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\section{Introduction}  \subsection{The negative comovement problem} One implication of simple RBC-like models with steady state growth is that a persistent increase in the growth rate of productivity can trigger a decline in output. More generally, positive changes in productivity growth can have negative impact on hours worked, output or investment. For instance \cite{Viard1993}, \cite{Carroll1994} showed that a \textit{decline} in the productivity growth rate should elicit an immediate rise in the saving rate, \cite{Campbell1994}  showed that in a real business cycle model, a persistent decline in the productivity growth rate yielded the "perverse" effect of a rise in employment and output. In both \cite{Edge2007} and \cite{Boz2011}, a representative agent reduces her labor supply in response to a positive and persistent trend growth shock, due to the wealth effect. When the persistence of the shock is higher than a threshold (around 0.2 in \cite{Boz2011} calibration) the decline in labor supply leads to a fall in output even after that capital starts to accumulate. accumulate \cite{Butler}  \cite{Edge2007} argues that this negative co-movement property is consequence of assuming full information, to the extent that it can be mitigated or eliminated, for sensible parameter values, if we introduce imperfect information about productivity shocks. The reason is simple: negative co-movement appears with permanent changes in growth but not with transitory ones. If the agent is unsure about the nature of the shock, permanent ones will never hit with the same force, because now agents believe that the shock is transitory with some probability. Hence, income effects are mitigated and negative co-movements disappear. Driving those negative co-movements are large income effect generated by permanent or very persistent changes in productivity growth, overcoming substitution effects, inducing a decline in consumption and leisure. Any modification that atone the influence or the perceived magnitude of this income effect, will work against those negative co-movements. In this paper I'd like to explore how much we gain if we assume that the agent, on top of imperfect information about the nature of the shock, it doesn't fully trust the model for productivity evolution and seeks to limit the losses induced by model misspecification.