Estimation of Continuous and Discrete Time Co-integrated Systems with Stock and Flow Variables

This paper proposes an exact discrete time error correction model for co-integrated systems in continuous time and outlines a computationally efficient algorithm that leads to the Gaussian estimates of the model’s parameters. Its performance in estimation is assessed by contrasting our estimates with those obtained after applying Johansen’s discrete time approach to cointegrated systems. The data, for analysis, consist of two simulated systems; one comprised entirely of stock variables and another one formed by flow variables. In the results, we show that for the system with stock variables Johansen’s approach and ours perform similarly. For the system with flow variables, however, Johansen’s estimates show a persistent estimation bias with negligible improvements in larger samples, while ours yields a smaller bias that lowers as the sample size increases. As our model incorporates a moving average component in the error term that permits full dynamics, we argue that Johansen’s bias reflects the cost of ignoring aggregation in the specification.