Structural Impulse Response Functions Research Articles

Identification of vector autoregressive models with nonlinear contemporaneous structure

We propose a statistical identification procedure for recursive structural vector autoregressive (VAR) models that present a nonlinear dependence (at least) at the contemporaneous level. By applying and adapting results from the literature on causal discovery with continuous additive noise models, we show that, under certain conditions, a large class of structural VAR models is identifiable. We spell out these specific conditions and propose a scheme for the estimation of structural impulse response functions in a nonlinear setting. We assess the performance of this scheme in a simulation experiment. Finally, we apply it in a study on the effects of the macroeconomic shocks that propagate through the economy, allowing for asymmetry between responses from positive and negative impulses.

A role for confidence: volition regimes and news

The economic literature presents a variety of empirical models of the structural impulse response function (SIRF) in real consumption and real output following changes in confidence or sentiment, particularly in the US and EA. This paper replicates them on the orbit of a neokeynesian dynamic stochastic general equilibrium (NK-DSGE) model characterized in particular by macroeconomic agents and derived from start to finish. Trust is specifically modeled as an endogenous variable characterized by a coalescence of three processes governed by a degree of volition, the processes being permanent technology, transient technology, and noise technology. The first two processes affect the actual production technology with a delay of one lag, while the third does not at all. The short-run responses to changes in confidence are shown whenever the degree of willingness allows confidence to change real consumption and aggregate labor, thus being non-negligible. Whenever the degree of volition was, by contrast, negligible, exogenous shocks in noise technology would cause no fluctuation in actual consumption and actual power.

BGVAR: Bayesian Global Vector Autoregressions with Shrinkage Priors in R

This document introduces the R package BGVAR to estimate Bayesian global vector autoregressions (GVAR) with shrinkage priors and stochastic volatility. The Bayesian treatment of GVARs allows to include large information sets by mitigating issues related to overfitting. This often improves inference as well as out-of-sample forecasts. Computational efficiency is achieved by using C++ to considerably speed up time-consuming functions. To maximize usability, the package includes numerous functions for carrying out structural inference and forecasting. These include generalized and structural impulse response functions, forecast error variance, and historical decompositions as well as conditional forecasts.

Crude oil production and macroeconomic performance in Ghana

AbstractThe objective of this study was to investigate the impact of crude oil production on macroeconomic performance in Ghana. The study employed monthly data from January 2011 to December 2018. The structural vector autoregressive model was employed to analyse the impact of crude oil production on macroeconomic performance. The findings of the structural impulse response function revealed that crude oil production had no impact on the agricultural sector, services sector, exchange rate and inflation. However, crude oil production had a negative and positive impact on the manufacturing sector and fiscal balance, respectively. The findings imply that the government through Ghana National Petroleum Corporation (GNPC) and other major oil stakeholders should establish oil refineries, petroleum industries and fertiliser plants domestically to provide a forward linkage for the non‐oil sectors. Also, the government through the Ministry of Trade and Industry should develop the services sectors to meet international standards to provide a backward linkage to the oil sector and ensure the integration of the sectors into the oil industry. The government needs to intensify measures to make the manufacturing sector recover from the adverse effect of the production of crude oil.

External shocks and output composition: evidence from Nigeria

PurposeThe study investigates the impact of external shocks on output composition (consumption and investment) in Nigeria for the period 1981:Q1– 2018:Q4. Trade-weighted variables from the country's five major trading partners are constructed to capture the impact.Design/methodology/approachThe study employs a block exogeneity open economy structural vector autoregressive (SVAR) analysis in studying the stated relationship.FindingsThe study reveals that external shocks significantly affect consumption and investment in Nigeria. Results from the structural impulse response function suggest that foreign output, real effective exchange rate and foreign interest rate have significant negative effects on consumption and investment. Specifically, results from error variance decomposition show that foreign inflation and real effective exchange rate shocks are major drivers of fluctuations in consumption and investment in Nigeria. Interestingly, the study finds that oil price shock accounts for minor variations in consumption and investment in Nigeria.Research limitations/implicationsThe findings suggest that consumption and investment in Nigeria are substantially and largely driven by external shocks.Practical implicationsThere is need for the monetary authority and the Nigerian government to design appropriate policies to stabilise the naira and salvage the country's exchange rate from unexpected large swings so as to reduce the vulnerability of the economy to external shocks.Originality/valuePrevious studies on external shocks have concentrated on the impact of external shocks on aggregate variables such as output and inflation, while few studies on external shocks in Nigeria capture external shocks through single-country data. This study differs from previous similar studies in Nigeria in two ways. First, the study examines the impact of external shocks on output composition such as consumption and investment. Second, the study captures the impact of external shocks on the two components of gross domestic product (GDP) by constructing trade-weighted variables from Nigeria's five major trading partners.

