The findings provide insights into how Vietnam can enhance its export competitiveness and formulate sustainable export strategies. The empirical results indicate that rice production, yield, and global demand have a statistically significant and positive impact on rice exports. In contrast, both domestic prices and export prices are found to negatively affect rice export volumes, implying that higher price levels may reduce competitiveness or domestic availability. Meanwhile, domestic demand appears statistically insignificant, suggesting that export decisions are more closely tied to supply-side and global market dynamics. To assess the short-term dynamics and the adjustment mechanism toward long-run equilibrium, a Vector Error Correction Model (VECM) is estimated. The VECM results reveal that the system corrects deviations from the long-run path at a rate of approximately 0.62% per year, indicating a slow but steady convergence. In conclusion, the study recommends that Vietnamese policymakers prioritize improvements in rice yield per hectare and total production capacity. These are shown to be the most effective drivers of export growth. Additionally, measures to enhance global market access and reduce price volatility will further strengthen Vietnam’s position as a leading rice exporter in an increasingly competitive global market.
This research attempts to scrutinize the dynamic nexus between the aggregate derivatives market trading activity/volume and the macroeconomic information. We track the nonlinear impact of money supply, interest rates and gold prices along with the stock index, volatility indices and economic policy uncertainty index on India’s NSE derivative market and its sub-segments trading activity using a nonlinear autoregressive distributed lag model. This article makes contributions by filling the deficit in the available literature with reference to the understanding of the nexus of derivatives trading activity and macroeconomic information. First, we found evidence of the long-run equilibrium cointegration between money supply, gold prices, interest rates and aggregate derivatives market trading activity. Second, we found that derivatives market segments vary in macroeconomic variable sensitivity. Third, identifying macroeconomic variable-induced long- and short-term asymmetry across segments. Recognizing the asymmetrical relationship between macroeconomic information and derivatives trading activity helps investors formulate trading strategies and policymakers mitigate stock market volatility through proactive policy adjustments.
Key Takeaways
Evidence of the long-run equilibrium cointegration between money supply, gold prices, interest rates and aggregate derivatives market trading activity.
Derivative market segments vary in macroeconomic variable sensitivity.
Identifying macroeconomic variables-induced long- and short-term asymmetry across segments.
Rice is an important staple food in Nigeria, playing a critical role in the country’s food security, agricultural development, and economic growth. This research investigated how rice importation affected rice production and Nigeria's economic growth from 1990 to 2020 using time series data. The study aimed to understand the dynamics between rice importation, local production, and economic performance to inform policy decisions that promote agricultural sustainability. The data were analyzed with various econometrics models such as the trend model, Augmented Dickey-Fuller (ADF) test, Johansen Cointegration technique, Granger causality test, and simultaneous equation model. The results showed a significant gap between rice demand and supply in Nigeria and a long-run relationship between rice production, rice importation, and economic growth. While the gap indicated a high dependence on foreign rice to meet the rising domestic demand, the long-run relationship indicated that rice importation had a negative impact on the economy. The results also revealed causal relationships between rice production, rice importation, and GDP, and that rice importation had a negative and significant effect on Nigeria's economic growth and domestic rice production potential. Rice production in Nigeria was influenced by rice importation and population growth, while rice importation was affected by exchange rates and population growth. The study concluded that a sustained overdependence on rice importation has adverse consequences on Nigeria's economy and thereby suggested that the adoption of a multifaceted policy measure or strategy that emphasizes reducing rice importation, increasing domestic production of rice, and enhancing the standard of living for domestic rice producers is a key policy objective.
