Stat Question on OLS assumptions

From: David Wright (David_wright_at_spra.com)
Date: 07/28/04 

Date: Wed, 28 Jul 2004 02:01:13 GMT

I am having a debate.

In the standard model:

y = a + bx + u

y and u are defined as a random variables and x is a fixed variable.

The first assumption given for OLS is often given:

1. E(u(i))=0

Where u is defined as a random variable and i is given for 1 to N
observations.

Now, does this mean that the Expected value of each error is zero? Or that
the expected value of all the errors is zero? That is, shouldnt rather be
written:

2. E(u) = 0

Since E(ui) makes no sense, if i is the realization of variable u, then the
expected value of ui is undefined, since u is already been realized?

I have consulted many texts, and they all write E(ui)=0 and not E(u)=0.

If the texts are correct, then I am led to conclude that each observation has
its own radom variable u(i), so u is really a vector of random variables and
not a scalar random variable.

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