Econometrics

Panel Data Models

All of the linear and nonlinear models may be analyzed with special forms of panel data, including:

• Fixed and random effects
• Multilevel random effects
• Latent class models
• Random parameters (mixed) models
• Unbalanced panels for all models
• Unlimited panel data set size
• Arellano/Bond DPD with many variations
• IV and GMM estimators

Model Estimation and Analysis

Over 100 model formulations for continuous, discrete, limited and censored dependent variables are provided, including:

• Linear and nonlinear regression
• Robust estimation
• Binary choice
• Ordered choice models
• Unordered multinomial choice
• Censoring and truncation
• Sample selection models
• Count data
• Loglinear models
• Stochastic frontier and DEA
• Survival analysis
• Time series models
• Panel data models

Data Description and Graphics

• Descriptive statistics for cross sections and panels
• Tables of means and quantiles
• Time series
• Graphics tools
• Discriminant analysis

Count Data

The widest range of specifications for count data of any package is provided, including several newly developed models:

• Poisson and negative binomial models
• New specifications for NB models
• Gamma, generalized Poisson, Polya
• Aeppli
• Zero inflation and hurdle
• Fixed and random effects
• Latent class

Statistical Analysis

Programming language allows extension of supported estimators:

• Nonlinear estimation
• Delta method for functions of parameters
• Simulation: Krinsky and Robb
• Testing and restrictions
• Post estimation analysis
• Predictions
• Marginal effects

Data Environments

Nearly every model may be extended to a variety of frameworks including:

• Data transformations
• Cross section
• Panel data
• Time series manipulation

Programming and Numerical Analysis

Programming language including matrix and data manipulation commands is provided for building new estimators:

• MAXIMIZE/MINIMIZE for user supplied functions
• Matrix programming with LIMDEP
• Scientific calculator
• Numerical analysis tools, integration and differentiation
• Simulation based estimation
• Program Gibbs samplers

Frontier and Efficiency Analysis

All forms of the stochastic frontier model are provided:

• Fixed and random effects
• Battese and Coelli
• Heteroscedasticity
• Technical inefficiency estimation
• This is the only package with both SFA and DEA.

Discrete Choice Models in LIMDEP

Discrete choice estimators for binary, multinomial, ordered, count and multivariate discrete data are provided:

• Binary choice - dozens of specifications
• Ordered choice
• Hierarchical ordered choice
• Panel data
• Multinomial logit
• Count data models

Modeling Individual Choice with NLOGIT

NLOGIT contains all of LIMDEP plus numerous extensions of the multinomial choice models that do not appear in LIMDEP, including:

• Nested logit model
• Generalized nested logit model
• Multinomial probit model
• Mixed (random parameters) logit model
• Latent class model
• Error components (RE) logit model
• Dynamic random effects MNL model
• General utility specifications
• Partial effects and elasticities
• Model simulation

(These features do not appear in LIMDEP.)

Time Series Analysis

A range of estimators for time series are provides including:

• ARMAX models
• GARCH and GARCH-in-mean models
• Spectral density estimation
• ACF and PACF
• Phillips-Perron tests
• Newey-West estimator

Accuracy

Extremely accurate computational methods are employed throughout. High marks are earned on all National Institute of Standards and Technology test problems, including:

• Descriptive statistics
• Analysis of variance
• Linear regression
• Nonlinear least squares

Post Estimation

Extensive tools for post estimation enable manipulation of model results along with other statistics and procedures.

Data Management

Data management tools are provided for input of data or internal generation with the random number generators, including:

• Data transformations
• Sampling and bootstrapping
• Bootstrap cross section observations or panel groups
• Weighted data
• Random number generation
• Cluster sampling and stratification

LIMDEP 9.0 is a major expansion of our premier software for cross section, panel and time series data analysis. Version 9.0 features numerous new estimation programs, a long list of enhancements to its user interface, additions to data manipulation commands, and improvements in the internal workings of the mathematical parts of the program. The new documentation, with over 2,500 pages, contains full reference guides for the program, background econometrics, and sample applications.

