1
$\begingroup$

From a discussion, I recieve a mathematic answer, I understand until one point

This decomposition can always be made by setting $\delta_c$ to be the expectation of $\varepsilon_{c,t}$ conditional on $c$ and $\gamma_t$ to be the expectation of $\varepsilon_{c,t}$ conditional on $t$

Can I ask what does this mean when saying "$\delta_c$ to be the expectation of $\varepsilon_{c,t}$ conditional on $c$"

$\endgroup$
4
$\begingroup$

Conditional expectation just means expectation conditional on some additional variable. I assume you already understand that expected value is is the average value or mean of a random variable and that the observed data can be viewed as the values of a collection of independent identically distributed random variables. Consequently, sample mean is defined as the expectation of the data with respect to the empirical distribution for the observed data so for a random sample $E[x]=\mu_x$.

Conditional expectation just means we are conditioning the expectation on some other set of variables. For example, suppose that at a university expected grade (X) of a sample of students is 8 (I am using Dutch grading system that is on scale 1-10), then let us suppose that expected grade of females in that sample is 9 and expected grade of males in that sample is 7. If we denote gender as a dummy where $D=1$ signifies females and $D=0$ signifies males, then in this case:

unconditional expected grade is $E[X]=8$

conditional expected grade, conditional on being female is $E[X|D=1]=9$

conditional expected grade, conditional on being male is $E[X|D=0]=7$

Thus saying that "$δ_c$ to be the expectation of $ε_{c,t}$ conditional on $c$" is just saying that $\delta_c$ is the expected value $\varepsilon$ conditional on what values $c$ take. For example, if $c$ is number of children you have $\delta_c$ would be expected value $\varepsilon$ given the number of children you happen to have rather than an expectation for anyone with any number of children.

$\endgroup$
4
  • $\begingroup$ I think this part ("Thus saying that "$δ_c$ to be the expectation of $ε_{c,t}$ conditional on $c$" is just saying that $\delta_c$ is the expected value $\epsilon$ conditional on what values $c$ take") should be ("Thus saying that "$δ_c$ to be the expectation of $ε_{c,t}$ conditional on $c$" is just saying that $\delta_c$ is the expected value of $ε_{c,t}$ conditional on what values $c$ take"). I mean $ε_{c,t}$ rather than $\epsilon$ $\endgroup$
    – Louise
    Jun 5 at 21:59
  • 1
    $\begingroup$ @Knowledge-chaser yes I omitted subscripts for brevity sake but by $\epsilon$ I meant $\epsilon_{c,t}$ $\endgroup$
    – 1muflon1
    Jun 5 at 22:03
  • 1
    $\begingroup$ @Knowledge-chaser oh I noticed I was using epsilon instead of varepsilon I will edit that probably that was bit confusing $\endgroup$
    – 1muflon1
    Jun 5 at 22:07
  • $\begingroup$ Yes, it is exactly what I mean, thank you , 1muflon1 $\endgroup$
    – Louise
    Jun 6 at 6:24

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.