The greatest difficulty with this question is that the term "effective" is a relative rather than an absolute one. A tax code is effective if it achieves its purpose. Without knowing what the purpose is of a tax code, it's impossible to measure its effectiveness.
For example, one could imagine a tax code designed for the (absurd) purpose of enriching people born under the astrological sign of Gemini and impoverishing people born under the sign of Pisces. If the code achieved this purpose, it would be effective. Whether we like or dislike the purpose of a tax code is irrelevant to the question of whether it achieves its intended goals.
If, for example, the goal of taxation is to promote income equality, one can look at how changes in a tax code correlate with the GINI coefficient, a measure of income inequality. The difficulty here, though, is that tax codes are not the only factors affecting income inequality.
Next, an effective tax code should be one that most people consider fair. If it is considered unfair or punitive, people will go to great lengths to evade taxes and an underground economy will flourish. Similarly, part of efficiency is that the code is sufficiently simple so that compliance can be readily enforced and monitored and so that evasion is difficult.