Which test is the most convincing?

#1
Brief background: I’m examining mediation rates in China (a form of dispute resolution). I have a panel dataset with N=24 provinces and T=30 years (1985-2014). For each province-year, I observe mediation rates and host of economic/demographic information.

Anecdotal reports suggest that in 2006 or soon thereafter, the Chinese government began bolstering its mediation system and encouraging its use. My goal is to test this assertion. Unfortunately, I’m unable to quantify the “effort” the government exerts in promoting mediation.

What is the most convincing way to test this assertion? My ideas are listed below. Please evaluate. For all ideas, assume that I am regressing mediation rates on variables thought to influence mediation rates.
  1. Include a time polynomial (such as year and year^2) in the regression. If year is negative and year^2 is positive, this is evidence of a parabolic trend, even after controlling for other factors. Proceed by determining whether the minimum of the parabola is around year 2006.
  2. Include year fixed effects. After these effects are estimated, graph their magnitudes against time. Progressively increasing year fixed effects after 2006 would indicate more effort.
  3. Include a linear time trend with a kink at 2006. Determine whether the post 2006 trend is significantly larger than the pre 2006 trend. Unlike the other ideas, this one assumes that we know where the change occurs.
  4. Include a lagged dependent variable in the regression, that is, a lag of the mediation rate. Perhaps the best measure of “effort” is the previous year’s mediation rate. After controlling for other factors, I can determine whether this effort proxy is positive and significant.
Do you have other ideas? Is there any reason to use a combination of these ideas? Please suggest. Thanks for your help!