The weak identification problem arises naturally in macroeconomic models. Consequently, instrumental variables methods produce puzzling results more often than what is empirically plausible. We propose novel methods to address puzzles usually featured in two of the main equations in macro models, namely the New-Keynesian Phillips Curve (NKPC) and the Euler Equation (EE). For the former, difficulties to estimate a positive slope without incurring a degree of stickiness incompatible with the micro evidence are widely known. We address the matter in the first chapter, proposing a richer framework of a multi-sector economy with price-setting heterogeneity. The procedure generates positive and roughly unchanging slope coefficients across econometric settings, as well as degrees of stickiness in line with the micro data, both regarding the entire economy and the cross section of sectors. Importantly, all of these estimates move consistently with implications by theory when modifying the model assumptions. The second chapter focuses on the estimation of the elasticity of intertemporal substitution (EIS), central parameter of the EE in models of dynamic choice. There, we argue that the use of officially reported consumption data – which is usually filtered, smoothed, interpolated, etc – distorts estimates of the EIS. A generalised model to unfilter available consumption data is proposed, suitable for several types of data – macro and micro – at different frequencies. Estimations based on unfiltered consumption produce considerably more stable estimates of the EIS, regardless of the econometric approach and the type of consumption data used. Results also seem less sensitive to the presence of weak instruments, compared to officially reported data.