The literature was initially quite pessimistic about the possibility to consistently estimate risk-aversion parameters consistently (and more generally all models' parameters), as highlighted by

Carroll, Christopher Dixon, 2001, "Death to the Log-Linearized Consumption Euler Equation! (And Very Poor Health to the Second-Order Approximation)," The B.E. Journal of Macroeconomics, 1(1).

However, provided the time horizon is long enough, there is some hope to estimate the parameters consistently from micro-data, as discussed by:

Attanasio, Orazio, P. and Hamish Low, 2004, "Estimating Euler equations," Review of Economic Dynamics, 7, 405–435.

Regarding the macroeconomic literature, the issue of consistent estimation cannot be investigated at all with macro data, as aggregation over individuals is only possible under strict conditions. For a study illustrating how "the size of the bias increases with the level of aggregation", see for instance:

Cutanda, A., J.M. Labeaga, and J.A. Sanchis-Llopis, 2020, "Aggregation biases in empirical Euler consumption equations: evidence from Spanish data," Empirical Economics, 58, 957–977.

The literature was initially quite pessimistic about the possibility to consistently estimate risk-aversion parameters consistently (and more generally all models' parameters), as highlighted by

Carroll, Christopher Dixon, 2001, "Death to the Log-Linearized Consumption Euler Equation! (And Very Poor Health to the Second-Order Approximation)," The B.E. Journal of Macroeconomics, 1(1).

However, provided the time horizon is long enough, there is some hope to estimate the parameters consistently from micro-data, as discussed by:

Attanasio, Orazio, P. and Hamish Low, 2004, "Estimating Euler equations," Review of Economic Dynamics, 7, 405–435.

Regarding the macroeconomic literature, the issue of consistent estimation cannot be investigated at all with macro data, as aggregation over individuals is only possible under strict conditions. For a study illustrating how "the size of the bias increases with the level of aggregation", see for instance:

Cutanda, A., J.M. Labeaga, and J.A. Sanchis-Llopis, 2020, "Aggregation biases in empirical Euler consumption equations: evidence from Spanish data," Empirical Economics, 58, 957–977.

Well, this does not identify which is precisely the original paper showing the inconsistency between the micro and macro estimates, but rather tend to give support to the thesis according to which macro estimates are inconsistent, and micro estimates can be consistent for the true parameters, under some reasonable conditions.