BGVAR: Bayesian Global Vector Autoregressions with Shrinkage Priors in R

This document introduces the R library BGVAR to estimate Bayesian global vector autoregressions (GVAR) with shrinkage priors and stochastic volatility. The Bayesian treatment of GVARs allows us to include large information sets by mitigating issues related to overfitting. This improves inference and often leads to better out-of-sample forecasts. Computational efficiency is achieved by using C++ to considerably speed up time-consuming functions. To maximize usability, the package includes numerous functions for carrying out structural inference and forecasting. These include generalized and structural impulse response functions, forecast error variance and historical decompositions as well as conditional forecasts.

Understanding the exchange rate pass-through to consumer prices in Vietnam: the SVAR approach

PurposeThe purpose of this paper is to examine the degree of the exchange rate pass-through (ERPT) to the consumer price index (CPI) at both aggregated and disaggregated levels in Vietnam. Updated data of the nominal effective exchange rate (NEER) and bilateral exchange rate (BiER) have been utilized in this study for the comparison purposes.Design/methodology/approachAdvanced time-series approaches such as a structural vector autoregressive framework, structural impulse response functions (SIRFs), and structural forecast-error variance decomposition (SFEVD) are utilized in this paper.FindingsEmpirical findings from this paper present an incomplete degree of the ERPT to the aggregated CPI. The ERPT based on the BiER is observed to have substantially larger magnitude than the NEER-based pass-through. For the disaggregated level, the degree of the ERPT varies considerably across sub-components of the CPI, with a higher magnitude of the ERPT elasticity being found from the BiER estimations. The index of housing and construction materials has the largest ERPT based on the BiER, followed by the food and foodstuffs (1.00 and 0.56, respectively). The macroeconomic and financial environments as well as an economic integration into the global market may be the main causes of a higher ERPT in Vietnam in comparison with other ASEAN countries.Research limitations/implicationsThe significant and incomplete pass-through of the exchange rate in Vietnam can affect firms’ and households’ budget planning, savings and profits. This finding generally implies that the cost of devaluation of the domestic currency affects the society as the whole in terms of welfare. The State Bank of Vietnam should carefully consider the overall effect of welfares when formulating and implementing strategies of currency devaluation. In addition, the Vietnamese economy becomes more sensitive to external vulnerabilities via changes of the exchange rate during an increasingly economic integration into the global market. In order to maintain inflation stability, it is vitally important to reduce the impact of exchange rate movements on the domestic prices, both aggregated and disaggregated levels, by pursuing either monetary policy credibility or inflation targeting.Originality/valuePrevious studies on the ERPT literature in the Asia region or for emerging countries focus mainly on the aggregated data of the CPI. Previous studies were conducted before the global financial crisis in 2008/2009. The current paper is the first of its kind to examine the pass-through from exchange rates to consumer prices in Vietnam using both aggregated and disaggregated data.

Bayesian inference on structural impulse response functions

I propose to estimate structural impulse responses from macroeconomic time series by doing Bayesian inference on the Structural Vector Moving Average representation of the data. This approach has two advantages over Structural Vector Autoregressions. First, it imposes prior information directly on the impulse responses in a flexible and transparent manner. Second, it can handle noninvertible impulse response functions, which are often encountered in applications. Rapid simulation of the posterior distribution of the impulse responses is possible using an algorithm that exploits the Whittle likelihood. The impulse responses are partially identified, and I derive the frequentist asymptotics of the Bayesian procedure to show which features of the prior information are updated by the data. The procedure is used to estimate the effects of technological news shocks on the U.S. business cycle. Bayesian inference Hamiltonian Monte Carlo impulse response function news shock nonfundamental noninvertible partial identification structural vector autoregression structural vector moving average Whittle likelihood C11 C32