New Models

• Probit model with endogenous right hand side variable
• Models for count data
  • Polya-Aeppli and generalized Poisson models for count data
  • New form of the negative binomial model for count data
  • Negative binomial model with sample selection
• Dynamic probit model for panel data
• Numerous new forms of the stochastic frontier model
  • Several forms of the Battese/Coelli model
  • Stochastic frontier model with sample selection
  • Data envelopment analysis for efficiency analysis
• Cox model with time varying covariates
• Parametric survival models with sample selection
• Ordered choice models
  • Generalized ordered probit
  • Hierarchical ordered probit
  • Zero inflated ordered probit
  • Bivariate ordered probit
  • Ordered probit with sample selection
• Propensity score matching methods
• Quantile regression model
• Nested random effects model
• Binomial, power, beta, Rayleigh and geometric loglinear models
• Discriminant and classification analysis

Panel Data Versions of Nearly All Models

A major theme of this revision is panel data. LIMDEP now offers panel data estimators for nearly all the models that are supported by the program. These estimators represent significant innovations in the capabilities of econometric software. To our knowledge, they do not exist in any other program. The estimators are of three broad classes:

• True fixed effects: You can fit fixed effects models with up to 50,000 dummy variable coefficients, to almost all of LIMDEP's models. (In a custom extension of this method, we used LIMDEP's algorithm to fit a probit model with over 150,000 dummy variable coefficients.) This is a true fixed effects estimator in which the dummy variable coefficients are actually computed, not swept out of the model. (In the process, we (in collaboration with Paul Allison) have remedied a major shortcoming in the longstanding negative binomial fixed effects model proposed by Hausman, Hall and Griliches in use since 1984.)
• Random parameters: Full random coefficients have been proposed at several places in the literature, but almost exclusively in the setting of the linear regression model, Poisson model, and binary logit model. This version of LIMDEP extends the maximum simulated likelihood technique for random parameters models to all the models supported by LIMDEP, and several new ones that have not appeared previously, such as the sample selection model and a suite of 10 new 'loglinear' models.
• Latent classes: Once again, this is a model that has appeared in the literature virtually exclusively in the Poisson regression model. We have extended it to over 30 different model forms, including probit, logit, tobit, truncation, Poisson, negative binomial, stochastic frontier, and so on.

Some of these have been extended to multiple equation settings as well, including forms of the bivariate probit model and sample selection models.

We have also extended the linear regression model with panel data in several directions, including the addition of the Hausman and Taylor estimator for random effects and the Arellano, Bond, and Bover GMM estimator for dynamic panel data models. We have also built a random coefficients estimator for the linear regression model which does not require every group to have more observations than there are variables in the model. The program panel data treatment of the linear model also adds a number of features which will make estimation much easier.

Extensions of Existing Models and Techniques

• Random effects multinomial logit model for panel data
• Multilevel and nested multilevel random effects models
• Extensions of several models for latent heterogeneity and heteroscedasticity

Extensions of Estimation and Analysis Methods

• Variance corrections in all models for clustered and complex survey data
• Jackknife estimator for asymptotic variances
• Linear constraints in general maximum likelihood estimation
• Generalized maximum entropy estimation for multinomial logit models
• Simulation analysis for binary choice models
• Extensions of plotting and histogram programs
• Export functions for model results
• Many extensions of the programming tools for writing procedures and new estimators
• Krinsky and Robb estimators for standard errors for nonlinear functions

One full set of hard copy manuals is included with each single user licenser order and with each site license order. The LIMDEP 9.0 documentation consists of three guides: the LIMDEP 9.0 Reference Guide and the LIMDEP 9.0 Econometric Modeling Guides, Volumes 1 and 2. The NLOGIT 4.0 documentation consists of four guides: the three LIMDEP guides and the NLOGIT Reference Guide.

