Real wages-employment relationship in Finnish manufacturing: a VAR approach

Granger's concept of causality and the vector autoregressive(VAR) technique is used to investigate the real wages-employment relationship in Finnish manufacturing. The stationarity of the time series is examined and a number of co-integration tests for the adequacy of a pure VAR specification performed. The results using a bivariate VAR model based on a lag structure determined by Akaike's information criterion suggests that real wages Granger-cause employment. The slight non-constancy of the model suggests, however, that the conclusion concerning the nature of the real wages-emploment relationship should be treated with causion.     

Forecasting macro variables with a Qual VAR business cycle turning point index

One criticism of Vector Autoregression (VAR) forecasting is that macroeconomic variables tend not to behave as linear functions of their own past around business cycle turning points. A large amount of literature therefore focuses on nonlinear forecasting models, such as Markov switching models, which only indirectly capture the relation with turning points. This article investigates a direct approach to using information on turning points from the National Bureau of Economic Research (NBER) chronology to model and forecast macroeconomic data. Our Qual VAR model includes a truncated normal latent business cycle index that is negative during NBER recessions and positive during expansions. We motivate our forecasting exercise by demonstrating that if starting from a linear specification, a truncated normal variable is an omitted variable, then forecasts of the remaining variables will become nonlinear functions of their own past. We apply the Qual VAR model to recursive out-of-sample forecasting and find that the Qual VAR improves on out-of-sample forecasts from a standard VAR.     

Bootstrapping Smooth Functions of Slope Parameters and Innovation Variances in VAR(∞) Models*

It is common to conduct bootstrap inference in vector autoregressive (VAR) models based on the assumption that the underlying data‐generating process is of finite‐lag order. This assumption is implausible in practice. We establish the asymptotic validity of the residual‐based bootstrap method for smooth functions of VAR slope parameters and innovation variances under the alternative assumption that a sequence of finite‐lag order VAR models is fitted to data generated by a VAR process of possibly infinite order. This class of statistics includes measures of predictability and orthogonalized impulse responses and variance decompositions. Our approach provides an alternative to the use of the asymptotic normal approximation and can be used even in the absence of closed‐form solutions for the variance of the estimator. We illustrate the practical relevance of our findings for applied work, including the evaluation of macroeconomic models.     

ESTIMATING THE RANK OF COINTEGRATION AFTER ESTIMATING THE ORDER OF A VECTOR AUTOREGRESSION*

Small sample properties are studied for the maximum likelihood test in determining the rank of cointegration. Firstly, some statistical methods are developed to determine the lag order of the vector auto-regressive (VAR) processes with unit roots. The asymptotic x² distribution of the likelihood ratio statistic is proved. Then the asymptotic standard normal distribution of the t-ratio is established for coefficients of differenced variables in the error correction representation. The t-ratio can be used to test the significance of individual coefficients in the highest order term of VAR processes without using any information on co-integration. The small sample properties of the likelihood ratio test, the t-test, AIC, and BIC are explored by simulations which are found indispensable in finding the order of VAR processes possibly with unit roots. Furthermore, and most importantly, our simulation shows that the trace test for finding the rank of co-integration does not depend much on the lag order selection criteria. Whichever procedure is used to find the lag order of a VAR process, the trace or the maximum eigen value test may on average give a similar rank of co-integration though this can be wrong.     

再论我国制造业增加值率下降的原因* ——基于WIOD数据的分析

针对我国制造业在国际横向比较中明显偏低且下降尤为明显的现象,本文从逻辑和经验两方面分析技术、结构、分配因素和产品内分工的影响。通过逻辑分析和来自WIOD的数据比对,本文发现：（1）产品内分工的发展必然带来增加值率的下降;（2）产品内国际分工从最末端的组装环节向我国延伸,是导致我国制造业增加值率偏低且不断下降的主要原因。本文研究结果意味着,我国制造业在内部形成了较强的拉动效应,而对服务业的拉动效应较弱。     

The Effects of Monetary Policy Shocks in the USA: A Forecast‐Augmented VAR Approach

