Like there are lists of unsolved problems in Mathematics, Physics, and Chemistry, Wikipedia also has a list of the 11 unsolved questions in economics. Sounds interesting? Take a look.
1. What caused the Industrial Revolution?
2. What is the proper size and scope of government?
3. How can heterogeneous production goods be included in a mathematically trackable intertemporal equilibrium constrution?
4. What truly caused the Great Depression?
5. Can we explain the Equity Premium Puzzle?
6. How is it possible to provide causal explanations using the purely logical constructions of mathematical economics?
7. Can we create an equivalent of Black-Scholes for futures contract pricing?
8. What is the microeconomic foundation of inflation?
9. Is the money supply endogenous?
10. How does price formation occur? Why do some markets achieve Pareto efficiency?
11. What causes the variation of income among ethnic groups?
I think some problems are quite solid (like the one on the size and scope of government, maybe more generally, organizations and institutions, also the other on EPP) therefore need careful investigation, but some of them, particularly those problems on causalities (one of them should be listed on unsolved problems in philosophy), are really too broad and too hard to tackle.
Hat tip to Mike Moffatt.