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Self-selection or sample selection models are applied when the individuals in the sample are not randomly chosen from the population from which one would like to draw inferences. In the prototypical self-selection model, interest centers on estimating the parameters of a regression equation (often labeled ``outcome equation'') from observations on individuals who self-selected into the sample on the basis of a criterion that is correlated with the dependent variable of the outcome equation.

To illustrate, suppose we are interested in estimating the expected income of a randomly chosen individual if she were working as a lawyer. Computing the average income of those who actually work as lawyers is likely to be an upward biased estimate since those observed as lawyers probably chose their profession because they are talented for this line of work and expect to earn a relatively high income.

The solution to the self-selection problem proposed by Heckman (1979) is to propose and estimate a model of the self-selection decision. That is, Heckman's solution adds a ``decision equation'' to the outcome equation. Formally, the model consists of the following two equations:

The self-selection problem arises if and are correlated, i.e. the (unobservable part of the) decision to select into the sample is correlated with the (unobservable part of the) outcome of interest.

12.3.1 Parametric Model

In Heckman (1979) 's classical solution to the problem it is assumed that and are jointly normally distributed:

We illustrate heckman with simulated data where the error terms in the decision and outcome equations are strongly correlated:

The distributional assumption ( 12.18 ) of the parametric self-selection model is, more than anything else, made for convenience. If, however, ( 12.18 ) is violated then the heckman estimator is not consistent. Hence, there is ample reason to develop consistent estimators for self-selection models with weaker distributional assumptions.

Powell (1987) considers a semiparametric self-selection model that combines the two-equation structure of ( 12.16 ) with the following weak assumption about the joint distribution of the error terms:

Note that for any two observations and with but we can difference out the unknown function by subtracting the regression functions for and

In ( 12.21 ), we tacitly assume that we have already obtained an estimate of Under assumption ( 12.20 ), we get a single index model for the decision equation in place of the Probit model ( 12.19 ) in the parametric case:

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JavaScript port of Asciidoctor produced by Opal, a Ruby to JavaScript cross compiler

License: MIT


Created: May 19, 2013 08:46

Last updated: March 31, 2015 02:01

Last pushed: March 30, 2015 13:02

Size: 6.9 MB




Open issues:

This project uses to transcompile Asciidoctor —a modern implementation of AsciiDoc—from Ruby to JavaScript to produce , bringing AsciiDoc to the browser!


Asciidoctor.js is direct port of Asciidoctor from Ruby to JavaScript using , a Ruby-to-JavaScript transcompiler. It consists of a Rake build script that executes the Opal compiler on the Asciidoctor source code to produce the asciidoctor.js script. A Grunt build is used to assemble and prepare the distribution files, using the Rake build underneath.

Opal parses the Ruby code and any required libraries, then rewrites the code into JavaScript under the Opal namespace. The resulting JavaScript can be executed within any JavaScript runtime environment (such as a browser).

To interact with the generated code, you either invoke the JavaScript APIs directly, or you can invoke native JavaScript objects from within the Ruby code prior to compilation.

To build , you’ll need some tools:

and npm

Rake and Bundle

Start by cloning the source from GitHub:

Next, switch to the directory and run npm’s command followed by Bower’s command:

You’re now ready to build asciidoctor.js.

To build asciidoctor.js, simple run the Grunt task from the root of the project:

This command produces some files in the directory:

(includes core and extensions)


(no extensions API)


(extensions API only)


(docbook backends : docbook45 and docbook5)


(core, extension and Opal. Docbook isn’t the main target of webapp, for this reason we choose to keep it separate)


dist/npm (to use with Npm)


(no extensions API, will automatically load docbook backends)

Each file has a and version.

You’ll see these scripts in action when you run the examples, described next.

To build the examples, simply run the Rake task from the root of the project:

This command produces another JavaScript file in the directory, . This script includes:

a string that contains an AsciiDoc source document