This paper empirically tests the expectations hypothesis on both daily EONIA swap rates and monthly EURIBOR rates extended backwards with German LIBOR rates. In addition, we quantify the size of the risk premia in the money market at maturities of one, three, six and nine months. Using implied forward and spot rates in a cointegrated VAR model, we find that the data support the expectations hypothesis in the euro area and in Germany prior to 1999. We find that risk premia are relatively limited at the shorter maturities but more significant at maturities of six and nine months. Furthermore, the results on LIBOR/EURIBOR rates tentatively indicate a downward shift in the structure of the risk premia after the introduction of the euro.

This paper employs response surface regressions based on simulation experiments to calculate asymptotic distribution functions for the Johansen-type likelihood ratio tests for cointegration. These are carried out in the context of the models recently proposed by Pesaran, Shin, and Smith (1997) that allow for the possibility of exogenous variables integrated of order one. The paper calculates critical values that are very much more accurate than those available previously. The principal contributions of the paper are a set of data files that contain estimated asymptotic quantiles obtained from response surface estimation and a computer program for utilizing them. This program, which is freely available via the Internet, can be used to calculate both asymptotic critical values and P values. JEL Classification Number: C22 Keywords: cointegration tests, Johansen tests, vector autoregressions, exogenous variables, response surfaces, critical values, approximate

Abstract: I implement two major approaches to identifying the equilibrium exchange rate. First, the concept of purchasing power parity is tested and used to define the equilibrium real exchange rate for the Indonesian rupiah, Korean won, Malaysian ringgit, Philippine peso, Singapore dollar, Taiwanese dollar and the Thai baht. The calculated PPP rates are then used to evaluate whether these seven East Asian currencies were overvalued. The purchasing power parity calculations are performed on broad price indices, price indices of tradable goods, and price indices of export goods using the Johansen and Horvath-Watson cointegration test procedures. As of May 1997, the baht, ringgit and peso were overvalued according to this criterion. While the overvaluations are not large, they do appear to be persistent. Robustness checks for sensitivity to deflator, sample period, and numeraire currency are undertaken. Second, I calculate the implied equilibrium rates from a monetary model augmented by a proxy variable for productivity trends. The monetary models imply less substantial deviations from equilibrium. Furthermore, the results do not closely correspond to those obtained from the PPP calculations. Interestingly, both methods indicate that the Korean won was undervalued even before its recent discrete drop in value.

In a model with housing collateral, the ratio of housing wealth to human wealth shifts the conditional distribution of asset prices and consumption growth. A decrease in house prices reduces the collateral value of housing, increases household exposure to idiosyncratic risk, and increases the conditional market price of risk. Using aggregate data for the US, we find that a decrease in the ratio of housing wealth to human wealth predicts higher returns on stocks. Conditional on this ratio, the covariance of returns with aggregate risk factors explains eighty percent of the cross-sectional variation in annual size and book-to-market portfolio returns. 1

Standard tests for the cointegrating rank of a vector autoregressive (VAR) process have nonstandard limiting distributions which depend on the characteristics of intercept terms and time trends in the system. In practice these characteristics are often unknown. Therefore modified tests are proposed with limiting distributions which do not depend on the characteristics of deterministic terms under the null hypothesis. One type of tests makes use of lag augmentation, that is, a VAR process of order p + 1 is fitted when the true order is p while the tests are based on the coefficient matrices of the first p lags only. It is shown that Ø 2 limiting distributions are obtained in this way. The price for this simplicity will be reduced power, however. Therefore, we also consider LM (Lagrange multiplier) type tests. These tests are shown to have nonstandard limiting distributions which do not depend on deterministic terms and have better local power than competing LR (likelihood ratio) test...

Federal Bank of St. Louis.

Acknowledgements: We thank Andy Levin for invaluable discussions of econometric issues.

Abstract not found

This paper assesses the effect of changes in solar zenith angle (SZA) and sensor changes on reflectances in channel 1, channel 2, and normalized difference vegetation index (NDVI) from the advanced very high resolution radiometer (AVHRR) Pathfinder land data set for the period July 1981 through September 1994. First, the effect of changes in SZA on channel reflectances and NDVI is derived from equations of radiative transfer in vegetation media. Starting from first principles, it is rigorously shown that the NDVI of a vegetated surface is a function of the maximum positive eigenvalue of the radiative transfer equation within the framework of the theory used and its assumptions. A sensitivity analysis of this relation indicates that NDVI is minimally sensitive to SZA changes, and this sensitivity decreases as leaf area increases. Second, statistical methods are used to analyze the relationship between SZA and channel reflectances or NDVI. It is shown that the use of ordinary least squares can generate spurious regressions because of the nonstationary property of time series. To avoid such a confusion, we use the notion of cointegration to analyze the relation between SZA and AVHRR data. Results are consistent with the conclusion of theoretical analysis from equations of radiative transfer. NDVI is not related to SZA in a statistically significant manner except for biomes with relatively low leaf area. From the theoretical and empirical analysis, we conclude that the NDVI data generated from the AVHRR Pathfinder land data set are not contaminated by trends introduced from changes in solar zenith angle due to orbital decay and changes in satellites (NOAA-7, 9, 11). As such, the NDVI data can be used to analyze interannual variability of global vegetation activity.

Cointegration occurs when the long run multiplier of a vector autoregressive model exhibits rank reduction. Priors and posteriors of the parameters of the cointegration model are therefore proportional to priors and posteriors of the long run multiplier given that it has reduced rank. Rank reduction of the long run multiplier is modelled using a decomposition resulting from its singular value decomposition. It specifies the long run multiplier matrix as the sum of a matrix that equals the product of the adjustment parameters and the cointegrating vectors, i.e. the cointegration specification, and a matrix that models the deviation from cointegration. Priors and posteriors for the parameters of the cointegration model are obtained by restricting the latter matrix to zero in the prior and posterior of the unrestricted long run multiplier. The special decomposition of the long run multiplier results in unique posterior densities. This theory leads to a complete Bayesian framework for cointegration analysis. It includes prior specification, simulation schemes for obtaining posterior distributions and determination of the cointegration rank via Bayes factors. We illustrate the analysis with several simulated series, the UK data