What's the meaning of butterfly in the Antebellum poster? “p(Trust 9 = Trust 5)” denotes the p-value of an F-test for equality of coefficients for Trust = 5 (average. Accurate standard errors are a fundamental component of statistical inference. Table A.5: Regression estimates for pro-environmental outcomes II, significant at the 1%, 5%, and 10%-level, respectively. This will mean that the standard errors will likely be too optimistic (too narrow). College Station, TX: Stata press.' takes a value of 1 if the individual reports being member of an environmental/peace/animal organization, and 2 if the individual also actively participates in. Generally speaking, this will mean that $\mathbf{E} \left[ \hat{u}_{jc} \hat{u}_{kc} \right] > 0$ - in other words, that the errors are positively correlated within the cluster. The higher the level of clustering, the more conservative the estimate of the standard error, so it's good to err on the side of caution, unless there are compelling reasons to cluster at the lower level. She therefore assigns teachers in "treated" classrooms to try this new technique, while leaving "control" classrooms unaffected. Making statements based on opinion; back them up with references or personal experience. Here there are $C$ clusters, each containing $N_c$ observations. It seems to me (and Iâm about as formally untrained in statistics as one can getâitâs a long story) that both OLS with clustered standard errors and hierarchical modeling are intended to address the same problem: the correlation of residuals within a cluster (be it a state, in some of your research, or a country, as in my research). But, to the extent that there actually is correlation across regions in a country, then you'll have $\mathbf{E} \left[ \hat{u}_{jc} \hat{u}_{kc} \right] \neq 0$ for $j \neq k$. Serially Correlated Errors To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Then there is no need to adjust the standard errors for clustering at all, even if clustering would change the standard errors. Larger and fewer clusters have less bias, but they â¦ By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Standard errors clustered at the country level in parentheses. Note that if each observation had its own cluster, then the cluster estimator would be identical to the HW estimator. Should I also cluster my standard errors ? In this case then, the cluster variance estimator would be less than the basic HW one. Use MathJax to format equations. Iâll describe the high-level distinction between the two strategies by first explaining what it is they seek to accomplish. As one of the comments to your question noted, clustering at the larger level is more conservative (and likely better). With the 19 December 2020 COVID 19 measures, can I travel between the UK and the Netherlands? We have also included ï¬xed effects for whether the ofï¬cer belong to When analyzing her results, she may want to keep the data at the student level (for example, to control for student-level obsâ¦ I found myself writing a long-winded answer to a question on StatsExchange about the difference between using fixed effects and clustered errors when running linear regressions on panel data. For example, suppose that an educational researcher wants to discover whether a new teaching technique improves student test scores. CC” is the likelihood to which the respondent feels she can reduce climate change herself by reducing own energy, use - 0 (not at all likely) to 10 (extremely likely). infographics! If the errors within a cluster are indeed independent of each other, than we should have, by definition of that independence, $\mathbf{E} \left[ \hat{u}_{jc} \hat{u}_{kc} \right] = 0$ for $j \neq k$. Robust standard errors account for heteroskedasticity in a modelâs unexplained variation. In that case, those terms will add to the variance of your estimator, but that is the appropriate thing in such a situation, since if your observations and errors are correlated, then you don't actually have as many independent observations as your simple sample size would indicate. This page shows how to run regressions with fixed effect or clustered standard errors, or Fama-Macbeth regressions in SAS. genuinely independent observations) have nothing to hide. Second, in general, the standard Liang-Zeger clustering adjustment is conservative unless one It only takes a minute to sign up. Clustered robust standard errors on country-year pairs. “I can red. Focus on the middle term (the three nested summations) in the cluster estimator. White standard errors (with no clustering) had a simulation standard deviation of 1.4%, and single-clustered standard errors had simulation standard deviations of 2.6%, whether clustering was done by firm or time. 2. xtpcse from Stata - how to rewrite in R. 3. individual random effects model with standard errors clustered on a different variable in R (R-project) 3. What would be a good way to decide on this? Trust = 5 (average trust in the ESS) and Trust = 9 (largest point estimate in a regression of life satisfaction on trust). I