CPANEL Procedure

MODEL Statement

MODEL response = <effects> </ options>;

The MODEL statement specifies the regression model, the error structure that is assumed for the regression residuals, and the estimation technique to be used. The response variable (response) on the left side of the equal sign is regressed on the independent variables (effects), which are listed after the equal sign. You can specify any number of MODEL statements. For each MODEL statement, you can specify only one response.

For information about constructing the model effects, see the section Specification and Parameterization of Model Effects in Chapter 4, Shared Concepts.

You can label models. Model labels are used in the printed output to identify the results for different models. If you do not specify a label, the model is referred to by numerical order wherever necessary. You can label models by prefixing the MODEL statement by a label followed by a colon as follows:

label: MODEL …;

The MODEL statement supports many options, some more specific than others. Table 3 summarizes the options available in the MODEL statement. These are subsequently discussed in detail in the order in which they are presented in the table.

Table 3: Summary of MODEL Statement Options

Option	Description
Estimation Technique Options
AMACURDY	Fits a one-way model by using the Amemiya-MaCurdy estimator
BTWNG	Fits the between-groups model
BTWNT	Fits the between-time-periods model
DYNDIFF	Fits a dynamic panel model by using first-differences GMM
DYNSYS	Fits a dynamic panel model by using system GMM
FDONE	Fits a one-way model by using first differences
FIXONE	Fits a one-way fixed-effects model
FIXONETIME	Fits a one-way fixed-effects model for time effects
FIXTWO	Fits a two-way fixed-effects model
HTAYLOR	Fits a one-way model by using the Hausman-Taylor estimator
IVBTWNG	Fits a between-groups regression model by using instrumental variables
IVFIXONE	Fits a one-way fixed-effects model by using instrumental variables
IVFIXONETIME	Fits a one-way time fixed-effects model for time effects by using instrumental variables
IVFIXTWO	Fits a two-way fixed-effects model by using instrumental variables
IVG2SLS	Fits a generalized two-stage least squares model by using instrumental variables
IVPOOLED	Fits the pooled regression model by using instrumental variables
IVRANONE	Fits a one-way random-effects model by using instrumental variables
IVRANTWO	Fits a two-way random-effects model by using instrumental variables
POOLED	Fits the pooled regression model
RANONE	Fits a one-way random-effects model
RANTWO	Fits a two-way random-effects model
Estimation Control Options
BIASCORRECTED	Computes bias-corrected two-step GMM variances for instrumental variables models and dynamic panel models
GMM=	Specifies one-step or two-step GMM for instrumental variables models and dynamic panel models
NOINT	Suppresses the intercept
VCOMP=	Specifies the type of variance component estimation for random-effects estimation
Dynamic Panel Estimation Options
ARTESTS=	Specifies the maximum lag of AR(m) tests
DLAGS=	Specifies the number of dependent variable lags to include
GINV=	Specifies the generalized inverse method
MAXBAND=	Limits the number of instruments
Alternative Variances Options
CLUSTER	Corrects covariance for intracluster correlation
HAC	Specifies a heteroscedasticity- and autocorrelation-consistent (HAC) covariance
HCCME=	Specifies a heteroscedasticity-corrected covariance matrix estimator (HCCME)
MAXBAND=	Limits the number of instruments
ROBUST	Computes robust variances
Printed Output Options
CORRB	Prints the parameter correlation matrix
COVB	Prints the parameter covariance matrix
NOLABEL	Suppresses variable labels
PRINTFIXED	Estimates and prints the fixed effects

You can specify the following options after a slash (/).

Estimation Technique Options

These options specify the assumed error structure and estimation method. You can specify more than one option, in which case the analysis is repeated for each. The default is FIXONE (one-way fixed effects).

All estimation methods are described in detail in the section Details: CPANEL Procedure.

