Unrestricted Vector Autoregression Research Articles

Government Expenditures and Revenues: Evidence from Asymmetric Modeling

1. IntroductionExamining the empirical relationship between government revenues and expenditures is a crucial step in understanding the future path of the budget deficit. Four alternative explanations have been used to describe the relationship between these variables in the budgetary process: (i) the tax-and-spend hypothesis, (ii) the spend-and-tax hypothesis, (iii) the fiscal synchronization hypothesis, and (iv) the institutional separation hypothesis. The issue of which hypothesis best describes the nature of the budgetary process has yet to be resolved in the literature. However, existing research has implicitly assumed that the state of the budget and whether or not the budget deficit (or surplus) is worsening or improving does not matter. We argue that government decision-makers may take these factors into account when determining expenditures and tax policy. As such, this article reexamines the tax-spend debate by using a more robust econometric technique that allows for asymmetry in the relationship between revenues and expenditures.Until now, the empirical evidence on the tax-spend debate has focused almost exclusively on two conventional econometric techniques. Depending on the cointegrating properties between revenues and expenditures, these techniques are based on either variations of the unrestricted vector autoregression (UVAR) or the vector autoregression error correction model (ECM).1 If, for example, the two budgetary variables are not cointegrated, then the application of causality2 tests requires the use of stationary variables in the UVAR model.3 On the other hand, if the two budgetary variables are cointegrated, then the application of causality tests requires an ECM specification.It is important to note that the ECM specification implicitly assumes that the adjustment process of expenditures and revenues due to disequilibrium between the variables is strictly symmetric. Indeed, if the adjustment is asymmetric, then the symmetric adjustment implicitly assumed in the conventional techniques to ascertain causality implies model misspecification. This specification error may lead to misguided and perhaps inappropriate fiscal policy decisions. Accurate estimation of the revenue and expenditure process is especially important as changes in taxes and spending alter incentives for work, investment, and productive activity (CEA 2004). Thus, the anticipated behavioral responses of households and businesses may be better captured by more general models that allow for asymmetry in the tax-spend relationship. To this end, this article examines the existence of cointegration between revenues and expenditures and the corresponding ECM specification by using the recently developed techniques of asymmetric modeling. In particular, we employ the threshold autoregression (TAR) and momentum threshold autoregression (M-TAR) models developed by Enders and Granger (1998) and Enders and Siklos (2001). Within the context of these models, we shed new light on whether budget surpluses versus budget deficits (or an improving budget versus a worsening budget) have asymmetric effects on the dynamic behavior of expenditures and revenues.There is an a priori rationale for modeling asymmetry in the budget and for the response of its components to disequilibrium. This rationale can be categorized into four factors. First, the fiscal policymakers may respond differently to a deviation of the deficit or surplus from its long-run trend. One would expect, for example, that the response would be more aggressive if the deficit was greater than its long-run trend than if it was less than its trend.Second, it is widely acknowledged that there is a very close connection between the budget and the business cycle through automatic fiscal stabilizers and discretionary fiscal measures. To the extent that the business cycle is asymmetric, the associated change in the budget may also be asymmetric. …

An Assessment of the Usefulness of Money for Policy in the Philippines

This study assesses the usefulness of money for policy in the Philippines. The basic idea behind the use of monetary aggregates for policy is that observed fluctuations in money anticipate movements in the ultimate objective of monetary policy, such as inflation control. The paper examines the stability of key empirical relationships, including the behavior of velocity and the presence of cointegrating relationships among money and variables of interest to policymakers. In general, results indicate that the stability of velocity and the presence of cointegrating relationships lend some limited support to the potential usefulness of money for policy. The ability of money to predict inflation is examined using Granger causality tests and an unrestricted vector autoregression (VAR) that examines the relative contribution of innovations in money to the variance of the forecast errors in inflation. In general, money's ability to predict inflation is less clear-cut and seems to be dependent on the ordering and lag lengths of the variables used in the VAR and the definition of money used.

