<p>Please don't mess with the round d symbol.
You are using it alone as a epsilon change on each variables, but <span class="math-container">$\partial C_t/\partial e_t$</span> represents a partial differentiation.
And basically, there's nothing wrong with what you've said.</p>
<p>In general, we could think the effect of productivity shock on consumption is positive, i.e. <span class="math-container">$\partial C_t/\partial e_t &gt; 0$</span> as you have mentioned.
What does this mean? <strong>When <span class="math-container">$e_t$</span> increases (or decreases) a small amount, <span class="math-container">$C_t$</span> will increase (or decrease).</strong></p>
<p>So yes. If you do an exercise of negative productivity shock, the consumption will decrease and the IRF will be negative since <span class="math-container">$\partial C_t/\partial e_t &gt; 0$</span>.</p>

CC BY-SA 4.0
2024-10-06T06:14:44.903Z
2024-10-06T06:14:44.903Z
JiYong Jung
<p>Should the IRF of consumption to negative productivity shock be negative or positive? I would think negative but I am little bit confused because IRF is a set of partial derivatives correct? Then, if <span class="math-container">$\partial e_t$</span> &lt;0 and since shock decreases consumption, <span class="math-container">$\partial C_t &lt;0$</span>, so, <span class="math-container">$\partial C_t/ \partial e_t$</span> have to be &gt; 0. What am I doing wrong? Can someone help me please? Thank you.</p>

<macroeconomics>
IRF of consumption to negative productivity shock
Hyun Jung
# IRF of consumption to negative productivity shock

(Asked by: username_0 on 2024-10-06)

Should the IRF of consumption to negative productivity shock be negative or positive? I would think negative but I am little bit confused because IRF is a set of partial derivatives correct? Then, if $\partial e\_t$ <0 and since shock decreases consumption, $\partial C\_t <0$, so, $\partial C\_t/ \partial e\_t$ have to be > 0. What am I doing wrong? Can someone help me please? Thank you.

**Tags:** macroeconomics

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## 1 answers

### Answer by username_1 on 2024-10-06. Score: 0 | Accepted answer

Please don't mess with the round d symbol.
You are using it alone as a epsilon change on each variables, but $\partial C\_t/\partial e\_t$ represents a partial differentiation.
And basically, there's nothing wrong with what you've said.

In general, we could think the effect of productivity shock on consumption is positive, i.e. $\partial C\_t/\partial e\_t > 0$ as you have mentioned.
What does this mean? **When $e\_t$ increases (or decreases) a small amount, $C\_t$ will increase (or decrease).**

So yes. If you do an exercise of negative productivity shock, the consumption will decrease and the IRF will be negative since $\partial C\_t/\partial e\_t > 0$.


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