Identify the following statements as true false or uncertain...

Identify the following statements as True, False or uncertain, and explain your answer. 1) Weighted least squares is the same as robust standard errors from OLS. ii) The omitted variable problem causes biased parameter estimates in the least squares regression model and proxy variables will eliminate the bias. iii) An F-test can be used to test either a single restriction (one linear test of the parameters) or any linear combinations of restrictions (multiple linear tests of the parameters). iv) We know that under the Gauss-Markov conditions for the population error term from the Least Squares Estimator is BLUE (i.e. a Best Linear Unbiased Estimator). If this is true, why is it that Least Squares estimates can provide poor estimates of the population parameters?

Transcript

00:02 The first statement is false.

00:14 While both methods, weightedly squares and robust standard errors, are used to alleviate the problem of heteroscadisticity, where the error terms have different variants.

00:31 The two methods are very different.

00:34 I can make a quick comparison as follows.

00:45 Weighted list square requires the data.

00:48 To be transformed.

01:00 And so it produces a very different result to ols.

01:17 Meanwhile, for the method of robust standard error, no data transformation is needed and the estimates you get from robust standard error are the same as ols.

01:47 The only difference is the standard the standard error is become larger.

02:04 Weighted list square is actually an older methodology, and robust standard error is now popular.

02:14 One reason why weighted list square is not very popular is because it requires a strong assumption of the structure of the covariance variance matrix.

02:28 For robust standard error, we do have some assumption, but the assumption is much more relaxed.

03:03 So we can say this method is less restrictive.

03:11 That is part one.

03:13 And for the second statement, this is false.

03:23 When we have omitted variable problem, you need...

03:30 It's better to have instrumental variables.

03:43 Actually, i can put this as uncertain because proxy variable can help with omitted variable bias.

04:08 So i will give a comparison between instrumental variable and proxy variable.

04:19 Anyway, instrumental variable is a more standard way to deal with the omitted variable bias.

04:31 Okay, so you need a proxy variable when your variable of interest, let's say x, is either poorly measured or an observed.

05:14 And you will have an instrumental variable when your x is endogenous.

05:29 There are several reasons that x can be endogenous and you should look up in.

05:35 In your textbook.

05:40 So the proxy variable can help with omitted variable bias by replacing the unobserved x.

06:14 The instrumental variable will help with omitted variable bias, will help reduce this bias by ruling out the endogenous part of x.

06:46 And the last difference, a good proxy variable should be a good representation of x and should be correlated with the outcome variable.

06:58 The proxy should be able to explain the outcome variable.

07:08 Let's say the outcome variable denoted y...

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