The assessment of productivity change over time together with its decomposition into efficiency changes and technology changes can be carried out using the so-called Malmquist index which was first introduced by Caves et al.  based on an idea of Malmquist . Following Fare et al.  the input-based adjacent Malmquist index between time periods t and t+1 is given by MPI(xt+1,yt+1,xt,yt)=[dCRSt(xt+1,yt+1)dCRSt(xt,yt) dCRSt+1(xt+1,yt+1)dCRSt+1(xt,yt)]1/2, Where dCRSt(xt,yt) and dCRSt+1(xt,yt) represent the distance functions  of the production bundle (xt, yt) from the CRS technology frontiers in periods t and t+1 respectively whilst dCRSt(xt+1,yt+1) and dCRSt+1(xt+1,yt+1) represent the corresponding distance functions for the production bundle (xt+1, yt+1), i.e. dCRSτ(xφ,yφ)=max{θ>0:(xφ/θ,yφ) ∈ TCRSτ}, where TCRSτ={(xτ,yτ): ∑j=1nλjτxj,iτ≤xiτ , i=1,2,…m,∑j=1nλjτyj,rτ≥yrτ ,r=1,2,…,s, λjτ≥0, j=1,2,…,n}, for τ = {t, t +1} and φ = {t, t +1} and are equal to the reciprocal of the Farell measures of technical efficiency.