Bayesian Vector Autoregressive Model Research Articles

Large quarterly Bayesian vector autoregression model for the modern Russian economy

It is often difficult to choose the necessary variables when we are forecasting the economic dynamics. On the one hand, vector autoregression (VAR) models can solve this problem by taking into account a sufficiently large number of variables. However, on the other hand, excessive parametrization of such models is not always justified, because it is often possible to choose such a small combination of variables the predictive power of which will be no worse than unlimited VARs with a large number of variables and lags. Bayesian methods help to solve this problem by introducing a priori restrictions on the VAR coefficients. The main goal of this work is to build a Large quarterly Bayesian vector autoregression (QBVAR) for the modern Russian economy. The hypotheses of the study: 1) BVAR(p) models reveal their maximum potential with a small number of variables, but with a large number of lags, 2) The Minnesota prior distribution is not always the best option for the modern Russian economy in the BVAR(p) model. As a result of the analysis, it turned out that for a number of the most important macroeconomic variables (GDP, inflation, key rate, unemployment, wages), Normal-Flat / Wishart-type priors turned out to be the optimal. In case of 29 input variables and two lags, the predictive power of the QBVAR(2) model is worse than the equivalent frequency VAR(2) or VECM(2). However, when it was possible to find the optimal combinations of variables, QBVAR(p) turned to be several times more accurate than its analogous frequency VAR(p) for all important macro indicators. In addition, the stiffness parameters of the considered a priori distributions decreases with increasing lags entering the model, i. e. the higher the order of the model with the minimum optimal set of variables, the tighter the distribution is necessary to obtain more accurate predictions. For the Russian realities, it is necessary to use very tight priors, 6–8 variables and 9–12 lags in a quarterly representation.

Inflation forecasting in turbulent times

AbstractIn the recent years many countries were hit by a series of macroeconomic shocks, most notably as a consequence of the COVID-19 pandemic and Russia’s invasion in Ukraine, raising inflation rates to multi-decade highs and suspending well-documented macroeconomic relationships. To capture these tail events, we propose a mixed-frequency Bayesian vector autoregressive (BVAR) model with Student t-distributed innovations or with stochastic volatility. Whereas inflation, industrial production, as well as oil and gas prices are available at monthly frequencies, real gross domestic product (GDP) is observed at a quarterly frequency. Thus, we apply a mixed-frequency setup using the forward-filtering–backward-sampling algorithm to generate monthly real GDP growth rates. We forecast inflation in those euro area countries that extensively import energy from Russia and therefore have been heavily exposed to the recent oil and gas price shocks. To measure the forecast performance of the mixed-frequency BVAR model, we compare our inflation forecasts with those generated by a battery of competing inflation forecasting models. The proposed BVAR models dominate the competition for all countries in terms of the log predictive density score.

Energy price reforms, exchange rate devaluation and macroeconomic instability: Evidence from Bayesian VAR identified with sign‐and‐zero restrictions

AbstractThis study sets out to examine the effects of the interaction of subsidy removal on premium motor spirit (PMS) and exchange rate devaluation on macroeconomic instability in Nigeria. In this regard, this study adopted the Bayesian vector autoregressive model (BVAR) identified with sign‐and‐zero restrictions for annual data between 1985 and 2022. The empirical results reveal that both the removal of subsidies on PMS and the devaluation of the naira exchange rate significantly undermine real gross domestic product (GDP) growth and raise inflationary pressures in Nigeria. One important implication of this finding is that the ongoing subsidy reforms in the energy sector and associated devaluation of the naira exchange rate raise the risk of stagflation in Nigeria. Secondly, the simulation shows that simultaneous subsidy removal on PMS and exchange rate devaluation can trigger macroeconomic instability. This finding implies that stabilising PMS price and the exchange rate is key to achieving macroeconomic stability in Nigeria. Thus, this study recommends that Nigeria should be cautious and act quickly to cushion the price of PMS from the vagaries of foreign exchange market fluctuations to improve macroeconomic stability in the country.

Diagnostic analystics in the Bayesian vector autoregressive model

The vector autoregressive model is extensively employed in macroeconomics, finance, and the natural sciences. However, it often encounters the issue of over-parametrization, resulting in undesirable behavior within the model. In this paper, we utilize the Bayesian vector autoregressive model as a tool to tackle this problem. Additionally, we employ the Bayesian local influence method to detect possible extreme observations under the model. We use posterior inference to estimate related parameters and construct Bayesian perturbation schemes for priors, variance, and data perturbations. Bayesian local influence is conducted based on three objective functions: Bayes factor, ϕ divergence, and posterior mean. To demonstrate the effectiveness of the diagnostics, we conduct numerical simulations. In the real data example, we use US inflation, unemployment, and interest rate data to verify this method's effectiveness.

