# GAUSS tscsFit Example

### Introduction

The following is an example of implementing the tscsFit procedure. This program provides estimates for the classic Grunfeld dataset [grunfeld.dat]. These data were originally found in PhD dissertation of Y. Grunfeld (University of Chicago, 1958). The data is a balanced dataset covering 10 firms [firm = 1, ..., 10] for 20 years (1935-1950) [ year = 1935, ..., 1954].

The program follows 2.6.1 from 'Econometric Analysis of Panel Data', Baltagi, 2005. It estimates the model

$$investment_{it} = a + B_{1}firmValue_{it} + B_{2}capitalStock_{it} + u_{it}$$ $$u_{it} = c_{i} + v_{it}$$

## Estimate the Model

This example uses the formula string syntax which requires no data loading prior to calling the procedure. This greatly simplifies the required code.

new;
cls;
library tsmt;

// Create file name with full path
dataset = getGAUSSHome \$+ "pkgs/tsmt/examples/grunfeld.dat";

// Call tscsFit
call tscsFit(dataset, "investment ~ firm_value + capital", "firm");

## Output

The printed results include the OLS dummy variable estimates (also known as the within or fixed effects estimates), the constrained pooled ols model, and the feasible gls error components model:

===============================================================================
tscsmt Version 3.0.0
===============================================================================
Data Set:  grunfeld.dat
-------------------------------------------------------------------------------

----------------------- OLS DUMMY VARIABLE RESULTS  ----------------------

---------------------------------
Dependent variable:  investment
---------------------------------

Observations          :  200
Number of Groups      :  10
Degrees of freedom    :  188
Residual SS           :  523478.147
Std error of est      :  52.768
Total SS (corrected)  :  2244352.274
F                     =  309.014      with 2,188 degrees of freedom
P-value               =  0.000

Variable          Coef.     Std. Coef.   Std. Error     t-Stat       P-Value
----------------------------------------------------------------------------
firm_value      0.110124     0.353129     0.011857     9.287901       0.000
capital         0.310065     0.679292     0.017355    17.866564       0.000

Group Number        Dummy Variable    Standard Error

1           -70.296717            49.707959
2           101.905814            24.938323
3          -235.571841            24.431616
4           -27.809295            14.077754
5          -114.616813            14.165433
6           -23.161295            12.668739
7           -66.553474            12.842973
8           -57.545657            13.993146
9           -87.222272            12.891893
10            -6.567844            11.826891

F-statistic for equality of dummy variables :
F(9, 188) = 49.1766        P-value:  0.0000

------------------- OLS ESTIMATE OF CONSTRAINED MODEL ---------------------

---------------------------------
Dependent variable:  investment
---------------------------------

Observations          :  200
Number of Groups      :  10
Degrees of freedom    :  197
R-squared             :  0.812
Rbar-squared          :  0.811
Residual SS           :  1755850.484
Std error of est      :  94.408
Total SS (corrected)  :  9359943.929
F                     =  426.576      with 3,197 degrees of freedom
P-value               =  0.000

Variable          Coef.     Std. Coef.   Std. Error     t-Stat       P-Value
----------------------------------------------------------------------------
CONSTANT      -42.714369          ---     9.511676    -4.490730       0.000
firm_value      0.115562     0.700416     0.005836    19.802589       0.000
capital         0.230678     0.320268     0.025476     9.054808       0.000

---------------------------------------------------------------------------
FULL, RESTRICTED, AND PARTIAL R-SQUARED TERMS--DUMMY VARIABLES ARE CONSTRAINED
-------------------------------------
TABLE OF R-SQUARED TERMS
-------------------------------------
R-squared--full model:        0.944
R-squared--constrained model: 0.812
Partial R-squared:            0.702
-------------------------------------

----------------------------------------------------------------------------
FULL, RESTRICTED, AND PARTIAL R-SQUARED TERMS--X VARIABLES ARE CONSTRAINED
-------------------------------------
TABLE OF R-SQUARED TERMS
-------------------------------------
R-squared--full model:        0.944
R-squared--constrained model: 0.760
Partial R-squared:            0.767
-------------------------------------

---------------------- GLS ERROR COMPONENTS RESULTS  ----------------------

---------------------------------
Dependent variable:  investment
---------------------------------

Observations          :  200
Number of Groups      :  10
Degrees of freedom    :  197
Residual SS           :  548904.055
Std error of est      :  52.786
Total SS (corrected)  :  2381390.625
F                     =  229.041      with 3,197 degrees of freedom
P-value               =  0.000
Std. errors of error terms:
Individual constant terms: 84.201
White noise error        : 52.768

Variable          Coef.     Std. Coef.   Std. Error     t-Stat       P-Value
----------------------------------------------------------------------------
CONSTANT      -57.834415          ---    28.898935    -2.001265       0.047
firm_value      0.109781     0.384782     0.010493    10.462658       0.000
capital         0.308113     0.659550     0.017180    17.933910       0.000

Group Number        Random Components

1            -9.524296
2           157.891024
3          -172.895804
4            29.911980
5           -54.679009
6            34.346132
7            -7.897758
8             0.672638
9           -28.139350
10            50.314444

Lagrange Multiplier Test for Error Components Model

Null hypothesis:  Individual error components do not exist.

Chi-squared statistic (1): 798.3793
P-value: 0.0000

Hausman (1978) Chi-Squared Specification Test

Null hypothesis:  Error components model is the correct specification.

Chi-squared statistic (2) = 2.3304
P-value = 0.3119    

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