Examining the Evolution of Agriculture Productivity in the European Union

Time-Series Tests

Conceptually, long-run convergence implies that economies are driven to ‘steady-state’ equilibrium with equalised per capita income. Encapsulated in this definition are two fundamental issues. First, there is the question of how to identify those economies which converge towards steady-state equilibrium, and second there is the question of what is the ‘steady-state’ equilibrium towards which economies are progressing in the long-run. According to Bernard and Durlauf (1995) convergence can be defined as follows:

The intuition behind equation (1) is clear. Convergence between two economies, let i and j, occurs if the long-run forecasts of GDP per worker for both economies are equal at a fixed time t. The associated econometric test is known as the bivariate Augmented Dickey Fuller (hereafter ADF) test and takes the following general form²:

Long run convergence implies two properties; firstly disparities across economies are disappearing and secondly a movement towards long run equilibrium is occurring. However, the unit root test is directed at ‘catching-up’ convergence only, i.e. the first of the two properties. In order to assess for long-run convergence also, then it must be the case that the coefficient on the time trend is equal to zero (). Thus, long run convergence between two economies occurs if and (Oxley & Greasley, 1995).