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 term structure of interest rates in Australia: an application of long run structural modelling

The term structure of interest rates in Australia, using data of different types as well as frequencies covering the period 1991(11) to 2000(9) is investigated using a relatively new modelling strategy previously untested on Australian interest rate data. Developed by Pesaran and Shin (2002), this strategy incorporates long-run structural relationships in an otherwise unrestricted vector autoregression model (VAR). The econometric tests indicate that in Australia, contrary to popular belief, long-term interest rates more often than not lead shorter-term interest rates, at least for the interest rates and time period under investigation. While these findings are not conclusive, if they are an accurate representation of interest rate behaviour, this does pose a major challenge for the monetary policy in Australia. The findings are consistent with the recent experience of the USA as well (Sarno and Thornton, 2003). The findings of the study based on recent rigorous time-series techniques tend to cast doubts ...

A Search for a Structural Phillips Curve

The foundation of the New Keynesian Phillips curve (NKPC) is a model of price setting with nominal rigidities that implies that the dynamics of inflation are well explained by the evolution of real marginal costs. In this paper, we analyze whether this is a structurally invariant relationship. We first estimate an unrestricted time-series model for inflation, unit labor costs, and other variables, and present evidence that their joint dynamics are well represented by a vector autoregression (VAR) with drifting coefficients and volatilities. We then apply a two-step minimum distance estimator to estimate deep parameters of the NKPC. Given estimates of the unrestricted VAR, we estimate parameters of the NKPC by minimizing a quadratic function of the restrictions that this theoretical model imposes on the reduced form. Our results suggest that it is possible to reconcile a constant-parameter NKPC with the drifting-parameter VAR; therefore, we argue that the price-setting model is structurally invariant.

Forecasting performance of multivariate time series models with full and reduced rank: an empirical examination

Since Quenouille's influential work on multiple time series, much progress has been made towards the goal of parameter reduction and model fit. Relatively less attention has been paid to the systematic evaluation of out-of-sample forecast performance of multivariate time series models. In this paper, we update the hog data set studied by Quenouille (and other researchers who followed him). We re-estimate his model with extended observations (1867–1966), and generate recursive one- to four-steps-ahead forecasts for the period of 1967 through 2000. These forecasts are compared to forecasts from an unrestricted vector autoregression, a reduced rank regression model, an index model and a cointegration-based error correction model. The error correction model that takes into account both nonstationarity of the data and rank reduction performs best at all four forecasting horizons. However, differences among competing models are statistically insignificant in most cases. No model consistently encompasses the others at all four horizons.

Dynamic Relationships among GCC Stock Markets and Nymex Oil Futures

Daily relationships among stock markets of the Gulf Cooperation Council (GCC) members, excluding Qatar, form two equilibrium relationships with varying predictive power. The Saudi market leads, followed by Bahrain and United Arab Emirates. Kuwait, which is dominated by momentum traders, and Oman have the weakest links with the other GCC markets. Only the Saudi index can predict—and be predicted by—New York Mercantile Exchange oil futures prices. Therefore these markets are candidates for diversified regional portfolios at the country level. The trading day effect is weak for all GCC markets and oil futures prices but remains consistent with findings for the U.S. stock market. (JEL C22, F3, Q49)

Inflation in India: An Analysis Using Post-Liberalisation Data

Using the post liberalization data on monetary aggregates and nominal effective exchange rates this paper tries to see if there still exists causality between these variables. With an unrestricted Vector Auto Regression framework we check for the granger causality existing among these variables. An attempt is also made to see which one of the three monetary aggregate, among reserve money, narrow money and broad money, explain the inflation in a better way. The granger causality tests and the analysis of unrestricted VAR models suggests strong linkage between both growth in all the three monetary aggregates and changes in nominal exchange rate on inflation in India. Even though no clear evidence is found as to which of the monetary aggregates best explains inflation, from the VAR model there is sufficient reason to believe that the broad money measure (M3) is better. It has also been observed that the explanatory power of these variables in explaining inflation is not high any more.

Testing for the Cointegrating Rank of a VAR Process with Level Shift at Unknown Time

A systems cointegration rank test is proposed that is applicable for vector autoregressive (VAR) processes with a structural shift at unknown time. The structural shift is modeled as a simple shift in the level of the process. It is proposed to estimate the break date first on the basis of a full unrestricted VAR model. Two alternative estimators are considered and their asymptotic properties are derived. In the next step the deterministic part of the process including the shift size is estimated and the series are adjusted by subtracting the estimated deterministic part. A Johansen type test for the cointegrating rank is applied to the adjusted series. The test statistic is shown to have a well-known asymptotic null distribution that does not depend on the break date. The performance of the procedure in small samples is investigated by simulations.

