gmmFitIV

Purpose

Estimate instrumental variables model using the generalized method of moments.

Format

gOut = gmmFitIV(y, x[, gCtl])
gOut = gmmFitIV(y, x[, z[, gCtl]])
gOut = gmmFitIV(dataset, formula[, gCtl])
gOut = gmmFitIV(dataset, formula[, inst_list[, gCtl]])
Parameters:
  • y (Nx1 matrix) – dependent data vector
  • x (NxK matrix) – independent data matrix.
  • z (NxK matrix) – Optional input, instrumental variables data matrix. If z is excluded, the linear model of y and x is estimated.
  • dataset (string) – name of dataset.
  • formula (string) –

    formula string of the model.

    e.g "y ~ X1 + X2", y is the name of dependent variable, X1 and X2 are names of independent variables;

    e.g. "y ~ .", . means including all variables except dependent variable y.

  • inst_list (string) –

    Optional input. Formula string representing the instrumental variables to be included in the model.

    e.g. "pcturban + price + age + zip" specifies that the variables pcturban, price, age, and zip should be used as instrumental variables.

  • gCtl (struct) –

    Optional argument. An instance of an gmmControl structure

    gCtl.method string, GMM method to be used.
    ”onestep”:One-step GMM
    ”twostep”:Two-step GMM
    ”iterative”:Iterative GMM
    ”CU”:Continuous updating GMM.

    Default = "twostep"

    gCtl.vceType string, variance-covariance matrix type.
    ”unadj”:Unadjusted, non-robust SE.
    ”robust”:Heteroscedastic robust SE.
    ”hac”:Heteroscedastic-autocorrelation robust SE.

    Default = "robust"

    gCtl.wType string, type of weight matrix used. Ignored for one-step case.
    ”unadj”:Unadjusted, non-robust SE.
    ”robust”:Heteroscedastic robust SE.
    ”hac”:Heteroscedastic-autocorrelation robust SE.

    Default = "robust"

    gCtl.hacKernel string, type of kernel used for estimation of HAC robust weight matrix and/or variance-covariance matrix. Ignored if not using "hac" weight matrix and/or variance-covariance matrix.

    Note

    Bandwidth is determined using the Newey-West optimal lag length selection method.

    ”bartlett”:Bartlett kernel.
    ”parzen”:Parzen kernel.
    ”quad”:Quadraticspectral kernel.

    Default = "bartlett"

    gCtl.gmmlags Scalar, Scalar, user specified lag truncation for HAC weight matrix and variance computations.
    gCtl.wInitMat data matrix, initial weight matrix to be used. If specified the matrix is used as initial weighting matrix and overrides specification of gCtl.wInit.
    gCtl.wInit string, type of initial weight matrix used. If data matrix, the specified matrix is used as initial weighting matrix. Else:
    ”identity”:Identity matrix.
    ”unadj”:Weight matrix \(1/n*inv(Z'Z)\). Assumes moments are i.i.d. Default = "unadj"
    gCtl.gIter instance of gmmIterative structure. This structure houses the tolerances for convergence for iterative GMM. Ignored if iterative GMM is not specified. The members include:
    gCtl.gIter.maxIter:
     scalar, maximum number of iterations. Default = 500.
    gCtl.gIter.paramTol:
     scalar, tolerance level for convergence based on parameter estimates. Default = 1e-6.
    gCtl.gIter.wTol:
     scalar, tolerance level for convergence based on weight matrix estimates. Default = 1e-6.
    gCtl.noconstant scalar, specified to indicate if constant is included in model. Only valid if data vector input method is used. Set to 1 to exclude constant from model. Constant is always first parameter in parameter vector. Default = 0 [constant included].For dataset and string formula method to remove constant from model specify "-1" as first dependent variable: e.g.: "y ~ -1 + X1 + X2"
    gCtl.varNames string array, dependent variable names. Only used for data vector input case. Default = X1, X2, ...
    gCtl.instNames string array, instrumental variable names. Only used for data vector input case. Default = Z1, Z2, ...
Returns:

gOut (struct) –

instance of gmmOut struct containing the following members:

gOut.paramEst column vector of final estimates. Constant, if included in model, is the first element.
gOut.wFinal matrix, final weighting matrix.
gOut.covPar matrix, estimated variance-covariance matrix.
gOut.numParams scalar, number of parameters estimated in model.
gOut.numMoments scalar, number of moments.
gOut.numObs scalar, number of observations.
gOut.numInstruments scalar, number of instruments.
gOut.numMoments scalar, number of moments.
gOut.JStat scalar, Hansen statistic of overidentification.
gOut.df scalar, degrees of freedom.

Examples

Formula String

new;
cls;

/*
** Declare gmm_result to be a gmmOut struct
** to hold the results of the estimation
*/
struct gmmOut gmm_result;

// Create fully pathed dataset file name string
auto_dset = getGAUSSHome() $+ "examples/auto";

// Perform estimation, using a formula string specification
gmm_result = gmmFitIV(auto_dset, "mpg ~ weight + length");

The above code will print out the following report:

Dependent Variable:                       mpg
Number of Observations:                    74
Number of Moments:                          0
Number of Parameters:                       3
Degrees of freedom:                        71


                         Standard                Prob
Variable     Estimate      Error     t-value     >|t|
-----------------------------------------------------

CONSTANT    47.884873    7.506021     6.380     0.000
weight      -0.003851    0.001947    -1.978     0.052
length      -0.079593    0.067753    -1.175     0.244


Instruments: weight, length, Constant

Data Matrix

new;
cls;

data = loadd(getGAUSSHome() $+ "examples/hsng.dat");

y = data[., 12];
x = data[., 11 7];
z = data[., 7 8 14:16];

/*
** Declare gctl to be a gmmControl struct
** and fill with default settings
*/
struct gmmControl gctl;
gctl = gmmControlCreate();

// Set desired estimation options
gctl.wInit = "unadj";

// Set method
gctl.method = "twostep";

// Set variance type
gctl.vceType = "robust";

// Weight matrix type
gctl.wType = "robust";

struct gmmOut gOut;
gOut = gmmFitIV(y, x, z, gctl);

The above code will print out the following report:

Dependent Variable:                       Y
Number of Observations:                  50
Number of Moments:                        0
Number of Parameters:                     3
Degrees of freedom:                      47


                         Standard                Prob
Variable     Estimate      Error     t-value     >|t|
-----------------------------------------------------

Beta1      112.122713   10.545763    10.632     0.000
Beta2        0.001464    0.000404     3.627     0.001
Beta3        0.761548    0.264387     2.880     0.006


Instruments: Z1, Z2, Z3, Z4, Z5, Z6

Hansen Test Statistic of the Moment Restrictions
Chi-Sq(   3) =        6.9753314
P-value of J-stat:     0.072688216

Remarks

The supported dataset types are CSV, Excel (XLS, XLSX), HDF5, GAUSS Matrix (FMT), GAUSS Dataset (DAT), Stata (DTA) and SAS (SAS7BDAT, SAS7BCAT).

See also

Functions gmmControlCreate(), gmmFit()