The analysis of asymmetric relationships among macroeconomic variables has attracted considerable attention in the empirical econometrics literature in recent decades. However, the one-step estimation of the nonlinear autoregressive distributed lag (NARDL) model faces an important theoretical challenge arising from the relationship between the positive and negative partial sums of the explanatory variables. These problems include: (a) severe multicollinearity between the positive and negative partial sums (POS and NEG), which may lead to singularity of the matrix of explanatory variables, X'X, thereby making the matrix non-invertible and preventing the regression coefficients from being obtained; (b) in ARDL and NARDL approaches, the exogeneity of the explanatory variables must be verified. If the exogeneity assumption is not confirmed, an exogeneity test is required; and (c) more importantly, in the one-step NARDL approach, the asymptotic distribution of the Wald statistic used to test symmetry is not chi-square due to the non-normality of its asymptotic distribution. Therefore, inference based on this statistic may not be sufficiently reliable. Cho et al. [1] explicitly identify these problems and, following a series of mathematical derivations, show that they can be addressed by employing a two-step FMOLS–ECM approach. Accordingly, this study investigates the asymmetric relationship between money supply and the exchange rate by employing this framework and comparing its results with those obtained from the one-step NARDL approach. The findings confirm the existence of endogenous money supply and a significant asymmetry in the long-run relationship between money supply and the exchange rate.