Unrestricted VAR Research Articles

Computer-Automated Single-Equation General-to-Specific Reduction Procedures for Vector Autoregressions

Vector autoregressive models are widely used in empirical macroeconomics. Unfortunately, they are subject to the curse of dimensionality. Single-equation general-to-specific reduction procedures using PcGets are proposed to overcome the problem: Starting from the unrestricted VAR, standard testing procedures eliminate statistically-insignificant variables in every equation of the VAR, with diagnostic tests checking the validity of reductions. Weak exogeneity conditions are derived for the efficiency of such single-equation reduction procedures. In Monte Carlo experiments the proposed reduction strategy recovers the DGP from a large unrestricted VAR with size and power close to commencing from the DGP itself. The application to a US monetary system illustrates its feasibility for the analysis of large macroeconomic data sets.

The Effect of Exchange Rate on Bilateral Trade Balance: New Evidence from Malaysia and Thailand

This paper attempts to identify the major economic factors that influence the bilateral trade balances of Malaysia and Thailand with the US and Japan. To this end, an unrestricted VAR model was estimated using quarterly frequency data from 1980: I to 1996: IV. The Johansen results indicate a stable long‐run relation between trade and three macro variables: exchange rate, domestic income and foreign income. The main findings of this paper are: (i) the real effective exchange rate is an important variable in the trade balance equation and devaluation improves the trade balances of both economies in the long‐run; (ii) the other important variables that determine trade balance include domestic and foreign incomes; (iii) the results indicate no J‐curve effect and causal run from exchange rate to trade balance, (iv) the real effects of devaluation are distributed over a period of eight to nine quarters.

Long-Horizon Exchange Rate Predictability?

Several authors have recently investigated the predictability of exchange rates by fitting a sequence of long-horizon error-correction equations. We show by means of a simulation study that, in small to medium samples, inference from this regression procedure depends on the null hypothesis that is used to generate empirical critical values. The standard assumption of a stationary error-correction term between exchange rates and fundamentals biases the results in favor of predictive power. Our results show that evidence of long-horizon predictability weakens when using empirical critical values generated under the more stringent null of no cointegration. Likewise, results are weakened using critical values generated under the null that exchange rates and fundamentals are generated by an unrestricted VAR with no integration restrictions.

Forecasting industrial employment figures in Southern California: A Bayesian vector autoregressive model

In this paper, we construct a Bayesian vector autoregressive model to forecast the industrial employment figures of the Southern California economy. The model includes both national and state variables. The root mean squared error (RMSE) and the Theil's U statistics are used in selecting the Bayesian prior. The out-of-sample forecasts derived from each model and prediction of the turning points show that the Bayesian VAR model outperforms the ARIMA and the unrestricted VAR models. At longer horizons the BVAR model appears to do relatively better than alternative models. A prior that becomes increasingly looser produces more accurate forecasts than a tighter prior in the BVAR estimations.

Post-stabilization inflation dynamics in Slovenia

This paper investigates the inflation process in Slovenia through an examination of some commonly used determinants of inflation in transition economies. Granger causality tests and an analysis of unrestricted VAR models suggest a strong linkage between both growth in broader monetary aggregates and changes in the tolar-deutsche mark exchange rate on retail price inflation. While the growth in wages affects inflation, it appears that both changes in the exchange rate and growth in monetary aggregates provide the initial impulse. A discussion of the present money-exchange rate policy framework and its influence on inflation is also provided.

Dynamics of Private and Public Real Estate Markets

Using five assets (T-bills, bonds, stocks, and both public and private real estate), this study investigates how cointegration of capital markets affects the dynamics of public and private real estate markets. The results show that the price indices of the five assets are nonstationary and cointegrated. Some implications for the long-term equilibrium relationship for portfolio diversification, price discovery and prediction are discussed. In a Granger causality framework, error-correction augmented VAR models (VECM) and unrestricted VAR models are compared with respect to the conclusion regarding the interaction between public and private real estate returns. VECM is also shown to improve the prediction of private real estate returns relative to an unrestricted VAR model. These results raise questions about previous research studies regarding the dynamics between public and private real estate returns. It is shown that the long-term equilibrium relationship establishes a feedback between the two real estate markets, but the private market seems to informationally lead the public one. Possible explanations are also explored.

Some tests on the effects of inflation targeting in New Zealand, Canada, and the UK

There is no empirical evidence that inflation targeting has changed macroeconomic variables in the unrestricted VAR context. There are two possible interpretations for this result. One is that inflation targeting may truly have no significant impacts on macroeconomic variables. The alternative scenario might be that the number of parameters in our model is so large relative to the number of observations that our tests do not have enough power to reject the null hypothesis of no structural changes. Further statistical investigations are desirable as more data become available and alternative models are devised.