AMACURDY: requests Amemiya-MaCurdy estimation for a model that has correlated individual (cross-sectional) effects. You specify the correlated effects by using the CORRELATED statement.
BTWNG: estimates a between-groups model.
BTWNT: estimates a between-time-periods model.
DYNDIFF: estimates a dynamic panel by using the generalized method of moments (GMM) on equations that are formed by first differencing.
DYNSYS: estimates a dynamic panel by using GMM on the system that combines first-differenced equations and level equations.
FDONE: estimates a one-way model by using first-differenced methods.
FIXONE: estimates a one-way fixed-effects model that corresponds to cross-sectional effects only.
FIXONETIME: estimates a one-way fixed-effects model that corresponds to time effects only.
FIXTWO: estimates a two-way fixed-effects model.
HTAYLOR: requests Hausman-Taylor estimation for a model that has correlated individual (cross-sectional) effects. You specify the correlated effects by using the CORRELATED statement.
IVBTWNG: requests instrumental variables regression for between-groups estimation for a model that has endogenous effects. You specify the endogenous effects by using the ENDOGENOUS statement, and you specify external instruments by using the INSTRUMENTS statement. You can choose to use two-stage least squares or GMM to estimate the model.
IVFIXONE: requests instrumental variables regression for one-way fixed-effects estimation for a model that has endogenous effects. You specify the endogenous effects by using the ENDOGENOUS statement, and you specify external instruments by using the INSTRUMENTS statement. You can choose to use two-stage least squares or GMM to estimate the model.
IVFIXONETIME: requests instrumental variables regression for one-way time fixed-effects estimation for a model that has endogenous effects. You specify the endogenous effects by using the ENDOGENOUS statement, and you specify external instruments by using the INSTRUMENTS statement. You can choose to use two-stage least squares or GMM to estimate the model.
IVFIXTWO: requests instrumental variables regression for two-way fixed-effects estimation for a model that has endogenous effects. You specify the endogenous effects by using the ENDOGENOUS statement, and you specify external instruments by using the INSTRUMENTS statement. You can choose to use two-stage least squares or GMM to estimate the model.
IVG2SLS: requests instrumental variables regression for generalized two-stage least squares estimation for a model that has endogenous effects. You specify the endogenous effects by using the ENDOGENOUS statement, and you specify external instruments by using the INSTRUMENTS statement. You can choose to use two-stage least squares or GMM to estimate the model.
IVPOOLED: requests instrumental variables regression for pooled regression. You specify the endogenous effects by using the ENDOGENOUS statement, and you specify external instruments by using the INSTRUMENTS statement. You can choose to use two-stage least squares or GMM to estimate the model.
IVRANONE: requests instrumental variables regression for one-way random-effects estimation for a model that has endogenous effects. You specify the endogenous effects by using the ENDOGENOUS statement, and you specify external instruments by using the INSTRUMENTS statement. You can choose to use two-stage least squares or GMM to estimate the model.
IVRANTWO: requests instrumental variables regression for two-way random-effects estimation for a model that has endogenous effects. You specify the endogenous effects by using the ENDOGENOUS statement, and you specify external instruments by using the INSTRUMENTS statement. You can choose to use two-stage least squares or GMM to estimate the model.
POOLED: estimates a pooled (OLS) model.
RANONE: estimates a one-way random-effects model.
RANTWO: estimates a two-way random-effects model.

Estimation Control Options

These options define parameters that control the estimation and can be specific to the chosen technique (for example, how to estimate variance components in a random-effects model).

BIASCORRECTED

computes the bias-corrected covariance matrix of the two-step generalized method of moments (GMM) estimator. This statement is valid only when you perform either dynamic panel estimation or instrumental variables regression.

CLUSTER

specifies the cluster correction for the covariance matrix. You can specify this option when you specify HCCME=0, 1, 2, or 3.

GMM=ONESTEP | TWOSTEP

specifies the number of GMM stages to use in the estimation. This statement is valid only when you perform either dynamic panel estimation or instrumental variables regression.

You can specify the following values:

ONESTEP: uses one-step GMM, which is computationally simple but dependent on model assumptions.
TWOSTEP: uses two-step GMM, which is computationally intensive but more robust to violations of model assumptions.

By default, GMM=ONESTEP.

The following statements perform two-step GMM in a dynamic panel model, which is requested by the DYNDIFF option in the MODEL statement. You can use similar statements for a dynamic panel estimation that uses a full system of difference and level equations by specifying the DYNSYS option instead of the DYNDIFF option in the MODEL statement. The endogenous variable is Sales, and the GMM-style instruments is the predetermined variable Price. Both sets of instruments are included only in the difference equations.

proc cpanel data =  mylib.a;
   id firm year;
   model Sales = Price / dyndiff GMM = TWOSTEP;
   endogenous Sales / eq = diff;
   predetermined Price / eq = diff;
run;

The following statements perform two-step GMM in an instrumental variables model. The endogenous variables are X2 and Z2, and the external instruments are G1 and G2.

proc cpanel data =  mylib.a;
   id firm year;
   model Y = X1 X2 Z1 Z2 / ivfixone GMM = TWOSTEP;
   endogenous X2 Z2;
   instruments G1 G2;
run;

The IVFIXONE option in the MODEL statement requests IV one-way fixed-effects estimation. You can request other types of IV estimation by specifying IVBTWNG, IVFIXONETIME, IVFIXTWO, IVG2SLS, IVPOOLED, IVRANONE, or IVRANTWO instead of IVFIXONE in the MODEL statement.

HAC <(options)>

specifies the heteroscedasticity- and autocorrelation-consistent (HAC) covariance matrix estimator. This option is not available for between-groups or between-time-periods models, and cannot be combined with the HCCME= option.

You can specify the following options within parentheses and separated by spaces:

ADJUSTDF

makes a small-sample adjustment to the degrees of freedom in the covariance calculation.

BANDWIDTH=number | method

specifies the fixed bandwidth value or bandwidth selection method to be used in the kernel function. You can specify either a fixed value (number) or one of the methods listed after number.

number

specifies a fixed value of the bandwidth parameter.

ANDREWS | AN

specifies the Andrews (1991) bandwidth selection method.