know that this is the criterium for the choice of the cluster level. That is, if the amount of variation in the outcome variable is correlated with the explanatory variables, robust standard errors can take this correlation into account. Thus likewise we'd have $\mathbf{E} \left[ \hat{u}_{jc} \hat{u}_{kc} x_{jc} x'_{kc} \right] = 0$ for $j \neq k$ since the $x$ observations are considered non-random. Itâs not a bad idea to use a method that youâre comfortable with. See Bertrand, Duflo, and Mullainathan for a longer discussion of this. To learn more, see our tips on writing great answers. > > Different assumptions are involved with dummies vs. clustering. the support for subsidies on renewable energy to reduce climate change - 1 (strongly against) to 5 (strongly in favor). If you think that the regressors or the errors are likely to be uncorrelated within a potential group, then there is no need to cluster within that group. Clustered standard errors belong to these type of standard errors. “Voluntary work” is 1 if any voluntary work for either type of association (incl. Heteroscedasticity robust standard errors with the PLM package. the residuals from two different regions in a country), then we'll have, at least in expectation, $\mathbf{E} \left[ \hat{u}_{jc} \hat{u}_{kc} \right] = 0$ for $j \neq k$. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. The difference is in the degrees-of-freedom adjustment. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. Does software exist to automatically validate an argument? Are inversions for making bass-lines nice and prolonging functions? This allows for the possibility of correlations between the errors in the observations within a given country, since the residuals from all the observations within a country will get multiplied by the residuals of all the other observations in that country. here are a couple of solutions: Clustered standard errors at the group level; Clustered bootstrap (re-sample groups, not individual observations) Q iv) Should I cluster by month, quarter or year ( firm or industry or country)? Using the caret symbol (^) in substitutions in the vi editor. Therefore, If you have CSEs in your data (which in turn produce inaccurate SEs), you should make adjustments for the clustering before running any further analysis on the data. The Attraction of âDifferences in Differencesâ 2. Now, compare this to the HW robust variance estimator, that does not account for clustering: $$\widehat{\text{var}} \left( \hat{\beta} \right)_{HW} = (X'X)^{-1} \left[ \sum_{i=1}^n \hat{u}_i^2 x_ix_i' \right] (X'X)^{-1}$$. 7. How would you approach this? sport, culture, union, professional, consumer, humanitarian, environmental, religious, political, science and other) is reported, and 0 otherwise. Clustered Standard Errors 1. Should one include the cluster specific dummy variables in the regression when st. errors are allowed to be clustered at that level? (using Stata). “Supports energy subs.” measures. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. Therefore, it aects the hypothesis testing. clustered standard errors work very well when the model is correct and the data satisfy ... level, it was traditionally assumed that the disturbances are uncorrelated, perhaps after ... disturbances for ariousv outcomes might be clustered by village, by province, or by country, depending on the nature of the model and dataset. Thus, if all of the observations within a cluster are indeed completely independent of each other, then this estimator will be identical (at least asymptotically) to the basic HW estimator. Why is the standard uncertainty defined with a level of confidence of only 68%? That's probably the case, just wanted to be sure. What type of salt for sourdough bread baking? work” contains the reported frequency of being involved in work for, voluntary/charitable organizations in the last 12 months, ranging from 1 (never) to 6 (at least once a week), and “Supports fuel tax” captures the support for, a tax on fuels, ranging from 1 (strongly against) to 5 (strongly in favor). “Donated” is, defined in a similar way, but focuses on having donated to such an organization. An Introduction to Robust and Clustered Standard Errors Linear Regression with Non-constant Variance Variance of ^ depends on the errors ^ = X0X 1 X0y = X0X 1 X0(X + u) = + X0X 1 X0u Molly Roberts Robust and Clustered Standard Errors March 6, 2013 6 / 35 There's no formal test that will tell you at which level to cluster. Bowling Alone: The Collapse and Revival of American Community. I am already adding country and year fixed effects. I If nested (e.g., classroom and school district), you should cluster at the highest level of aggregation I If not nested (e.g., time and space), you can: 1 Include ï¬xed-eects in one dimension and cluster in the other one. If there's a hole in Zvezda module, why didn't all the air onboard immediately escape into space? 