The Macroeconomics of Employment and Wages in Mexico

The main objective of this article is to study some aspects of the labor market in Mexico, on the basis of an econometric model. Starting with an unrestricted VAR, the author finds two cointegration vectors, one with employment and output, and one with nominal wages, minimum wages, the price index, and labor productivity. A congruent model with the growth rates of the variables, and including the cointegration vectors, is finally estimated. On the basis of this model the author carries out an analysis of the effects of macroeconomic variables upon employment and nominal wages.

Cointegration in return series and its effect on short‐term prediction

Refers to previous research on the relationship between returns for different asset classes and on cointegration; and applies Johansen’s (1988) methodology to develop a prediction model. Uses 1978‐1995 data on five US asset classes (treasury bills, long‐term bonds, large capitalization common stocks, unsecuritized real estate and securitized real estate equity) to investigate cointegration between them. Shows that the index of unsecuritized real estate is positively related to treasury bills and negatively related to long‐term bonds and securitized real estate; and that returns for it can be forecast more accurately by using VECM models rather than unrestricted VAR models. Considers the implications for portfolio allocation, compares the results with other research fundings and calls for further research.

Impulse response and forecast error variance asymptotics in nonstationary VARs

Estimated impulse responses and forecast error decompositions are shown to be inconsistent at long horizons in unrestricted VARs with some unit roots. Predictions from unrestricted VARs also do not converge to the optimal predictors over long forecast horizons. In contrast, reduced rank regressions produce impulse responses and forecast error variance estimates that are consistent and predictions that are asymptotically optimal, provided the cointegrating rank is correctly specified or consistently estimated by an order selector such as PIC. Some simulations show these findings to be relevant in finite samples in VARs with some unit roots and cointegration.

An Empirical Investigation of Money Demand: Evidence from a Cash-In-Advance Model

This paper investigates the empirical performance of a cash-in-advance model of money demand in which the income velocity of money may be nonstationary. Generalized method of moments is used to estimate parameters from first-order conditions but, unlike much of the existing empirical work on money/asset pricing models, the Euler equations are not assumed to hold exactly. Instrumental variables methods are used to estimate the model parameters, with careful attention paid to the choice of valid instruments. The estimated parameters are used to solve the model and its predictions are compared with those of an unrestricted VAR.

Post Stabilization Inflation Dynamics in Slovenia

This paper investigates the inflation process in Slovenia through an examination of some commonly used determinants of inflation in transition economies. Granger causality tests and an analysis of unrestricted VAR models suggest a strong linkage between both growth in broader monetary aggregates and changes in the tolar–deutsche mark exchange rate on retail price inflation. While the growth in wages affects inflation, it appears that both changes in the exchange rate and growth in monetary aggregates provide the initial impulse. A discussion of the present money–exchange rate policy framework and its influence on inflation is also provided.

Post Stabilization Inflation Dynamics in Slovenia

This paper investigates the inflation process in Slovenia through an examination of some commonly used determinants of inflation in transition economies. Granger causality tests and an analysis of unrestricted VAR models suggest a strong linkage between both growth in broader monetary aggregates and changes in the tolar-deutsche mark exchange rate on retail price inflation. While the growth in wages affects inflation, it appears that both changes in the exchange rate and growth in monetary aggregates provide the initial impulse. A discussion of the present money-exchange rate policy framework and its influence on inflation is also provided.

An Optimization-Based Econometric Framework for the Evaluation of Monetary Policy

This paper considers a simple quantitative model of output, interest rate and inflation determination in the United States, and uses it to evaluate alternative rules by which the Fed may set interest rates. The model is derived from optimizing behavior under rational expectations, both on the part of the purchasers of goods (who choose quantities to purchase given the expected path of real interest rates), and upon that of the sellers of goods (who set prices on the basis of the expected evolution of demand). Numerical parameter values are obtained in part by seeking to match the actual responses of the economy to a monetary shock to the responses predicted by the model. The resulting model matches the empirical responses quite well and, once due account is taken of its structural disturbances, can account for our data nearly as well as an unrestricted VAR. The monetary policy rule that most reduces inflation variability (and is best on this account) requires very variable interest rates, which in turn is possible only in the case of a high average inflation rate. But even in the case of a constrained-optimal policy, that takes into account some of the costs of average inflation and constrains the variability of interest rates so as to keep average inflation low, inflation would be stabilized considerably more and output stabilized considerably less than under our estimates of current policy. Moreover, this constrained-optimal policy also allows average inflation to be much smaller.

