R : Copyright 2005, The R Foundation for Statistical Computing
Version 2.1.1  (2005-06-20), ISBN 3-900051-07-0

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> ### * <HEADER>
> ###
> attach(NULL, name = "CheckExEnv")
> assign(".CheckExEnv", as.environment(2), pos = length(search())) # base
> ## add some hooks to label plot pages for base and grid graphics
> setHook("plot.new", ".newplot.hook")
> setHook("persp", ".newplot.hook")
> setHook("grid.newpage", ".gridplot.hook")
> 
> assign("cleanEx",
+        function(env = .GlobalEnv) {
+ 	   rm(list = ls(envir = env, all.names = TRUE), envir = env)
+            RNGkind("default", "default")
+ 	   set.seed(1)
+    	   options(warn = 1)
+ 	   delayedAssign("T", stop("T used instead of TRUE"),
+ 		  assign.env = .CheckExEnv)
+ 	   delayedAssign("F", stop("F used instead of FALSE"),
+ 		  assign.env = .CheckExEnv)
+ 	   sch <- search()
+ 	   newitems <- sch[! sch %in% .oldSearch]
+ 	   for(item in rev(newitems))
+                eval(substitute(detach(item), list(item=item)))
+ 	   missitems <- .oldSearch[! .oldSearch %in% sch]
+ 	   if(length(missitems))
+ 	       warning("items ", paste(missitems, collapse=", "),
+ 		       " have been removed from the search path")
+        },
+        env = .CheckExEnv)
> assign("..nameEx", "__{must remake R-ex/*.R}__", env = .CheckExEnv) # for now
> assign("ptime", proc.time(), env = .CheckExEnv)
> grDevices::postscript("systemfit-Examples.ps")
> assign("par.postscript", graphics::par(no.readonly = TRUE), env = .CheckExEnv)
> options(contrasts = c(unordered = "contr.treatment", ordered = "contr.poly"))
> options(warn = 1)    
> library('systemfit')
> 
> assign(".oldSearch", search(), env = .CheckExEnv)
> assign(".oldNS", loadedNamespaces(), env = .CheckExEnv)
> cleanEx(); ..nameEx <- "coef.systemfit"
> 
> ### * coef.systemfit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: coef.systemfit
> ### Title: Coefficients of systemfit object
> ### Aliases: coef.systemfit
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Not run: library( systemfit )
> 
> data( kmenta )
> attach( kmenta )
> demand <- q ~ p + d
> supply <- q ~ p + f + a
> labels <- list( "demand", "supply" )
> system <- list( demand, supply )
> 
> ## perform OLS on each of the equations in the system
> fitols <- systemfit( "OLS", system, labels )
> 
> ## print the coefficients
> coef( fitols )
eq 1 (Intercept)           eq 1 p           eq 1 d eq 2 (Intercept) 
      99.8954229       -0.3162988        0.3346356       58.2754312 
          eq 2 p           eq 2 f           eq 2 a 
       0.1603666        0.2481333        0.2483023 
> 
> 
> 
> cleanEx(); ..nameEx <- "coef.systemfit.equation"
> 
> ### * coef.systemfit.equation
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: coef.systemfit.equation
> ### Title: Coefficients of systemfit equation
> ### Aliases: coef.systemfit.equation
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Not run: library( systemfit )
> 
> data( kmenta )
> attach( kmenta )
> demand <- q ~ p + d
> supply <- q ~ p + f + a
> labels <- list( "demand", "supply" )
> system <- list( demand, supply )
> 
> ## perform OLS on each of the equations in the system
> fitols <- systemfit( "OLS", system, labels )
> 
> ## print the coefficients of the first equation
> coef( fitols$eq[[1]] )
(Intercept)           p           d 
 99.8954229  -0.3162988   0.3346356 
> 
> ## print the coefficients of the second equation
> coef( fitols$eq[[2]] )
(Intercept)           p           f           a 
 58.2754312   0.1603666   0.2481333   0.2483023 
> 
> 
> 
> cleanEx(); ..nameEx <- "confint.systemfit"
> 
> ### * confint.systemfit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: confint.systemfit
> ### Title: Confidence intervals of coefficients
> ### Aliases: confint.systemfit
> ### Keywords: models regression
> 
> ### ** Examples
> 
> ## Not run: library( systemfit )
> 
> data( kmenta )
> attach( kmenta )
> demand <- q ~ p + d
> supply <- q ~ p + f + a
> labels <- list( "demand", "supply" )
> system <- list( demand, supply )
> 
> ## perform OLS on each of the equations in the system
> fitols <- systemfit( "OLS", system, labels )
> 
> ## print the confidence interval of the coefficients
> confint( fitols )
                  2.5 %  97.5 %
eq 1 (Intercept) 84.031 115.760
eq 1 p           -0.508  -0.125
eq 1 d            0.239   0.430
eq 2 (Intercept) 33.975  82.576
eq 2 p           -0.041   0.362
eq 2 f            0.150   0.346
eq 2 a            0.042   0.455
> 
> 
> 
> cleanEx(); ..nameEx <- "confint.systemfit.equation"
> 
> ### * confint.systemfit.equation
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: confint.systemfit.equation
> ### Title: Confidence intervals of coefficients
> ### Aliases: confint.systemfit.equation
> ### Keywords: models regression
> 
> ### ** Examples
> 
> ## Not run: library( systemfit )
> 
> data( kmenta )
> attach( kmenta )
> demand <- q ~ p + d
> supply <- q ~ p + f + a
> labels <- list( "demand", "supply" )
> system <- list( demand, supply )
> 
> ## perform OLS on each of the equations in the system
> fitols <- systemfit( "OLS", system, labels )
> 
> ## print the confidence interval of the coefficients of the first equation
> confint( fitols$eq[[1]] )
             2.5 %  97.5 %
(Intercept) 84.031 115.760
p           -0.508  -0.125
d            0.239   0.430
> 
> ## print the confidence interval of the coefficients of the second equation
> confint( fitols$eq[[2]] )
             2.5 % 97.5 %
(Intercept) 33.975 82.576
p           -0.041  0.362
f            0.150  0.346
a            0.042  0.455
> 
> 
> 
> cleanEx(); ..nameEx <- "correlation.systemfit"
> 
> ### * correlation.systemfit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: correlation.systemfit
> ### Title: Correlation between Predictions from Equation i and j
> ### Aliases: correlation.systemfit
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Not run: library( systemfit )
> 
> data( kmenta )
> attach( kmenta )
> demand <- q ~ p + d
> supply <- q ~ p + f + a
> inst <- ~ d + f + a
> labels <- list( "demand", "supply" )
> system <- list( demand, supply )
> 
> ## perform 2SLS on each of the equations in the system
> fit2sls <- systemfit( "2SLS", system, labels, inst)
> print( fit2sls )

systemfit results 
method: 2SLS 

        N DF     SSR     MSE    RMSE       R2   Adj R2
demand 20 17 65.7291 3.86642 1.96632 0.754847 0.726005
supply 20 16 96.6332 6.03958 2.45756 0.639582 0.572004

The covariance matrix of the residuals
        demand  supply
demand 3.86642 4.35744
supply 4.35744 6.03958

The correlations of the residuals
         demand   supply
demand 1.000000 0.901724
supply 0.901724 1.000000

The determinant of the residual covariance matrix: 4.36424
OLS R-squared value of the system: 0.697214

2SLS estimates for demand  (equation 1 )
Model Formula: q ~ p + d
Instruments: ~d + f + a

             Estimate Std. Error   t value Pr(>|t|)    
(Intercept) 94.633304   7.920838 11.947385        0 ***
p           -0.243557   0.096484 -2.524313 0.021832   *
d            0.313992   0.046944  6.688695    4e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.966321 on 17 degrees of freedom
Number of observations: 20 Degrees of Freedom: 17 
SSR: 65.729088 MSE: 3.866417 Root MSE: 1.966321 
Multiple R-Squared: 0.754847 Adjusted R-Squared: 0.726005 


2SLS estimates for supply  (equation 2 )
Model Formula: q ~ p + f + a
Instruments: ~d + f + a

             Estimate Std. Error  t value Pr(>|t|)    
(Intercept) 49.532442  12.010526 4.124086 0.000795 ***
p            0.240076   0.099934 2.402347 0.028785   *
f            0.255606    0.04725 5.409637  5.8e-05 ***
a            0.252924   0.099655 2.537996 0.021929   *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 2.457555 on 16 degrees of freedom
Number of observations: 20 Degrees of Freedom: 16 
SSR: 96.633244 MSE: 6.039578 Root MSE: 2.457555 
Multiple R-Squared: 0.639582 Adjusted R-Squared: 0.572004 

> print( fit2sls$rcov )
         [,1]     [,2]
[1,] 3.866417 4.357440
[2,] 4.357440 6.039578
> 
> ## perform the 3SLS
> fit3sls <- systemfit( "3SLS", system, labels, inst )
> print( fit3sls )

systemfit results 
method: 3SLS 

        N DF      SSR     MSE    RMSE       R2   Adj R2
demand 20 17  65.7291 3.86642 1.96632 0.754847 0.726005
supply 20 16 107.9138 6.74461 2.59704 0.597508 0.522041

The covariance matrix of the residuals used for estimation
        demand  supply
demand 3.86642 4.35744
supply 4.35744 6.03958

The covariance matrix of the residuals
        demand  supply
demand 3.86642 5.00443
supply 5.00443 6.74461

The correlations of the residuals
        demand  supply
demand 1.00000 0.97999
supply 0.97999 1.00000

The determinant of the residual covariance matrix: 1.03320
OLS R-squared value of the system: 0.676177
McElroy's R-squared value for the system: 0.786468

3SLS estimates for demand  (equation 1 )
Model Formula: q ~ p + d
Instruments: ~d + f + a

             Estimate Std. Error   t value Pr(>|t|)    
(Intercept) 94.633304   7.920838 11.947385        0 ***
p           -0.243557   0.096484 -2.524313 0.021832   *
d            0.313992   0.046944  6.688695    4e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.966321 on 17 degrees of freedom
Number of observations: 20 Degrees of Freedom: 17 
SSR: 65.729088 MSE: 3.866417 Root MSE: 1.966321 
Multiple R-Squared: 0.754847 Adjusted R-Squared: 0.726005 


3SLS estimates for supply  (equation 2 )
Model Formula: q ~ p + f + a
Instruments: ~d + f + a