Tests of Rank in Reduced Rank Regression Models

There has recently been renewed research interest in the development of tests of the rank of a matrix. This article evaluates the performance of some asymptotic tests of rank determination in reduced rank regression models together with bootstrapped versions through simulation experiments. The bootstrapped procedures significantly improve on the performance of the corresponding asymptotic tests. The article also presents a Monte Carlo exercise comparing the forecasting performance of reduced rank and unrestricted vector autoregressive (VAR) models in which the former appear superior. The tests of rank considered here are then applied to construct reduced rank VAR models for leading indicators of U.K. economic activity. These more parsimonious multivariate representations display an improvement in forecasting performance over that of unrestricted VAR models.

The economic and statistical significance of spread forecasts: Evidence from the London Stock Exchange

This paper measures the economic and statistical significance of econometric forecasts of bid–ask spreads. The economic importance of these forecasts is assessed by considering the benefits of scheduling trades based on these forecasts. The unrestricted vector autoregression (VAR) model of Huang and Masulis [Rev. Financial Studies 12 (1999) 61] and the two-equation structural model of Huang and Stoll [Rev. Financial Studies 7 (1994) 179] are used to generate intraday h-step ahead forecasts of spreads for 50 stocks listed on the London Stock Exchange (LSE). The period corresponding to the minimum expected spread is then scheduled into the trading activity of the investor. The results indicate that when the unrestricted VAR model is used, the spreads incurred are around 35% lower than the spreads incurred by investors who do not schedule their trades. By contrast, spread discounts of only 5% are obtained when the two-equation structural model is used. The heterogeneity of the economic importance of the spread forecasts generated by the models is confirmed by tests of the statistical significance of the forecasts.

Further evidence on the credit view: the case of Finland

The present paper provides further empirical evidence on the credit view (i.e., bank credit availability has a positive impact on macroeconomic activity) by investigating the case of Finland. The Finnish economy suffered a severe recession in the early 1990s that was marked by widespread banking crisis and extensive government intervention. Using monthly data for the 1980–1996 period, unrestricted and restricted vector autoregression (VAR) models with GDP, money supply, consumer prices, bank credit, and exports were estimated. It is found that, while money supply had the largest effect on economic output, bank credit exhibited a fairly strong effect on output that exceeded price effects for the most part. Exports had little impact on fluctuations in GDP but did help to explain industrial output changes over time. Based on these results, it is concluded that there is empirical support for the credit view in Finland. By implication, government intervention in Finland to restore safety and soundness during the banking crisis likely limited further damage to the macroeconomy associated with disruption of credit intermediation services.

Potential inventory cost reductions using advanced time series forecasting techniques

This paper compares demand forecasts computed using the time series forecasting techniques of vector autoregression (VAR) and Bayesian VAR (BVAR) with forecasts computed using exponential smoothing and seasonal decomposition. These forecasts for three demand data series were used to determine three inventory management policies for each time series. The inventory costs associated with each of these policies were used as a further basis for comparison of the forecasting techniques. The results show that the BVAR technique, which uses mixed estimation, is particularly useful in reducing inventory costs in cases where the limited historical data offer little useful information for forecasting. The BVAR technique was effective in improving forecast accuracy and reducing inventory costs in two of the three cases tested. In the third case, unrestricted VAR and exponential smoothing produced the lowest experimental forecast errors and computed inventory costs. Furthermore, this research illustrates that improvements in demand forecasting can provide better cost reductions than relying on stochastic inventory models to provide cost reductions.

Public versus Private Education in Hawaii

This study presents a time-series evidence on the timing and degree of feedback relationship between participation in education and income growth in Hawaii. Using the unrestricted vector autoregression approach and two related measures of linear dependence and feedback, the results suggest that across all educational levels, i.e., K-12 and tertiary, participation in public education could be a good predictor of income growth in Hawaii. However, decomposing the feedback effect by frequency suggests that the dominance of public education over private education in explaining the variation in income growth to be concentrated mainly on the short-run to medium-run for tertiary level and long-run to permanent effect for K-12 level. Hawaii state legislature and educators should perhaps take these results as a motivation not to ignore the problems plaguing Hawaii's public schools but should work towards greater improvement and support for public education given its predicted significant overall contribution to the Hawaiian economy.