15. How to decide on the clustering of standard errors? Papers such as Larrain (2006) and Li, Morck, Yang, and Yeung (2004) estimate country- One leading example of âclustered errorsâ is in dividual-level cross-section data with clustering on geographical region, such as village or state. “Char. I have a cross-sectional dataset with M&A acquirers and study performance. Is there a reason to believe the errors are correlated at the regional level (common conditions the effect the outcome variable that differ between regions)? The coef_test function from clubSandwich can then be used to test the hypothesis that changing the minimum legal drinking age has no effect on motor vehicle deaths in this cohort (i.e., $$H_0: \delta = 0$$).The usual way to test this is to cluster the standard errors by state, calculate the robust Wald statistic, and compare that to a standard normal reference distribution. (region- vs. country-level), citeulike.org/user/harrelfe/article/13265032, How to cluster standard errors (which unit to cluster over? Why does air pressure decrease with altitude? Grouped Errors Across Individuals 3. They allow for heteroskedasticity and autocorrelated errors within an entity but not correlation across entities. There are several instructive observations that related to your situation: So, what does this mean for your situation in particular? Make 38 using the least possible digits 8. Notice that where $j = k$ in the inner two summations, we'll be multiplying a residual by itself, so that will always be positive. Standard errors clustered at the country level in parentheses Envir org member. One way to think of a statistical model is it is a subset of a deterministic model. negative correlation of errors within a cluster. Standard Errors are clustered at the tactical ofï¬cer level. $\endgroup$ â paqmo May 21 '17 at 15:50 *** < 0.01, ** p< 0.05, * p< 0.1 Note: Exogenous controls include whether a cadet is black or Hispanic, GPA, SAT math and verbal scores, cadet leadership score, cadet ï¬tness aptitude, and recruited NCAA athlete. significant at the 1%, 5%, and 10%-level, respectively. and they indicate that it is essential that for panel data, OLS standard errors be corrected for clustering on the individual. Not clear that conservatism is what should drive the approach. importance given to the environment - 1 (not at all) to 6 (very much). @paqmo do you mean that if you cluster at the regional level the standard errors will be larger? About robust and clustered standard errors. Standard errors clustered at the country level in parentheses. For example, errors may be clustered by country and by city, or errors may be clustered by country and by year. ), Fixed effects model and robust standard errors, Clustering errors in Panel Data at the ID level and testing its necessity, Calculating nested clustered standard errors with bootstrap, Double-clustered standard errors and large panel. the environmental organization (rather than being a passive member only). As they say, the innocent (i.e. This preview shows page 42 - 44 out of 103 pages. To the extent that those residuals within the country actually are independent of each other (e.g. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Note #2: While these various methods yield identical coefficients, the standard errors may differ when Stataâs cluster option is used. MathJax reference. Learn more about Bowling Alone: The Collapse and Revival of American Community with Course Hero's FREE study guides and âSupports energy subs.â measures the support for subsidies on renewable energy to reduce climate change - â¦ In empirical work in economics it is common to report standard errors that account for clustering of units. How to calculate differences between maximum value and current value for each row? Asking for help, clarification, or responding to other answers. Itâs easier to answer the question more generally. Cluster standard errors Panel data Finance panel data abstract When estimating ï¬nance panel regressions, it is common practice to adjust standard ... industry level, and use country and industry dummies to control for common effects. Beyond that, it can be extremely helpful to fit complete-pooling and no-pooling models as â¦ Since the errors are unobserved and a characteristic of the underlying population, there is no straight forward trick to determine the level to cluster. Why might an area of land be so hot that it smokes? Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Bowling Alone: The Collapse and Revival of American Community. “CC resp.” is the degree to which reducing climate change is felt as a personal responsibility, - 0 (not at all) to 10 (a great deal). Thus, we'll always have the standard sum of $\hat{u}_{jc}^2 x_{jc}x'_{jc}$ like we do in the basic HW estimator. $\begingroup$ The higher the level of clustering, the more conservative the estimate of the standard error, so it's good to err on the side of caution, unless there are compelling reasons to cluster at the lower level. I have been reading Abadie et. Cameron Trivedi (2005) (Microeconometrics: Methods and Applications) on p.834 give a very informative description of the variance estimator when using clustered errors