             Estimate Std. Error  t value Pr(>|t|)    
(Intercept) 52.197204  11.893372 4.388764 0.000458 ***
p            0.228589   0.099673 2.293388 0.035706   *
f            0.228158   0.043994 5.186139    9e-05 ***
a            0.361138   0.072889 4.954608 0.000143 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 2.597039 on 16 degrees of freedom
Number of observations: 20 Degrees of Freedom: 16 
SSR: 107.913821 MSE: 6.744614 Root MSE: 2.597039 
Multiple R-Squared: 0.597508 Adjusted R-Squared: 0.522041 

> print( "covariance of residuals used for estimation (from 2sls)" )
[1] "covariance of residuals used for estimation (from 2sls)"
> print( fit3sls$rcovest )
         [,1]     [,2]
[1,] 3.866417 4.357440
[2,] 4.357440 6.039578
> print( "covariance of residuals" )
[1] "covariance of residuals"
> print( fit3sls$rcov )
         [,1]     [,2]
[1,] 3.866417 5.004427
[2,] 5.004427 6.744614
> 
> ## examine the correlation between the predicted values
> ## of suppy and demand by plotting the correlation over
> ## the value of q
> r12 <- correlation.systemfit( fit3sls, 1, 2 )
> plot( q, r12, main="correlation between predictions from supply and demand" )
> 
> 
> 
> cleanEx(); ..nameEx <- "fitted.systemfit"
> 
> ### * fitted.systemfit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: fitted.systemfit
> ### Title: Fitted values
> ### Aliases: fitted.systemfit
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Not run: library( systemfit )
> 
> data( kmenta )
> attach( kmenta )
> demand <- q ~ p + d
> supply <- q ~ p + f + a
> labels <- list( "demand", "supply" )
> system <- list( demand, supply )
> 
> ## perform OLS on each of the equations in the system
> fitols <- systemfit( "OLS", system, labels )
> 
> ## print the fitted values
> fitted( fitols )
            eq1       eq2
 [1,]  97.41053  98.92925
 [2,]  99.57728 100.08251
 [3,]  99.53832 100.19787
 [4,]  99.70152 100.36979
 [5,] 102.29446 102.72620
 [6,] 102.06849 102.56269
 [7,] 102.46276 102.42403
 [8,] 102.83273 104.30737
 [9,] 101.71547 102.94896
[10,] 100.78922 100.35059
[11,]  95.58388  96.03328
[12,]  94.37826  94.12138
[13,]  95.65592  95.59902
[14,]  98.97700  97.78688
[15,] 104.31033 102.63791
[16,] 103.92569 104.09052
[17,] 104.79508 103.78669
[18,] 101.93124 102.37790
[19,] 103.48498 102.11329
[20,] 106.53086 104.51788
> 
> 
> 
> cleanEx(); ..nameEx <- "fitted.systemfit.equation"
> 
> ### * fitted.systemfit.equation
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: fitted.systemfit.equation
> ### Title: Fitted values
> ### Aliases: fitted.systemfit.equation
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Not run: library( systemfit )
> 
> data( kmenta )
> attach( kmenta )
> demand <- q ~ p + d
> supply <- q ~ p + f + a
> labels <- list( "demand", "supply" )
> system <- list( demand, supply )
> 
> ## perform OLS on each of the equations in the system
> fitols <- systemfit( "OLS", system, labels )
> 
> ## print the fitted values of the first equation
> fitted( fitols$eq[[1]] )
        1         2         3         4         5         6         7         8 
 97.41053  99.57728  99.53832  99.70152 102.29446 102.06849 102.46276 102.83273 
        9        10        11        12        13        14        15        16 
101.71547 100.78922  95.58388  94.37826  95.65592  98.97700 104.31033 103.92569 
       17        18        19        20 
104.79508 101.93124 103.48498 106.53086 
> 
> ## print the fitted values of the second equation
> fitted( fitols$eq[[2]] )
        1         2         3         4         5         6         7         8 
 98.92925 100.08251 100.19787 100.36979 102.72620 102.56269 102.42403 104.30737 
        9        10        11        12        13        14        15        16 
102.94896 100.35059  96.03328  94.12138  95.59902  97.78688 102.63791 104.09052 
       17        18        19        20 
103.78669 102.37790 102.11329 104.51788 
> 
> 
> 
> cleanEx(); ..nameEx <- "hausman.systemfit"
> 
> ### * hausman.systemfit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: hausman.systemfit
> ### Title: Hausman's Test
> ### Aliases: hausman.systemfit
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Not run: library( systemfit )
> 
> data( kmenta )
> attach( kmenta )
> demand <- q ~ p + d
> supply <- q ~ p + f + a
> inst <- ~ d + f + a
> labels <- list( "demand", "supply" )
> system <- list( demand, supply )
> 
> ## perform the estimation and report the results for the whole system
> fit2sls <- systemfit( "2SLS", system, labels, inst)
> fit3sls <- systemfit( "3SLS", system, labels, inst)
> 
> ## perform the hausman test on the first equation
> h <- hausman.systemfit( fit2sls, fit3sls )
> pval <- 1 - pchisq( h, dim( fit3sls$bcov )[1] )
> 
> print( h )
         [,1]
[1,] 2.535651
> print( pval )
          [,1]
[1,] 0.9243886
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "kmenta"
> 
> ### * kmenta
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: kmenta
> ### Title: Partly Artificial Data on the U. S. Economy
> ### Aliases: kmenta
> ### Keywords: datasets datasets
> 
> ### ** Examples
> 
> data(kmenta)
> 
> 
> 
> cleanEx(); ..nameEx <- "lrtest.systemfit"
> 
> ### * lrtest.systemfit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: lrtest.systemfit
> ### Title: Likelihood Ratio test for Equation Systems
> ### Aliases: lrtest.systemfit
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Not run: library( systemfit )
> data( kmenta )
> demand <- q ~ p + d
> supply <- q ~ p + f + a
> labels <- list( "demand", "supply" )
> system <- list( demand, supply )
> 
> ## unconstrained SUR estimation
> fitsur <- systemfit("SUR", system, labels, data=kmenta )
> print( fitsur )

systemfit results 
method: SUR 

        N DF      SSR     MSE    RMSE       R2   Adj R2
demand 20 17  65.6829 3.86370 1.96563 0.755019 0.726198
supply 20 16 104.0584 6.50365 2.55023 0.611888 0.539117

The covariance matrix of the residuals used for estimation
        demand  supply
demand 3.72539 4.13696
supply 4.13696 5.78444

The covariance matrix of the residuals
        demand  supply
demand 3.86370 4.92431
supply 4.92431 6.50365

The correlations of the residuals
         demand   supply
demand 1.000000 0.982348
supply 0.982348 1.000000

The determinant of the residual covariance matrix: 0.879285
OLS R-squared value of the system: 0.683453
McElroy's R-squared value for the system: 0.788722

SUR estimates for demand  (equation 1 )
Model Formula: q ~ p + d

             Estimate Std. Error   t value Pr(>|t|)    
(Intercept) 99.332894   7.514452 13.218913        0 ***
p           -0.275486   0.088509 -3.112513 0.006332  **
d             0.29855   0.041945  7.117605    2e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.96563 on 17 degrees of freedom
Number of observations: 20 Degrees of Freedom: 17 
SSR: 65.682902 MSE: 3.8637 Root MSE: 1.96563 
Multiple R-Squared: 0.755019 Adjusted R-Squared: 0.726198 


SUR estimates for supply  (equation 2 )
Model Formula: q ~ p + f + a

             Estimate Std. Error  t value Pr(>|t|)    
(Intercept) 61.966166   11.08079 5.592215    4e-05 ***
p            0.146884   0.094435 1.555397 0.139408    
f            0.214004   0.039868 5.367761  6.3e-05 ***
a            0.339304   0.067911 4.996283 0.000132 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 2.550226 on 16 degrees of freedom
Number of observations: 20 Degrees of Freedom: 16 
SSR: 104.05843 MSE: 6.503652 Root MSE: 2.550226 
Multiple R-Squared: 0.611888 Adjusted R-Squared: 0.539117 

> 
> ## SUR estimation with 2 restrictions
> Rrestr <- matrix(0,2,7)
> qrestr <- matrix(0,2,1)
> Rrestr[1,3] <-  1
> Rrestr[1,7] <- -1
> Rrestr[2,2] <- -1
> Rrestr[2,5] <-  1
> qrestr[2,1] <-  0.5
> fitsur2 <- systemfit("SUR", system, labels, data=kmenta,
+                       R.restr=Rrestr, q.restr=qrestr )
> print( fitsur2 )

systemfit results 
method: SUR 

        N DF      SSR     MSE    RMSE       R2   Adj R2
demand 20 17  63.9868 3.76393 1.94008 0.761345 0.733268
supply 20 16 101.4731 6.34207 2.51835 0.621530 0.550567

The covariance matrix of the residuals used for estimation
        demand  supply
demand 3.76491 4.45579
supply 4.45579 5.98832

The covariance matrix of the residuals
        demand  supply
demand 3.76393 4.70247
supply 4.70247 6.34207

The correlations of the residuals
         demand   supply
demand 1.000000 0.962476
supply 0.962476 1.000000

The determinant of the residual covariance matrix: 1.75786
OLS R-squared value of the system: 0.691438
McElroy's R-squared value for the system: 0.689596

SUR estimates for demand  (equation 1 )
Model Formula: q ~ p + d

             Estimate Std. Error   t value Pr(>|t|)    
(Intercept) 96.827525   7.466548 12.968179        0 ***
p           -0.279771   0.083971 -3.331764 0.002046  **
d            0.328631   0.020632 15.928109        0 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.940085 on 17 degrees of freedom
Number of observations: 20 Degrees of Freedom: 17 
SSR: 63.986801 MSE: 3.763929 Root MSE: 1.940085 
Multiple R-Squared: 0.761345 Adjusted R-Squared: 0.733268 


SUR estimates for supply  (equation 2 )
Model Formula: q ~ p + f + a

             Estimate Std. Error   t value Pr(>|t|)    
(Intercept) 52.938648   7.665482  6.906108        0 ***
p            0.220229   0.083971  2.622692 0.012832   *
f            0.232671   0.021215 10.967325        0 ***
a            0.328631   0.020632 15.928109        0 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 2.518346 on 16 degrees of freedom
Number of observations: 20 Degrees of Freedom: 16 
SSR: 101.473089 MSE: 6.342068 Root MSE: 2.518346 
Multiple R-Squared: 0.62153 Adjusted R-Squared: 0.550567 

