Correct choice of analytical statistic method for time series problem

Question

I want to make a statement about corruption (y) influenced by the ratification of the UN-convention-Against-Corruption "contract" (x). Luckily, most of them signed it within 3 years.

So, I have corruption data of the observed countries (y) 10 years before and 10 years after the ratification (x0) for those countries who signed the contract and those who did NOT sign.

• Thus, there are 2 control groups.
• It's a time series analysis.
• variable x is binary (ratified/not ratified; changing x to years of observations)

My questions:

1. What method could I employ to prove that the ratification had a negative effect on degree of corruption. (that is the hypothesis)
2. With what method could I analyse the assumed turning-point after x0 (the year of ratification)? I assume with some delay corruption will decrease. And I want to prove it with this turning point.
3. How do I compare the 2 time series of the control groups (ratified, not ratified)?
4. What are the correct names of these methods?

A few thoughts of mine to tackle this.

1. I thought I could calculate the mean of the corruption index over all countries per year. This is my new y-value for each year (x).
2. Then I would draw the regression line (what the correct name in time series?) for both control groups.
3. and then?

Any solid and clear hints are highly appreciated!