Perhaps some sort of multivariate outlier test is needed, but in this context it seems reasonable to me to think of trying to predict the 2012 indicators, $y$, based on the 1996 indicators, $x$ -- i.e., putting the data in roles of dependent and independent variables. If you fit a linear regression line using software that can compute the "$t$ residuals", AKA "Studentized deleted residuals", then that is the formal way of testing for an outlier in the $y$ direction. A absolute $t$ residual greater than $t_{\alpha/2,d}$ would be ``significant,'' where $d$ is the error degrees of freedom.
Another way to do the above is to fit a regression model with $y$ as the response and predictors $x$ and $I_i$, where $I_i$ is an indicator variable for the $i$th observation ($1$ for the $i$th observation, $0$ for all others). Then in the table of coefficients, the $t$ statistic for $I_i$ is the negative of the $i$th $t$ residual. This approach also reveals the substance of what is being done: this $t$ statistic measures the significance of accounting for the $i$th observation separately, over and above what is explained by $x$.