Bootstrap inference for impulse response functions in factor‐augmented vector autoregressions

SummaryIn this study, we consider residual‐based bootstrap methods to construct the confidence interval for structural impulse response functions in factor‐augmented vector autoregressions. In particular, we compare the bootstrap with factor estimation (Procedure A) with the bootstrap without factor estimation (Procedure B). Both procedures are asymptotically valid under the condition , where N and T are the cross‐sectional dimension and the time dimension, respectively. However, Procedure A is also valid even when with 0 ≤ c < ∞ because it accounts for the effect of the factor estimation errors on the impulse response function estimator. Our simulation results suggest that Procedure A achieves more accurate coverage rates than those of Procedure B, especially when N is much smaller than T. In the monetary policy analysis of Bernanke et al. (Quarterly Journal of Economics, 2005, 120(1), 387–422), the proposed methods can produce statistically different results.

Balanced Bootstrap Joint Confidence Bands for Structural Impulse Response Functions

Constructing joint confidence bands for structural impulse response functions based on a VAR model is a difficult task because of the non‐linear nature of such functions. We propose new joint confidence bands that cover the entire true structural impulse response function up to a chosen maximum horizon with a pre‐specified probability (1−α), at least asymptotically. Such bands are based on a certain bootstrap procedure from the multiple testing literature. We compare the finite‐sample properties of our method with those of existing methods via extensive Monte Carlo simulations. We also investigate the effect of endogenizing the lag order in our bootstrap procedure on the finite‐sample properties. Furthermore, an empirical application to a real dataset is provided.

Identification and Estimation of Dynamic Causal Effects in Macroeconomics Using External Instruments

An exciting development in empirical macroeconometrics is the increasing use of external sources of as-if randomness to identify the dynamic causal effects of macroeconomic shocks. This approach – the use of external instruments – is the time series counterpart of the highly successful strategy in microeconometrics of using external as-if randomness to provide instruments that identify causal effects. This lecture exposits this approach and provides conditions on instruments and control variables under which external instrument methods produce valid inference on dynamic causal effects, that is, structural impulse response functions. These conditions can help guide the search for valid instruments in applications. We consider two methods, a one-step instrumental variables regression and a two-step method that entails estimation of a vector autoregression. Under a restrictive instrument validity condition, the onestep method is valid even if the vector autoregression is not invertible, so comparing the two estimates provides a test of invertibility. Under a less restrictive condition, where multiple lagged endogenous variables are needed as control variables in the one-step method, the conditions for validity of the two methods are the same.

Output Hysteresis and Optimal Monetary Policy

We analyze the implications for monetary policy when deficient aggregate demand can cause a permanent loss in potential output, a phenomenon termed as hysteresis. In the model, incomplete stabilization of a temporary shortfall in demand reduces the return to innovation, thus reducing TFP growth and generating a permanent loss in output. The origin of output is contingent on the monetary policy rule. When the nominal interest rate is constrained at the zero lower bound, a central bank unable to commit to future policy actions suffers from hysteresis bias: it does not offset past losses in potential output. A new policy rule that targets zero output approximates the optimal policy by keeping output at the first-best level. Estimated structural impulse response functions for key variables align with predictions of the model. A quantitative model provides evidence of significant output resulting from endogenous growth over the Great Recession.

Balanced Bootstrap Joint Confidence Bands for Structural Impulse Response Functions

Constructing joint confidence bands for structural impulse response functions based on a VAR model is a difficult task because of the non-linear nature of such functions. We propose new joint confidence bands that cover the entire true structural impulse response function up to a chosen maximum horizon with a prespecified probability (1 − α), at least asymptotically. Such bands are based on a certain bootstrap procedure from the multiple testing literature. We compare the finite-sample properties of our method with those of existing methods via extensive Monte Carlo simulations. We also investigate the effect of endogenizing the lag order in our bootstrap procedure on the finite-sample properties. Furthermore, an empirical application to a real data set is provided.

