This paper presents a canonical, econometric model of contagion and investigates the conditions under which contagion can be distinguished from inter-dependence. In a two-country (market) setup it is shown that for a range of fundamentals the solution is not unique, and for sufficiently large values of the contagion coefficients it has interesting bifurcation properties with bimodal density functions. The extension of the model to herding behaviour is also briefly discussed. To identify contagion effects in the presence of inter-dependencies the equations for the individual markets or countries must contain country (market) specific forcing variables. This sheds doubt on the general validity of the correlation-based tests of contagions recently proposed in the literature which do not involve any country (market) specific fundamentals. Finally, we show that ignoring inter-dependence can introduce an upward bias in the estimate of the contagion coefficient, and using Monte Carlo experiments we further show that this bias could be substantial.