In general, the difference between the smoothed and the historical series is the measurement error. Thus, if measurement error is important, the two will deviate. What is strange is that the scale of the measurement error and the gini do not at all match. How exactly do you enter the measurement error? And which Dynare version are you using.
With interpolated data, your measurement error will always look more persistent and there are very good reasons for not interpolating, see [Data transformation for estimation). Moreover, all models are misspecified in some dimensions. This will often show up in measurement error. It being non-white noise is to be expected. It is the degree of this that matters.