This paper formulates a forward‐looking monetary policy function for the USA in a structural vector autoregression (VAR) model, by using forecasts of key macroeconomic variables, in addition to the ex post realised variables used in a standard VAR. Since this forecast‐augmented VAR (FOAVAR) uses both forecasted and realised variables, and the standard VAR uses only realised variables, the standard VAR is nested in the FOAVAR. I find that the Fed responds to forecasted macroeconomic variables more significantly than realised variables. I also find that the monetary policy shock in the FOAVAR generates impulse responses of variables that are consistent with the predictions of economic theories, while the policy shock in the standard VAR causes a price puzzle: an increase in the price level due to a contractionary policy shock. These results suggest that a monetary policy function identified in a standard VAR, by using only realised macroeconomic variables, may incorrectly represent the Fed's policy function.     

Forecasting the semiconductor industry cycles by bootstrap prediction intervals

In recent years, there has been a recognition that point forecasts of the semiconductor industry sales may often be of limited value. There is substantial interest for a policy maker or an individual investor in knowing the degree of uncertainty that attaches to the point forecast before deciding whether to increase production of semiconductors or purchase a particular share from the semiconductor stock market. In this article, I first obtain the bootstrap prediction intervals of the global semiconductor industry cycles by a vector autoregressive (VAR) model using monthly US data consisting of four macroeconomic and seven industry-level variables with 92 observations. The 24-step-ahead out-of-sample forecasts from various VAR setups are used for comparison. The empirical result shows that the proposed 11-variable VAR model with the appropriate lag length captures the cyclical behaviour of the industry and outperforms other VAR models in terms of both point forecast and prediction interval.     

Putting the present value model into practice: a comparison of two alternative approaches

A key issue around putting the present-value model into practice is how to construct the unobserved future expectations of the fundamental variables related to an asset. One approach is to fit a vector autoregression (VAR) for the fundamental variables and deduce their future expectations from the estimated VAR. An alternative is to directly specify the future expectations as unobserved components (UC) and use the Kalman filter to extract their estimates from the realized data. This article examines whether the predictions of the present-value model are consistent across the two approaches. Constructing the VAR and UC versions of the standard present-value model, we examine how the two versions compare in identifying the main driver of the US and UK housing markets. For the UK, the two approaches consistently attribute most variations in the price–rent ratio to the expected future risk premium for housing investment. For the US, however, the two approaches deliver considerably different results: the VAR version marks the expected risk-free rate of return, whereas the UC version singles out the expected risk premium as the main driver of the ratio. We conclude that the choice between the VAR and UC approaches is not a trivial issue related to utilizing the present-value model.     

The forecasting ability of a cointegrated VAR system of the UK tourism demand for France, Spain and Portugal

This paper uses the vector autoregressive (VAR) methodology as an alternative to Deaton and Muellbauer’s Almost Ideal Demand System (AIDS), to establish the long-run relationships between I(1) variables: tourism shares, tourism prices and UK tourism budget. With appropriate testing, the deterministic components and sets of exogenous and endogenous variables of the VAR are established, and Johansen’s rank test is used to determine the number of cointegrated vectors in the system. The cointegrated VAR structural form is identified and the long-run structural parameters are estimated. Theoretical restrictions such as homogeneity and symmetry are tested and not rejected by the VAR structure. The fully restricted cointegrated VAR model reveals itself a theoretically consistent and statistically robust means to analyse the long-run demand behaviour of UK tourists, and an accurate multi-step forecaster of the destinations’ shares when compared with unrestricted reduced form and first differenced VARs, or even with the structural AIDS model.     

The effects of monetary policy using structural factor analysis

The traditional Vector Autoregression (VAR) method is widely used to trace out the effects of monetary policy innovations on the economy. However, this method suffers from the curse of dimensionality, so that in practice VARs are estimated on a limited number of variables, leading to a potential missing information problem. In this article we use the method of structural factor analysis to evaluate the effects of monetary policy on key macroeconomic variables in a data rich environment. This methodology allows us to extract information on monetary policy and its impact on the economy from a much larger data set than is possible with the traditional VAR method. We propose two structural factor models. One is the Structural Factor Augmented Vector Autoregressive (SFAVAR) model and the other is the Structural Factor Vector Autoregressive (SFVAR) model. Compared to the traditional VAR, both models incorporate information from hundreds of data series, series that can be and are monitored by the central bank in setting policy. Moreover, the factors used are structurally meaningful, a feature that adds to the understanding of the ‘black box’ of the monetary transmission mechanism. Both models generate qualitatively reasonable impulse response functions. For the SFVAR model, both the price puzzle and the liquidity puzzle are eliminated.     

