Why use OLS when it is assumed there is heteroscedasticity?
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So I'm slowly going through the Stock and Watson book and I'm a bit confused on how to deal with the issue of homoscedacity/heteroscedacity. Specifically, it is mentioned that economic theory tells us that there's no reason for us to assume that errors will be homoscedastic, so their advice is that we assume heteroscedasticity and always use the heteroscedastic robust standard errors when performing our regression analysis. The way I'm being taught this material, in STATA for example, is that we just run the reg
command, always sure to include r
for robust standard error.
My question(s) is this: if our default position is to assume heteroscedacticity, then is it also correct that OLS is no longer the best unbiased linear estimator as one of the Gauss-Markov assumptions is violated? And if this is the case, is it also correct that GLS would be the BLUE estimator? Lastly, if both of these assumptions are correct, why would we not just run GLS regressions as our default and not OLS?
Thanks.
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So I'm slowly going through the Stock and Watson book and I'm a bit confused on how to deal with the issue of homoscedacity/heteroscedacity. Specifically, it is mentioned that economic theory tells us that there's no reason for us to assume that errors will be homoscedastic, so their advice is that we assume heteroscedasticity and always use the heteroscedastic robust standard errors when performing our regression analysis. The way I'm being taught this material, in STATA for example, is that we just run the reg
command, always sure to include r
for robust standard error.
My question(s) is this: if our default position is to assume heteroscedacticity, then is it also correct that OLS is no longer the best unbiased linear estimator as one of the Gauss-Markov assumptions is violated? And if this is the case, is it also correct that GLS would be the BLUE estimator? Lastly, if both of these assumptions are correct, why would we not just run GLS regressions as our default and not OLS?
Thanks.
least-squares heteroscedasticity generalized-least-squares blue
New contributor
3
It would be good to get some clarification about your meaning of "GLS." My understanding of GLS is that you have to provide specific information about the error variances. What do you have in mind doing in the general (and by far most common) case when there is no such information directly available?
– whuber♦
12 hours ago
Hi, I'm not sure what to clarify. I'm not very familiar with the Generalized Least Squares method, but in your comment, is that the answer? Namely, that even assuming that our errors are heteroscedastic, we do an OLS regression anyways, because to do a GLS we need information on the error terms that we don't have? Sorry, this is all quite new to me, and I'm sure I've not phrased the question well. Thanks to all for their comments.
– anguyen1210
12 hours ago
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up vote
2
down vote
favorite
up vote
2
down vote
favorite
So I'm slowly going through the Stock and Watson book and I'm a bit confused on how to deal with the issue of homoscedacity/heteroscedacity. Specifically, it is mentioned that economic theory tells us that there's no reason for us to assume that errors will be homoscedastic, so their advice is that we assume heteroscedasticity and always use the heteroscedastic robust standard errors when performing our regression analysis. The way I'm being taught this material, in STATA for example, is that we just run the reg
command, always sure to include r
for robust standard error.
My question(s) is this: if our default position is to assume heteroscedacticity, then is it also correct that OLS is no longer the best unbiased linear estimator as one of the Gauss-Markov assumptions is violated? And if this is the case, is it also correct that GLS would be the BLUE estimator? Lastly, if both of these assumptions are correct, why would we not just run GLS regressions as our default and not OLS?
Thanks.
least-squares heteroscedasticity generalized-least-squares blue
New contributor
So I'm slowly going through the Stock and Watson book and I'm a bit confused on how to deal with the issue of homoscedacity/heteroscedacity. Specifically, it is mentioned that economic theory tells us that there's no reason for us to assume that errors will be homoscedastic, so their advice is that we assume heteroscedasticity and always use the heteroscedastic robust standard errors when performing our regression analysis. The way I'm being taught this material, in STATA for example, is that we just run the reg
command, always sure to include r
for robust standard error.
My question(s) is this: if our default position is to assume heteroscedacticity, then is it also correct that OLS is no longer the best unbiased linear estimator as one of the Gauss-Markov assumptions is violated? And if this is the case, is it also correct that GLS would be the BLUE estimator? Lastly, if both of these assumptions are correct, why would we not just run GLS regressions as our default and not OLS?
Thanks.
least-squares heteroscedasticity generalized-least-squares blue
least-squares heteroscedasticity generalized-least-squares blue
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asked 12 hours ago
anguyen1210
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It would be good to get some clarification about your meaning of "GLS." My understanding of GLS is that you have to provide specific information about the error variances. What do you have in mind doing in the general (and by far most common) case when there is no such information directly available?
– whuber♦
12 hours ago
Hi, I'm not sure what to clarify. I'm not very familiar with the Generalized Least Squares method, but in your comment, is that the answer? Namely, that even assuming that our errors are heteroscedastic, we do an OLS regression anyways, because to do a GLS we need information on the error terms that we don't have? Sorry, this is all quite new to me, and I'm sure I've not phrased the question well. Thanks to all for their comments.
– anguyen1210
12 hours ago
add a comment |
3
It would be good to get some clarification about your meaning of "GLS." My understanding of GLS is that you have to provide specific information about the error variances. What do you have in mind doing in the general (and by far most common) case when there is no such information directly available?
