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Programming Advice

My purpose in writing this paper was to make sure researchers (myself included) understood what each of the methods for estimating standard errors was actually doing. These pages are meant to help researchers use the correct techniques. Code which is easily available is more likely to be used. Since I program in Stata, most of the instructions below are for Stata. I have also included code in other languages (written by other generous academics) at the end of this page. Questions should be directed to the authors, as I am not familiar with the code. If you know how to do this in other languages, please let me know. I am happy to post links to the instructions. I have also posted a test data set (in text and in stata format) along with the standard errors estimated by several different methods using this data. You can use these results to verify that your routines are producing the same results. With all of the instructions, the programming instructions are in bold. The variable names which the user must specify are in italics. I have also included a sample of the Stata program which I used to run the simulations (i.e. simulated the data sets and then estimated the coefficients and standard errors). Although I have posted these instructions, I unfortunately, do not have time to respond to all programming questions.

Stata Programming Instructions

The standard command for running a regression in Stata is:

    regress dependent_variable independent­_variables, options

Clustered (Rogers) Standard Errors – One dimension

To obtain Clustered (Rogers) standard errors (and OLS coefficients), use the command:

    regress dependent_variable independent_variables, robust cluster(cluster_variable)

This produces White standard errors which are robust to within cluster correlation (clustered or Rogers standard errors). If you wanted to cluster by year, then the cluster variable would be the year variable. If you wanted to cluster by industry and year, you would need to create a variable which had a unique value for each industry-year pair. These standard errors would allow observations in the same industry/year to be correlated (i.e. different firms), but would assume that observations in the same industry, but different years, are assumed to be uncorrelated. To allow observations which share an industry or share a year to be correlated, you need to cluster by two dimensions (industry and year). These instructions follow.

For most estimation commands such as logits and probits, the previous form of the command will also work. For example, to run a logit with clustered standard errors you would use the command:

    logit dependent_variable independent_variables, robust cluster(cluster_variable)

Clustered Standard Errors – Two dimensions

The routines currently written into Stata allow you to cluster by only one variable (e.g. one dimension such as firm or time). Papers by Thompson (2006) and by Cameron, Gelbach and Miller (2006) suggest a way to account for multiple dimensions at the same time. This approach allows for correlations among different firms in the same year and different years in the same firm, for example. See their papers and mine for more details and caveats. I have written a Stata ado file to implement this estimation procedure. It runs a regression and calculates standard errors which account for two dimensions of within cluster correlation. The variables which record the two dimensions (e.g. a firm identifier and a time identifier) are specified in the required options: flcuster( ) and tcluster( ). There are also versions of the Stata ado file that estimates logit (logit2.ado), probit (probit2.ado), or tobit (tobit2.ado) models with clustering on two dimensions. The format is similar to the cluster2.ado command.

    cluster2 dependent_variable independent_variables, fcluster(cluster_variable_one)  tcluster(cluster_variable_two)

If there are multiple observations per firm-year (e.g. loan data sets which have multiple loans per firm in a given year), then the method described in my paper needs to be modified. In this case, instead of subtracting off the White variance matrix, you need to subtract off the variance matrix clustered by firm-year (i.e. for correlation among observations with the same firm AND the same year -- see Cameron, Gelbach, and Miller (2006) for details). The program has been modified to automatically check for this condition and use the correct third matrix. The program is also now compatible with the outreg procedure.

            The code for estimating clustered standard errors in two dimensions using R is available here.

Fama-MacBeth Standard Errors

Stata does not contain a routine for estimating the coefficients and standard errors by Fama-MacBeth (that I know of), but I have written an ado file which you can download. The ado file fm.ado runs a cross-sectional regression for each year in the data set. The program allows you to specify a by variable for Fama-MacBeth. Thus if in stead of running T cross-sectional regressions, you could run N time series regressions by specifying the firm identifier as the byfm( ) variable. If the option is not specified, it uses the time variable (as set by the tsset comment) as the by variable. The program is also now compatible with the outreg procedure.

The form of the command is:

    fm dependent_variable independent_variables, byfm(by_variable)

Prior to running the fm program, you need to use the tsset command. This tells Stata the name of the firm identifier and the time variable. The form of this command is:

    tsset firm_identifier time_identifier

The program will accept the Stata in and if commands, if you want to do the regression for only certain observations. Judson Caskey, who showed me how to use the tsset command in the FM program, has also modified the program. His version reports the number of positive or negative coefficients and the number which are significant (and positive or negative). Another version (xtfmb.ado) has been written by Daniel Hoechle. To install this ado file from with in Stata type net search xtfmb. A full description is in the help file.

Newey West for Panel Data Sets

The Stata command newey will estimate the coefficients of a regression using OLS and generate Newey-West standard errors. If you want to use this in a panel data set (so that only observations within a cluster may be correlated), you need to use the tsset command.

tsset firm_identifier time_identifier  

newey dependent_variable independent_variables, lag(lag_length) force

Where firm_identifier is the variable which denotes each firm (e.g. cusip, permn, or gvkey) and time_identifier is the variable that identifies the time dimension, such as year. This specification will allow for observations on the same firm in different years to be correlated (i.e. a firm effect). If you want to allow for observations on different firms but in the same year to be correlated you need to reverse the firm and time identifiers. If you are clustering on some other dimension besides firm (e.g. industry or country), you would use that variable instead. You can specify any lag length up to T-1, where T is the number of years per firm.

 

Fixed Effects

Stata can automatically include a set of dummy variable for each value of one specified variable.

The form of the command is:

    areg dependent_variable independent_variables, absorb(identifier_variable)

Where identifier_variable is a firm identifier (e.g. cusip, permn, or gvkey) if you want firm dummies or a time identifier (e.g. year) if you want year dummies. If you want to include both firm and time dummies, only one set can be included with the absorb option. The other must be included manually (e.g. by manually including a full set of time dummies among the independent variables, and then using the absorb option for the firm dummies).