Enerji, ekonomik faaliyetler ve üretim süreçlerinde temel bir girdi olarak öne çıkmaktadır. Ülkelerin ekonomik büyüme performansı ve dış ticareti üzerinde kritik bir rol oynayan enerji, sanayileşmenin hızla artması, küresel ekonominin gelişimi ve ticaretin serbestleşmesi gibi faktörlere bağlı olarak talep artışıyla karşı karşıyadır. Bu talebin en belirgin bir şekilde ortaya çıktığı alanlardan biri, sanayi sektörünün temel alt dalını oluşturan ve üretim süreçlerinde enerjiyi önemli ölçüde kullanan imalat sanayi sektörüdür. İmalat sanayi, üretimin ve tüketimin gerçekleştiği geniş bir yelpazede faaliyet gösteren ve çeşitli alt sektörleri kapsayan bir endüstri dalıdır. Bu endüstri dalı, malların üretiminden tasarımına, işleme süreçlerinden geri dönüşümüne ve tüketiciye ulaşıncaya kadar tüm aşamalarında enerjiyi kullanmaktadır. Özellikle hammaddenin işlenmesinden başlayarak tüketildiği son noktaya kadar üretim ve imalatla ilgili tüm endüstriyel faaliyetlerde kullanılan yoğun enerji tüketimi, sera gazı emisyonlarının önemli bir kaynağıdır. Gelişmekte olan ülkelerin büyüme sürecinde rol oynayan imalat sanayi Türkiye için kritik bir role sahiptir. GSYH içindeki payı %20’lerde olmasının yanı sıra toplam ihracatının %87’si gibi büyük bir kısmını oluşturmaktadır. 1991-2021 yıllarını kapsayan bu çalışmada Türkiye imalat sanayi enerji tüketiminin karbon emisyonu ve ihracatı arasındaki ilişki Johansen eşbütünleşme yöntemi ve Toda-Yamamoto nedensellik analizi kullanılarak test edilmiştir. Analiz sonuçlarına göre imalat sanayi ihracatı, enerji tüketimi ve karbon emisyonu arasında uzun dönemli bir ilişkinin olduğu belirlenmiştir. Toda-Yamamoto nedensellik analizine göre ise imalat sanayi ihracatı ile karbon emisyonu arasında çift yönlü nedensellik ilişkisi olduğu bu değişkenlerin karşılıklı olarak birbirini etkilediği, imalat sanayi enerji tüketiminden ihracata doğru tek yönlü bir nedensellik ilişkisinin varlığı tespit edilmiştir.
The main objective of this research was to examine the impacts of private and public physical capital accumulations on economic growth in Ethiopia for the period ranging from 1974/75-2017/18 by using Auto Regressive Distributed Lag (ARDL) Approach to Co-integration and Vector Error Correction Model. The result showed that real private capital accumulation had statistically insignificant impact while public capital accumulation had negative and statistically significant impact on economic growth of Ethiopia in the long-run. The result also revealed that human capital and labor force had positive and statistically significant impact while trade openness, macroeconomic instability and foreign aid had negative and statistically significant impact in determining economic growth of Ethiopia in the long-run. In addition, in the short-run private and public capital stocks had negative and statistically significant impact on economic growth of Ethiopia at first lag while human capital, labor force, trade openness, macroeconomic instability and foreign aid had positive and significant impact on economic growth of Ethiopia with lag. Overall, the policy implication of this study is that, given the long-run insignificant impact of private capital and negative significant impact of public capital stocks on economic growth, it is recommendable to reduce public capital investment in different sector investments rather better to encourage private sector participation on economic activities in Ethiopia.
This study analyses the effect of political stability and macroeconomic uncertainty on aggregate investment behaviour in Pakistan over the period 1960–2015. The Auto-Regressive Distributed Lags (ARDL) methodology is applied to explore both the long-run equilibrium relationship and short-run behaviour of investment. The macroeconomic uncertainty variable is derived from real exchange rate and is computed by the best-fitted GARCH model. The results reveal robust effects of political stability and macroeconomic uncertainty on overall investment activity in Pakistan. The government nationalisation policy, GDP growth, user cost of capital, credit availability and degree of openness are found to be the other key determining factors for investment both in long- and short-run. However, the favourable impact of physical infrastructure on investment holds in long-run only, while its effect is adverse though insignificantly in short-run. The findings support the neoclassical flexible accelerator principle and are consistent with economic theory. The volume of available funds is the binding constraint for investment and the McKinnon-Shaw hypothesis is validated in the short-run. Keywords: Aggregate Investment, Irreversibility, Macroeconomic Uncertainty, Political Stability, GARCH, ARDL, Bound Testing Approach, Pakistan
Demografik bir unsur olan nüfus, iktisadın teorik ve politik anlamda önemli konularından birini oluşturmaktadır. Sanayi Devrimi’nden sonraki süreçte dünya nüfusunun, kişi başına gelirden daha hızlı artması küresel doğal sermaye stokunu hızla aşındırmıştır. Beşerî faaliyetlerin neden olduğu tahribatın şiddeti, ekolojik ayak izinin biyolojik kapasiteyi aşması ile de kendisini göstermektedir. Birleşmiş Milletler Sürdürülebilir Kalkınma Hedefleri’nin merkezinde insanın ekonomik faaliyetleri ve onun ekolojik ayak izini azaltma çabasının yer alması, dikkatleri yeniden nüfus düzeyine çekmiştir. Bu çalışmada ekolojik ve ekonomik hedefler bağlamında Türkiye için optimal nüfus düzeyinin ne olması gerektiği ARDL yöntemiyle araştırılmıştır. Bulgular refah düzeyinin artırılması ve kaynakların sürdürülebilirliği açısından Türkiye’nin nüfus düzeyinin olması gerekenin çok üzerinde olduğunu göstermektedir.