Analysing Economic Growth and Environmental Quality: A Classical and Bayesian Approach

Abstract This empirical study investigates the intricate relationship between the ecological environment and economic growth within the context of Zhejiang Province, China - a region characterised by its rapid urbanisation and significant economic development. By analysing data spanning from 2011 to 2020, the research applies the Environmental Kuznets Curve (EKC) model, which hypothesises an inverted U-shaped relationship between environmental degradation and economic growth, within both classical and Bayesian statistical frameworks to examine the province’s per capita GDP. Findings from both statistical approaches reveal a distinct correlation between economic progression and environmental conditions, underscoring the Environmental Kuznets Curve hypothesis. Additionally, this study conducts a comparative analysis between Vector Autoregression (VAR) and Bayesian Vector Autoregression (BVAR) models to evaluate their predictive capabilities concerning the interplay between ecological health and economic advancement in Zhejiang. The BVAR model, with its incorporation of Bayesian statistics, demonstrates superior forecasting precision, providing valuable insights into the dynamics governing the relationship between economic growth and the ecological environment in Zhejiang Province.

Uncertainty, labour force participation and job search

This study examines the impact of labour force participation (LFP) on search behaviour and unemployment in response to uncertainty shocks. Using a Bayesian vector autoregression model, this study shows that an increase in uncertainty raises unemployment, lowers inflation and decreases LFP and search intensity. Then, a New Keynesian model that incorporates endogenous LFP and variable search intensity is constructed. Results show that both search intensity and participation are procyclical, which suggests a discouragement effect. However, with habit formation, the wealth effect outweighs the discouragement effect and induces an increase in LFP, resulting in a more significant decline in aggregate search intensity due to the expanded searcher pool. In the exogenous LFP model, search intensity is countercyclical, which dampens the unemployment rate. In the endogenous LFP model, the increased entry of non-participants cancels out the countercyclical search intensity of unemployed workers due to the large number of searchers.

Bayesian varying‐effects vector autoregressive models for inference of brain connectivity networks and covariate effects in pediatric traumatic brain injury

AbstractIn this article, we develop an analytical approach for estimating brain connectivity networks that accounts for subject heterogeneity. More specifically, we consider a novel extension of a multi‐subject Bayesian vector autoregressive model that estimates group‐specific directed brain connectivity networks and accounts for the effects of covariates on the network edges. We adopt a flexible approach, allowing for (possibly) nonlinear effects of the covariates on edge strength via a novel Bayesian nonparametric prior that employs a weighted mixture of Gaussian processes. For posterior inference, we achieve computational scalability by implementing a variational Bayes scheme. Our approach enables simultaneous estimation of group‐specific networks and selection of relevant covariate effects. We show improved performance over competing two‐stage approaches on simulated data. We apply our method on resting‐state functional magnetic resonance imaging data from children with a history of traumatic brain injury (TBI) and healthy controls to estimate the effects of age and sex on the group‐level connectivities. Our results highlight differences in the distribution of parent nodes. They also suggest alteration in the relation of age, with peak edge strength in children with TBI, and differences in effective connectivity strength between males and females.

Global supply chain disruptions and financial conditions

Supply chain disruptions have emerged as a critical factor influencing global economic conditions. This research examines the implications of global supply chain disruptions via Bayesian Vector Autoregression (BVAR) model as it relates to equity returns. The analysis reveals that supply chain shocks can be destabilizing via lower output, higher inflation and lower equity returns. These novel findings offer valuable insights for policymakers and investors.

