Description Usage Arguments Details Value Author(s) References

Computes the SPS estimator for a two-stage structural model, as well as a sample estimate of the alpha parameter controlling the degree of combination between the OLS and TSLS estimators.

1 | ```
sps.internal(y,X,Z,REF="TSLS",ALPHA=FALSE,n.btj=10)
``` |

`y` |
Numeric: A vector of observations, representing the outcome variable. |

`X` |
Numeric: A matrix of observations, whose number of columns
corresponds to the number of predictors in the model, and the number
of rows should be conformal with the number of entries in |

`Z` |
Numeric: A matrix of observations representing the
intrumental variables (IVs) in the first-stage structural equation. The
number of IVs should be at least as large as the number of
endogenous variables in |

`REF` |
Character: Controls the choice of the |

`ALPHA` |
Logical: If TRUE, the function returns the value of the
sample estimate of the parameter controlling the respective
contribution of the |

`n.btj` |
Numeric: The number of boostrap iterations performed, when computing the SPS estimator, when using the JIVE as reference estimator. This option is only relevant, when JIVE has been selected as the reference estimator. These iterations are used to compute the various components entering in the calculation of the SPS estimator. |

See documentaion for the sps.est function. Users should use the sps.est function, instead.

`list` |
The first term (est) is a vector of estimates for the coefficients of interest, and the second term (alpha) representing the estimate of the contribution of the OLS to the combined SPS estimator. |

Cedric E. Ginestet <cedric.ginestet@kcl.ac.uk>

Judge, G.G. and Mittelhammer, R.C. (2004). A semiparametric basis for combining esti- mation problems under quadratic loss. Journal of the American Statistical Association, 99(466), 479–487.

Judge, G.G. and Mittelhammer, R.C. (2012a). An information theoretic approach to econo- metrics. Cambridge University Press.

Judge, G. and Mittelhammer, R. (2012b). A risk superior semiparametric estimator for over-identified linear models. Advances in Econometrics, 237–255.

Judge, G. and Mittelhammer, R. (2013). A minimum mean squared error semiparametric combining estimator. Advances in Econometrics, 55–85.

Mittelhammer, R.C. and Judge, G.G. (2005). Combining estimators to improve structural model estimation and inference under quadratic loss. Journal of econometrics, 128(1), 1–29.

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