Infinite-variance,alpha-stable shocks in monetary SVAR

This paper outlines a theory of what might be going wrong in the monetary SVAR (structural vector autoregression) literature and provides supporting empirical evidence. The theory is that macroeconomists may be attempting to identify structural forms that do not exist, given the true distribution of the innovations in the reduced-form VAR. This paper shows that this problem occurs whenever (1) some innovation in the VAR has an infinite-variance distribution and (2) the matrix of coefficients on the contemporaneous terms in the VAR's structural form is nonsingular. Since (2) is almost always required for SVAR analysis, it is germane to test hypothesis (1). Hence, in this paper, we fit α-stable distributions to the residuals from 3-lag and 12-lag monetary VARs, and, using a parametric-bootstrap method, we reject the null hypotheses of finite variance (or equivalently, α = 2) for all 12 error terms in the two VARs. These results are mostly robust to a sample break at the February 1984 observations. Moreover, ARCH tests suggest that the shocks from the subperiod VARs are homoskedastic in seven of 24 instances. Next, we compare the fits of the α-stable distributions with those of t distributions and a GARCH(1,1) shock model. This analysis suggests that the time-invariant α-stable distributions provide the best fits for two of six shocks in the VAR(12) specification and three of six shocks in the VAR(3). Finally, we use the GARCH model as a filter to obtain homoskedastic shocks, which also prove to have α < 2, according to ML estimates.     

A Litterman BVAR approach for production forecasting of technology industries

Forecasting the production of technology industries is important to entrepreneurs and governments, but usually suffers from market fluctuation and explosion. This paper aims to propose a Litterman Bayesian vector autoregression (LBVAR) model for production prediction based on the interaction of industrial clusters. Related industries within industrial clusters are included into the LBVAR model to provide more accurate predictions. The LBVAR model possesses the superiority of Bayesian statistics in small sample forecasting and holds the dynamic property of the vector autoregression (VAR) model. Two technology industries in Taiwan, the photonics industry and semiconductor industry are used to examine the LBVAR model using a rolling forecasting procedure. As a result, the LBVAR model was found to be capable of providing outstanding predictions for these two technology industries in comparison to the autoregression (AR) model and VAR model.     

Financial Development and Economic Growth: An Egg‐and‐Chicken Problem?

This study uses a Granger causality procedure to investigate the relationship between financial development and economic growth. The authors estimate a vector autoregression (VAR) model for nine OECD countries and China. They argue that a time-series approach is superior to a cross-sectional one and that the VAR framework avoids technical problems common in other time-series models. Evidence is presented of bidirectional causality between financial development and growth in half of the countries and reverse causality in three others. There is little support for the hypothesis that finance "leads" growth, and caution must be exercised in making general conclusions about this relationship.     

Is public capital productive in Europe?

This paper addresses the issue of whether and by how much public investment or public capital can increase GDP. In comparison with the literature on the subject, we apply many different methodologies to answer these questions. A vector autoregressive (VAR) model (for France, Italy, Germany, the UK and the USA), a panel composed of 6 European countries (Austria, Belgium, France, Germany, Italy and the Netherlands) and a regional panel (French regions) are estimated. Public investment is shown to be a significant determinant of output; this is also true for public capital but to a lesser extent than public investment with a VAR methodology. The size of the estimated coefficient is also more realistic than those obtained in the literature. This empirical result confirms that the focus of some economists on safeguarding the level of public investment is not misplaced. The debate on the introduction of a ‘golden rule of public finance’ in the European Monetary Union is legitimate in this respect.     

When did unsystematic monetary policy have an effect on inflation?

