The past carries a heavy weight to cast off for Mexico, and the heavy lifting takes political will and cooperation to cast off.
Factors from the past:
1) The PRI presided over the only hyperinflation in Mexico's history.
The tradeoff to bring inflation back down has been a factor weighing against GDP growth (Phillips curve) as the money supply has had to be restricted. During the PAN presidency, inflation has been brought down to low and stable levels around 5%, sometimes lower, but at a cost. In the long term, this is good for the investments that will help Mexico grow and reduce poverty.
2) The PRI nationalized (stole) oil companies form foreigners in the 1930's and set up PEMEX as a government run company in charge of oil production /processes (also government run electric company, gas, phone lines, etc). While Mexico did manage to cast off many of its hundreds of state owned enterprises like Britain and other countries all of the world did to stop draining all its fund on inefficient government run bureaucracies, it is still holding on to the companies that were stupidly made public companies in the wording of its constituion, including PEMEX. After 70 years, it is approaching such levels of debt and falling production that it is a drag on GDP. The same is rapidly starting to happen to Venezuela's more recently nationalized oil companies.
3) The PRI presided over a huge debt overhand in the 1980's as they relied on oil revenues for decades until oil prices plunged as they always do in their commodity cycle. They spend money like drunken sailors during high oil prices and when prices plunge they had difficulty paying back debt, plunging the nation in debt crisis in the 1980's and leaving the nation with about as much debt as it had GDP. Now it is down to about 20% of GDP, but this decrease in spending to pay down debt has been a temporary drag in growth.
Mexico is just another example of the failings of socialism. The clean-up dirty work takes a lot of political will, but can result in a long and sustained period of growth.
With its economy now increasingly open to trade over the years, Mexico can do what Hong Kong and Japan have done coming out of tough export markets to grow more rapidly like the Asian tigers did for decades, in part by opening to the world and learning and adapting technologies and foreign companies transferring technology and training.