To create a full set of dummy variables from an indexed variable such as year you can use the following command:

    tabulate index_variable, gen(dummy_variable)

This will create a set of dummy variables (e.g. dummy_variable1, dummy_variable2, etc), which are equal to one if the index_variable takes on its first value and zero otherwise (in the case of dummy_variable1).

A more elegant way to do this is to use the xi command (as recommended by Prof Nandy). This allows you to include a set of dummy variables for any categorical variable (e.g. year or firm), including multiple categorical values. To include both year and firm dummies, the command is:

    xi: areg dependent_variable independent_variables i.year, absorb(firm_identifier)

where year is the categorical variable for year and firm_identifier is the categorical variable for firm. The coefficients on T-1 of the year variables will be reported, the coefficients on the firm dummy variables will not. To see the coefficients on both sets of  dummy variables you would use the command:

    xi: reg dependent_variable independent_variables i.year i.firm_identifier

 

Generalized Least Squares

When the residuals are correlated within a cluster, not only are the OLS standard errors biased but the slope coefficients are not efficient. One method for taking advantage of the additional information in the residuals (and generating more efficient estimates) is to estimate a random effects model using a generalized least squares approach. I used the xtreg command to estimate the GLS results reported in the paper.

The form of the command is:

    xtreg dependent_variable independent_variables, i(firm_idenifier)

As with the regress commend, standard errors which are robust to within cluster correlation can be produced by including the option cluster(firm_idenifier)

    xtreg dependent_variable independent_variables, i(firm_idenifier) cluster(firm_idenifier)

 

Bootstrapped Standard Errors

The Stata command bootstrap will allow you to estimate the standard errors using the bootstrap method. This will run the regression multiple times and use the variability in the slope coefficients as an estimate of their standard deviation (intuitively like I did with my simulations).

The form of this command is:

    bootstrap “regress  dependent_variable independent_variables” _b, reps(number_of_repetitions)

Where number_of_repetitions samples will be drawn with replacement from the original sample. Each time the regression will be run and the slope coefficients will be saved, since _b is specified. Both the average slope and its standard deviation will be reported. As specified, the bootstrapped samples will be drawn a single observation at a time. If the observations within a cluster (year or firm) are correlated, then these bootstrapped standard errors will be biased. To account for the correlation within cluster it is necessary to draw clusters with replacement oppose observations with replacement. To do this in Stata, you need to add the cluster option. In this case, the command is:

    bootstrap “regress  dependent_variable independent_variables” _b, reps(number_of_repetitions) cluster(cluster_variable)

 


SAS Programming Instructions

Although I did not work in SAS, Tanguy Brachet was kind enough to explain how to do some of the estimation in SAS. A brief description follows.

Clustered Standard Errors

The standard command for running an OLS regression in SAS and getting the Clustered/Rogers standard errors is:

    proc surveyreg data=mydata;
            cluster cluster_variable;
            model dependent variable = independent variables;

This produces White standard errors which are robust to within cluster correlation (Rogers or clustered standard errors), when cluster_variable is the variable by which you want to cluster. If you clustered by firm it could be cusip or gvkey. If you clustered by time it could be year. SAS allows you to specify multiple variables in the cluster statement (e.g. firm and year). However, this does not produce standard errors clustered by two dimensions described in my paper.

Clustered Standard Errors – Two dimensions

SAS does not contain a routine to do this, but you can find SAS code for estimating standard errors clustered on two dimensions on this web site (Mark Ma).

Fixed Effects

If you want to include dummy variables for one dimension (time) and cluster by another dimension, you need to create the dummy variables. A simple way is as follows:

   data new;
            set old;
            year1 = (year=1991);
            year2 = (year=1992);
            year3 = (year=1993);
            year4 = (year=1994);
            year5 = (year=1995);

Alternative specifications can be found on Noah Stoffman’s pages. As SAS is not my traditional language, this code is provided just as information. I have used both the SAS and Stata code to verify that the results produced by both sets of instructions (SAS and Stata) are the same based on a test data set.


R Programming Instructions

The programs in R are written by Mahmood Arai. Questions can be directed to him.

Clustered Standard Errors – Two dimensions

 


Simulated Data Sets

    Many of the results in the paper are based on simulating data sets with a specified dependence (firm and/or time effect). For those who are interested in seeing how this was done or for researchers who want simulation results for different data structures, I have posted a stripped down version of the simulation program. This program simulates a data set with a firm effect and then estimates the coefficients using OLS and Fama-MacBeth. The program estimates OLS standard errors, standard errors clustered by firm, and Fama-MacBeth standard errors. The results are saved for each iteration, and the means and standard deviations are calculated and displaced. To run the program simulation.do, you need to type

    do simulation firm_effect_x firm_effect_r number_of years

where firm_effect_x is the percent of the independent variable’s variance which is due to the firm effect [i.e. rho(x)], firm_effect_r is the percent of the residual’s variance which is due to the firm effect [i.e. rho(r)], and number_of_years is the number of time periods per firm in the data set. Rho(x) and rho(r) should be between 0 and 1.0. The data set will have 5,000 observations (although this can be changed), so the number of firms is 5,000/number_of_years. Other parameters can be changed by editing the program. This example is just meant to provide intuition of how I did the simulations. If you have questions about this page, you are welcome to e-mail me. I can not promise an immediate response, but I will try to get back to you. I unfortunately, can’t help you debug your stata (or non-stata) programs. However, by posting these instructions I hope to make it easier to use the methods discussed in my paper.


If you find errors or corrections, please e-mail me.

Mitchell A. Petersen