Extra manual sets may be purchased in conjunction with a multi-user site license.

LIMDEP 9.0 Documentation

The LIMDEP 9.0 set of manuals, with over 2,500 pages, contains full reference guides for the program, background econometrics, and sample applications. The LIMDEP documentation consists of two parts:

LIMDEP 9.0 Reference Guide

The LIMDEP 9.0 Reference Guide provides all instructions for operating the program, including installation, invocation, and most of the basic setup operations that precede model estimation. These operations include reading and transforming data and setting the sample. This manual also describes the optimization procedures, how to use the matrix algebra package and scalar scientific calculator as stand alone tools and as part of LIMDEP programs, what sorts of results are produced by the program, and some of the common features of the model estimation programs, such as how to do post estimation analysis of model results. Two other components of the Reference Guide are a summary of how the model commands are documented in the Econometric Modeling Guide and a complete listing of the program diagnostics.

LIMDEP 9.0 Econometric Modeling Guide, Volume 1 and Volume 2

The 38 chapters of this guide are arranged in two volumes. These provide the econometric background, LIMDEP commands, and examples with data, commands and results. Topics are arranged by modeling framework, not by program command. There are chapters on

• Descriptive statistics
• Linear regression
• Panel data analysis
• Heteroscedasticity
• Binary choice models
• Models for count data
• Censored and truncated data
• Survival models

and many others. Each model fit by the program is fully documented. The full set of formulas for all computations are shown in this manual with the full mathematical documentation of the models. Additional chapters in this guide show how to do numerical analysis, how to program your own estimators, and provide a full listing of diagnostics.

NLOGIT 4.0 Documentation

NLOGIT 4.0 includes all of LIMDEP 9.0. The complete NLOGIT 4.0 set of manuals, with over 3,000 pages, consists of the three LIMDEP 9.0 guides plus a separate NLOGIT 4.0 Reference Guide.

NLOGIT 4.0 Reference Guide

With over 500 pages, the NLOGIT 4.0 Reference Guide includes complete instructions for specifying and estimating discrete choice models with NLOGIT. To provide a total picture of the use of NLOGIT in analyzing discrete choice data, the NLOGIT Reference Guide incorporates documentation of the foundational discrete choice models described in detail in the LIMDEP Econometric Modeling Guide, including binary choice and ordered choice models. Second, we have included extensive explanatory text and dozens of examples, with applications, for every technique and model presented.

Specifications

• Poisson regression
• Negative binomial: NB1, NB2, NB-P
• Negative binomial with heterogeneity
• Gamma model for over- or underdispersion
• Generalized Poisson and Polya-Aeppli
• Latent heterogeneity - normal or log-gamma
• Hurdle model
• Underreporting
• Box-Cox functional form
• Zero inflation models
  • ZIP(tau) and ZINB(tau)
  • Covariates ZIP and ZINB
• Zero inflation with endogenous regime
• Sample selection
  • Sample selection models, Poisson and negative binomial
  • Incidental truncation
  • Heterogeneity and underreporting
  • Endogenous underreporting

Data features

• Censoring
• Truncation
• Unobserved heterogeneity

Estimation and inference

• Marginal effects and average partial effects
• Fit measures (Pearson and deviance)
• Predictions
• Restrictions and hypothesis - Wald, LR, LM tests
• Overdispersion tests
• Robust covariance matrices: cluster, sandwich
• Tests for hurdle effects

Panel data models

• Fixed effects
  • Conditional
  • Unconditional: up to 50,000 dummy variable coefficients
  • Marginal effects
  • Predictions
• Random effects
  • Log-gamma
  • Lognormal
• Random parameters
• Latent class models
• Latent class with zero inflation
• Split population and latent class models

• 

Model frameworks for production or cost

• Normal-half normal
• Normal-truncated normal
• Normal-exponential
• Normal-gamma