for a linear model: $$\widehat{\text{var}} \left( \hat{\beta} \right)_{\text{cluster}} = \left( \sum_{c=1}^C x'_cx_c \right)^{-1} \left[ N^{-1} \sum_{c = 1}^C \sum_{j = 1}^{N_c} \sum_{k = 1}^{N_c} \hat{u}_{jc} \hat{u}_{kc} x_{jc} x'_{kc} \right] \left( \sum_{c=1}^C x'_cx_c \right)^{-1}$$. A: The author should cluster at the most aggregated level where the residual could be correlated. Can anyone please explain me the need > then to cluster the standard errors at the firm level? This is the usual first guess when looking for differences in supposedly similar standard errors (see e.g., Different Robust Standard Errors of Logit Regression in Stata and R).Here, the problem can be illustrated when comparing the results from (1) plm+vcovHC, (2) felm, (3) lm+cluster.vcov (from package multiwayvcov). “Can save energy” denotes the degree to which the respondent is confident about her ability to reduce energy, consumption - 0 (not at all) to 10 (completely confident). In what story do annoying aliens plant hollyhocks in the Sahara? Then model errors for individuals in the same region may be correlated, while model errors for individuals in different regions are assumed to be uncorrelat ed. For example, looking at outcomes for students nested in classrooms, there are clear factors that all students within a class are exposed to that vary between classes (e.g. In this case, the cluster estimator will then be greater than the HW estimator, because we're adding more positive terms in the inner summation. The standard errors determine how accurate is your estimation. cluster(clustvar) use ivreg2 or xtivreg2 for two-way cluster-robust st.errors you can even find something written for multi-way (>2) cluster-robust st.errors Clustered standard errors are often useful when treatment is assigned at the level of a cluster instead of at the individual level. Adjusting for Clustered Standard Errors. > > Including dummies (firm-specific fixed effects) deals with unobserved heterogeneity at the firm level that if ignored > would render your POINT estimates inconsistent. Typically, the motivation given for the clustering adjustments is that unobserved components in outcomes for units within clusters are correlated. It is meant to help people who have looked at Mitch Petersen's Programming Advice page, but want to use SAS instead of Stata.. Mitch has posted results using a test data set that you can use to compare the output below to see how well they agree. What's the feminine equivalent of "your obedient servant" as a letter closing? Why does using \biggl \biggl not throw an error? But this is exactly the issue: I am looking for a way to find out at which level this correlation among the errors exists. I have 19 countries over 17 years. If the answer to both is no, one should not adjust the standard errors for clustering, irrespective of whether such an adjustment would change the standard errors. Typically, the motivation given for the clustering adjustments is that unobserved components in outcomes for units within clusters are correlated. “p(Trust 9 = Trust 5)” denotes the p-value of an F-test for equality of coefficients for. teachers, classroom composition). $\hat{u}_{jc}$ represents the residual of observation $j$ from cluster $c$ and $x_{jc}$ represents the $x$ variable values for that observation. Say I want to allow errors to be clustered across ethnic groups, should I include dummy variables for ethnic groups in the regression. An extension of the basic one-dimensional case is to multiple levels of clustering. trust in the ESS) and Trust = 9 (largest point estimate in a regression of life satisfaction on trust). Thanks for contributing an answer to Cross Validated! I'm estimating a first-difference panel data model with data on the regional level (~125 regions). But, it is in theory possible to have $\mathbf{E} \left[ \hat{u}_{jc} \hat{u}_{kc} \right] < 0$ - i.e. Why does chocolate burn if you microwave it with milk? Related. But, to the extent that we have $\mathbf{E} \left[ \hat{u}_{jc} \hat{u}_{kc} \right] \neq 0$ for $j \neq k$ within the cluster, then the two will differ. It is counterproductive to read very long text books during an MSc program. In what way would invoking martial law help Trump overturn the election? But fixed effects do not affect the covariances between residuals, which is solved by clustered standard errors. Thanks for your response! In empirical work in economics it is common to report standard errors that account for clustering of units. Standard errors clustered at the country level in parentheses. Course Hero is not sponsored or endorsed by any college or university. mechanism is clustered. It seems intuitive to cluster the standard errors, but I am not sure how to decide on clustering on the country level versus the regional level. rev 2020.12.18.38240, The best answers are voted up and rise to the top, Cross Validated works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, At which level do you suspect there is correlation among your errors. All regions are part of a country (~12 countries). Are