NEWEYWEST<(C=number)> | NW <(C=number)>

specifies the bandwidth selection method of Newey and West (1994) You can also specify C=number to calculate the lag selection parameter; by default, C=12.

SAMPLESIZE<(options)> | SS<(options)>

calculates the bandwidth according to the following equation based on the sample size,

b equals gamma upper T Superscript r Baseline plus c

where b is the bandwidth parameter; T is the sample size; and , r, and c are values that you specify using the following options within parentheses and separated by spaces:

CONSTANT=number: specifies the constant c in the equation. By default, CONSTANT=0.5.
GAMMA=number: specifies the coefficient in the equation. By default, GAMMA=0.75.
INTSS: specifies that the bandwidth parameter be an integer; that is, , where denotes the largest integer less than or equal to x.
RATE=number: specifies the growth rate r in the equation. By default, RATE=0.3333.

By default, BANDWIDTH=ANDREWS.

KERNEL=BARTLETT | PARZEN | QS | TH | TRUNCATED

specifies the type of kernel function. You can specify the following values:

BARTLETT: specifies the Bartlett kernel function.
PARZEN: specifies the Parzen kernel function.
QS: specifies the quadratic spectral kernel function.
TH: specifies the Tukey-Hanning kernel function.
TRUNCATED: specifies the truncated kernel function.

By default, KERNEL=QS.

KERNELLB=number

specifies the lower bound of the kernel weight value. Any kernel weight less than number is regarded as 0, which accelerates the calculation in large samples, especially for the quadratic spectral kernel function. By default, KERNELLB=0.

PREWHITENING

requests prewhitening in the covariance calculation.

The following statements perform one-way fixed-effects estimation by using the Newey-West bandwidth and a Bartlett kernel based on a prewhitened gradient vector:

proc cpanel data =  mylib.a;
   id firm year;
   model Y = X1 X2 Z1 Z2 / ivfixone gmm=twostep
   hac(bandwidth=neweywest(c=12) kernel=bartlett prewhitening);
run;

HCCME=0 | 1 | 2 | 3

specifies the type of adjustment to the HCCME covariance matrix. You can specify the values 0 through 3, which indicate the type of covariance adjustment.

NOINT

suppresses the intercept parameter from the model.

ROBUST

computes the robust covariance matrix. This option can be applied to dynamic panel models, instrumental variables regression models, and static panel models. For dynamic panel models and instrumental variables regression models, the option provides heteroscedasticity-corrected standard errors according to the GMM estimation method. The following statements perform IV fixed-effects regression with robust standard errors:

proc cpanel data =  mylib.a;
   id firm year;
   model Y = X1 X2 Z1 Z2 / ivfixone gmm=twostep robust;
   endogenous X2 Z2;
   instruments G1 G2;
run;

For static panel models, this option produces cross-sectional clustered standard errors when HCCME=0. The following statements perform one-way fixed-effects regression with clustered standard errors:

proc cpanel data =  mylib.a;
   id firm year;
   model Y = X1 X2 Z1 Z2 / fixone robust;
run;

VCOMP=FB | NL | SA | WH | WK

specifies the type of variance component estimate to use. You can specify the following values:

FB: uses the Fuller-Battese method.
NL: uses the Nerlove method.
SA: uses the Swamy-Arora method.
WH: uses the Wallace-Hussain method.
WK: uses the Wansbeek-Kapteyn method.

By default, VCOMP=SA.

Dynamic Panel Estimation Options

These options are specific to dynamic panel estimation, which you obtain by specifying the DYNDIFF or DYNSYS option in the MODEL statement.

ARTESTS=integer

specifies the maximum order of the test for the presence of autoregression (AR) effects. By default, ARTESTS=2.

DLAGS=integer

specifies the number of dependent-variable lags to use as regressors. By default, DLAGS=1.

GINV=G2 | G4

specifies what type of generalized inverse to use. You can specify the following values:

G2: uses the G2 generalized inverse.
G4: uses the G4 generalized inverse.

The difference between G2 and G4 becomes evident when you invert singular matrices. The G2 generalized inverse drops rows and columns from singular matrices to produce a viable inverse. The G4 inverse, on the other hand, is the Moore-Penrose generalized inverse, which averages the variance effects between collinear rows. The G4 inverse is usually more stable, but it is computationally intensive. By default, GINV=G2. If you have trouble reproducing published results, often the solution is to switch to GINV=G4.

MAXBAND=integer

if specified, sets the maximum number of GMM-style instruments per observation, for each variable. Because the number of GMM-style instruments grows quadratically with the number of time periods, this option makes estimation more feasible when you have many time periods.

Printed Output Options

These options alter how results are presented.

CORRB: prints the matrix of estimated correlations between the parameter estimates.
COVB: prints the matrix of estimated covariances between the parameter estimates.
NOLABEL: suppresses variable labels from the printed output.
PRINTFIXED: estimates and prints the fixed effects in models where they would normally be absorbed within the estimation.

Last updated: July 09, 2026