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Re: LSE MSc as a PhD Track Degree
One thing to remember. Almost everyone who enters the EME will have the exact same goal as you (i.e. to use this programme as a signal of ability and get into a good PhD programme). Therefore, you must be realistic in how you measure yourself against your potential classmates. I'm not saying it is, but it could be a big fish, small pond type of situation, where you're currently at, and that your masters grades might suffer when doing the EME, since the programme is very selective and attracts only the brightest of students.
Personally, I think it is borderline dumb to give up a place at any top 15 for the EME at LSE. If you're looking at the top 15/20, all incoming students have demonstrated high levels of aptitude, so any variance in actual admission will solely depend on research experience & the strength and connections of your letter writers (none of which can be remedied via the EME route). Furthermore, there is no absolute guarantee that you'll even get into said school again next year, since the pool of applicants might change, and you might've just made the cut this round, hypothetically. In addition, the benefit of doing the EME only materialises when you apply in 2 years, not next year, since EME grades won't be available when you apply, and, to adcoms, the value of being enrolled in LSE's EME is borderline helpful at best, considering that you've already gotten a place in a top 20, which points to the fact that you're already academically very capable.
edit: I just realised you were talking about the MSc Econ, and not the markedly more rigorous MSc EME. It is a terrible idea to put off a top 20 admit for that. I know someone who graduated from LSE couple years back, and is now in a top 20. He ended up with a 60+ score average (you need 70 average for a Distinction). He mentioned that the quality of instruction is quite bad there, and that very few actually manage to get Distinction, and even then, out of that group, only 1 or 2 made it into top 10, while the rest got into top 15/20. Mind you, my acquaintance scored first in his cohort from our undergrad institution many years ago, when he was doing his undergrad.