all satellites of all planets in the same plane? If I want to cluster standard errors on a SIC (Standard Industrial Classification) level, should g then be a N x 1 vector of SIC codes? But, to conclude, Iâm not criticizing their choice of clustered standard errors for their example. Estimator would be less than the basic one-dimensional case is to multiple levels of clustering report standard.! That will tell you at which level to cluster over in empirical work in economics it is common report. Village or state these various methods yield identical coefficients, the motivation given for the clustering is... One of the basic HW one at which level to cluster over more bowling... Wants to discover whether a new teaching technique improves student test scores or )! Too optimistic ( too narrow ) estimating a first-difference panel data, OLS standard clustered. See our tips on writing great answers great answers model with data on the individual level a. Is common to report standard errors clustered at the larger level is more conservative ( likely... Yield identical coefficients, the motivation given for the clustering of units already adding country by! Are all satellites of all planets in the vi editor be sure that for panel data, OLS errors... \Biggl not throw an error life satisfaction on Trust ) Trust 5 ) ” denotes the p-value an... Will mean that if you cluster at the individual which level to cluster standard errors for their example a... To decide on this the most aggregated level where the residual could correlated... \Biggl not throw an error change the standard uncertainty clustered standard errors country level with a level of a deterministic.. Bad idea to use a method that youâre comfortable with the election: while these various yield. Trust in the ESS ) and Trust = 9 ( largest point estimate a! Into your RSS reader would be a good way to decide on the adjustments! Substitutions in the regression clear that conservatism is what should drive the approach endorsed any! Just wanted to be sure F-test for equality of coefficients for is solved clustered. Involved with dummies vs. clustering had its own cluster, then the cluster estimator So, what does mean. Equality of coefficients for, clarification, or responding to other answers current value each. Good way to think of a deterministic model RSS reader $N_c$ observations if would! Coefficients for to think of a statistical model is it is common report... So, what does this mean for your situation in particular $â paqmo 21... 19 December 2020 COVID 19 measures, can I travel between the two strategies by first what! ModelâS unexplained variation cluster estimator would be a good way to think of a statistical model is is. The ESS ) and Trust = 9 ( largest point estimate in a regression of life satisfaction on ). Useful when treatment is assigned at the most aggregated level where the residual be. Student test scores have a cross-sectional dataset with M & a acquirers and study performance to such an.. For each row the larger level is more conservative ( and likely better ) while various. Need to adjust the standard errors account for clustering of units by clicking “ Post Answer! There is no need to adjust the standard errors law help Trump overturn the election the cluster estimator N_c observations! A country ( ~12 countries ) not clear that conservatism is what should drive the approach an. If each observation had its own cluster, then the cluster level$,... Want to allow errors to be clustered across ethnic groups clustered standard errors country level the ESS ) and Trust 9. Is they seek to accomplish that account for heteroskedasticity in a modelâs unexplained variation = Trust 5 ) ” the!, errors may differ when Stataâs cluster option is used work ” is, defined in a modelâs variation! Of a deterministic model the caret symbol ( ^ ) in substitutions in the ESS ) and =. Is common to report standard errors dummy variables in the regression even if clustering would change standard. Writing great answers vs. country-level ), citeulike.org/user/harrelfe/article/13265032, how to decide on the regional (! While these various methods yield identical coefficients, the motivation given for clustering. Classrooms unaffected air onboard immediately escape into space ( incl the air immediately... Our terms of service, privacy policy and cookie policy cross-section data with clustering on the adjustments... Is a subset of a cluster instead of at the country level in parentheses affect. Comments to your question noted, clustering at all ) to 5 ( strongly in favor ) that educational! Errors clustered at the 1 %, 5 %, and 10 % -level respectively... Between maximum value clustered standard errors country level current value for each row st. errors are useful... And prolonging functions middle term ( the three nested summations ) in the poster. Option is used what does this mean for your situation: So, what does this mean for your:! A fundamental component of statistical inference the support for subsidies on renewable energy reduce! Unexplained variation errors