– whuber♦
12 hours ago
Hi, I'm not sure what to clarify. I'm not very familiar with the Generalized Least Squares method, but in your comment, is that the answer? Namely, that even assuming that our errors are heteroscedastic, we do an OLS regression anyways, because to do a GLS we need information on the error terms that we don't have? Sorry, this is all quite new to me, and I'm sure I've not phrased the question well. Thanks to all for their comments.
– anguyen1210
12 hours ago
3
3
It would be good to get some clarification about your meaning of "GLS." My understanding of GLS is that you have to provide specific information about the error variances. What do you have in mind doing in the general (and by far most common) case when there is no such information directly available?
– whuber♦
12 hours ago
It would be good to get some clarification about your meaning of "GLS." My understanding of GLS is that you have to provide specific information about the error variances. What do you have in mind doing in the general (and by far most common) case when there is no such information directly available?
– whuber♦
12 hours ago
Hi, I'm not sure what to clarify. I'm not very familiar with the Generalized Least Squares method, but in your comment, is that the answer? Namely, that even assuming that our errors are heteroscedastic, we do an OLS regression anyways, because to do a GLS we need information on the error terms that we don't have? Sorry, this is all quite new to me, and I'm sure I've not phrased the question well. Thanks to all for their comments.
– anguyen1210
12 hours ago
Hi, I'm not sure what to clarify. I'm not very familiar with the Generalized Least Squares method, but in your comment, is that the answer? Namely, that even assuming that our errors are heteroscedastic, we do an OLS regression anyways, because to do a GLS we need information on the error terms that we don't have? Sorry, this is all quite new to me, and I'm sure I've not phrased the question well. Thanks to all for their comments.
– anguyen1210
12 hours ago
add a comment |
2 Answers
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oldest
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5
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Because GLS is BLUE if you know the form of heteroskedasticity (and correlated errors). If you misspecify the form of heteroscedasticity, GLS estimates will lose their nice properties.
Under heteroscedasticity, OLS remains unbiased and consistent, but you lose efficiency.
So unless you're certain of the form of heteroscedasticity, it makes sense to stick with unbiased and consistent estimates from OLS. Then adjust inference for heteroskedasticity using robust standard errors which are valid asymptotically if you don't know the form of heteroscedasticity.
A hybrid approach is to do your best at specifying the form of heteroskedasticity but still apply robust standard errors for inference. See Resurrecting weighted least squares (PDF).
Modeling is all about tradeoffs and resources. If you are convinced there is nothing to be learned from modeling the form of heteroscedasticity, then specifying its form is a waste of time. I would argue that there is usually something to be learned in empirical applications. But tradition/convention nudges us away from studying heteroscedasticity, looking at the variances, since all they are is "error".
add a comment |
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OLS is still unbiased when the data are correlated (provided the mean model is true). The net effect of heteroscedasticity is that it offsets the errors, so that the 95% CI for the regression is, at times, too tight and at other times too wide. Even still, you can correct the standard errors by using the sandwich or heteroscedasticity consistent standard error (HC) estimator. Technically, this is not "ordinary least squares" but it results in the same effect summary measures: a slope, interecept, and 95% CIs for their values, just no global test, or F-tests, and no validity to prediction intervals.
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
5
down vote
accepted
Because GLS is BLUE if you know the form of heteroskedasticity (and correlated errors). If you misspecify the form of heteroscedasticity, GLS estimates will lose their nice properties.
Under heteroscedasticity, OLS remains unbiased and consistent, but you lose efficiency.
So unless you're certain of the form of heteroscedasticity, it makes sense to stick with unbiased and consistent estimates from OLS. Then adjust inference for heteroskedasticity using robust standard errors which are valid asymptotically if you don't know the form of heteroscedasticity.
A hybrid approach is to do your best at specifying the form of heteroskedasticity but still apply robust standard errors for inference. See Resurrecting weighted least squares (PDF).
Modeling is all about tradeoffs and resources. If you are convinced there is nothing to be learned from modeling the form of heteroscedasticity, then specifying its form is a waste of time. I would argue that there is usually something to be learned in empirical applications. But tradition/convention nudges us away from studying heteroscedasticity, looking at the variances, since all they are is "error".
add a comment |
up vote
5
down vote
accepted
Because GLS is BLUE if you know the form of heteroskedasticity (and correlated errors). If you misspecify the form of heteroscedasticity, GLS estimates will lose their nice properties.
Under heteroscedasticity, OLS remains unbiased and consistent, but you lose efficiency.
So unless you're certain of the form of heteroscedasticity, it makes sense to stick with unbiased and consistent estimates from OLS. Then adjust inference for heteroskedasticity using robust standard errors which are valid asymptotically if you don't know the form of heteroscedasticity.
A hybrid approach is to do your best at specifying the form of heteroskedasticity but still apply robust standard errors for inference. See Resurrecting weighted least squares (PDF).
