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This principal objective of this paper is the construction and evaluation of a Pesaran-type core quarterly econometric model of the Trinidad and Tobago economy using data covering the period 1970-1998. It represents the first step in the construction of a more comprehensive model of the Trinidad and Tobago economy with this core at the centre. Such a model will be used for forecasting and for policy evaluation. In the paper, the econometric methodology to be employed is presented and discussed. This is followed by a description of the hypothesized long-run relations in the core model which are derived from economic theory as well a discussion about the associated problems relating to the corresponding data to be used. The core model is estimated after testing for unit roots and cointegration vectors. The Error Correction form of the model is then derived and evaluated. Persistence profiles based on system wide shocks are derived and discussed. Forecasts derived from the model are those obtained from benchmark ARIMA models.