# Presenting the error term in a quantile regression specification

Let $Y_i$ be the response and $X_i$ be the independent variables. Whenever I've seen a quantile regression specification they'll go:

$Q_{\tau}(Y_i | X_i) = a(\tau) + b(\tau) X_i$

Or, alternatively:

$Q_{Y_i}(\tau|X_i) = a(\tau) + b(\tau) X_i$

where $X_i$ is a vector of independent variable observations for cross-section $i$ and $b(\tau)$ is a vector of coefficient estimates for some $\tau \in [0,1]$.

These are the two alternatives I see throughout the different examples in "Economic Applications of Quantile Regressions".

However, I want to specify an error term in my quantile regression equation. How would I go about doing this? Further, I'd like to ask why those worked examples in that book (all from different papers) don't specify an error term?

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