> 
> ## perform LR-test
> lrtest.systemfit( fitsur2, fitsur )
$df
[1] 2

$lr
[1] 13.85483

$p
[1] 0.0009805345

> 
> 
> 
> cleanEx(); ..nameEx <- "nlsystemfit"
> 
> ### * nlsystemfit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: nlsystemfit
> ### Title: Nonlinear Equation System Estimation
> ### Aliases: nlsystemfit
> ### Keywords: models regression nonlinear
> 
> ### ** Examples
> 
> library( systemfit )
> data( ppine )
> 
> hg.formula <- hg ~ exp( h0 + h1*log(tht) + h2*tht^2 + h3*elev + h4*cr)
> dg.formula <- dg ~ exp( d0 + d1*log(dbh) + d2*hg + d3*cr + d4*ba  )
> labels <- list( "height.growth", "diameter.growth" )
> inst <- ~ tht + dbh + elev + cr + ba
> start.values <- c(h0=-0.5, h1=0.5, h2=-0.001, h3=0.0001, h4=0.08,
+                   d0=-0.5, d1=0.009, d2=0.25, d3=0.005, d4=-0.02 )
> model <- list( hg.formula, dg.formula )
> 
> model.ols <- nlsystemfit( "OLS", model, start.values, data=ppine, eqnlabels=labels )
Warning: NA/Inf replaced by maximum positive value
Warning: NA/Inf replaced by maximum positive value
> print( model.ols )

nlsystemfit results 
method: OLS 

convergence achieved after 104 iterations
nlsystemfit objective function value: 271.151618810351 

                  N  DF      SSR      MSE     RMSE       R2   Adj R2
height.growth   166 161 259.4263 1.611343 1.269387 0.405302 0.390527
diameter.growth 166 161  11.7253 0.072828 0.269867 0.753083 0.746949

The covariance matrix of the residuals
                height.growth diameter.growth
height.growth        1.611343      -0.0518970
diameter.growth     -0.051897       0.0728282

The correlations of the residuals
                height.growth diameter.growth
height.growth        1.000000       -0.151500
diameter.growth     -0.151500        1.000000

The determinant of the residual covariance matrix: 0.114658

OLS estimates for height.growth (equation 1)
Model Formula: hg ~ exp(h0 + h1 * log(tht) + h2 * tht^2 + h3 * elev + h4 * cr)

    Estimate Std. Error   t value Pr(>|t|)    
h0 -0.512559   0.470294 -1.089869 0.277399    
h1  0.420753   0.208105  2.021835 0.044849   *
h2 -0.000112   0.000301  -0.37318 0.709506    
h3  0.000154    2.2e-05   6.90088        0 ***
h4  0.084599   0.014649  5.774931        0 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.269387 on 161 degrees of freedom
Number of observations: 166 Degrees of Freedom: 161 
SSR: 259.426272 MSE: 1.611343 Root MSE: 1.269387 
Multiple R-Squared: 0.405302 Adjusted R-Squared: 0.390527 


OLS estimates for diameter.growth (equation 2)
Model Formula: dg ~ exp(d0 + d1 * log(dbh) + d2 * hg + d3 * cr + d4 * ba)

    Estimate Std. Error    t value Pr(>|t|)    
d0 -0.266069    0.11046  -2.408747 0.017137   *
d1  0.170404   0.055619   3.063776 0.002563  **
d2  0.124853   0.012866   9.704127        0 ***
d3  0.019871   0.014038   1.415515 0.158849    
d4 -0.014953   0.001012 -14.780279        0 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.269867 on 161 degrees of freedom
Number of observations: 166 Degrees of Freedom: 161 
SSR: 11.725347 MSE: 0.072828 Root MSE: 0.269867 
Multiple R-Squared: 0.753083 Adjusted R-Squared: 0.746949 

> 
> model.sur <- nlsystemfit( "SUR", model, start.values, data=ppine, eqnlabels=labels )
Warning: NA/Inf replaced by maximum positive value
Warning: NA/Inf replaced by maximum positive value
> print( model.sur )

nlsystemfit results 
method: SUR 

convergence achieved after 68 iterations
nlsystemfit objective function value: 319.440887464005 

                  N  DF      SSR     MSE     RMSE      R2   Adj R2
height.growth   166 161 259.7675 1.61346 1.270221 0.40452 0.389726
diameter.growth 166 161  11.8850 0.07382 0.271699 0.74972 0.743502

The covariance matrix of the residuals used for estimation
                height.growth diameter.growth
height.growth        1.611343      -0.0518970
diameter.growth     -0.051897       0.0728282

The covariance matrix of the residuals
                height.growth diameter.growth
height.growth        1.613463      -0.0863410
diameter.growth     -0.086341       0.0738201

The correlations of the residuals
                height.growth diameter.growth
height.growth        1.000000       -0.250175
diameter.growth     -0.250175        1.000000

The determinant of the residual covariance matrix: 0.111651

SUR estimates for height.growth (equation 1)
Model Formula: hg ~ exp(h0 + h1 * log(tht) + h2 * tht^2 + h3 * elev + h4 * cr)

    Estimate Std. Error   t value Pr(>|t|)    
h0 -0.471577   0.462561 -1.019492 0.309499    
h1  0.385882   0.204106  1.890597 0.060475   .
h2  -5.6e-05   0.000294 -0.191342 0.848498    
h3  0.000164    2.2e-05  7.432781        0 ***
h4  0.085797    0.01472  5.828495        0 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.270221 on 161 degrees of freedom
Number of observations: 166 Degrees of Freedom: 161 
SSR: 259.767467 MSE: 1.613463 Root MSE: 1.270221 
Multiple R-Squared: 0.40452 Adjusted R-Squared: 0.389726 


SUR estimates for diameter.growth (equation 2)
Model Formula: dg ~ exp(d0 + d1 * log(dbh) + d2 * hg + d3 * cr + d4 * ba)

    Estimate Std. Error    t value Pr(>|t|)    
d0 -0.302906   0.111744  -2.710711 0.007442  **
d1   0.13194   0.055714   2.368151 0.019064   *
d2  0.143449   0.012657  11.333291        0 ***
d3  0.017366   0.014151   1.227122 0.221568    
d4 -0.014986      0.001 -14.991626        0 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.271699 on 161 degrees of freedom
Number of observations: 166 Degrees of Freedom: 161 
SSR: 11.885037 MSE: 0.07382 Root MSE: 0.271699 
Multiple R-Squared: 0.74972 Adjusted R-Squared: 0.743502 

> 
> model.2sls <- nlsystemfit( "2SLS", model, start.values, data=ppine,
+    eqnlabels=labels, inst=inst )
Warning: NA/Inf replaced by maximum positive value
Warning: NA/Inf replaced by maximum positive value
> print( model.2sls )

nlsystemfit results 
method: 2SLS 

convergence achieved after 74 iterations
nlsystemfit objective function value: 9.99962954935783e-06 

                  N  DF      SSR      MSE     RMSE       R2   Adj R2
height.growth   166 161 273.3067 1.697557 1.302903 0.373483 0.357918
diameter.growth 166 161  17.2811 0.107336 0.327621 0.636089 0.627048

The covariance matrix of the residuals
                height.growth diameter.growth
height.growth        1.697557       -0.221047
diameter.growth     -0.221047        0.107336

The correlations of the residuals
                height.growth diameter.growth
height.growth        1.000000       -0.517918
diameter.growth     -0.517918        1.000000

The determinant of the residual covariance matrix: 0.133347

2SLS estimates for height.growth (equation 1)
Model Formula: hg ~ exp(h0 + h1 * log(tht) + h2 * tht^2 + h3 * elev + h4 * cr)
Instruments: ~tht + dbh + elev + cr + ba

    Estimate Std. Error   t value Pr(>|t|)    
h0 -1.934212   1.395188 -1.386345 0.167558    
h1  1.039302   0.651917  1.594225 0.112847    
h2 -0.001006   0.000969 -1.037716 0.300959    
h3  0.000139    2.9e-05  4.709071    5e-06 ***
h4  0.089886   0.015815  5.683735        0 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.302903 on 161 degrees of freedom
Number of observations: 166 Degrees of Freedom: 161 
SSR: 273.306739 MSE: 1.697557 Root MSE: 1.302903 
Multiple R-Squared: 0.373483 Adjusted R-Squared: 0.357918 


2SLS estimates for diameter.growth (equation 2)
Model Formula: dg ~ exp(d0 + d1 * log(dbh) + d2 * hg + d3 * cr + d4 * ba)
Instruments: ~tht + dbh + elev + cr + ba

    Estimate Std. Error    t value Pr(>|t|)    
d0  -0.62896   0.142345  -4.418566  1.8e-05 ***
d1  0.009037   0.081199   0.111295 0.911521    
d2  0.230997    0.02898   7.971021        0 ***
d3  0.004896   0.017024   0.287578  0.77404    
d4 -0.013305   0.001201 -11.076569        0 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.327621 on 161 degrees of freedom
Number of observations: 166 Degrees of Freedom: 161 
SSR: 17.281057 MSE: 0.107336 Root MSE: 0.327621 
Multiple R-Squared: 0.636089 Adjusted R-Squared: 0.627048 

> 
> model.3sls <- nlsystemfit( "3SLS", model, start.values, data=ppine,
+                                     eqnlabels=labels, inst=inst )
Warning: NA/Inf replaced by maximum positive value
Warning: NA/Inf replaced by maximum positive value
> print( model.3sls )

nlsystemfit results 
method: 3SLS 

convergence achieved after 98 iterations
nlsystemfit objective function value: 1.02447662459866e-15 

                  N  DF      SSR      MSE     RMSE       R2   Adj R2
height.growth   166 161 273.3067 1.697557 1.302903 0.373483 0.357918
diameter.growth 166 161  17.2589 0.107198 0.327411 0.636557 0.627527

The covariance matrix of the residuals used for estimation
                height.growth diameter.growth
height.growth        1.697557       -0.221047
diameter.growth     -0.221047        0.107336

The covariance matrix of the residuals
                height.growth diameter.growth
height.growth        1.697557       -0.220725
diameter.growth     -0.220725        0.107198

The correlations of the residuals
                height.growth diameter.growth
height.growth        1.000000       -0.517496
diameter.growth     -0.517496        1.000000

The determinant of the residual covariance matrix: 0.133255

3SLS estimates for height.growth (equation 1)
Model Formula: hg ~ exp(h0 + h1 * log(tht) + h2 * tht^2 + h3 * elev + h4 * cr)
Instruments: ~tht + dbh + elev + cr + ba