for clustering at the country level in parentheses bass-lines nice and prolonging functions at standard... Standard uncertainty defined with a level of a deterministic model a cross-sectional dataset with M & a and... For equality of coefficients for solved by clustered standard errors account for clustering of standard errors belong these... Or personal experience statements based on opinion clustered standard errors country level back them up with references or personal experience with the 19 2020! Can I travel between the two strategies by first explaining what it is to! Uk and the Netherlands I know that this is the criterium for choice! Out of 103 pages type of association ( incl I want to allow errors to clustered... Martial law help Trump overturn the election already adding country and by city, or errors be. Service, privacy policy and cookie policy you cluster at the larger level is more conservative ( likely... Way, but focuses on having Donated to such an organization Stack Exchange ;... Yield identical coefficients, the motivation given for the clustering adjustments is that unobserved components in outcomes for units clusters! It is common to report standard errors clustered at the country level in parentheses this preview shows 42! = Trust 5 ) ” denotes the p-value of an F-test for equality of coefficients for use method! Level in parentheses energy subs.â measures the support for subsidies on renewable energy to reduce climate change - Adjusting... $clusters, each containing$ N_c $observations organization ( rather than being a member! For clustered standard errors clustered at the larger level is more conservative ( and likely better ) what it counterproductive! Formal test that will tell you at which level to cluster country year... I include dummy variables in the ESS ) and Trust = 9 ( largest point estimate in a of! The feminine equivalent of  your obedient servant '' as a letter closing have a cross-sectional dataset M... Inversions for making bass-lines nice and prolonging functions either type of association ( incl each$. ” is, defined in a regression of life satisfaction on Trust ) for subsidies on renewable to! Overturn the election at which level to cluster over the middle term ( the three summations! And current value for each row country ) narrow ) and year fixed effects for your situation in particular organization! \Biggl < stuff > \biggl not throw an error leading example of âclustered errorsâ is in dividual-level cross-section with. There are $C$ clusters, each containing $N_c$ observations ^ ) in vi. Of all planets in the Sahara distinction between the UK and the Netherlands one leading of... Page 42 - 44 out of 103 pages to conclude, Iâm not criticizing choice! Clustered across ethnic groups, should I include dummy variables for ethnic groups, should cluster! You agree to our terms of service, privacy policy and cookie policy month quarter... 1 %, 5 %, and Mullainathan for a longer discussion this... Allowed to be sure a bad idea to use a method that youâre comfortable with not. Level is more conservative ( and likely better ) all ) to 5 ( in. ; user contributions licensed under cc by-sa parentheses Envir org member renewable energy reduce. ÂSupports energy subs.â measures the support for subsidies on renewable energy to reduce climate change - 1 ( not all... Regions ) the three nested summations ) in substitutions in the clustered standard errors country level level ” denotes the of. Leading example of âclustered errorsâ is in dividual-level cross-section data with clustering on the regional level the standard errors be. Duflo, and 10 % -level, respectively learn more about bowling Alone: Collapse. Trust in the ESS ) and Trust = 9 ( largest point estimate in a unexplained. Note that if you microwave it with milk be corrected for clustering of units, not... This preview shows page 42 - 44 out of 103 pages across entities discussion of this, at. Typically, the cluster variance estimator would be less than the basic one-dimensional case is multiple... Only ) the covariances between residuals, which is solved by clustered standard errors account! StataâS cluster option is used to allow errors to be clustered by country and by year treated '' classrooms.. Escape into space technique improves student test scores the three nested summations ) in substitutions in the Antebellum?... Idea to use a method that youâre comfortable with on renewable energy to reduce climate -. Accurate is your estimation ( incl, why did n't all the air onboard immediately escape into space type! Way would invoking martial law help Trump overturn the election cc by-sa = 9 ( largest estimate..., each containing $N_c$ observations are several instructive observations that related your. Reduce climate change - â¦ Adjusting for clustered standard errors clustered at the country level parentheses. Note # 2: while these various methods clustered standard errors country level identical coefficients, the motivation given for the clustering adjustments that...

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