Carbon Market Efficiency and Economic Policy Uncertainty: Evidence from a TVP-VAR Model

This paper examines the dynamic linkages among economic policy uncertainty (EPU), the green bond market, the carbon market, and the macroeconomy using the time-varying parameter vector autoregressive (TVP-VAR) model with monthly data spanning from January 2016 to December 2021. Additionally, it assesses the robustness and accuracy of the empirical results through the Bayesian vector autoregressive (BVAR) model. The findings indicate that EPU negatively affects the green bond market in the short term but has a positive impact in the medium and long term. Conversely, EPU has a positive impact on the carbon market in the short term but a negative impact in the medium and long term. Furthermore, the green bond market negatively influences the carbon market in both the short and medium to long term. These results suggest that emerging markets, such as the green bond and carbon markets, are influenced by EPU. The adverse impact of the green bond market on the carbon market, however, contributes to expediting China’s attainment of its low-carbon objectives. Appropriate economic policies can play a vital role in accelerating the transition to a low-carbon economy. The study also reveals that the US-China trade war has expedited the development of green capital markets in China, despite its impact on the green economic transition in the country. These findings provide insights for the government and investors to formulate suitable strategies for risk mitigation.

Bayesian Markov switching model for BRICS currencies' exchange rates

AbstractExchange rate modeling has always fascinated researchers because of its complex macroeconomic dynamics. This study documents the exchange rate dynamics of major emerging economies after accounting for their macroeconomic cycles and explores the Bayesian Vector Error Correction Model (VECM) Markov Regime switching model, which uses time‐varying transition probabilities. The main objective is to study the exchange rate dynamics of Brazil, Russia, India, China, and South Africa (BRICS) vis‐à‐vis the US dollar. The Bayesian setup uses two hierarchal shrinkage priors, the normal‐gamma (NG) prior and the Litterman prior, for parameters' estimation. These shrinkage priors allow for a more comprehensive assessment of the regime‐specific coefficients. The model performed well in differentiating between the two regimes for all currencies. The Russian ruble was identified to be the most depreciated currency, whereas the African Rand was the most appreciated. The evaluation of model features revealed that many regime‐specific coefficients differed significantly from their common mean. A forecasting exercise was then performed for the out‐of‐sample period to assess the model's performance. A significant improvement was observed over the basic random walk (RW) model and the linear Bayesian vector autoregression (BVAR) model.

Analysing the Nexus between the Financial Sector and Economic Growth in Nigeria: A Comparative Investigation using, BVAR, Linear Regression (OLS), and PPML Models

Aims: This study aims to analyze the complex relationship between the financial sector and economic growth in Nigeria. The study aims to provide comprehensive insights into this nexus by employing a comparative investigation using three distinct models: Linear Regression, Poisson Pseudo Maximum Likelihood (PPML), and Bayesian Vector Autoregression (BVAR).
 Methodology: The study then applied three different models, with a specific focus on the BVAR(2) model, supported by various diagnostic tests and stability assessments. The inclusion of Linear regression analysis and Poisson Pseudo Maximum Likelihood Estimator (PPML) enhances the depth of the study, providing nuanced insights into the impact of specific financial sector variables on economic growth.
 Results: The BVAR (2) model emerges as the optimal choice, demonstrating its reliability in capturing dynamic interactions and offering a powerful tool for policymakers. Specific results, such as the significant negative impact of D(CPS) in the regression analysis and the high R-squared in PPML, provide actionable insights into areas requiring policy interventions and underscore the substantial contribution of the financial sector to economic growth.
 Conclusion: The comparative assessment of model performances, favoring the BVAR model, guides future research and policy considerations, providing a reliable framework for further investigations. The study's insights are positioned as valuable for policymakers seeking to enhance economic growth through strategic interventions in the financial sector. Overall, the abstract succinctly encapsulates the aims, methodology, results, and concluding implications of the study on the nexus between the financial sector and economic growth in Nigeria.

Economic Growth and Inflation Tradeoffs within Global Stagflation: Evidence from the Vietnam Economy

The paper analyzes the interaction of economic growth and inflation rate on accounting for both sources of capital investment and global shocks. The analysis method is a time-varying coefficient Bayesian vector autoregression (TVC-BSVAR) model applied in a quarterly data sample of the Vietnam economy over Q2/2001–Q4/2022. The global factors, including the world economic growth and the inflation rate, are the most important drivers of domestic growth and inflation rate. A greater world growth rate raises the domestic growth rate while a higher world inflation rate increases the domestic inflation rate. If the world economy falls into stagflation with declining growth and a rising inflation rate, Vietnam’s economic growth reduces while the inflation surges. The monetary and fiscal policy can be employed to recover domestic economic growth but with an associated surge in the domestic inflation rate.

Food insecurity and water management shocks in Saudi Arabia: Bayesian VAR analysis.