    Estimate Std. Error   t value Pr(>|t|)    
h0 -1.934213   1.630889 -1.185987 0.237375    
h1  1.039303   0.762051  1.363822 0.174527    
h2 -0.001006   0.001132 -0.888047  0.37584    
h3  0.000139    3.4e-05  4.050146  7.9e-05 ***
h4  0.089886   0.018485  4.862684    3e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.302903 on 161 degrees of freedom
Number of observations: 166 Degrees of Freedom: 161 
SSR: 273.306743 MSE: 1.697557 Root MSE: 1.302903 
Multiple R-Squared: 0.373483 Adjusted R-Squared: 0.357918 


3SLS estimates for diameter.growth (equation 2)
Model Formula: dg ~ exp(d0 + d1 * log(dbh) + d2 * hg + d3 * cr + d4 * ba)
Instruments: ~tht + dbh + elev + cr + ba

    Estimate Std. Error   t value Pr(>|t|)    
d0 -0.626883   0.166212 -3.771585 0.000227 ***
d1  0.009485   0.090192  0.105166 0.916375    
d2  0.230775   0.032921  7.009984        0 ***
d3  0.004688   0.019878  0.235859 0.813842    
d4 -0.013309     0.0014 -9.503644        0 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.327411 on 161 degrees of freedom
Number of observations: 166 Degrees of Freedom: 161 
SSR: 17.258855 MSE: 0.107198 Root MSE: 0.327411 
Multiple R-Squared: 0.636557 Adjusted R-Squared: 0.627527 

> 
> 
> 
> cleanEx(); ..nameEx <- "ppine"
> 
> ### * ppine
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ppine
> ### Title: Tree Growth Data for Ponderosa Pine
> ### Aliases: ppine
> ### Keywords: datasets datasets
> 
> ### ** Examples
> 
> data(ppine)
> 
> 
> 
> cleanEx(); ..nameEx <- "predict.systemfit"
> 
> ### * predict.systemfit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: predict.systemfit
> ### Title: Predictions from Equation System Estimation
> ### Aliases: predict.systemfit
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Not run: library( systemfit )
> data( kmenta )
> demand <- q ~ p + d
> supply <- q ~ p + f + a
> labels <- list( "demand", "supply" )
> system <- list( demand, supply )
> 
> ## OLS estimation
> fitols <- systemfit("OLS", system, labels, data=kmenta )
> 
> ## calculate predicted values and limits
> predict( fitols )
    eq1.pred  eq2.pred
1   97.41053  98.92925
2   99.57728 100.08251
3   99.53832 100.19787
4   99.70152 100.36979
5  102.29446 102.72620
6  102.06849 102.56269
7  102.46276 102.42403
8  102.83273 104.30737
9  101.71547 102.94896
10 100.78922 100.35059
11  95.58388  96.03328
12  94.37826  94.12138
13  95.65592  95.59902
14  98.97700  97.78688
15 104.31033 102.63791
16 103.92569 104.09052
17 104.79508 103.78669
18 101.93124 102.37790
19 103.48498 102.11329
20 106.53086 104.51788
> 
> 
> 
> cleanEx(); ..nameEx <- "predict.systemfit.equation"
> 
> ### * predict.systemfit.equation
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: predict.systemfit.equation
> ### Title: Predictions from Equation System Estimation
> ### Aliases: predict.systemfit.equation
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Not run: library( systemfit )
> data( kmenta )
> demand <- q ~ p + d
> supply <- q ~ p + f + a
> labels <- list( "demand", "supply" )
> system <- list( demand, supply )
> 
> ## OLS estimation
> fitols <- systemfit("OLS", system, labels, data=kmenta )
> 
> ## print the predicted values of the first equation
> predict( fitols$eq[[1]] )
        1         2         3         4         5         6         7         8 
 97.41053  99.57728  99.53832  99.70152 102.29446 102.06849 102.46276 102.83273 
        9        10        11        12        13        14        15        16 
101.71547 100.78922  95.58388  94.37826  95.65592  98.97700 104.31033 103.92569 
       17        18        19        20 
104.79508 101.93124 103.48498 106.53086 
> 
> ## print the predicted values of the second equation
> predict( fitols$eq[[2]] )
        1         2         3         4         5         6         7         8 
 98.92925 100.08251 100.19787 100.36979 102.72620 102.56269 102.42403 104.30737 
        9        10        11        12        13        14        15        16 
102.94896 100.35059  96.03328  94.12138  95.59902  97.78688 102.63791 104.09052 
       17        18        19        20 
103.78669 102.37790 102.11329 104.51788 
> 
> 
> 
> cleanEx(); ..nameEx <- "print.confint.systemfit"
> 
> ### * print.confint.systemfit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: print.confint.systemfit
> ### Title: Print confidence intervals of coefficients
> ### Aliases: print.confint.systemfit
> ### Keywords: models regression
> 
> ### ** Examples
> 
> ## Not run: library( systemfit )
> 
> data( kmenta )
> attach( kmenta )
> demand <- q ~ p + d
> supply <- q ~ p + f + a
> labels <- list( "demand", "supply" )
> system <- list( demand, supply )
> 
> ## perform OLS on each of the equations in the system
> fitols <- systemfit( "OLS", system, labels )
> 
> ## calculate and print the confidence intervals
> ## of all coefficients
> ci <- confint( fitols )
> print( ci, digits=4 )
                   2.5 %   97.5 %
eq 1 (Intercept) 84.0310 115.7599
eq 1 p           -0.5076  -0.1250
eq 1 d            0.2388   0.4305
eq 2 (Intercept) 33.9751  82.5757
eq 2 p           -0.0408   0.3615
eq 2 f            0.1502   0.3460
eq 2 a            0.0416   0.4550
> 
> ## calculate and print the confidence intervals
> ## of the coefficients of the second equation
> ci2 <- confint( fitols$eq[[2]] )
> print( ci2, digits=4 )
              2.5 %  97.5 %
(Intercept) 33.9751 82.5757
p           -0.0408  0.3615
f            0.1502  0.3460
a            0.0416  0.4550
> 
> 
> 
> cleanEx(); ..nameEx <- "print.nlsystemfit.equation"
> 
> ### * print.nlsystemfit.equation
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: print.nlsystemfit.equation
> ### Title: print.nlsystemfit.equation
> ### Aliases: print.nlsystemfit.equation
> ### Keywords: models regression nonlinear
> 
> ### ** Examples
> 
> library( systemfit )
> data( ppine )
> 
> hg.formula <- hg ~ exp( h0 + h1*log(tht) + h2*tht^2 + h3*elev + h4*cr)
> dg.formula <- dg ~ exp( d0 + d1*log(dbh) + d2*hg + d3*cr + d4*ba  )
> labels <- list( "height.growth", "diameter.growth" )
> inst <- ~ tht + dbh + elev + cr + ba
> start.values <- c(h0=-0.5, h1=0.5, h2=-0.001, h3=0.0001, h4=0.08,
+                   d0=-0.5, d1=0.009, d2=0.25, d3=0.005, d4=-0.02 )
> model <- list( hg.formula, dg.formula )
> 
> model.ols <- nlsystemfit( "OLS", model, start.values, data=ppine, eqnlabels=labels )
Warning: NA/Inf replaced by maximum positive value
Warning: NA/Inf replaced by maximum positive value
> print( model.ols )

nlsystemfit results 
method: OLS 

convergence achieved after 104 iterations
nlsystemfit objective function value: 271.151618810351 

                  N  DF      SSR      MSE     RMSE       R2   Adj R2
height.growth   166 161 259.4263 1.611343 1.269387 0.405302 0.390527
diameter.growth 166 161  11.7253 0.072828 0.269867 0.753083 0.746949

The covariance matrix of the residuals
                height.growth diameter.growth
height.growth        1.611343      -0.0518970
diameter.growth     -0.051897       0.0728282

The correlations of the residuals
                height.growth diameter.growth
height.growth        1.000000       -0.151500
diameter.growth     -0.151500        1.000000

The determinant of the residual covariance matrix: 0.114658

OLS estimates for height.growth (equation 1)
Model Formula: hg ~ exp(h0 + h1 * log(tht) + h2 * tht^2 + h3 * elev + h4 * cr)

    Estimate Std. Error   t value Pr(>|t|)    
h0 -0.512559   0.470294 -1.089869 0.277399    
h1  0.420753   0.208105  2.021835 0.044849   *
h2 -0.000112   0.000301  -0.37318 0.709506    
h3  0.000154    2.2e-05   6.90088        0 ***
h4  0.084599   0.014649  5.774931        0 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.269387 on 161 degrees of freedom
Number of observations: 166 Degrees of Freedom: 161 
SSR: 259.426272 MSE: 1.611343 Root MSE: 1.269387 
Multiple R-Squared: 0.405302 Adjusted R-Squared: 0.390527 


OLS estimates for diameter.growth (equation 2)
Model Formula: dg ~ exp(d0 + d1 * log(dbh) + d2 * hg + d3 * cr + d4 * ba)

    Estimate Std. Error    t value Pr(>|t|)    
d0 -0.266069    0.11046  -2.408747 0.017137   *
d1  0.170404   0.055619   3.063776 0.002563  **
d2  0.124853   0.012866   9.704127        0 ***
d3  0.019871   0.014038   1.415515 0.158849    
d4 -0.014953   0.001012 -14.780279        0 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.269867 on 161 degrees of freedom
Number of observations: 166 Degrees of Freedom: 161 
SSR: 11.725347 MSE: 0.072828 Root MSE: 0.269867 
Multiple R-Squared: 0.753083 Adjusted R-Squared: 0.746949 

> 
> model.3sls <- nlsystemfit( "3SLS", model, start.values, data=ppine,
+                                     eqnlabels=labels, inst=inst )
Warning: NA/Inf replaced by maximum positive value
Warning: NA/Inf replaced by maximum positive value
> print( model.3sls )

nlsystemfit results 
method: 3SLS 

convergence achieved after 98 iterations
nlsystemfit objective function value: 1.02447662459866e-15 

                  N  DF      SSR      MSE     RMSE       R2   Adj R2
height.growth   166 161 273.3067 1.697557 1.302903 0.373483 0.357918
diameter.growth 166 161  17.2589 0.107198 0.327411 0.636557 0.627527

The covariance matrix of the residuals used for estimation
                height.growth diameter.growth
height.growth        1.697557       -0.221047
diameter.growth     -0.221047        0.107336

The covariance matrix of the residuals
                height.growth diameter.growth
height.growth        1.697557       -0.220725
diameter.growth     -0.220725        0.107198

The correlations of the residuals
                height.growth diameter.growth
height.growth        1.000000       -0.517496
diameter.growth     -0.517496        1.000000

