I don't know any specific measure which Republicans did better, but I think you are attributing some things to party or political reasons with no evidence.
What evidence would you like to see, specifically?
Keep in mind:
(1) This is not an experimental science, where we can run history a hundred times, tweaking variables, until we've isolated exactly what is causing what. Even with the most careful analysis, we're going to be stuck making guesses based on the best available evidence. Sometimes those guesses may be little better than blind guesswork -- but if they're AT ALL better than blind guesswork, that's still going to be better than going with our gut instincts, or trying to reason from a priori assumptions, which are the approaches most people take.
(2) Like it or not, we need to make high-stakes political decisions on an ongoing basis, without waiting for better evidence. Elections are happening every two years, at least, and they are potentially EXTREMELY high impact events. Taking no position and waiting for better evidence just isn't an option here. Even not voting is a position of sorts. So, the question comes down to whether we make a decision that is in line with the best available evidence, however shaky, or whether we make one contrary to such evidence.
For example, the teen birth rate, crime rate, and divorce rate all began declining about 1992 and continued.
True. Yet those things don't actually explain the Republican/Democrat difference. Let's look at the murder rate only the period after 1992 (through 2020, when the preliminary reading was 6.6). So, how do Republicans look versus Democrats in that time? Well, turns out the murder rate FELL 3.8 points, net, during the Democratic administrations and ROSE 1.1 points during the Republican administrations. That's a short period of time, so you can say the sample size is too small to be meaningful, but that ends up a little like the guy who kills his parents and then pleads for mercy because he's an orphan. We narrowed down to post-1992 in an attempt to erase the Democratic advantage that shows when we include all available data, so disqualifying the narrower test because it's narrow would be a Catch-22 situation.
Similarly, I have data for birth rates of 15 to 17 year olds from 1992-2000. Here is the per-year decline in that rate by president:
Clinton 1.375
Bush 0.75
Obama 1.50
Trump 0.75
Again, small sample size, but a big difference between Democratic and Republican eras, even after we specify post-1992.
https://datacenter.kidscount.org/da...573,869,36,868,867/2829,6,8,7,251/15589,15590
And there's another way to reality-check the idea that Democratic/liberal leadership is better on that front. If my hypothesis is right, and the reason the Democratic eras are so much better at lowering teen birth rates is related to more liberal policies, rather than random chance, then we'd expect that to show up at the state level, as well. In other words, if I'm right, we'd expect to see low teen birth rates in very liberal states and high ones in very conservatives states. Turns out that's exactly what we see -- teen birth rates are over four times as high in the most conservative states than the most liberal ones. In fact, of the bottom ten teen birth rates in the US, ALL TEN were states that went against Trump in both elections. There's only a single conservative state with first-world-level teen birth rates: Utah. Coincidence? It's certainly consistent with the hypothesis that liberal leadership helps to achieve low teen birth rates, just as the presidential-era data suggests.
https://www.cdc.gov/nchs/pressroom/sosmap/teen-births/teenbirths.htm
Can you name any policies of either party that led to the declines of these three factors?
Absolutely. Take crime as an example. A lot of crime is stimulated by dysfunctional cities, and Democrats do more to invest in cities, making them less dysfunctional. That includes efforts to lower poverty, like child tax credits and higher minimum wages. It includes efforts to keep at-risk kids off the street, from subsidized childcare to enhanced after-school activities, and even things like midnight basketball. It also includes efforts to promote mixed-income settlement patterns, which fights against slum formation. Democrats are also better about addressing pollution, and one factor in the decline of violent crime rates has been reducing lead poisoning. Then there's gun control. I know it's an emotionally difficult thing for conservatives to accept that gun control lowers crime rates, but it does. When Clinton pushed through the Brady Bill, the conservatives predicted crime would spike because it would be harder for people to arm themselves, while the liberals predicted it would fall. Turns out the liberals were right.
These arguments can be frustrating because they feel like they go in circles. Like Democrats say, let's do X, Y, and Z, because doing so will bring about good results A, B, and C. Then, when they do it, and A, B, and C actually happen the conservatives insist it's a coincidence and demand to know what policies the Democrats enacted that brought about A, B, and C. And, of course, the conservatives dismiss those, notwithstanding the real-world events. And that brings me back to my opening question: what evidence do you want to see? Since it's not an experimental science, we're never going to have 100% conclusive evidence.
The best we can do is make our choices based on the evidence we have at the moment, however shaky it might be. And the fact it's so difficult to find a stat that favors Republican-led eras (or conservative-dominated states, for that matter) should be telling us something. If you're stuck on a desert island and have two fresh water sources to drink from, and you drink from one a few times and are fine, but you drink from the other a few times and get violently ill, which one are you going to choose to drink from next? Even without lab equipment to prove there's something wrong with the water in that second source, you're forced to choose, so it's just a matter of whether you go with the best available evidence, however shaky, or stubbornly insist on continuing to try your luck, and hoping you don't actually die from dysentery.