frontierCost - WeAreCAS

Q: What is the primary purpose of the frontierCost action?

The frontierCost action is designed for analyzing stochastic frontier cost models.

Q: How do I specify the input data for the analysis?

You use the "table" parameter to specify the input table containing the data to be analyzed.

Q: How can I define the stochastic frontier model to be estimated?

You define the model using the "model" parameter. Within this parameter, you specify the dependent variable(s) using "depVars" and the explanatory effects using the "effects" parameter.

Q: What types of frontier models are supported by the frontierCost action?

The action supports three types of frontier models, specified via the "type" subparameter in "modelOptions": "EXPONENTIAL" (the default), "HALF" (half-normal), and "TRUNCATED" (truncated-normal).

Q: How can I obtain estimates for technical efficiency in the output table?

You can request technical efficiency estimates using the "output" parameter. Specifically, use the "te1" and "te2" subparameters to specify the variable names for technical efficiency type 1 and type 2, respectively.

Q: Is it possible to perform hypothesis tests on the regression parameters?

Yes, you can use the "tests" parameter to specify linear hypotheses about the regression parameters. The action supports Wald, Lagrange multiplier (LM), and likelihood ratio (LR) tests.

Q: How are classification variables handled in the model?

You can specify classification variables using the "class" parameter. This parameter allows you to define options such as the parameterization method ("param"), the reference level ("ref"), and the sort order ("order") for the categorical variables.

Q: What optimization algorithms are available for parameter estimation?

The "optimizer" parameter's "algorithm" option allows you to choose from several techniques, including "CONJUGATEGRADIENT", "DOUBLEDOGLEG", "NEWTONRAPHSONWITHLINESEARCH" (the default), "NEWTONRAPHSONWITHRIDGING", "QUASINEWTON", "TRUSTREGION", or "NONE".

Q: How can I save specific display tables, such as parameter estimates, as CAS tables?

You can use the "outputTables" parameter to list the specific display tables you wish to save as CAS tables using the "names" subparameter.

Q: Can I provide custom initial values for the model parameters?

Yes, the "initialvalues" parameter allows you to specify a list of initial values for the parameters to start the optimization process.

Description

The frontierCost action analyzes stochastic frontier cost models. It estimates the cost efficiency of decision-making units by formulating a cost function that accounts for both random error and non-negative inefficiency components. This action is essential for benchmarking performance and identifying deviations from the optimal cost frontier given input prices and output levels.

Settings

Parameter	Description
table	Specifies the input data table to be analyzed. This is a required parameter.
model	Specifies the dependent variable, explanatory effects (regressors), and specific model options (like efficiency type). This is a required parameter.
class	Specifies the classification variables to be used in the analysis.
bounds	Imposes simple boundary constraints on the parameter estimates.
optimizer	Controls the nonlinear optimization process, including the algorithm (e.g., Newton-Raphson, Conjugate Gradient) and convergence criteria.
output	Specifies details for the output data table, which can contain predicted values, residuals, and technical efficiency estimates (te1, te2).
restrictions	Specifies linear restrictions to be imposed on the parameter estimates.
tests	Specifies linear hypotheses about the regression parameters to be tested (Wald, Lagrange Multiplier, Likelihood Ratio).
weight	Specifies the variable to be used as the observation weight.
freq	Specifies the variable to be used as the observation frequency.

Data Preparation View data prep sheet

Creation of Simulated Cost Data

Generates a dataset simulating cost, output, and input prices for 100 firms, including a random inefficiency term.

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1
2	DATA casuser.cost_data;
3	call streaminit(12345);
4	DO i = 1 to 100;
5	log_output = rand('Normal', 1, 0.5);
6	log_price1 = rand('Normal', 0.5, 0.2);
7	log_price2 = rand('Normal', 0.5, 0.2);
8	v = rand('Normal', 0, 0.1);
9	u = abs(rand('Normal', 0, 0.2));
10	log_cost = 0.5 + 0.8log_output + 0.4log_price1 + 0.6*log_price2 + v + u;
11	OUTPUT;
12	END;
13
14	RUN;
15
16	PROC CASUTIL;
17	load
18	DATA=casuser.cost_data casout="cost_data" replace;
19
20	RUN;
21

Examples

Estimates a simple Cobb-Douglas stochastic frontier cost model using the default exponential distribution for efficiency.

SAS® / CAS Code Code awaiting community validation

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1
2	PROC CAS;
3	frontier.frontierCost TABLE="cost_data", model={depVars={{name="log_cost"}}, effects={{vars={"log_output", "log_price1", "log_price2"}}}};
4
5	RUN;
6

Result :
Generates parameter estimates for the cost function and the inefficiency variance components.

Estimates a model specifying a Half-Normal efficiency distribution, custom optimization settings, and generates an output table containing technical efficiency scores.

SAS® / CAS Code Code awaiting community validation

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1
2	PROC CAS;
3	frontier.frontierCost TABLE="cost_data", model={depVars={{name="log_cost"}}, effects={{vars={"log_output", "log_price1", "log_price2"}}}, modelOptions={type="HALF"}}, optimizer={algorithm="QUASINEWTON", maxit=200}, OUTPUT={casOut={name="frontier_scores", replace=true}, te1="TechEff", pred="PredictedCost"};
4
5	RUN;
6

Result :
Produces model estimates using the Half-Normal type and creates a CAS table 'frontier_scores' containing technical efficiency (TechEff) and predicted cost values.

FAQ

What is the primary purpose of the frontierCost action?

How do I specify the input data for the analysis?

How can I define the stochastic frontier model to be estimated?

What types of frontier models are supported by the frontierCost action?

How can I obtain estimates for technical efficiency in the output table?

Is it possible to perform hypothesis tests on the regression parameters?

How are classification variables handled in the model?

What optimization algorithms are available for parameter estimation?

How can I save specific display tables, such as parameter estimates, as CAS tables?

Can I provide custom initial values for the model parameters?

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Table of Contents

Description

Creation of Simulated Cost Data

Examples

Basic Stochastic Frontier Cost Model

Advanced Model with Half-Normal Efficiency and Output

FAQ

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