Life expectancy reflects a population's overall health and prosperity. This study applies the Auto-Regressive Distributed Lag (ARDL) method to analyze how oil use influences the link between GDP growth and life expectancy in Malaysia from 1980 to 2020. The results show that while GDP growth boosts life expectancy in both the short and long term, dependence on oil negatively affects it. Wealth accumulation positively contributes to longevity, whereas healthcare budget distribution surprisingly reduces life expectancy. These findings highlight the complex relationship between economic development and environmental conditions, suggesting the need for policies that support both growth and environmental sustainability to improve public health outcomes.
Energy abundance is driving the global economy. But this comes at a price: our energies to extract energy from fossil fuels and renewable energy sources are costing us dearly in terms of land. The pollution generated by the production and consumption of energy, including the combustion of biomass, is changing the ecology of the entire planet. This study aims to analyze the contributions of renewable and non-renewable energies in Saudi Arabia to long-term global climate change. This study is based on the Auto-Regressive Distributive Lags (ARDL) approach that is proposed by Pesaranc et al during the period 1990-2019. The empirical estimate yields interesting results. There is a relationship between climate change, renewable and non-renewable energy in the long term.
Purpose: This study investigates the dynamic relationship between macro-economic variables, specifically FDI and economic growth (GDP per capita), and their impact on GHG emissions in Zambia. Using time series data from 1990 to 2022, this investigation tested the Environmental Kuznets Curve (EKC) and Pollution Haven Hypothesis (PHH). Materials and Methods: The econometric analysis made use of the Vector Error Correction Model (VECM) to evaluate the short run and long run relationship among the variables while the granger causality test was used to analyze the causal relationship among the variables. Findings: The findings revealed that the EKC does not hold in Zambia, indicating a U-shaped relationship between economic growth and GHG emissions. Furthermore, FDI in Zambia supports environmental sustainability, aligning with the Pollution Halo Hypothesis (PHAH) rather than the PHH at least at the low level of current Zambia’s output. The granger causality results indicated that there exists a positive unidirectional causal relationship from GDP per capita to GHG emissions and no causality relationship among the rest of the variables. Unique contribution to Theory, Practice and Policy: These results provide insights for policymakers to balance economic growth with environmental sustainability hence the study suggested policy recommendations aimed at strengthening regulations, promoting green technology, and attracting sustainable foreign investment.
Tax revenues are considered the most significant source of public income when implementing fiscal policy within a country. Whether positive or negative, changes in tax revenue can lead to various shifts in states' economic, social, and political dynamics, making tax revenues highly critical for governments. On the other hand, taxes, as a significant expenditure for businesses, can be substantially influenced by economic and political factors. Considering these factors, this study examines the relationship between economic policy uncertainty and total tax revenues in Türkiye. The relationship between uncertainty and tax revenues was tested using Johansen Cointegration, Dynamic Ordinary Least Squares (DOLS), Fully Modified Ordinary Least Squares (FMOLS), and Canonical Cointegrating Regression (CCR) statistical model analyses. In addition to uncertainty and tax revenue, the econometric model included interest rates, unemployment rates, exchange rates, and industrial production indices as control variables. The analysis utilised quarterly time series data spanning from 2008Q1 to 2023Q4. The Johansen test indicated a long-run cointegration relationship between total tax revenue and political and economic uncertainty in Türkiye. Furthermore, the regression coefficient results derived from DOLS, FMOLS and CCR methods revealed that uncertainty significantly reduces total tax revenues. In conclusion, the study found that economic policy uncertainty has a negative impact on tax revenues due to the adverse effects it creates within the economic system.
This study examines how forensic auditing influences bank performance in Nigeria, using annual data from 2013 to 2023. By applying the autoregressive distributed lag (ARDL) model and validating the results with fully modified ordinary least squares (FMOLS), the study provides a comprehensive analysis of forensic auditing's impact on the banking sector. The findings reveal that forensic auditing plays a crucial role in enhancing financial reporting accuracy, fraud detection, and risk management. By minimizing fraudulent activities and ensuring compliance with regulatory standards, forensic auditing fosters a more secure and efficient banking environment. Additionally, the study underscores its role in restoring stakeholder confidence, as greater transparency and accountability lead to increased trust in financial institutions. Banks that integrate forensic auditing are better positioned to detect irregularities early, mitigate risks, and improve overall operational efficiency and profitability. Given these insights, the study recommends that banks enhance their Anti-Money Laundering (AML) mechanisms by adopting stronger forensic auditing frameworks. This proactive approach can help identify and prevent money laundering activities, ultimately safeguarding the integrity of Nigeria's financial system.