An Optimization-Based Econometric Framework for the Evaluation of Monetary Policy

This paper considers a simple quantitative model of output, interest rate and inflation determination in the United States, and uses it to evaluate alternative rules by which the Fed may set interest rates. The model is derived from optimizing behavior under rational expectations, both on the part of the purchasers of goods (who choose quantities to purchase given the expected path of real interest rates), and upon that of the sellers of goods (who set prices on the basis of the expected evolution of demand). Numerical parameter values are obtained in part by seeking to match the actual responses of the economy to a monetary shock to the responses predicted by the model. The resulting model matches the empirical responses quite well and, once due account is taken of its structural disturbances, can account for our data nearly as well as an unrestricted VAR. The monetary policy rule that most reduces inflation variability (and is best on this account) requires very variable interest rates, which in turn is possible only in the case of a high average inflation rate. But even in the case of a constrained-optimal policy, that takes into account some of the costs of average inflation and constrains the variability of interest rates so as to keep average inflation low, inflation would be stabilized considerably more and output stabilized considerably less than under our estimates of current policy. Moreover, this constrained-optimal policy also allows average inflation to be much smaller.

Stock Market Returns, Expected Returns, and Economic Fundamentals in an Emerging Market: The Case of Korea

This paper investigates the feedback relationship between stock market returns and economic fundamentals in an emerging market. Starting from an intertemporal consumption-based CAPM (CCAPM), we obtain a restricted VAR model for stock returns and macroeconomic variables. We then apply this model to Korea and find statistically significant departures from the restrictions implied by CCAPM. Consequently, an unrestricted VAR model is used to analyze the variations of expected and unexpected returns in the Korean stock market. It is shown that the expected market returns vary with a set of macroeconomic variables, and that the predictable component is substantial. Reflecting richer dynamics in the data, relative to the usual single equation modeling in the literature, the estimated VAR model shows considerable predictive ability for both real economic activity and real returns. Using the model for a variance decomposition of unexpected returns, we find that, although we cannot directly observe the market's revision of expected future dividend growth, we can estimate a large part of the revision with the news in the expected industry output growth from our VAR model. Finally, we also find that economic fundamentals can explain only a small portion of the variation in unexpected returns in the Korean stock market.

The interaction between the frequency of market quotations, spread and volatility in the foreign exchange market

There is an empirical relationship between volatility, average spread, and number of quotations in the foreign exchange spot market. The estimation procedure involves two steps. In the first one the optimal functional form between these variables is determined through a maximization procedure of the unrestricted VAR, involving the Box—Cox transformation. The second step uses the two-stage least squares method to estimate the transformed variables in a simultaneous equation system framework. The results indicate that the number of quotations successfully approximates activity in the spot market. Furthermore, the number of quotations and temporal dummies reduce significantly the conditional heteroskedasticity e⁄ect. We also discuss information aspects of the model as well as its implications for financial informational theories. Inter- and intra-day patterns of the three variables are also revealed.

Causality testing in models of spatial market integration: A comment on an article by Stefan Dercon

In his article Stefan Dercon makes a number of comments on an earlier article by Alexander and Wyeth [1994], the most important of which is that part of the testing procedure proposed by Alexander and Wyeth is statistically incorrect. In fact the authors were aware of this, as they show by using the correct methods explained by Stefan Dercon in all their other work published in the area, both prior and subsequent to the JDS article (see, for example, Alexander [1993], Alexander and Barrow [1994], Alexander and Rendall [1995] and Alexander and Wyeth [1995]). The real error in the article referred to by Stefan Dercon was that it failed to clarify why the authors went ahead and used unrestricted VARs for causality testing even though the procedure was not strictly correct.

A BVAR model for the connecticut economy

AbstractA Bayesian vector autoregressive (BVAR) model is developed for the Connecticut economy to forecast the unemployment rate, nonagricultural employment, real personal income, and housing permits authorized. The model includes both national and state variables. The Bayesian prior is selected on the basis of the accuracy of the out‐of‐sample forecasts. We find that a loose prior generally produces more accurate forecasts. The out‐of‐sample accuracy of the BVAR forecasts is also compared with that of forecasts from an unrestricted VAR model and of benchmark forecasts generated from univariate ARIMA models. The BVAR model generally produces the most accurate short‐ and long‐term out‐of‐sample forecasts for 1988 through 1992. It also correctly predicts the direction of change.

The performance of alternative VAR models in forecasting exchange rates

The purpose of this research is to analyze the forecasting accuracy of full vector autoregressive (FVAR), mixed vector autoregressive (MVAR), and Bayesian vector autoregressive (BVAR) models of the US dollar/yen, US dollar/Canadian dollar, and US dollar/Deutsche mark exchange rates. The VAR specifications are based on a monetary/asset model of exchange rate determination. Out-of-sample results (1983:1–1989:12) indicate that the forecasting performance of restricted VARs (MVARs and BVARs) is substantially better than that of unrestricted VARs (FVARs). Overall, the results show that a monetary/asset model in a VAR representation does have forecasting value for some exchange rates.