The determinant of the residual covariance matrix: 0.133255

3SLS estimates for height.growth (equation 1)
Model Formula: hg ~ exp(h0 + h1 * log(tht) + h2 * tht^2 + h3 * elev + h4 * cr)
Instruments: ~tht + dbh + elev + cr + ba

    Estimate Std. Error   t value Pr(>|t|)    
h0 -1.934213   1.630889 -1.185987 0.237375    
h1  1.039303   0.762051  1.363822 0.174527    
h2 -0.001006   0.001132 -0.888047  0.37584    
h3  0.000139    3.4e-05  4.050146  7.9e-05 ***
h4  0.089886   0.018485  4.862684    3e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.302903 on 161 degrees of freedom
Number of observations: 166 Degrees of Freedom: 161 
SSR: 273.306743 MSE: 1.697557 Root MSE: 1.302903 
Multiple R-Squared: 0.373483 Adjusted R-Squared: 0.357918 


3SLS estimates for diameter.growth (equation 2)
Model Formula: dg ~ exp(d0 + d1 * log(dbh) + d2 * hg + d3 * cr + d4 * ba)
Instruments: ~tht + dbh + elev + cr + ba

    Estimate Std. Error   t value Pr(>|t|)    
d0 -0.626883   0.166212 -3.771585 0.000227 ***
d1  0.009485   0.090192  0.105166 0.916375    
d2  0.230775   0.032921  7.009984        0 ***
d3  0.004688   0.019878  0.235859 0.813842    
d4 -0.013309     0.0014 -9.503644        0 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.327411 on 161 degrees of freedom
Number of observations: 166 Degrees of Freedom: 161 
SSR: 17.258855 MSE: 0.107198 Root MSE: 0.327411 
Multiple R-Squared: 0.636557 Adjusted R-Squared: 0.627527 

> 
> 
> 
> cleanEx(); ..nameEx <- "print.nlsystemfit.system"
> 
> ### * print.nlsystemfit.system
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: print.nlsystemfit.system
> ### Title: print.nlsystemfit.system
> ### Aliases: print.nlsystemfit.system
> ### Keywords: models regression nonlinear
> 
> ### ** Examples
> 
> library( systemfit )
> data( ppine )
> 
> hg.formula <- hg ~ exp( h0 + h1*log(tht) + h2*tht^2 + h3*elev + h4*cr)
> dg.formula <- dg ~ exp( d0 + d1*log(dbh) + d2*hg + d3*cr + d4*ba  )
> labels <- list( "height.growth", "diameter.growth" )
> inst <- ~ tht + dbh + elev + cr + ba
> start.values <- c(h0=-0.5, h1=0.5, h2=-0.001, h3=0.0001, h4=0.08,
+                   d0=-0.5, d1=0.009, d2=0.25, d3=0.005, d4=-0.02 )
> model <- list( hg.formula, dg.formula )
> 
> model.ols <- nlsystemfit( "OLS", model, start.values, data=ppine, eqnlabels=labels )
Warning: NA/Inf replaced by maximum positive value
Warning: NA/Inf replaced by maximum positive value
> print( model.ols )

nlsystemfit results 
method: OLS 

convergence achieved after 104 iterations
nlsystemfit objective function value: 271.151618810351 

                  N  DF      SSR      MSE     RMSE       R2   Adj R2
height.growth   166 161 259.4263 1.611343 1.269387 0.405302 0.390527
diameter.growth 166 161  11.7253 0.072828 0.269867 0.753083 0.746949

The covariance matrix of the residuals
                height.growth diameter.growth
height.growth        1.611343      -0.0518970
diameter.growth     -0.051897       0.0728282

The correlations of the residuals
                height.growth diameter.growth
height.growth        1.000000       -0.151500
diameter.growth     -0.151500        1.000000

The determinant of the residual covariance matrix: 0.114658

OLS estimates for height.growth (equation 1)
Model Formula: hg ~ exp(h0 + h1 * log(tht) + h2 * tht^2 + h3 * elev + h4 * cr)

    Estimate Std. Error   t value Pr(>|t|)    
h0 -0.512559   0.470294 -1.089869 0.277399    
h1  0.420753   0.208105  2.021835 0.044849   *
h2 -0.000112   0.000301  -0.37318 0.709506    
h3  0.000154    2.2e-05   6.90088        0 ***
h4  0.084599   0.014649  5.774931        0 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.269387 on 161 degrees of freedom
Number of observations: 166 Degrees of Freedom: 161 
SSR: 259.426272 MSE: 1.611343 Root MSE: 1.269387 
Multiple R-Squared: 0.405302 Adjusted R-Squared: 0.390527 


OLS estimates for diameter.growth (equation 2)
Model Formula: dg ~ exp(d0 + d1 * log(dbh) + d2 * hg + d3 * cr + d4 * ba)

    Estimate Std. Error    t value Pr(>|t|)    
d0 -0.266069    0.11046  -2.408747 0.017137   *
d1  0.170404   0.055619   3.063776 0.002563  **
d2  0.124853   0.012866   9.704127        0 ***
d3  0.019871   0.014038   1.415515 0.158849    
d4 -0.014953   0.001012 -14.780279        0 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.269867 on 161 degrees of freedom
Number of observations: 166 Degrees of Freedom: 161 
SSR: 11.725347 MSE: 0.072828 Root MSE: 0.269867 
Multiple R-Squared: 0.753083 Adjusted R-Squared: 0.746949 

> 
> model.3sls <- nlsystemfit( "3SLS", model, start.values, data=ppine,
+                                     eqnlabels=labels, inst=inst )
Warning: NA/Inf replaced by maximum positive value
Warning: NA/Inf replaced by maximum positive value
> print( model.3sls )

nlsystemfit results 
method: 3SLS 

convergence achieved after 98 iterations
nlsystemfit objective function value: 1.02447662459866e-15 

                  N  DF      SSR      MSE     RMSE       R2   Adj R2
height.growth   166 161 273.3067 1.697557 1.302903 0.373483 0.357918
diameter.growth 166 161  17.2589 0.107198 0.327411 0.636557 0.627527

The covariance matrix of the residuals used for estimation
                height.growth diameter.growth
height.growth        1.697557       -0.221047
diameter.growth     -0.221047        0.107336

The covariance matrix of the residuals
                height.growth diameter.growth
height.growth        1.697557       -0.220725
diameter.growth     -0.220725        0.107198

The correlations of the residuals
                height.growth diameter.growth
height.growth        1.000000       -0.517496
diameter.growth     -0.517496        1.000000

The determinant of the residual covariance matrix: 0.133255

3SLS estimates for height.growth (equation 1)
Model Formula: hg ~ exp(h0 + h1 * log(tht) + h2 * tht^2 + h3 * elev + h4 * cr)
Instruments: ~tht + dbh + elev + cr + ba

    Estimate Std. Error   t value Pr(>|t|)    
h0 -1.934213   1.630889 -1.185987 0.237375    
h1  1.039303   0.762051  1.363822 0.174527    
h2 -0.001006   0.001132 -0.888047  0.37584    
h3  0.000139    3.4e-05  4.050146  7.9e-05 ***
h4  0.089886   0.018485  4.862684    3e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.302903 on 161 degrees of freedom
Number of observations: 166 Degrees of Freedom: 161 
SSR: 273.306743 MSE: 1.697557 Root MSE: 1.302903 
Multiple R-Squared: 0.373483 Adjusted R-Squared: 0.357918 


3SLS estimates for diameter.growth (equation 2)
Model Formula: dg ~ exp(d0 + d1 * log(dbh) + d2 * hg + d3 * cr + d4 * ba)
Instruments: ~tht + dbh + elev + cr + ba

    Estimate Std. Error   t value Pr(>|t|)    
d0 -0.626883   0.166212 -3.771585 0.000227 ***
d1  0.009485   0.090192  0.105166 0.916375    
d2  0.230775   0.032921  7.009984        0 ***
d3  0.004688   0.019878  0.235859 0.813842    
d4 -0.013309     0.0014 -9.503644        0 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.327411 on 161 degrees of freedom
Number of observations: 166 Degrees of Freedom: 161 
SSR: 17.258855 MSE: 0.107198 Root MSE: 0.327411 
Multiple R-Squared: 0.636557 Adjusted R-Squared: 0.627527 

> 
> 
> 
> cleanEx(); ..nameEx <- "print.systemfit"
> 
> ### * print.systemfit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: print.systemfit
> ### Title: Print output of systemfit estimation
> ### Aliases: print.systemfit
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Not run: library( systemfit )
> 
> data( kmenta )
> attach( kmenta )
> demand <- q ~ p + d
> supply <- q ~ p + f + a
> labels <- list( "demand", "supply" )
> system <- list( demand, supply )
> 
> ## perform OLS on each of the equations in the system
> fitols <- systemfit( "OLS", system, labels )
> 
> ## print the results
> print( fitols )

systemfit results 
method: OLS 

        N DF     SSR     MSE    RMSE       R2   Adj R2
demand 20 17 63.3317 3.72539 1.93013 0.763789 0.735999
supply 20 16 92.5511 5.78444 2.40509 0.654807 0.590084

The covariance matrix of the residuals
        demand  supply
demand 3.72539 4.13696
supply 4.13696 5.78444

The correlations of the residuals
         demand   supply
demand 1.000000 0.891179
supply 0.891179 1.000000

The determinant of the residual covariance matrix: 4.43485
OLS R-squared value of the system: 0.709298

OLS estimates for demand  (equation 1 )
Model Formula: q ~ p + d

             Estimate Std. Error   t value Pr(>|t|)    
(Intercept) 99.895423   7.519362 13.285093        0 ***
p           -0.316299   0.090677 -3.488177 0.002815  **
d            0.334636   0.045422  7.367285    1e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.930127 on 17 degrees of freedom
Number of observations: 20 Degrees of Freedom: 17 
SSR: 63.33165 MSE: 3.725391 Root MSE: 1.930127 
Multiple R-Squared: 0.763789 Adjusted R-Squared: 0.735999 


OLS estimates for supply  (equation 2 )
Model Formula: q ~ p + f + a

             Estimate Std. Error  t value Pr(>|t|)    
(Intercept) 58.275431   11.46291 5.083825 0.000111 ***
p            0.160367   0.094884 1.690134 0.110388    
f            0.248133   0.046188 5.372263  6.2e-05 ***
a            0.248302   0.097518 2.546227 0.021567   *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 2.405087 on 16 degrees of freedom
Number of observations: 20 Degrees of Freedom: 16 
SSR: 92.551058 MSE: 5.784441 Root MSE: 2.405087 
Multiple R-Squared: 0.654807 Adjusted R-Squared: 0.590084 

