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Re: Is a master from TSE or PSE highly recognized for a top PhD in economics in the U
They both have a good record of placing into top 10 USD PhD programs. But it'll only be the best students in each program that end up at top 10 US PhD programs - 1-3 students per year to the top 10 US PhDs. In other words, the faculty of these schools can probably send an accurate and trusted signal, but your actual signal depends on you having better academic performance than almost your entire cohort, which is impossible for us to predict and also difficult for you to predict.
If you apply to both programs and get offers, the main factors of consideration are: (i) which program you like more; (ii) which department (TSE/PSE) you like more, because there's a decent chance that you'll eventually remain in the department as a PhD student. Other considerations are lifestyle and cost. The effect of either program on your chances to top 10 US PhD programs is less important than any of those, because it only matters to a hypothetical scenario with small ex-ante probability. (furthermore, that'd be the most optimistic scenario, and rational people should focus on hedging against pessimistic scenarios, as a type of risk aversion)
I think the best tracks for students interested in doctoral studies are "Economic Theory and Econometrics" in TSE and "APE" in PSE, but this is something you should figure out yourself by checking their websites.