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Federal Register / Vol. 86, No. 142 / Wednesday, July 28, 2021 / Rules and Regulations
of $0.009 and $0.0119suggesting that under these rates the provider can cover the marginal cost of a minute of calling as well as cover their fixed costs. Similarly, six contracts in the Second Mandatory Data Collection report providers earning perminute rates net of site commissions of less than $0.01, including the REDACTED
contract for the REDACTED. Indeed, the cost of an additional minute may be de minimis, with the cost of both originating and terminating a call being near zero. Thus, a material majority of contracts would be able to recover their costs under the new interim rate caps. Given that the estimates presented here are based on the upper bound of costs for a contract, that the Commission leaned toward understating demand responsiveness, the true share of contracts that are costcovering is likely larger.

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Appendix B
Sensitivity Testing: Additional Statistical Analysis of Cost Data 1. The Commission analyzes inmate calling services providers responses to the Second Mandatory Data Collection to determine whether certain characteristics of inmate calling services contracts can be shown to have a meaningful association with contract costs on a per-minute basis, as reported by the providers. In this Appendix, the Commission frequently refers to inmate calling services providers by short names or acronyms. These providers are: ATN, Inc.
ATN; CenturyLink Public Communications, Inc. CenturyLink; Correct Solutions, LLC
Correct; Combined Public Communications CPC; Crown Correctional Telephone, Inc.
Crown; Global TelLink Corporation GTL;
ICSolutions, LLC ICSolutions; Legacy Long Distance International, Inc. Legacy; NCIC
Inmate Communications NCIC; Pay Tel Communications, Inc. Pay Tel; Prodigy Solutions, Inc. Prodigy; and Securus Technologies, LLC Securus. The Commission previously performed this analysis in Appendix B of the 2020 ICS
FNPRM. That analysis found that provider identity and the state a facility is located in were by far the most important predictors of a contracts per-minute costs. It also found that other facility and contract variables, such as the average daily populations of the facilities covered by the contract, the type of those facilities prison or jail, and the rurality of the facilities, had virtually no additional predictive power. In comments submitted to the Commission, the finding that per-minute costs were not significantly impacted by facility size and type was criticized. This Appendix repeats the analysis from Appendix B of the 2020 ICS
FNPRM using updated data.
2. To perform the analysis, the Commission uses a recognized statistical method named least absolute shrinkage and selection operator Lasso to identify which, if any, variables serve as accurate predictors of perminute contract costs for calling services.
This method identifies predictors of an outcome variablein the case the logarithm of costs per minuteby trading off the goodness of fit against the complexity of the model, as measured by the number of predictors. As used here, the Lasso model
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seeks to identify factors that are predictive of an inmate calling service providers costs per minute, balancing a number of competing considerations. Lasso is especially useful in situations like this where many variables, and interactions among those variables, can potentially predict outcomes. Given that the Commission is interested in determining the potential cost effects of many categorical variables as well as their interactions with one another, the overall number of potential variables is extremely large, and estimating the effects of all variables on costs via more traditional methods such as linear regression is infeasible. In the Lasso model, the Commission finds the main predictors of costs per minute to be provider identity and the state where the contracts facilities are located. The Commission also finds that facility type whether the facility is a prison or jail is a predictor of costs per minute, although not as strong as provider identity and state. Finally, the Commission finds that a wide range of other variables have less, or essentially no, predictive power.
3. The Commission chooses the inmate calling services contract as the unit of observation for the analysis for two reasons.
First, providers bid for contracts rather than separately bidding for each individual facility, which indicates that commercial decisions are made at the contract level.
Second, many contracts cover more than one facility, but several providers did not report data on those facilities separately, which precludes any meaningful analysis at the facility level. As in Appendix A, jails with average daily populations of less than 1,000
are included in the totals to ensure that the sensitivity analysis is comprehensive among the total dataset of 2,900 contracts. But, because the Commission does not address jails with average daily populations of less than 1,000 in the Report and Order for purposes of arriving at revised interim rate caps based on the Second Mandatory Data Collection, the Commission does not include any results based on such jails in this Appendix. The Commission focuses on the logarithm of costs per minute as the dependent variablei.e., the Commission seeks to evaluate what factors are predictive of an inmate calling service providers costs per minute. The contract variables that the Commission considers in the analysis are as follows:
The identity of the inmate calling services provider;
The states in which the correctional facilities covered by a contract are located;
The Census divisions and regions in which the facilities covered by a contract are located;
The type of facility prison or jail;
An indicator for joint contracts i.e., contracts for which an inmate calling services provider subcontracts with another inmate calling services provider;
Contract average daily population;
Contract average daily population bins average daily population 25; average daily population 50; average daily population 100; average daily population 250; average daily population 500; average daily population 1,000; average daily population 5,000;

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Rurality of the facilities covered by the contract rural, if all the facilities covered by the contract are located in a census block designated by the Bureau of Census as rural;
urban, if all facilities are located in a census block not designated as rural; or mixed, if the contract covers facilities in census blocks designated as both rural and not rural; and Various combinations i.e., multiplicative interactions among the above variables.
4. Lasso and Costs per Minute. The Lasso results indicate economically significant differences in costs per minute across different providers and states. The provider identity and state variables retained by Lasso as predictors of cost explain approximately 67% of the variation in costs across contracts.
Provider identity is an especially meaningful predictor of costs; a Lasso model with it alone explains over 60% of the variation in costs across contracts. The differences in costs measured by the provider identity variable may reflect systematic differences in costs across providers, but they are more likely indicative of systematic differences in the way costs are calculated and reported to the Commission by providers. The differences in cost measured by the state variables may reflect statewide differences in costs arising from different regulatory frameworks or other state-specific factors.
Lasso results also indicate differences in costs per minute by facility type prison or jail, rurality, and region. However, these variables are not economically significant:
When retained as predictors by Lasso, these variables explain less than 1% of the variation in costs that are explained by the provider identity and state variables alone.
5. A group of contracts representing a significant fractionabout 11%of observations contained insufficient information to ascertain the rurality of facilities included in those contracts. As a result, in the baseline model that includes all contracts, the Commission interprets the effect of the rurality variables as differences from the contracts for which the Commission does not have rurality information. To ensure that this is a sound approach, the Commission uses a sample selection model to confirm that the factors that may be associated with a contract not having sufficient rurality information are not significantly correlated with costs. The Commission estimates a Heckman sample selection model where selection is for observations that contain rurality information. The dependent variable and controls in this model were chosen to be the same as the ones in Lasso. The Commission finds that the coefficient on the inverse Mills ratio is not significant at reasonable levels of significance p-value is 0.21, allaying potential concerns about sample selectivity.
The Commission also conducts the analysis using only the contracts that contain rurality information and obtain Lasso results that are similar to the results the Commission obtains with the baseline model.
6. The Commission also explores the differences in the costs reported by the top three providers by size using a doubleselection Lasso model. Double-selection Lasso is a method of statistical inference that
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