The degree of contagion is frequently measured by the size and significance of linear correlation coefficients. In this paper, we show that such linear measures are inappropriate for three reasons: contagion is likely to be nonlinear, the structural contagion model is unknown, and the contagion itself will be time-varying. Instead, we use a time-varying coefficient method to give a time-varying, unbiased measure of bilateral contagion between two countries, which shows that simple correlation measures over-estimate the average contagion from the source country and how the degree of contagion varies over the sample period. To illustrate, we use Greece as an exemplar source country and Belgium, France, Italy, Ireland, Netherlands, Portugal, and Spain as recipient countries over the period 2009 to 2022.