The existing conditions of domestic agricultural production and the resulting products will not be able to fruitfully address the increasing food demand due to the limited fertile land and water resources in Saudi Arabia. Moreover, the escalating threat of a hotter climate, the deterioration in precipitation, and harsh droughts in Saudi Arabia have reduced the predictability of water management efficiency and resulted in the exhaustion of water bodies and serious degradation of ecosystems that have directly affected agricultural systems and indirectly, food security. This study also aims to assess the impact of water efficiency on food insecurity in Saudi Arabia. The study applied the Bayesian Vector Autoregressive (BVAR) model for the reference period for the data extended from 2000-2020. Likewise, we used both impulse response functions (IRFs) and forecasting variance error decomposition (FVED) through 1000 Monte Carlo simulations according to the BVAR model to examine both the response of food insecurity to the shocks on water management efficiency used for various purposes and the decomposition of error variance in food insecurity. The results show that food insecurity was not observed throughout this study. The results of the BVAR analysis indicate that in the short run, the coefficients of water use efficiency are significant based on the Food Insecurity Multidimensional Index (FIMI). Also, the BVAR model provides a better forecast with an interdependence on water use efficiency for agricultural purposes and FIMI. Moreover, the results obtained from IRFs have shown a significant effect of water efficiency on FIMI. Water use efficiency for agriculture and industrial purposes reduces food insecurity while increasing water for services use increases food insecurity. Water use efficiency is the key factor affecting food insecurity in the short run. The results reveal that the water use efficiency shocks will decrease food insecurity. The shocks experienced by food insecurity can be predicted as self-shock over a span of ten years. Emphasis is given to the task of water management that may support food security in Saudi Arabia through implementing and enhancing the water use efficiency as an integral part of achieving the SDGs in Saudi Arabia.

Retracted: Application of Bayesian Vector Autoregressive Model in Regional Economic Forecast

Retracted: Application of Bayesian Vector Autoregressive Model in Regional Economic Forecast

Density forecast combinations: The real‐time dimension

AbstractEuro area real‐time density forecasts from three dynamic stochastic general equilibrium (DSGE) and three Bayesian vector autoregression (BVAR) models are compared with six combination methods over the sample 2001Q1–2019Q4. The terms information and observation lag are introduced to distinguish time shifts between data vintages and actuals used to compute model weights and compare the forecast, respectively. Bounds for finite mixture combinations are presented, allowing for benchmarking them given the models. Empirically, combinations with limited weight variation often improve upon the individual models for the output and the joint forecasts with inflation. This reflects overconfident BVAR forecasts before the Great Recession. For inflation, a BVAR model typically performs best.

A modelling framework for equity portfolio projections under different carbon price scenarios

It is recognised that climate risks (including carbon pricing policy) are a new source of risk for the financial system. We propose a modelling framework for medium-term projections of stock returns under different carbon price scenarios. First, we construct a green factor to augment the classic capital asset pricing model (CAPM) and capture a firm’s exposure to climate policy risks. Then, we project to 2040 the factors of the CAPM, conditional on different carbon price pathways, using the estimated medium-scale Bayesian vector autoregressive model (MBVAR). Finally, we project the stock returns of each firm in the portfolio. Our scenarios suggest that the impacts of a carbon price policy are not confined to the most polluting firms (mining and quarrying, transportation and storage firms) for the effect of systematic risk. Moreover, in the short term, the negative impacts of a carbon price policy are more accentuated under a disorderly than an orderly transition. In the medium term, the projections suggest that the stock market progressively adapts to new conditions and believes in the benefits of rigorous carbon policies to incentivise the transition to a low-carbon economy. The proposed toolbox may represent effective support for investors in preparing portfolios for climate transition risks in the context of uncertainty regarding the timing of the introduction of a carbon policy. For policymakers, it can help shed light on how policies to prevent or mitigate climate change effects can affect financial stability.

ANALISIS DIAGNOSTIK VARIABEL CUACA UNTUK ESTIMASI POLA CURAH HUJAN DI MEDAN MENGGUNAKAN MODEL BAYESIAN VECTOR AUTOREGRESSIVE