> 
> 
> 
> cleanEx(); ..nameEx <- "print.systemfit.equation"
> 
> ### * print.systemfit.equation
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: print.systemfit.equation
> ### Title: Print output of systemfit estimation
> ### Aliases: print.systemfit.equation
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Not run: library( systemfit )
> 
> data( kmenta )
> attach( kmenta )
> demand <- q ~ p + d
> supply <- q ~ p + f + a
> labels <- list( "demand", "supply" )
> system <- list( demand, supply )
> 
> ## perform OLS on each of the equations in the system
> fitols <- systemfit( "OLS", system, labels )
> 
> ## print the results
> print( fitols$eq[[1]] )

OLS estimates for demand  (equation 1 )
Model Formula: q ~ p + d

             Estimate Std. Error   t value Pr(>|t|)    
(Intercept) 99.895423   7.519362 13.285093        0 ***
p           -0.316299   0.090677 -3.488177 0.002815  **
d            0.334636   0.045422  7.367285    1e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.930127 on 17 degrees of freedom
Number of observations: 20 Degrees of Freedom: 17 
SSR: 63.33165 MSE: 3.725391 Root MSE: 1.930127 
Multiple R-Squared: 0.763789 Adjusted R-Squared: 0.735999 

> 
> 
> 
> cleanEx(); ..nameEx <- "residuals.systemfit"
> 
> ### * residuals.systemfit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: residuals.systemfit
> ### Title: Residuals of systemfit object
> ### Aliases: residuals.systemfit
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Not run: library( systemfit )
> 
> data( kmenta )
> attach( kmenta )
> demand <- q ~ p + d
> supply <- q ~ p + f + a
> labels <- list( "demand", "supply" )
> system <- list( demand, supply )
> 
> ## perform OLS on each of the equations in the system
> fitols <- systemfit( "OLS", system, labels )
> 
> ## print the residuals
> residuals( fitols )
          eq1        eq2
1   1.0744708 -0.4442544
2  -0.3902787 -0.8955081
3   2.6246816  1.9651334
4   1.8024842  1.1342118
5   1.9455436  1.5138013
6   1.1745134  0.6803121
7   1.5302384  1.5689661
8  -2.9327287 -4.4073714
9  -1.3654672 -2.5989581
10  2.0307798  2.4694121
11 -0.1488821 -0.5982785
12 -1.9542622 -1.6973834
13 -1.1209171 -1.0640179
14 -0.2200033  0.9701222
15  1.4866729  3.1590873
16 -3.7006906 -3.8655164
17 -1.2730806 -0.2646900
18 -2.0022429 -2.4488950
19  1.7380247  3.1097065
20 -0.2988561  1.7141205
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "residuals.systemfit.equation"
> 
> ### * residuals.systemfit.equation
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: residuals.systemfit.equation
> ### Title: Residuals of systemfit equation
> ### Aliases: residuals.systemfit.equation
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Not run: library( systemfit )
> 
> data( kmenta )
> attach( kmenta )
> demand <- q ~ p + d
> supply <- q ~ p + f + a
> labels <- list( "demand", "supply" )
> system <- list( demand, supply )
> 
> ## perform OLS on each of the equations in the system
> fitols <- systemfit( "OLS", system, labels )
> 
> ## print the residuals of the first equation
> residuals( fitols$eq[[1]] )
         1          2          3          4          5          6          7 
 1.0744708 -0.3902787  2.6246816  1.8024842  1.9455436  1.1745134  1.5302384 
         8          9         10         11         12         13         14 
-2.9327287 -1.3654672  2.0307798 -0.1488821 -1.9542622 -1.1209171 -0.2200033 
        15         16         17         18         19         20 
 1.4866729 -3.7006906 -1.2730806 -2.0022429  1.7380247 -0.2988561 
> 
> ## print the residuals of the second equation
> residuals( fitols$eq[[2]] )
         1          2          3          4          5          6          7 
-0.4442544 -0.8955081  1.9651334  1.1342118  1.5138013  0.6803121  1.5689661 
         8          9         10         11         12         13         14 
-4.4073714 -2.5989581  2.4694121 -0.5982785 -1.6973834 -1.0640179  0.9701222 
        15         16         17         18         19         20 
 3.1590873 -3.8655164 -0.2646900 -2.4488950  3.1097065  1.7141205 
> 
> 
> 
> cleanEx(); ..nameEx <- "se.ratio.systemfit"
> 
> ### * se.ratio.systemfit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: se.ratio.systemfit
> ### Title: Ratio of the Standard Errors
> ### Aliases: se.ratio.systemfit
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Not run: library( systemfit )
> 
> data( kmenta )
> attach( kmenta )
> demand <- q ~ p + d
> supply <- q ~ p + f + a
> inst <- ~ d + f + a
> labels <- list( "demand", "supply" )
> system <- list( demand, supply )
> 
> ## perform 2SLS on each of the equations in the system
> fit2sls <- systemfit( "2SLS", system, labels, inst )
> fit3sls <- systemfit( "3SLS", system, labels, inst )
> 
> ## print the results from the fits
> print( fit2sls )

systemfit results 
method: 2SLS 

        N DF     SSR     MSE    RMSE       R2   Adj R2
demand 20 17 65.7291 3.86642 1.96632 0.754847 0.726005
supply 20 16 96.6332 6.03958 2.45756 0.639582 0.572004

The covariance matrix of the residuals
        demand  supply
demand 3.86642 4.35744
supply 4.35744 6.03958

The correlations of the residuals
         demand   supply
demand 1.000000 0.901724
supply 0.901724 1.000000

The determinant of the residual covariance matrix: 4.36424
OLS R-squared value of the system: 0.697214

2SLS estimates for demand  (equation 1 )
Model Formula: q ~ p + d
Instruments: ~d + f + a

             Estimate Std. Error   t value Pr(>|t|)    
(Intercept) 94.633304   7.920838 11.947385        0 ***
p           -0.243557   0.096484 -2.524313 0.021832   *
d            0.313992   0.046944  6.688695    4e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.966321 on 17 degrees of freedom
Number of observations: 20 Degrees of Freedom: 17 
SSR: 65.729088 MSE: 3.866417 Root MSE: 1.966321 
Multiple R-Squared: 0.754847 Adjusted R-Squared: 0.726005 


2SLS estimates for supply  (equation 2 )
Model Formula: q ~ p + f + a
Instruments: ~d + f + a

             Estimate Std. Error  t value Pr(>|t|)    
(Intercept) 49.532442  12.010526 4.124086 0.000795 ***
p            0.240076   0.099934 2.402347 0.028785   *
f            0.255606    0.04725 5.409637  5.8e-05 ***
a            0.252924   0.099655 2.537996 0.021929   *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 2.457555 on 16 degrees of freedom
Number of observations: 20 Degrees of Freedom: 16 
SSR: 96.633244 MSE: 6.039578 Root MSE: 2.457555 
Multiple R-Squared: 0.639582 Adjusted R-Squared: 0.572004 

> print( fit3sls )

systemfit results 
method: 3SLS 

        N DF      SSR     MSE    RMSE       R2   Adj R2
demand 20 17  65.7291 3.86642 1.96632 0.754847 0.726005
supply 20 16 107.9138 6.74461 2.59704 0.597508 0.522041

The covariance matrix of the residuals used for estimation
        demand  supply
demand 3.86642 4.35744
supply 4.35744 6.03958

The covariance matrix of the residuals
        demand  supply
demand 3.86642 5.00443
supply 5.00443 6.74461

The correlations of the residuals
        demand  supply
demand 1.00000 0.97999
supply 0.97999 1.00000

The determinant of the residual covariance matrix: 1.03320
OLS R-squared value of the system: 0.676177
McElroy's R-squared value for the system: 0.786468

3SLS estimates for demand  (equation 1 )
Model Formula: q ~ p + d
Instruments: ~d + f + a

             Estimate Std. Error   t value Pr(>|t|)    
(Intercept) 94.633304   7.920838 11.947385        0 ***
p           -0.243557   0.096484 -2.524313 0.021832   *
d            0.313992   0.046944  6.688695    4e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.966321 on 17 degrees of freedom
Number of observations: 20 Degrees of Freedom: 17 
SSR: 65.729088 MSE: 3.866417 Root MSE: 1.966321 
Multiple R-Squared: 0.754847 Adjusted R-Squared: 0.726005 


3SLS estimates for supply  (equation 2 )
Model Formula: q ~ p + f + a
Instruments: ~d + f + a

             Estimate Std. Error  t value Pr(>|t|)    
(Intercept) 52.197204  11.893372 4.388764 0.000458 ***
p            0.228589   0.099673 2.293388 0.035706   *
f            0.228158   0.043994 5.186139    9e-05 ***
a            0.361138   0.072889 4.954608 0.000143 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 2.597039 on 16 degrees of freedom
Number of observations: 20 Degrees of Freedom: 16 
SSR: 107.913821 MSE: 6.744614 Root MSE: 2.597039 
Multiple R-Squared: 0.597508 Adjusted R-Squared: 0.522041 

> print( "covariance of residuals used for estimation (from 2sls)" )
[1] "covariance of residuals used for estimation (from 2sls)"
> print( fit3sls$rcovest )
         [,1]     [,2]
[1,] 3.866417 4.357440
[2,] 4.357440 6.039578
> print( "covariance of residuals" )
[1] "covariance of residuals"
> print( fit3sls$rcov )
         [,1]     [,2]
[1,] 3.866417 5.004427
[2,] 5.004427 6.744614
> 
> ## examine the improvement of 3SLS over 2SLS by computing
> ## the ratio of the standard errors of the estimates
> improve.ratio <- se.ratio.systemfit( fit2sls, fit3sls, 2 )
> print( "summary values for the ratio in the std. err. for the predictions" )
[1] "summary values for the ratio in the std. err. for the predictions"
> print( summary( improve.ratio ) )
     object     
 Min.   :1.001  
 1st Qu.:1.062  
 Median :1.156  
 Mean   :1.151  
 3rd Qu.:1.238  
 Max.   :1.331  
> 
> 
> 
> cleanEx(); ..nameEx <- "summary.nlsystemfit.equation"
> 
> ### * summary.nlsystemfit.equation
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: summary.nlsystemfit.equation
> ### Title: summary.nlsystemfit.equation
> ### Aliases: summary.nlsystemfit.equation
> ### Keywords: models regression nonlinear
> 
> ### ** Examples
> 
> library( systemfit )
> data( ppine )
> 
> hg.formula <- hg ~ exp( h0 + h1*log(tht) + h2*tht^2 + h3*elev + h4*cr)
> dg.formula <- dg ~ exp( d0 + d1*log(dbh) + d2*hg + d3*cr + d4*ba  )
> labels <- list( "height.growth", "diameter.growth" )
> inst <- ~ tht + dbh + elev + cr + ba
> start.values <- c(h0=-0.5, h1=0.5, h2=-0.001, h3=0.0001, h4=0.08,
+                   d0=-0.5, d1=0.009, d2=0.25, d3=0.005, d4=-0.02 )
> model <- list( hg.formula, dg.formula )
> 
> model.ols <- nlsystemfit( "OLS", model, start.values, data=ppine, eqnlabels=labels )
Warning: NA/Inf replaced by maximum positive value
Warning: NA/Inf replaced by maximum positive value
> print( model.ols )

nlsystemfit results 
method: OLS 

convergence achieved after 104 iterations
nlsystemfit objective function value: 271.151618810351 

