Academic journal article National Institute Economic Review

Forecasting the Swiss Economy Using VECX* Models: An Exercise in Forecast Combination across Models and Observation Windows

Academic journal article National Institute Economic Review

Forecasting the Swiss Economy Using VECX* Models: An Exercise in Forecast Combination across Models and Observation Windows

Article excerpt

This paper uses vector error correction models of Switzerland for forecasting output, inflation and the short-term interest rate. It considers three different ways of dealing with forecast uncertainties. First, it investigates the effect on forecasting performance of averaging over forecasts from different models. Second, it considers averaging forecasts from different estimation windows. It is found that averaging over estimation windows is at least as effective as averaging over different models and both complement each other. Third, it examines whether using weighting schemes from the machine learning literature improves the average forecast. Compared to equal weights the effect of alternative weighting schemes on forecast accuracy is small in the present application.

Key words: Bayesian model averaging; choice of observation window; long-run structural vector autoregression

JEL Classifications: C53; C32

I. Introduction

Forecasting macroeconomic variables is of importance for market participants and policymakers alike. Although great care is generally taken in designing a specific forecasting model, the true forecast uncertainty is often underestimated because various sources of forecasting errors, like parameter and model uncertainties, are not taken into account properly. (l) This paper considers the problem of forecast uncertainty in the context of a long-run structural vector error correcting model of the Swiss economy. The model includes the effective nominal exchange rate of the Swiss franc, real gross domestic product (GDP), the real money stock, measured by M2, the three-month interest rate, inflation and the ratio of domestic to foreign prices as endogenous variables, and foreign output, the foreign interest rate and the oil price as exogenous variables. We first present an overidentified long-run vector error correction model with exogenous variables (VECX* model) and use it for forecasting. The model contains five long-run relations identified as the purchasing power parity, money demand, output convergence, uncovered interest parity, and the Fisher equation.

We then allow for forecast uncertainty along three different dimensions. First, we deal with model uncertainty. When deciding on a specific model, one always has to make choices like, e.g., the number of lags to include, the number of cointegrating relations to assume, the long-run restrictions to impose, and the data-generating processes to adopt for the exogenous variables. In this paper, we confine ourselves to a class of models that differ only with respect to these characteristics instead of considering entirely different model types. To allow for model uncertainty we apply Bayesian model averaging and combine forecasts from several plausible specifications of the model.

Second, economic relations can be subject to structural breaks. Pesaran and Timmerman (2007) proposed to take this into account by estimating a model over different observation windows and then pooling the forecasts. While estimation is more efficient if all available data are used when the models are stable, the occurrence of structural breaks, which are often difficult to identify and measure accurately with statistical methods, might bias the forecasts. One pragmatic way to deal with this is to average forecasts from models estimated over different estimation windows. Since economic theory is more informative regarding the nature of the long-run relations, in this exercise we do not allow for parameter uncertainty of the long-run coefficients, but consider alternative estimates of the short-run coefficients computed over different observation windows starting in the fourth quarter of each year between 1965 and 1976.

Third, we assess the usefulness of different weighting schemes in model averaging, such as equal weights, Akaike (AIC) weights and weighting schemes advanced in the machine-learning literature (Yang, 2004; Sancetta, 2006). …

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