An important stylized fact to emerge from VAR estimates is that exogenous monetary policy shocks (also labelled unsystematic monetary policy) have a delayed, persistent, hump-shaped effect on inflation. I argue that this empirical pattern is fragile. In particular, it disappears when one examines periods without large shifts in the level of inflation (such as 1984–2005). An important consequence is that the hump-shaped VAR estimated response of inflation is not appropriate to fit stylized models of the response of inflation around a stable steady state inflation level.     

The effects of monetary policy in the Czech Republic: an empirical study

In this paper, we examine the effects of Czech monetary policy on the economy within the vector auto regression (VAR), structural VAR, Bayesian VAR with sign restrictions, and factor-augmented VAR, frameworks. We document a well-functioning transmission mechanism similar to the euro area countries, especially in terms of persistence of monetary policy shocks. Subject to various sensitivity tests, we find that a contractionary monetary policy shock has a negative effect on the degree of economic activity and the price level, both with a peak response after one year or so. Regarding prices at the sectoral level, tradables adjust faster than non-tradables, which is in line with microeconomic evidence on price stickiness. There is no price puzzle, as our data come from a single monetary policy regime. There is a rationale in using the real-time output gap instead of current GDP growth, as using the former results in much more precise estimates. The results indicate a rather persistent appreciation of the domestic currency after a monetary tightening, with a gradual depreciation afterwards.     

Precious metals,oil and the exchange rate: contemporaneous spillovers

We investigate the contemporaneous spillovers among precious metals, crude oil and the US$ exchange rate. We contend that conventional reduced-form vector autoregressive (VAR) models based on lead/lag relations do not fully capture the interactions among these series as these models ignore the contemporaneous effects. Using a Structural VAR model, we identify these contemporaneous spillovers, which are shown to be strong and asymmetric. We further show that not taking into consideration the contemporaneous interactions among these assets leads to inaccurate findings and inevitably to inaccurate interpretations of the causal relations among them.     

Measuring the effects of monetary policy in Pakistan: a factor-augmented vector autoregressive approach

This paper examines the effects of monetary policy on macroeconomic variables in Pakistan’s economy using a data-rich environment. We used the factor-augmented vector autoregressive (FAVAR) methodology, which contains 115 monthly variables for the period 1992:01 to 2010:12. We compared the results of VAR and FAVAR model and the results showed that FAVAR model explains the effects of monetary policy which are consistent with the theory and better than the VAR model. VAR model shows the existence of price puzzle and liquidity puzzle in Pakistan while FAVAR model did not provide any evidence of puzzles. Interest rate negatively influences prices, hence interest rate is a good instrument for controlling inflation in Pakistan but it takes a lag of 5 months. The transmission of monetary policy shock is faster in case of prices as compared to output in Pakistan. FAVAR model supports the effectiveness of interest rate channel in Pakistan.     

Forecasting with a state space time-varying parameter VAR model: Evidence from the Euro area

Standard VAR and Bayesian VAR models are proven to be reliable tools for modeling and forecasting, yet they are still linear and they do not consider time-variation in parameters. VAR modeling is subject to the Lucas critique and fails to take into account the inherent nonlinearities of the economy, while it can only be utilized in the analysis of stationary series and in many cases stationarity assumptions are too restrictive. A novel time-varying multivariate state-space estimation method for vector autoregression models is introduced. For the time-varying parameter model (TVP-VAR), the parameters are estimated using a multivariate specification of the standard Kalman filter (Harvey, 1990) combined with a suitable extension of the univariate methodology framework of Kim and Nelson (1999). The TVP-VAR model as well as standard VARs and Bayesian VARs, are used in a comparative investigation of their predicting performance for the monthly IP, CPI and Euribor rate of the EU economy. The total period covers 1999:1–2011:2 with an out-of-sample testing period of 2007:2 to 2011:2, which included the US sub-prime and the EU debt crisis sub-periods. The results varied across the investigated time series and indicated that the TVP-VAR model consistently outperforms the other models in case of the EU monthly CPI, while different specifications of the VAR and BVAR models for the IP and Euribor series provide with better forecasting performance. Interestingly, the robustness analysis showed that the TVP-VAR model provided with enhanced predictability in particular during “crisis times”.