Purpose
This study empirically analyses the relationship between China’s economic growth and higher education, specifically examining the background of China’s higher education expansion that commenced in 1999.
Design/methodology/approach
The research employs the Autoregressive Distributed Lag (ARDL) model with annual data, choosing the number of entrants and graduates as measures of higher education.
Findings
As results emerge, economic progress exerts a positive influence on entrants at the short-cycle tertiary level, whereas it negatively affects Master’s entrants in both the long run and short run. Furthermore, an increase in graduates from Bachelor’s or Master’s programmes hampers economic growth.
Practical implications
The findings imply that the talents cultivated by higher education do not match the demands of economic development since the expansion. It is recommended that there should be strategic planning for quantity adjustment and quality improvement across different tertiary levels to better fit market needs.
Originality/value
Extensive research efforts have looked at education as a whole without differentiating between various tertiary levels when assessing its impact on the economy. This article categorises higher education into four levels and explores their connections to economic growth. In addition, earlier research has predominantly relied on enrollment series as a measure of higher education. This article utilises the indicators of entrants and graduates so as to assess their relationships with economic growth from the perspective of supply and demand.
Ushbu tadqiqotning maqsadi hududlarda amalga oshirilayotgan islomiy investitsiya loyihalarining kengayishiga taʼsir etuvchi omillarning bogʻliqligini oʻrganishga qaratilgan. Hududlarda islomiy investitsiya loyihalari miqdori va unga taʼsir etishi mumkin boʻlgan mustaqil omillarning 2004-yildan 2024-yilgacha vaqtli qatorlardagi maʼlumotlari tahlil qilingan. Tadqiqotimizda VAR modelidan foydalanildi. Tadqiqotimizning natijasiga koʻra, tanlab olingan mustaqil omillarning islomiy investitsiya loyihalariga qisqa muddatda ijobiy bogʻliqligi aniqlandi.
Klasik üretim faktörlerinin günümüzdeki ekonomik büyümeyi yeterince açıklayamaması, büyüme teorileri konusunda yeni çalışmaların artışına neden olmuştur. Bu kapsamda geliştirilen içsel büyüme teorileri içerisinde beşerî sermayenin ekonomik büyüme sürecinde büyük önemi bulunmaktadır. Bu çalışmanın amacı Türkiye’de beşerî sermayenin ekonomik büyüme üzerine etkisini 1995Q1-2023Q4 dönemi için incelemektir. Çalışmada ekonometrik model olarak Johansen Eşbütünleşme Analizi kullanılmıştır. Araştırma sonucunda; yüksek öğretimde okullaşma ve üniversite mezunu istihdam oranının artmasının büyümeyi uzun dönemde pozitif etkilerken, MEB ve YÖK bütçelerinin genel kamu bütçesi içindeki payının artmasının büyümeye etkisinin istatistiki olarak anlamsız olduğu bulgusuna ulaşılmıştır.
The study examined the influence of real exchange rates fluctuations on the trade balance in Botswana. The main objectives were to assess the effects of real exchange rates on the trade balance and determine whether the Marshall – Lerner condition and the J-curve theory hold for Botswana using quarterly time series data from 1995 to 2022. The Johansen Cointegration and Vector Error Correction Model (VECM) were used to assess the impact of real exchange rates on the trade balance. The findings suggest that real exchange rates have a negative impact on the trade balance in the long run, indicating that the Marshall – Lerner condition is not valid. This implies that a weakening of the Botswana Pula does not affect the country’s net exports. In the short run, the coefficient of the real exchange rate was negative but statistically insignificant, indicating the absence of the J-curve effect. This indicates that Botswana’s net exports performance is not affected by the devaluation of the domestic currency. The study recommends that currency misalignment should be avoided. Furthermore, the study's findings revealed that real exchange rates affect the trade balance in both the short run and long run; therefore policy makers should maintain the current monetary and managed float exchange rate policies.
