KLEIN.RPF

KLEIN.RPF demonstrates estimation by two-stage least squares using the equations of Klein's Model I. See, for instance, Greene(2012), p 332 for a description of the model. This is a small (U.S.) macro model with three structural equations and three identities. The example file HANSEN.RPF also uses this model to demonstrate specification testing in instrumental variables models and GRN7P333.RPF in the Greene(2012) textbook examples estimates the model using a wide variety of other methods, such as three-stage least squares and Full Information Maximum Likelihood. (The SIMULEST.RPF example applies those to a different model).

The endogenous explanatory variables are (current) PROFIT, PRIVWAGE and PROD (production). The exogenous and pre-determined variables from the model are CONSTANT, TREND, the policy variables GOVTWAGE, GOVTEXP and TAXES and lags of CAPITAL, PROD and PROFIT. The instruments (the full list of exogenous and pre-determined variables) are listed on an INSTRUMENTS instruction. Note that you are required to include CONSTANT if it's appropriate (which it usually is).

instruments constant trend govtwage taxes govtexp $

capital{1} prod{1} profit{1}

The equations themselves are estimated by two-stage least squares using the LINREG instruction with the INSTRUMENTS option. Note that you do not need to do "two-stage" estimates yourself—all the required calculations are done by the LINREG.

linreg(inst) cons

# constant profit{0 1} wagebill

linreg(inst) invst

# constant profit{0 1} capital{1}

linreg(inst) privwage

# constant prod{0 1} trend

Full Program

calendar(a) 1920
open data klein.prn
data(format=prn,org=obs) 1920:1 1941:1
table
set wagebill = privwage + govtwage

set capital = klagged1+invst
set trend    = year-1920

instruments constant trend govtwage taxes govtexp $
             capital{1} prod{1} profit{1}
linreg(inst) cons
# constant profit{0 1}   wagebill
linreg(inst) invst
# constant profit{0 1}   capital{1}
linreg(inst) privwage
# constant prod{0 1} trend

Output

This is the output from the TABLE instruction, which shows basic statistics on the variables.

Series Obs Mean Std Error Minimum Maximum

YEAR 22 1930.5000000 6.4935866 1920.0000000 1941.0000000

CONS 22 53.3500000 7.3477402 39.8000000 69.7000000

PROFIT 22 16.7000000 4.2142615 7.0000000 23.5000000

PRIVWAGE 22 36.0181818 6.3601914 25.5000000 53.3000000

INVST 22 1.3318182 3.4797901 -6.2000000 5.6000000

KLAGGED1 22 199.5681818 10.6113321 180.1000000 216.7000000

PROD 22 59.3681818 10.8535878 44.3000000 88.4000000

GOVTWAGE 22 4.9863636 2.0083861 2.2000000 8.5000000

GOVTEXP 22 4.6863636 2.3807353 2.4000000 13.8000000

TAXES 22 6.6500000 2.1113638 3.4000000 11.6000000

These are the output from the three LINREG instructions for the three structural equations. These show summary statistics which are appropriate for two-stage least squares. In particular, there are no $R^2 $ (which are only appropriate for least squares estimators) and there is a J-specification test.

Linear Regression - Estimation by Instrumental Variables

Dependent Variable CONS

Annual Data From 1921:01 To 1941:01

Usable Observations 21

Degrees of Freedom 17

Mean of Dependent Variable 53.995238095

Std Error of Dependent Variable 6.860865557

Standard Error of Estimate 1.135658590

Sum of Squared Residuals 21.925247348

J-Specification(4) 7.1007

Significance Level of J 0.1306592

Durbin-Watson Statistic 1.4851

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. Constant 16.554755765 1.467978697 11.27725 0.00000000

2. PROFIT 0.017302212 0.131204584 0.13187 0.89663371

3. PROFIT{1} 0.216234041 0.119221677 1.81371 0.08741342

4. WAGEBILL 0.810182698 0.044735057 18.11069 0.00000000

Linear Regression - Estimation by Instrumental Variables

Dependent Variable INVST

Annual Data From 1921:01 To 1941:01

Usable Observations 21

Degrees of Freedom 17

Mean of Dependent Variable 1.2666666667

Std Error of Dependent Variable 3.5519478224

Standard Error of Estimate 1.3071490861

Sum of Squared Residuals 29.046858465

J-Specification(4) 1.4693

Significance Level of J 0.8320728

Durbin-Watson Statistic 2.0853

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. Constant 20.27820894 8.38324890 2.41890 0.02707053

2. PROFIT 0.15022182 0.19253359 0.78024 0.44597984

3. PROFIT{1} 0.61594358 0.18092585 3.40440 0.00337550

4. CAPITAL{1} -0.15778764 0.04015207 -3.92975 0.00107972

Linear Regression - Estimation by Instrumental Variables

Dependent Variable PRIVWAGE

Annual Data From 1921:01 To 1941:01

Usable Observations 21

Degrees of Freedom 17

Mean of Dependent Variable 36.361904762

Std Error of Dependent Variable 6.304401335

Standard Error of Estimate 0.767155325

Sum of Squared Residuals 10.004963969

J-Specification(4) 10.1152

Significance Level of J 0.0385316

Durbin-Watson Statistic 1.9634

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. Constant 0.0659443264 1.1533129884 0.05718 0.95506996

2. PROD 0.4388590651 0.0396026616 11.08155 0.00000000

3. PROD{1} 0.1466738215 0.0431639485 3.39806 0.00342209

4. TREND 0.1303956872 0.0323883889 4.02600 0.00087642