The territory of Indonesia is located in a strategic position in the tropics. Indonesia is in a position where the equator passes, making it vulnerable to changes in weather and climate. Big cities are increasingly facing many global challenges, so that the effects of climate change are causing urban areas to become more vulnerable to disasters. The city of Medan is one of the big cities that has been recognized as having different characteristics from the surrounding climate, which still has quite a lot of natural elements. Various community activities in Medan City can change the composition of the atmosphere which causes changes in the characteristics of the microclimate which will affect the weather and climate. Weather and climate have a dynamic relationship with other weather elements such as air humidity, air temperature and rainfall. Weather and climate patterns often do not match the pattern they should and are difficult to predict. The main elements of weather are temperature and rainfall, knowing the temperature and rainfall of an area can be used as material to describe the weather in that area. In expressing rainfall in an area, the relationship between air humidity, air temperature and wind direction and speed is very influential. Knowing the pattern of rainfall is very important to do in several activities. So that a diagnostic analysis of weather variables is needed to estimate rainfall patterns in the city of Medan using the bayesian vector autoregressive (BVAR) model. The estimation results using the Bayesian Vector Autoregressive (BVAR) model for Medan City found that the highest rainfall occurred in September at 571.87 mm and the lowest occurred in January at 54.59 mm with a method accuracy rate of 4.75% which indicates that the use of the BVAR method in estimation is very accurate

Global Demand and Supply Sentiment: Evidence From Earnings Calls*

AbstractThis paper quantifies global demand and supply conditions and compares two major global recessions: the 2009 Great Recession and the COVID‐19 pandemic. First, we compute demand and supply sentiment by applying Natural Language Processing techniques on earnings call transcripts. Second, we corroborate our sentiment measure by identifying demand and supply shocks using a structural Bayesian vector autoregression model. The results highlight sharp contrast in the size of supply and demand conditions over time and across sectors. While the Great Recession was characterized by weak demand, COVID‐19 caused sizable disruptions to both demand and supply, with varying relative importance across major sectors. Furthermore, certain sub‐sectors, such as professional and business services, internet retail, and grocery/department stores, fared better than others during the pandemic.

Application of Bayesian Vector Autoregressive Models in the Analysis of Quasi Money and Money Supply: A Case Study of Nigeria

Aims: The aim of this study is to model the relationship between Nigerian quasi money and money supply using the Bayesian Vector Autoregressive (BVAR) model.
 Study design: The study collected and analyzed monthly data from the Central Bank of Nigeria (CBN) money and credit statistics over an 8-year period (November 2015 to December 2022). The analysis utilized both Vector Autoregressive (VAR) Model and BVAR model to examine the dynamics between these variables and their implications for monetary policy.
 Methodology: The study employed the Bayesian Vector Autoregressive (BVAR) model to analyze the relationship between Nigerian quasi money and money supply. Monthly data from the Central Bank of Nigeria (CBN) over an 8-year period was collected and subjected to both Vector Autoregressive (VAR) Model and BVAR model for analysis.
 Results: The findings indicated that there is no long-run relationship between Nigerian narrow money and quasi money, but quasi money does granger cause changes in narrow money, and vice versa. This suggests a multi-directional effect between the two variables. The BVAR model consistently outperformed the VAR model in terms of higher Adjusted-R² values, indicating its stronger ability to explain the variance in the data. The BVAR model provided a more robust and accurate representation of the relationship between these variables. The model exhibited stability and the absence of heteroscedasticity in the residuals, indicating a stable relationship between the variables. The impulse response function showed an immediate impact of changes in narrow money on the overall money supply in Nigeria.
 Conclusion: This study contributes to existing knowledge by empirically examining the relationship between Nigerian narrow money and quasi money and also concluded that there existed no co-integrating relationship between narrow money and quasi money, which has important implications for effective monetary policy strategies, particularly in Nigeria.

The macroeconomic effects of exchange rate movements in a commodity-exporting developing economy

This paper empirically examines the macroeconomic effects of exchange rate movements and their transmission mechanisms (trade and financial channels) in Mongolia, a net debtor in foreign currency and a commodity-exporting developing economy, using Structural Bayesian Vector Autoregression (SBVAR) models. Our findings suggest that both the financial and trade channels of exchange rates are operative and have a notable impact at the macroeconomic level. We identify a significant financial channel, causing GDP contractions and affecting investments, particularly in sensitive sectors such as manufacturing and construction in response to DWER depreciation shocks. The traditional trade channel, driven by NEER depreciation, leads to increased net exports with pass-through to CPI. Despite these effects on key macro variables, exchange rate shocks do not substantially destabilize the economy. Foreign shocks, including federal funds rates, China's GDP, and copper prices, have a more pronounced impact. The trade channel plays a crucial role in the transmission of external demand and commodity price shocks, while the financial channel is essential in the transmission of commodity price shocks.