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Various inflation forecasting models are compared using a simulated out-of-sample forecasting framework. We focus on the question of whether monetary aggregates are useful for forecasting inflation, but unlike previous work we examine a wide range of forecast horizons and allow for estimated as well as theoretically specified cointegrating relationships in some of our models. Our findings indicate that there are forecasting gains from allowing monetary aggregates to enter into prediction models via cointegrating restrictions among money, prices, and output derived from a simple version of the quantity theory, but only when the cointegrating relations are specified a priori based on economic theory. When estimated cointegrating relations are used in a vector error correction (VEC) model, a vector autoregression (VAR) model in differences predicts better. These results hold, even during the 1990s, and evidence is presented suggesting that previous findings of a breakdown in the cointegrating relationship among prices, money, and output is the result of a failure of M2 as a measure of the money stock, and is not due to money demand instabilities. Two Monte Carlo experiments that lend credence to our findings are also reported on. The first shows that cointegration vector parameter estimation error is crucial when using VEC models for forecasting, and helps to explain previous findings of the failure of VEC models to forecast better than VAR models. The second shows that random walk and other atheoretical models routinely forecast better than correctly specified alternative models, due to parameter estimation error, indicating that caution needs to be exercised when interpreting the results of such comparisons, particularly when making statements concerning the usefulness of empirical models for use in policy-setting.

In this paper we examine the extent to which fluctuations in a number of macroeconomic variables impact on the volume of federal litigation cases. In particular, the impact of aggregate U.S. GDP, consumption, inflation, unemployment, and interest rates on the volume of antitrust, bankruptcy, contract, personal injury, and product liability cases between the years 1960 and 2000 is examined using Granger causal analysis and vector autoregression models (see e.g. Granger (1988)). Our empirical findings suggest that there are several linkages between macroeconomic variables and the volume of litigation cases, in broad agreement with the findings of Siegelman and Donohue (1995), who find that unemployment is an important determinant of the (number and) quality of employment cases filed. Most noteworthy, we find that there is a causal linkage from output, consumption and inflation to the total volume of federal litigation, so that predictions of future litigation volume can be improved by using information contained in current macroeconomic aggregates. Causation in the other direction (i.e. from the volume of litigation to macroeconomic activity) is not found in the data, however. Based on impulse response analysis, it is seen that shocks to income, consumption and inflation immediately lead to an increase in the volume of litigation, with shocks to inflation having the largest impact, and shocks to consumption having a rather moderate impact. In addition, the long run impact that shocks to each of these variables has on the volume of litigation is positive, regardless of whether the VAR or VEC model is used. Here, again, the impact of consumption is quite moderate, though. Additionally, similar results arise when examining the relation between various individual measures of federal litigation volume and the macroeconomy. Thus, the volume of federal litigation does not appear to be immune to the business cycle, a finding which is in broad agreement with the findings of Siegelman and Donohue.