Mean of the one sided (inefficiency) component

• E[U] = zero mean, the standard case
• E[U] = nonzero constant mean
• E[U] = a'z

Variance of the one sided (inefficiency) component

• Var[U] = homoscedastic
• Var[U] = exp(c'z) (heteroscedastic)

Variance of the firm specific (symmetric) component

• Var[v] = homoscedastic
• Var[v] = exp(d'w) (heteroscedastic)

Doubly heteroscedastic

Estimates of inefficiency measures with all formulations

Panel data formulations

• Random effects in specifications
• Fixed effects
  • Fixed effect in production (cost) function
  • Truncation model with fixed effects
  • Fixed effects in mean of one sided component
  • Fixed effects in variance of one sided component
• Random parameters
• Latent class
• Battese and Coelli panel data models

Frontier and Efficiency Analysis: Data Envelopment Analysis

Analysis in parallel with stochastic frontier estimation and analysis (the only package available that has both of these methods in one program)

• Input and output oriented inefficiency - retained in the data set for further analysis
• Constant, increasing or nonincreasing returns to scale
• Economic and allocative inefficiency
• Bootstrapped confidence intervals for efficiency scores
• Malmquist total factor productivity indexes for panel data
• Listing of 'peer' firms with results

LIMDEP is the only program that provides tools for both stochastic frontier analysis and data envelopment analysis.

• 

Model Estimation and Analysis: Ordered Choice Models

Ordered choice models include the following:

• Ordered probit, logit, Gompertz, complementary log log
• Marginal effects
  • Standard errors computed by the delta method
  • Effects for binary variables
• Restrictions
  • Wald, LM, LR tests
  • Linear restrictions
• Predictions
• Heteroscedasticity
  • LR and LM test
  • Maximum likelihood estimation
• Censored data
• Stratification
• Choice based sampling
• Robust covariance matrix, sandwich, cluster
• Sample selection model
  • Maximum likelihood ordered probit with selection
  • Ordered probit selection criterion
• Panel data
  • Fixed effects
  • Random effects
  • Random parameters
  • Latent class
• Discrete hazard model, ordered extreme value
• Hierarchical ordered probit - thresholds are functions of variables
• Zero inflated ordered probit - correlated with main equation
• Bivariate ordered probit

• 

LIMDEP AND NLOGIT are written for use on Windows driven microcomputers. LIMDEP and NLOGIT are generally compatible with Windows 95 and later Windows operating systems. For Windows Vista, the Help systems used by LIMDEP and NLOGIT are no longer installed as standard in Windows Vista, and Microsoft has released an update.

The programs require 16 megabytes of memory and occupy approximately 10 megabytes on the local hard disk drive.

Program Limits at a Glance

we are often asked about LIMDEP and NLOGIT's specific internal limits. The following limits are relevant to the most common applications.

Active Data Set
Variables	900
Observations	3,000,000+
Total cells in data area	limited by memory
Namelists	25
Variables in namelist	100

Command Entry
Characters in one command	2500
Characters in a stored procedure	2500
Commands in a stored procedure	10
Stored procedures	50

Model Size, General & Specific
Number of parameters	150
Equations for SURE & 3SLS	30
Equations for WALD, NLSURE, GMM	20

Panel Data Models
Groups in fixed & random effects	Linear models: unlimited Nonlinear models: 50,000
Regressors in fixed & random effects	150
Groups x Regressors	unlimited
Intervals in TVCs for survival	50
Periods in fixed effects (Chamberlain) logit	100
Groups in time series/cross section	100

NLOGIT
Number of alternatives	100
Branches in tree	25
Limbs in tree	10
Trunks in tree	5
Number of attributes & constants	125

Matrix & Scalar Algebra
Number of active matrices	100
Number of active named scalars	50
Size of a matrix	50,000 cells
Rows in data matrix	unlimited

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