Modeling is all about tradeoffs and resources. If you are convinced there is nothing to be learned from modeling the form of heteroscedasticity, then specifying its form is a waste of time. I would argue that there is usually something to be learned in empirical applications. But tradition/convention nudges us away from studying heteroscedasticity, looking at the variances, since all they are is "error".
add a comment |
up vote
5
down vote
accepted
up vote
5
down vote
accepted
Because GLS is BLUE if you know the form of heteroskedasticity (and correlated errors). If you misspecify the form of heteroscedasticity, GLS estimates will lose their nice properties.
Under heteroscedasticity, OLS remains unbiased and consistent, but you lose efficiency.
So unless you're certain of the form of heteroscedasticity, it makes sense to stick with unbiased and consistent estimates from OLS. Then adjust inference for heteroskedasticity using robust standard errors which are valid asymptotically if you don't know the form of heteroscedasticity.
A hybrid approach is to do your best at specifying the form of heteroskedasticity but still apply robust standard errors for inference. See Resurrecting weighted least squares (PDF).
Modeling is all about tradeoffs and resources. If you are convinced there is nothing to be learned from modeling the form of heteroscedasticity, then specifying its form is a waste of time. I would argue that there is usually something to be learned in empirical applications. But tradition/convention nudges us away from studying heteroscedasticity, looking at the variances, since all they are is "error".
Because GLS is BLUE if you know the form of heteroskedasticity (and correlated errors). If you misspecify the form of heteroscedasticity, GLS estimates will lose their nice properties.
Under heteroscedasticity, OLS remains unbiased and consistent, but you lose efficiency.
So unless you're certain of the form of heteroscedasticity, it makes sense to stick with unbiased and consistent estimates from OLS. Then adjust inference for heteroskedasticity using robust standard errors which are valid asymptotically if you don't know the form of heteroscedasticity.
A hybrid approach is to do your best at specifying the form of heteroskedasticity but still apply robust standard errors for inference. See Resurrecting weighted least squares (PDF).
Modeling is all about tradeoffs and resources. If you are convinced there is nothing to be learned from modeling the form of heteroscedasticity, then specifying its form is a waste of time. I would argue that there is usually something to be learned in empirical applications. But tradition/convention nudges us away from studying heteroscedasticity, looking at the variances, since all they are is "error".
edited 11 hours ago
answered 12 hours ago
Heteroskedastic Jim
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add a comment |
up vote
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OLS is still unbiased when the data are correlated (provided the mean model is true). The net effect of heteroscedasticity is that it offsets the errors, so that the 95% CI for the regression is, at times, too tight and at other times too wide. Even still, you can correct the standard errors by using the sandwich or heteroscedasticity consistent standard error (HC) estimator. Technically, this is not "ordinary least squares" but it results in the same effect summary measures: a slope, interecept, and 95% CIs for their values, just no global test, or F-tests, and no validity to prediction intervals.
add a comment |
up vote
0
down vote
OLS is still unbiased when the data are correlated (provided the mean model is true). The net effect of heteroscedasticity is that it offsets the errors, so that the 95% CI for the regression is, at times, too tight and at other times too wide. Even still, you can correct the standard errors by using the sandwich or heteroscedasticity consistent standard error (HC) estimator. Technically, this is not "ordinary least squares" but it results in the same effect summary measures: a slope, interecept, and 95% CIs for their values, just no global test, or F-tests, and no validity to prediction intervals.
add a comment |
up vote
0
down vote
up vote
0
down vote
OLS is still unbiased when the data are correlated (provided the mean model is true). The net effect of heteroscedasticity is that it offsets the errors, so that the 95% CI for the regression is, at times, too tight and at other times too wide. Even still, you can correct the standard errors by using the sandwich or heteroscedasticity consistent standard error (HC) estimator. Technically, this is not "ordinary least squares" but it results in the same effect summary measures: a slope, interecept, and 95% CIs for their values, just no global test, or F-tests, and no validity to prediction intervals.
OLS is still unbiased when the data are correlated (provided the mean model is true). The net effect of heteroscedasticity is that it offsets the errors, so that the 95% CI for the regression is, at times, too tight and at other times too wide. Even still, you can correct the standard errors by using the sandwich or heteroscedasticity consistent standard error (HC) estimator. Technically, this is not "ordinary least squares" but it results in the same effect summary measures: a slope, interecept, and 95% CIs for their values, just no global test, or F-tests, and no validity to prediction intervals.
answered 11 hours ago
AdamO
31.8k257135
31.8k257135
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It would be good to get some clarification about your meaning of "GLS." My understanding of GLS is that you have to provide specific information about the error variances. What do you have in mind doing in the general (and by far most common) case when there is no such information directly available?
– whuber♦
12 hours ago
Hi, I'm not sure what to clarify. I'm not very familiar with the Generalized Least Squares method, but in your comment, is that the answer? Namely, that even assuming that our errors are heteroscedastic, we do an OLS regression anyways, because to do a GLS we need information on the error terms that we don't have? Sorry, this is all quite new to me, and I'm sure I've not phrased the question well. Thanks to all for their comments.
– anguyen1210
12 hours ago