Parameterised post Newtonian (PPN) parameters γ and β (which should equal unity if general relativity is valid) are estimated through the analyses of four years of LAGEOS 1 and LAGEOS 2 data. To reduce the chance of possible imprinting of general relativistic effects which could be contained in the Earth gravity model used, several low order spherical harmonic coefficients are solved in the orbit estimation and propagation process. After convergence is reached, the solved PPN parametersand γ and β are kept fixed at their solved values and scaling coefficients are introduced to explore the possibility of open parameter space in the accelerations due to the Schwarzschild field, frame dragging and de Sitter (geodesic) precession. It is found that some parameter space is available in the radial acceleration component, which could be taken up by including post-post-Newtonian components of general relativity, or it could be due to some other radial acceleration component that is not adequately modelled. The inclusion of scale coefficients in the least-squares process proves to be a valuable tool in evaluating the solutions for γ and β. A comparison with results obtained for the PPN parameters by other authors utilising different techniques such as VLBI and radar measurements to planets and probes are made.