This article studies how to identify hidden factors in multivariate time series process. This problem is important because, when the series are driven by a set of common factors, (a) a large number of parameters may be needed to obtain an adequate representation of the system and (b) the estimated parameters will be highly correlated. Therefore, a complex and badly defined relationship can appear when, in fact, a simpler and parsimonious model in terms of a few common factors can be operating. This article develops a methodology to identify the number of factors and to build a simplifying transformation to represent the series. It is proved that the number of factors is equal to the rank of the covariance matrices and the parameter matrices of the infinite moving average representation of the process. The eigenvectors of these matrices will provide the canonical transformation. The method is illustrated with one example, using series of the price of wheat in five provinces of Spain in the 19th century. The standard approach to build a vector autore-gressive integrated moving average model showed a complex relationship with all kinds of feedback operating. When the methodology developed in the article was applied, however, two factors were identified and a clearer and simpler representation of the system was achieved.
This paper develops a multivariate regression theory for integrated processes which simplifies and extends much earlier work. Our framework allows for both stochastic and certain deterministic regressors, vector autoregressions and regressors with drift. The main focus of the paper is statistical inference. The presence of nuisance parameters in the asymptotic distributions of regression F-tests is explored and new transformations are introduced to deal with these dependencies. Some specializations of our theory are considered in detail. In models with strictly exogenous regressors we demonstrate the validity of conventional asymptotic theory for appropriately constructed Wald tests. These tests provide a simple and convenient basis for specification robust inferences in this context. Single equation regression tests are also studied in detail. Here it is shown that the asymptotic distribution of the Wald test is a mixture of the chi square of conventional regression theory and the standard unit root theory. The new result accommodates both extremes and intermediate cases.
This paper continues the theoretical investigation of Park and Phillips [7]. We develop an asymptotic theory of regression for multivariate linear models that accommodates integrated processes of different orders, nonzero means, drifts, time trends and cointegrated regressors. The framework of analysis is general but has a common architecture that helps to simplify and codify what would otherwise be a myriad of isolated results. A good deal of earlier research by the authors and by others comes within the new framework. Special models of some importance are considered in detail, such as VAR systems with multiple lags and cointegrated variants.
Recent work on the theory of regression with integrated process is reviewed. This work is particularly relevant in economics where many financial series and macroeconomic time series exhibit nonstationary characteristics and are often well modeled individually as simple ARIMA processes. The theory makes extensive use of weak convergence methods and allows for integrated processes that are driven by quite general weakly dependent and possibly heterogeneously distributed innovations. The theory also includes near integrated time series, which have roots near unity, and cointegrated series, which move together over time but are individually nonstationary. A general framework for asymptotic analysis is given which involves limiting Gaussian functionals and extends the LAN and LAMN families of conventional asymptotic theory. An application to the Gaussian AR(1) is reported.
This paper develops a general asymptotic theory of regression for processes which are integrated of order one. The theory
includes vector autoregressions and multivariate regressions amongst integrated processes that are driven by innovation sequences
which allow for a wide class of weak dependence and heterogeneity. The models studied cover cointegrated systems such as those
advanced recently by Granger and Engle and quite general linear simultaneous equations systems with contemporaneous regressor
error correlation and serially correlated errors. Problems of statistical testing in vector autoregressions and multivariate
regressions with integrated processes are also studied. It is shown that the asympotic theory for conventional tests involves
major departures from classical theory and raises new and important issues of the presence of nuisance parameters in the limiting
distribution theory.
Information about faults plays an important role in fault diagnosis and control reconfiguration. This paper proposes a fault estimation method which involves a two step procedure. The first step is used to generate the residual from inputs and outputs of the system. In the second step, a fault estimator is used to estimate faults using the residual signal. The design problem of the fault estimator is solved using linear inverse system theory. A simple example is used to illustrate the method taken.
This paper is concerned with the investigation of reduced rank coefficient models for multiple time series. In particular, autoregressive processes which have a structure to their coefficient matrices similar to that of classical multivariate reduced rank regression are studied in detail. The estimation of parameters and associated asymptotic theory are derived. The exact correspondence between the reduced rank regression procedure for multiple autoregressive processes and the canonical analysis of Box & Tiao (1977) is briefly indicated. To illustrate the methods, U.S. hog data are considered.