                  N  DF      SSR      MSE     RMSE       R2   Adj R2
height.growth   166 161 259.4263 1.611343 1.269387 0.405302 0.390527
diameter.growth 166 161  11.7253 0.072828 0.269867 0.753083 0.746949

The covariance matrix of the residuals
                height.growth diameter.growth
height.growth        1.611343      -0.0518970
diameter.growth     -0.051897       0.0728282

The correlations of the residuals
                height.growth diameter.growth
height.growth        1.000000       -0.151500
diameter.growth     -0.151500        1.000000

The determinant of the residual covariance matrix: 0.114658

OLS estimates for height.growth (equation 1)
Model Formula: hg ~ exp(h0 + h1 * log(tht) + h2 * tht^2 + h3 * elev + h4 * cr)

    Estimate Std. Error   t value Pr(>|t|)    
h0 -0.512559   0.470294 -1.089869 0.277399    
h1  0.420753   0.208105  2.021835 0.044849   *
h2 -0.000112   0.000301  -0.37318 0.709506    
h3  0.000154    2.2e-05   6.90088        0 ***
h4  0.084599   0.014649  5.774931        0 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.269387 on 161 degrees of freedom
Number of observations: 166 Degrees of Freedom: 161 
SSR: 259.426272 MSE: 1.611343 Root MSE: 1.269387 
Multiple R-Squared: 0.405302 Adjusted R-Squared: 0.390527 


OLS estimates for diameter.growth (equation 2)
Model Formula: dg ~ exp(d0 + d1 * log(dbh) + d2 * hg + d3 * cr + d4 * ba)

    Estimate Std. Error    t value Pr(>|t|)    
d0 -0.266069    0.11046  -2.408747 0.017137   *
d1  0.170404   0.055619   3.063776 0.002563  **
d2  0.124853   0.012866   9.704127        0 ***
d3  0.019871   0.014038   1.415515 0.158849    
d4 -0.014953   0.001012 -14.780279        0 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.269867 on 161 degrees of freedom
Number of observations: 166 Degrees of Freedom: 161 
SSR: 11.725347 MSE: 0.072828 Root MSE: 0.269867 
Multiple R-Squared: 0.753083 Adjusted R-Squared: 0.746949 

> 
> model.3sls <- nlsystemfit( "3SLS", model, start.values, data=ppine,
+                                     eqnlabels=labels, inst=inst )
Warning: NA/Inf replaced by maximum positive value
Warning: NA/Inf replaced by maximum positive value
> print( model.3sls )

nlsystemfit results 
method: 3SLS 

convergence achieved after 98 iterations
nlsystemfit objective function value: 1.02447662459866e-15 

                  N  DF      SSR      MSE     RMSE       R2   Adj R2
height.growth   166 161 273.3067 1.697557 1.302903 0.373483 0.357918
diameter.growth 166 161  17.2589 0.107198 0.327411 0.636557 0.627527

The covariance matrix of the residuals used for estimation
                height.growth diameter.growth
height.growth        1.697557       -0.221047
diameter.growth     -0.221047        0.107336

The covariance matrix of the residuals
                height.growth diameter.growth
height.growth        1.697557       -0.220725
diameter.growth     -0.220725        0.107198

The correlations of the residuals
                height.growth diameter.growth
height.growth        1.000000       -0.517496
diameter.growth     -0.517496        1.000000

The determinant of the residual covariance matrix: 0.133255

3SLS estimates for height.growth (equation 1)
Model Formula: hg ~ exp(h0 + h1 * log(tht) + h2 * tht^2 + h3 * elev + h4 * cr)
Instruments: ~tht + dbh + elev + cr + ba

    Estimate Std. Error   t value Pr(>|t|)    
h0 -1.934213   1.630889 -1.185987 0.237375    
h1  1.039303   0.762051  1.363822 0.174527    
h2 -0.001006   0.001132 -0.888047  0.37584    
h3  0.000139    3.4e-05  4.050146  7.9e-05 ***
h4  0.089886   0.018485  4.862684    3e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.302903 on 161 degrees of freedom
Number of observations: 166 Degrees of Freedom: 161 
SSR: 273.306743 MSE: 1.697557 Root MSE: 1.302903 
Multiple R-Squared: 0.373483 Adjusted R-Squared: 0.357918 


3SLS estimates for diameter.growth (equation 2)
Model Formula: dg ~ exp(d0 + d1 * log(dbh) + d2 * hg + d3 * cr + d4 * ba)
Instruments: ~tht + dbh + elev + cr + ba

    Estimate Std. Error   t value Pr(>|t|)    
d0 -0.626883   0.166212 -3.771585 0.000227 ***
d1  0.009485   0.090192  0.105166 0.916375    
d2  0.230775   0.032921  7.009984        0 ***
d3  0.004688   0.019878  0.235859 0.813842    
d4 -0.013309     0.0014 -9.503644        0 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.327411 on 161 degrees of freedom
Number of observations: 166 Degrees of Freedom: 161 
SSR: 17.258855 MSE: 0.107198 Root MSE: 0.327411 
Multiple R-Squared: 0.636557 Adjusted R-Squared: 0.627527 

> 
> 
> 
> cleanEx(); ..nameEx <- "summary.nlsystemfit.system"
> 
> ### * summary.nlsystemfit.system
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: summary.nlsystemfit.system
> ### Title: summary.nlsystemfit.system
> ### Aliases: summary.nlsystemfit.system
> ### Keywords: models regression nonlinear
> 
> ### ** Examples
> 
> library( systemfit )
> data( ppine )
> 
> hg.formula <- hg ~ exp( h0 + h1*log(tht) + h2*tht^2 + h3*elev + h4*cr)
> dg.formula <- dg ~ exp( d0 + d1*log(dbh) + d2*hg + d3*cr + d4*ba  )
> labels <- list( "height.growth", "diameter.growth" )
> inst <- ~ tht + dbh + elev + cr + ba
> start.values <- c(h0=-0.5, h1=0.5, h2=-0.001, h3=0.0001, h4=0.08,
+                   d0=-0.5, d1=0.009, d2=0.25, d3=0.005, d4=-0.02 )
> model <- list( hg.formula, dg.formula )
> 
> model.ols <- nlsystemfit( "OLS", model, start.values, data=ppine, eqnlabels=labels )
Warning: NA/Inf replaced by maximum positive value
Warning: NA/Inf replaced by maximum positive value
> print( model.ols )

nlsystemfit results 
method: OLS 

convergence achieved after 104 iterations
nlsystemfit objective function value: 271.151618810351 

                  N  DF      SSR      MSE     RMSE       R2   Adj R2
height.growth   166 161 259.4263 1.611343 1.269387 0.405302 0.390527
diameter.growth 166 161  11.7253 0.072828 0.269867 0.753083 0.746949

The covariance matrix of the residuals
                height.growth diameter.growth
height.growth        1.611343      -0.0518970
diameter.growth     -0.051897       0.0728282

The correlations of the residuals
                height.growth diameter.growth
height.growth        1.000000       -0.151500
diameter.growth     -0.151500        1.000000

The determinant of the residual covariance matrix: 0.114658

OLS estimates for height.growth (equation 1)
Model Formula: hg ~ exp(h0 + h1 * log(tht) + h2 * tht^2 + h3 * elev + h4 * cr)

    Estimate Std. Error   t value Pr(>|t|)    
h0 -0.512559   0.470294 -1.089869 0.277399    
h1  0.420753   0.208105  2.021835 0.044849   *
h2 -0.000112   0.000301  -0.37318 0.709506    
h3  0.000154    2.2e-05   6.90088        0 ***
h4  0.084599   0.014649  5.774931        0 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.269387 on 161 degrees of freedom
Number of observations: 166 Degrees of Freedom: 161 
SSR: 259.426272 MSE: 1.611343 Root MSE: 1.269387 
Multiple R-Squared: 0.405302 Adjusted R-Squared: 0.390527 


OLS estimates for diameter.growth (equation 2)
Model Formula: dg ~ exp(d0 + d1 * log(dbh) + d2 * hg + d3 * cr + d4 * ba)

    Estimate Std. Error    t value Pr(>|t|)    
d0 -0.266069    0.11046  -2.408747 0.017137   *
d1  0.170404   0.055619   3.063776 0.002563  **
d2  0.124853   0.012866   9.704127        0 ***
d3  0.019871   0.014038   1.415515 0.158849    
d4 -0.014953   0.001012 -14.780279        0 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.269867 on 161 degrees of freedom
Number of observations: 166 Degrees of Freedom: 161 
SSR: 11.725347 MSE: 0.072828 Root MSE: 0.269867 
Multiple R-Squared: 0.753083 Adjusted R-Squared: 0.746949 

> 
> model.3sls <- nlsystemfit( "3SLS", model, start.values, data=ppine,
+                                     eqnlabels=labels, inst=inst )
Warning: NA/Inf replaced by maximum positive value
Warning: NA/Inf replaced by maximum positive value
> print( model.3sls )

nlsystemfit results 
method: 3SLS 

convergence achieved after 98 iterations
nlsystemfit objective function value: 1.02447662459866e-15 

                  N  DF      SSR      MSE     RMSE       R2   Adj R2
height.growth   166 161 273.3067 1.697557 1.302903 0.373483 0.357918
diameter.growth 166 161  17.2589 0.107198 0.327411 0.636557 0.627527

The covariance matrix of the residuals used for estimation
                height.growth diameter.growth
height.growth        1.697557       -0.221047
diameter.growth     -0.221047        0.107336