Dynamic analysis of the German day-ahead electricity spot market

This paper analyzes the dynamic behavior of day-ahead spot prices in the German electricity spot market due to positive structural shocks in wind and solar power. It uses a dynamic structural vector autoregressive model to estimate the related structural impulse response functions. The estimates suggest that wind power shocks have a more prolonged negative effect on spot prices than solar power shocks. Significant autocorrelations of wind power for larger lags indicate these results. The total negative merit order effect of a solar power shock is larger when using a reasonable model specification. One reason might be that solar power shocks coincide with demand peaks. However, results regarding the relation of the effects of wind and solar should be dealt with carefully because these results do not hold for all specifications. Past static estimates show differences in the total average negative merit order effects. These estimates might be overstated if wind and solar power dynamics are transferred to the merit order effects.

Joint Confidence Sets for Structural Impulse Responses

Many users of structural VAR models are primarily interested in learning about the shape of structural impulse response functions. This requires joint inference about sets of structural impulse responses, allowing for dependencies across time as well as across response functions. Such joint inference is complicated by the fact that the joint distribution of structural impulse response becomes degenerate when the number of structural impulse responses of interest exceeds the number of model parameters, as is often the case in applied work. This degeneracy may be overcome by transforming the estimator appropriately. We show that the joint Wald test is invariant to this transformation and converges to a nonstandard distribution, which can be approximated by the bootstrap, allowing the construction of asymptotically valid joint confidence sets for any subset of structural impulse responses, regardless of whether the joint distribution of the structural impulse responses is degenerate or not. We demonstrate by simulation the coverage accuracy of these sets in finite samples under realistic conditions. We make the case for representing these joint confidence sets in the form of shotgun plots rather than joint confidence bands for impulse response functions. Several empirical examples demonstrate that this approach not only conveys the same information as confidence bands about the statistical significance of response functions, but provides economically relevant additional information about the shape of response functions that is lost when reducing the joint confidence set to two-dimensional bands

Inference on impulse response functions in structural VAR models

Skepticism toward traditional identifying assumptions based on exclusion restrictions has led to a surge in the use of structural VAR models in which structural shocks are identified by restricting the sign of the responses of selected macroeconomic aggregates to these shocks. Researchers commonly report the vector of pointwise posterior medians of the impulse responses as a measure of central tendency of the estimated response functions, along with pointwise 68% posterior error bands. It can be shown that this approach cannot be used to characterize the central tendency of the structural impulse response functions. We propose an alternative method of summarizing the evidence from sign-identified VAR models designed to enhance their practical usefulness. Our objective is to characterize the most likely admissible model(s) within the set of structural VAR models that satisfy the sign restrictions. We show how the set of most likely structural response functions can be computed from the posterior mode of the joint distribution of admissible models both in the fully identified and in the partially identified case, and we propose a highest-posterior density credible set that characterizes the joint uncertainty about this set. Our approach can also be used to resolve the long-standing problem of how to conduct joint inference on sets of structural impulse response functions in exactly identified VAR models. We illustrate the differences between our approach and the traditional approach for the analysis of the effects of monetary policy shocks and of the effects of oil demand and oil supply shocks.

STRUCTURAL INFERENCE WITH LONG-RUN RECURSIVE EMPIRICAL MODELS

This paper investigates conditions under which a long-run recursive model can be used to identify a structure. Economists frequently employ this type of empirical model. I define the class of long-run partially recursive structures. If an economic system is a member of this class, then certain long-run recursive empirical models will obtain some of the structural impulse response functions. This sufficient condition for a structure is first shown in a vector autoregression. A well-known example from the literature is used to illustrate this particular class of structures and to present some useful applications of the result. Then the result is shown in models of cointegrated time series. Necessary conditions for a long-run recursive model to identify structure are addressed in the conclusion.

Structural information in recursive VAR orderings

This paper investigates structural models that will permit a Cholesky decomposition of the covariance matrix of VAR residuals to identify some structural impulse response functions. Cholesky decompositions are found to be useful identification tools for the set of partially recursive structural models. A partially recursive structure is defined as any block recursive system where the equations in one block can be recursively ordered and where the structural shocks are uncorrelated. Using this class of models, we derive necessary and sufficient conditions for the moving average representation from a Cholesky decomposition to identify structure. The paper concludes by discussing implications of these results for empirical research.