For an m-variate (“partially”) nonstationary vector autoregressive process {Yt}, we consider the autoregressive model Φ(L)Yt = εt, where Φ(L) = I − Φ1L − … − ΦpL and det{Φ(z)} = 0 has d < m roots equal to unity and all other roots are outside the unit circle. It is also assumed that rank {Φ(1)} = r, r = m − d, so that each component of the first differences Wt = Yt − Yt − 1 is stationary. The relation of the model to error correction models and co-integration (Engle and Granger 1987) is discussed. The process {Yt} has the error correction representation Φ(L)(1 − L)Yt = −P2(Ir − Λr)Q2Yt-1 + εt, where Q(Im − Φ(1))P = J = diag(Id, Λr) is in Jordan canonical form and Q' = [Q1, Q2]. It follows that the transformation Zt = QYt = [Z 1t, Z 2t] is such that the d × 1 process Z1t is nonstationary with Z1t − Z1t-1 stationary while Z2t is stationary. Asymptotic distribution theory for least squares parameter estimators of the model is first considered. A Gaussian partial reduced rank estimation procedure that explicitly incorporates the unit root structure in the model is then presented, and an asymptotically equivalent two-step reduced rank estimation procedure is also considered. A numerical example is presented to illustrate the methods and concepts. The finite sample properties of the estimators are also briefly examined through a small Monte Carlo sampling experiment.
Cointegrated multiple time series share at least one common trend. Two tests are developed for the number of common stochastic trends (i.e., for the order of cointegration) in a multiple time series with and without drift. Both tests involve the roots of the ordinary least squares coefficient matrix obtained by regressing the series onto its first lag. Critical values for the tests are tabulated, and their power is examined in a Monte Carlo study. Economic time series are often modeled as having a unit root in their autoregressive representation, or (equivalently) as containing a stochastic trend. But both casual observation and economic theory suggest that many series might contain the same stochastic trends so that they are cointegrated. If each of n series is integrated of order 1 but can be jointly characterized by k > n stochastic trends, then the vector representation of these series has k unit roots and n — k distinct stationary linear combinations. Our proposed tests can be viewed alternatively as tests of the number of common trends, linearly independent cointegrating vectors, or autoregressive unit roots of the vector process. Both of the proposed tests are asymptotically similar. The first test (qf) is developed under the assumption that certain components of the process have a finite-order vector autoregressive (VAR) representation, and the nuisance parameters are handled by estimating this VAR. The second test (qc) entails computing the eigenvalues of a corrected sample first-order autocorrelation matrix, where the correction is essentially a sum of the autocovariance matrices. Previous researchers have found that U.S. postwar interest rates, taken individually, appear to be integrated of order 1. In addition, the theory of the term structure implies that yields on similar assets of different maturities will be cointegrated. Applying these tests to postwar U.S. data on the federal funds rate and the three- and twelve-month treasury bill rates provides support for this prediction: The three interest rates appear to be cointegrated.
We show that maximum‐likelihood analysis of the reduced‐rank regression model exploits a fundamental inequality result of matrix theory when a normally distributed error structure with unknown covariance is assumed. This approach closely parallels the corresponding analysis when the covariance matrix is known (Davies and Tso, 1980) and demonstrates straightforwardly the intimate connection between reduced‐rank regression and canonical analysis. A geometric interpretation of the analysis is given.
Box and Tiao (1977) established the correspondence between non-stationary roots and canonical correlations of an AR(1) process. In this paper, we give an alternative, more direct, proof of the correspondence and extend a special case of that result to AR(p) processes. The usefulness of these results for multiple time series modelling is also briefly discussed.
We consider a nonstationary vector autoregressive process which is integrated of order 1, and generated by i.i.d. Gaussian errors. We then derive the maximum likelihood estimator of the space of cointegration vectors and the likelihood ratio test of the hypothesis that it has a given number of dimensions. Further we test linear hypotheses about the cointegration vectors.The asymptotic distribution of these test statistics are found and the first is described by a natural multivariate version of the usual test for unit root in an autoregressive process, and the other is a χ2 test.
In this paper we study the performance of various tests for normality (N), homoscedasticity (H) and serial independence (I) of regression residuals (u) under one, two and three directional departures from HO:u∼NHI.
We use the Lagrange multiplier procedure to derive efficient joint tests for residual normality, homoscedasticity and serial independence. The tests are simple to compute and asymptotically distributed as χ2.
SUMMARY This paper proposes a canonical transformation of a k-dimensional stationary autoregressive process. The components of the transformed process are ordered from least to most predictable.
The least predictable components are often nearly white noise which can reflect stable contemporaneous relationships among
the original variables. The most predictable can be nearly nonstationary representing the dynamic growth characteristic of
the series. The method is illustrated with a series with five variables.