Constructing and estimating a realistic optimizing model of monetary policy

A dynamic stochastic general-equilibrium (DSGE) model with real and nominal, both price and wage, rigidities succeeds in capturing some key nominal features of U.S. business cycles. Additive technology shocks, as well as multiplicative shocks, are introduced and shown to be crucial. Monetary policy is specified as an interest rate targeting rule following developments in the structural vector autoregression (VAR) literature. The interaction between real and nominal rigidities is essential to reproduce the liquidity effect of monetary policy. The model is estimated by maximum likelihood on U.S. data, and its fit is comparable to that of an unrestricted first-order VAR. Besides producing reasonable impulse responses and second moments, this model replicates a feature of U.S. business cycles, never captured by previous research with DSGE models, that an increase in interest rates predicts a decrease in output two to six quarters in the future.

Residual-Based Tests for Normality in Autoregressions: Asymptotic Theory and Simulation Evidence

Existing results for the asymptotic validity of the Jarque–Bera test in vector autoregressive (VAR) models assume stationarity. In applied work, however, researchers often work with possibly integrated and cointegrated process. We prove the asymptotic validity of the Jarque–Bera test for vector error-correction (VEC) models and for unrestricted VAR models with possibly integrated or cointegrated variables. We also propose the use of bootstrap critical values in stationary VAR models and in VEC models. We show that the bootstrap version of the Jarque–Bera test is considerably more accurate in small samples than the asymptotic test, even for processes with roots close to unity.

Common Trends and Cycles in European Industrial Production: Exchange Rate Regimes and Economic Convergence

We analyse monthly data on six European industrial production series to ascertain the presence of common cycles and trends. Particular attention is paid to the exchange rate regime, with the Bretton Woods and Exchange Rate Mechanism (ERM) regimes being analysed separately. We employ recently developed techniques in vector autoregressive (VAR) modelling (a) to test for and estimate both common trends and common cycles, (b) to estimate VAR models subject to these ‘common feature’ restrictions, (c) to compare and contrast these models with those obtained from an alternative approach, that of estimating unrestricted levels VAR models, and (d) to present a permanent–transitory decomposition of the series that is based on the common trends found in the systems. We find limited evidence of convergence during the ERM, and this is of a long‐run nature. In the short run, asymmetric shocks seem to have produced a divergence compared with the earlier Bretton Woods regime. There is also some evidence of German ‘leadership’ over Belgium, France and the Netherlands.

Population forecasting with endogenous migration: an application to trans-Tasman migration.

"This article focuses on forecasting migration between Australia and New Zealand (trans-Tasman migration), which is largely visa-free and therefore resembles internal migration. Net trans-Tasman migration is a major component of New Zealand population change and is embedded in this article in a Bayesian or unrestricted vector autoregression (VAR) model, which includes foreign and domestic economic variables. When time series of net migration are available, this approach provides a useful input into forecasting population growth in the short run in the absence of major policy changes. This conclusion applies equally to interregional migration and to unrestricted international migration between economically integrated nations."

Population growth and development: the case of Bangladesh

This paper raises the question whether population growth is exogenous or endogenous with respect to the development process of Bangladesh during the last three decades. The results of an unrestricted vector autoregression model indicate that population growth does not Granger cause real GDP per capita. On the contrary, the results clearly indicate that real GDP per capita Granger causes population growth. Based on the results one may conclude that population growth is endogenous in the development process of Bangladesh. This is reflected both in the Granger causality tests and the decompositions of variances of detrended real GDP per capita and population growth.

Monetary Policy in a Stochastic Equilibrium Model with Real and Nominal Rigidities

A dynamic stochastic general-equilibrium (DSGE) model with real and nominal rigidities succeeds in capturing some key nominal features of U.S. business cycles. Additive technology shocks, as well as multiplicative shocks, are introduced. Monetary policy is specified following the developments in the structural vector autoregression (VAR) literature. Interaction between real and nominal rigidities is essential to reproduce the liquidity effect of monetary policy. The model is estimated by maximum likelihood on U.S. data, and its fit is comparable to that of an unrestricted first-order VAR. Besides producing reasonable impulse responses and second moments, this model replicates a feature of U.S. business cycles, never captured by previous research with DSGE models, that an increase in interest rates predicts a decrease in output two to six quarters in the future. Finally, some policy implications are discussed.