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Consider the following model: $$ y_{it}=\nu_{it}+\epsilon_{it}$$ $$\nu_{it}=\rho \nu_{it-1}+\zeta_{it}$$ Where $y_{it}$ is the income for $i$ at time $t$. $\epsilon_{it}$ is the idiosyncratic income shock. $\nu_{it}$ denotes the permanent component that follows an AR(1) process, like unobserved productivity. The only observed data is $\{y_{it}\}$. We assume that $\epsilon_{it}\sim N(0,\sigma_\epsilon^2)$ and $\zeta_{it}\sim N(0,\sigma_{\zeta}^2)$, and $0<|\rho|<1$ so that the process is stationary.

Can we identify $\rho, \sigma_{\epsilon}^2$ and $\sigma_{\zeta}^2$ in this case? And how do we estimate the parameters exactly?

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  • $\begingroup$ This is a partially observed Markov process, are you familiar with Kalman filtering? $\endgroup$ Commented Sep 21, 2022 at 3:16
  • $\begingroup$ @JohnMadden Thank you for your reply. No, I'm not familiar with Kalman Filtering. $\endgroup$ Commented Sep 21, 2022 at 4:19

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