The large depreciation of the rupiah in July and August 1997 was unexpected, and the ensuing currency crisis drew attention to anomalies in the domestic economy that cannot fail to have an impact on external confidence in its performance. Economic growth for 1997 will depend on how heavily the crisis affects economic activity during the second half of the year. Inflation had been projected at 6% for 1997, but accelerated depreciation had already begun to exert some upward pressure on prices by August. A slowdown had been feared for non-oil exports, but there were signs of acceleration even before the devaluation of the rupiah, especially for electrical and electronics products. The deficit on the current account of the balance of payments was expected to climb to 4% of GDP in 1997, but it was comfortably covered in the first half by substantial capital inflows. Foreign debt remained sizeable at $110 billion but foreign reserves had accumulated rapidly since late 1996. Foreign direct investment (FDI) approvals had experienced a decline in early 1997. This need not have led to a change in realised FDI, however, because approval levels had been artificially high previously, and profit expectations remained good. Controversies in the mining sector have caused concern about an apparent re-awakening of economic nationalism. The national 'Timor' car program continues to be plagued by hazards and doubts. The foremost source of uncertainty, however, remains the still unresolved question of the political leadership succession.
The purpose of this paper is to give a systematic account of the maximum likelihood inference concerning cointegration vectors in non-stationary vector value autoregressive time series with Gaussian errors. The hypothesis of r cointegration vectors is given a simple parametric formulation in terms of cointegration vectors and their weights. We then estimate and test linear hypotheses about these. We find that the asymptotic inference for the linear hypotheses can be performed by applying the usual ² test. We also give some very simple Wald test and their asymptotic properties. The methids are illustrated by data from the Danish and the Finnish economy on the demand for money.
This paper contains the likelihood analysis of vector autoregressive models allowing for cointegration. The author derives the likelihood ratio test for cointegrating rank and finds it asymptotic distribution. He shows that the maximum likelihood estimator of the cointegrating relations can be found by reduced rank regression and derives the likelihood ratio test of structural hypotheses about these relations. The author shows that the asymptotic distribution of the maximum likelihood estimator is mixed Gaussian, allowing inference for hypotheses on the cointegrating relation to be conducted using the Chi(" squared") distribution. Copyright 1991 by The Econometric Society.
This paper considers estimation and hypothesis testing in linear time series when some or all of the variables have (possibly multiple) unit roots. The motivating example is a vector autoregression with some unit roots in the companion matrix, which might include polynomials in time as regressors. Parameters that can be written as coefficients on mean zero, nonintegrated regressors have jointly normal asymptotic distribution, converging at the rate of T(superscript "one-half") In general, the other coefficients (including the coefficient on polynomials in time), and associated t and F test statistics, have nonstandard asymptotic distributions. Copyright 1990 by The Econometric Society.
This paper develops an asymptotic theory for residual based tests for cointegration. Attention is given to the augmented Dickey-Fuller (ADF) test and the Z(subscript "alpha") and Z(subscript "t") unit root tests. Two new tests are also introduced. The tests are shown to be asymptotically similar, and simple representations of their limiting distributions are given and asymptotic critical values are tabulated. The ADF and Z(subscript "t") tests are asymptotically equivalent. Power properties of the test are also studied. The tests are consistent if suitably constructed, but the ADF and Z(subscript "t") tests have slower rates of divergence under cointegration than the other tests. Copyright 1990 by The Econometric Society.
Under fairly general conditions, ordinary least squares and linear instrumental variables estimators are asymptotically normal when a regression equation has nonstationary right hand side variables. Standard formulas may be used to calculate a consistent estimate of the asymptotic variance-covariance matrix of the estimated parameter vector, even if the disturbances are conditionally heteroskedastic and autocorrelated. So inference may proceed in the usual way. The key requirements are that the nonstationary variables share a common unit root and that the unconditional mean of their first differences is nonzero. Copyright 1988 by The Econometric Society.
The relationship between cointegration and error correction models, first suggested by Granger, is here extended and used to develop estimation procedures, tests, and empirical examples. A vector of time series is said to be cointegrated with cointegrating vector a if each element is stationary only after differencing while linear combinations a8xt are themselves stationary. A representation theorem connects the moving average , autoregressive, and error correction representations for cointegrated systems. A simple but asymptotically efficient two-step estimator is proposed and applied. Tests for cointegration are suggested and examined by Monte Carlo simulation. A series of examples are presented. Copyright 1987 by The Econometric Society.
This paper studies the properties of maximum likelihood estimates of co-integrated systems. Alternative formulations of such models are considered including a new triangular system error correction mechanism. It is shown that full system maximum likelihood brings the problem of inference within the family that is covered by the locally asymptotically mixed normal asymptotic theory provided that all unit roots in the system have been eliminated by specification and data transformation. This result has far reaching consequences. It means that cointegrating coefficient estimates are symmetrically distributed and median unbiased asymptotically, that an optimal asymptotic theory of inference applies and that hypothesis tests may be conducted using standard asymptotic chi-squared sets.
