Arbitrage Pricing Theory based factor models characterize key parameters jointly and non-linearly, which complicates identification. We propose simultaneous inference methods that preserve equilibrium relations between all model parameters including ex-post sample-dependent ones, without assuming identification. Confidence sets that invert joint tests are derived, with analytical tractable solutions. These allow one to assess whether traded and untraded factors are priced risk-drivers, and to take account of cross-sectional intercepts. A formal test for traded factor assumptions is proposed. Simulation and empirical analyses are conducted with Fama-French factors. Simulation results underscore the information content of cross-sectional intercept and traded factor restrictions. Three empirical results are noteworthy: (1) The Fama-French three factors are priced before 1970; thereafter, we find no evidence favoring any factor relative to the market. (2) Heterogeneity is not sufficient to distinguish a priced momentum from profitability or investment risk. (3) Post 1970s, factors are rejected or weakly identified, depending on intercept restrictions or test portfolios.