The asymptotic distributions of cointegration tests are approximated using the Gamma distribution. The tests considered are for the I(1), the conditional I(1), as well as the I(2) model. Formulae for the parameters of the Gamma distributions are derived from response surfaces. The resulting approximation is flexible, easy to implement and more accurate than the standard tables previously published.
The primary purpose of this paper is to review a very few results on some basic elements of large sample theory in a restricted structural framework, as described in detail in the recent book by LeCam and Yang (1990, Asymptotics in Statistics: Some Basic Concepts . New York: Springer), and to illustrate how the asymptotic inference problems associated with a wide variety of time series regression models fit into such a structural framework. The models illustrated include many linear time series models, including cointegrated models and autoregressive models with unit roots that are of wide current interest. The general treatment also includes nonlinear models, including what have become known as ARCH models. The possibility of replacing the density of the error variables of such models by an estimate of it (adaptive estimation) based on the observations is also considered.
Under the framework in which the asymptotic problems are treated, only the approximating structure of the likelihood ratios of the observations, together with auxiliary estimates of the parameters, will be required. Such approximating structures are available under quite general assumptions, such as that the Fisher information of the common density of the error variables is finite and nonsingular, and the more specific assumptions, such as Gaussianity, are not required. In addition, the construction and the form of inference procedures will not involve any additional complications in the non-Gaussian situations because the approximating quadratic structure actually will reduce the problems to the situations similar to those involved in the Gaussian cases.
Time series variables that stochastically trend together form a cointegrated system. OLS and NLS estimators of the parameters of a cointegrating vector are shown to converge in probability to the true parameter value at the rate T11d for any positive d. These estim mators can be written asymptotically in terms of relatively simple nonnormal random matrices which do not depend on the parameters of th e system. These asymptotic representations form the basis for simple and fast Monte Carlo calculations of the limiting distributions of th ese estimators. Asymptotic distributions thus computed are tabulated for several cointegrated processes. Copyright 1987 by The Econometric Society.
Cointegration in Linear Dynamic Systems', Discussion paper,Cointegration: A Survey of Recent Develop-ments', Mimeo
- J Davidson
- Lse
- J J Dolado
- T Jenkinson
Davidson, J. (1986). 'Cointegration in Linear Dynamic Systems', Discussion paper, LSE. Dolado, J. J. and Jenkinson, T. (1988). 'Cointegration: A Survey of Recent Develop-ments', Mimeo, Institute of Economics and Statistics, Oxford University.
Testing for Cointegration’ Cowles Foundation discussion paper No
- P C B Phillips
Phillips, P. C. B. and Ouliaris, S. (1986). 'Testing for Cointegration', Cowles Founda-tion discussion paper No. 809.
An introduction to Multivariate Statistical AnalysisA Canonical Analysis of Multiple Time Series with Applications
- T W Anderson
- Wiley
- G E P Box
- G C Tiao
Anderson, T. W. (1984). An introduction to Multivariate Statistical Analysis. New York, Wiley. Box, G. E. P. and Tiao, G. C. (1981). 'A Canonical Analysis of Multiple Time Series with Applications', Biornetrika, Vol. 64, pp. 355-65.
The Demand for Money
- D E W Laidler
Laidler, D. E. W. (1985). 'The Demand for Money', Oxford, Philip Allan.
Time Series Analysis of Error Correction Models', in Studies in Econometrics
- C W J Granger
- A A Weiss
Granger, C. W. J. and Weiss, A. A. (1983). 'Time Series Analysis of Error Correction Models', in Studies in Econometrics, Time Series and Multivariate Statistics, in Karlin, S., Amemiya, T. and Goodman, L. A. (eds.), New York, Academic Press, pp. 25 5-78.
‘Optimal Inference in Cointegrated Systems’ Cowles Foundation discussion paper No
- P C B Phillips
Phillips, P. C. B. (1988). 'Optimal Inference in Cointegrated Systems', Cowles Foundation discussion paper No. 866.
Testing for Cointegration’
- P C B Phillips
- S Ouliaris
Cointegration in Linear Dynamic Systems’
- J Davidson
‘Cointegration in Linear Dynamic Systems’ Discussion paper LSE
- J Davidson
Cointegration: A Survey of Recent Developments
- J J Dolado