The covariance matrix of the residuals
                height.growth diameter.growth
height.growth        1.697557       -0.220725
diameter.growth     -0.220725        0.107198

The correlations of the residuals
                height.growth diameter.growth
height.growth        1.000000       -0.517496
diameter.growth     -0.517496        1.000000

The determinant of the residual covariance matrix: 0.133255

3SLS estimates for height.growth (equation 1)
Model Formula: hg ~ exp(h0 + h1 * log(tht) + h2 * tht^2 + h3 * elev + h4 * cr)
Instruments: ~tht + dbh + elev + cr + ba

    Estimate Std. Error   t value Pr(>|t|)    
h0 -1.934213   1.630889 -1.185987 0.237375    
h1  1.039303   0.762051  1.363822 0.174527    
h2 -0.001006   0.001132 -0.888047  0.37584    
h3  0.000139    3.4e-05  4.050146  7.9e-05 ***
h4  0.089886   0.018485  4.862684    3e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.302903 on 161 degrees of freedom
Number of observations: 166 Degrees of Freedom: 161 
SSR: 273.306743 MSE: 1.697557 Root MSE: 1.302903 
Multiple R-Squared: 0.373483 Adjusted R-Squared: 0.357918 


3SLS estimates for diameter.growth (equation 2)
Model Formula: dg ~ exp(d0 + d1 * log(dbh) + d2 * hg + d3 * cr + d4 * ba)
Instruments: ~tht + dbh + elev + cr + ba

    Estimate Std. Error   t value Pr(>|t|)    
d0 -0.626883   0.166212 -3.771585 0.000227 ***
d1  0.009485   0.090192  0.105166 0.916375    
d2  0.230775   0.032921  7.009984        0 ***
d3  0.004688   0.019878  0.235859 0.813842    
d4 -0.013309     0.0014 -9.503644        0 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.327411 on 161 degrees of freedom
Number of observations: 166 Degrees of Freedom: 161 
SSR: 17.258855 MSE: 0.107198 Root MSE: 0.327411 
Multiple R-Squared: 0.636557 Adjusted R-Squared: 0.627527 

> 
> 
> 
> cleanEx(); ..nameEx <- "summary.systemfit"
> 
> ### * summary.systemfit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: summary.systemfit
> ### Title: Print output of systemfit estimation
> ### Aliases: summary.systemfit
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Not run: library( systemfit )
> 
> data( kmenta )
> attach( kmenta )
> demand <- q ~ p + d
> supply <- q ~ p + f + a
> inst <- ~ d + f + a
> labels <- list( "demand", "supply" )
> system <- list( demand, supply )
> 
> ## perform OLS on each of the equations in the system
> fitols <- systemfit( "OLS", system, labels )
> 
> ## print the results
> summary.systemfit( fitols )

systemfit results 
method: OLS 

        N DF     SSR     MSE    RMSE       R2   Adj R2
demand 20 17 63.3317 3.72539 1.93013 0.763789 0.735999
supply 20 16 92.5511 5.78444 2.40509 0.654807 0.590084

The covariance matrix of the residuals
        demand  supply
demand 3.72539 4.13696
supply 4.13696 5.78444

The correlations of the residuals
         demand   supply
demand 1.000000 0.891179
supply 0.891179 1.000000

The determinant of the residual covariance matrix: 4.43485
OLS R-squared value of the system: 0.709298

OLS estimates for demand  (equation 1 )
Model Formula: q ~ p + d

             Estimate Std. Error   t value Pr(>|t|)    
(Intercept) 99.895423   7.519362 13.285093        0 ***
p           -0.316299   0.090677 -3.488177 0.002815  **
d            0.334636   0.045422  7.367285    1e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.930127 on 17 degrees of freedom
Number of observations: 20 Degrees of Freedom: 17 
SSR: 63.33165 MSE: 3.725391 Root MSE: 1.930127 
Multiple R-Squared: 0.763789 Adjusted R-Squared: 0.735999 


OLS estimates for supply  (equation 2 )
Model Formula: q ~ p + f + a

             Estimate Std. Error  t value Pr(>|t|)    
(Intercept) 58.275431   11.46291 5.083825 0.000111 ***
p            0.160367   0.094884 1.690134 0.110388    
f            0.248133   0.046188 5.372263  6.2e-05 ***
a            0.248302   0.097518 2.546227 0.021567   *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 2.405087 on 16 degrees of freedom
Number of observations: 20 Degrees of Freedom: 16 
SSR: 92.551058 MSE: 5.784441 Root MSE: 2.405087 
Multiple R-Squared: 0.654807 Adjusted R-Squared: 0.590084 

> 
> 
> 
> cleanEx(); ..nameEx <- "summary.systemfit.equation"
> 
> ### * summary.systemfit.equation
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: summary.systemfit.equation
> ### Title: Print output of systemfit estimation
> ### Aliases: summary.systemfit.equation
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Not run: library( systemfit )
> 
> data( kmenta )
> attach( kmenta )
> demand <- q ~ p + d
> supply <- q ~ p + f + a
> inst <- ~ d + f + a
> labels <- list( "demand", "supply" )
> system <- list( demand, supply )
> 
> ## perform OLS on each of the equations in the system
> fitols <- systemfit( "OLS", system, labels )
> 
> ## print the results
> summary.systemfit.equation( fitols$eq[[1]] )

OLS estimates for demand  (equation 1 )
Model Formula: q ~ p + d

             Estimate Std. Error   t value Pr(>|t|)    
(Intercept) 99.895423   7.519362 13.285093        0 ***
p           -0.316299   0.090677 -3.488177 0.002815  **
d            0.334636   0.045422  7.367285    1e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.930127 on 17 degrees of freedom
Number of observations: 20 Degrees of Freedom: 17 
SSR: 63.33165 MSE: 3.725391 Root MSE: 1.930127 
Multiple R-Squared: 0.763789 Adjusted R-Squared: 0.735999 

> 
> 
> 
> cleanEx(); ..nameEx <- "systemfit"
> 
> ### * systemfit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: systemfit
> ### Title: Equation System Estimation
> ### Aliases: systemfit
> ### Keywords: models regression
> 
> ### ** Examples
> 
> ## Not run: library( systemfit )
> data( kmenta )
> demand <- q ~ p + d
> supply <- q ~ p + f + a
> labels <- list( "demand", "supply" )
> system <- list( demand, supply )
> 
> ## OLS estimation
> fitols <- systemfit("OLS", system, labels, data=kmenta )
> print( fitols )

systemfit results 
method: OLS 

        N DF     SSR     MSE    RMSE       R2   Adj R2
demand 20 17 63.3317 3.72539 1.93013 0.763789 0.735999
supply 20 16 92.5511 5.78444 2.40509 0.654807 0.590084

The covariance matrix of the residuals
        demand  supply
demand 3.72539 4.13696
supply 4.13696 5.78444

The correlations of the residuals
         demand   supply
demand 1.000000 0.891179
supply 0.891179 1.000000

The determinant of the residual covariance matrix: 4.43485
OLS R-squared value of the system: 0.709298

OLS estimates for demand  (equation 1 )
Model Formula: q ~ p + d

             Estimate Std. Error   t value Pr(>|t|)    
(Intercept) 99.895423   7.519362 13.285093        0 ***
p           -0.316299   0.090677 -3.488177 0.002815  **
d            0.334636   0.045422  7.367285    1e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.930127 on 17 degrees of freedom
Number of observations: 20 Degrees of Freedom: 17 
SSR: 63.33165 MSE: 3.725391 Root MSE: 1.930127 
Multiple R-Squared: 0.763789 Adjusted R-Squared: 0.735999 


OLS estimates for supply  (equation 2 )
Model Formula: q ~ p + f + a

             Estimate Std. Error  t value Pr(>|t|)    
(Intercept) 58.275431   11.46291 5.083825 0.000111 ***
p            0.160367   0.094884 1.690134 0.110388    
f            0.248133   0.046188 5.372263  6.2e-05 ***
a            0.248302   0.097518 2.546227 0.021567   *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 2.405087 on 16 degrees of freedom
Number of observations: 20 Degrees of Freedom: 16 
SSR: 92.551058 MSE: 5.784441 Root MSE: 2.405087 
Multiple R-Squared: 0.654807 Adjusted R-Squared: 0.590084 

> 
> ## OLS estimation with 2 restrictions
> Rrestr <- matrix(0,2,7)
> qrestr <- matrix(0,2,1)
> Rrestr[1,3] <-  1
> Rrestr[1,7] <- -1
> Rrestr[2,2] <- -1
> Rrestr[2,5] <-  1
> qrestr[2,1] <-  0.5
> fitols2 <- systemfit("OLS", system, labels, data=kmenta,
+                       R.restr=Rrestr, q.restr=qrestr )
> print( fitols2 )

systemfit results 
method: OLS 

        N DF     SSR     MSE    RMSE       R2   Adj R2
demand 20 17 64.0034 3.76491 1.94034 0.761283 0.733199
supply 20 16 95.8131 5.98832 2.44710 0.642641 0.575636

The covariance matrix of the residuals
        demand  supply
demand 3.76491 4.45579
supply 4.45579 5.98832

The correlations of the residuals
         demand   supply
demand 1.000000 0.938415
supply 0.938415 1.000000

The determinant of the residual covariance matrix: 2.69142
OLS R-squared value of the system: 0.701962

OLS estimates for demand  (equation 1 )
Model Formula: q ~ p + d

              Estimate Std. Error   t value Pr(>|t|)    
(Intercept) 101.481708   6.159922 16.474512        0 ***
p            -0.316799   0.062915 -5.035322  1.4e-05 ***
d             0.318885   0.039852  8.001656        0 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.940337 on 17 degrees of freedom
Number of observations: 20 Degrees of Freedom: 17 
SSR: 64.00342 MSE: 3.764907 Root MSE: 1.940337 
Multiple R-Squared: 0.761283 Adjusted R-Squared: 0.733199 


OLS estimates for supply  (equation 2 )
Model Formula: q ~ p + f + a

            Estimate Std. Error  t value Pr(>|t|)    
(Intercept) 54.14942   7.551514  7.17067        0 ***
p           0.183201   0.062915 2.911859 0.006215  **
f           0.259528   0.039059 6.644583        0 ***
a           0.318885   0.039852 8.001656        0 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 2.447104 on 16 degrees of freedom
Number of observations: 20 Degrees of Freedom: 16 
SSR: 95.813088 MSE: 5.988318 Root MSE: 2.447104 
Multiple R-Squared: 0.642641 Adjusted R-Squared: 0.575636 

> 
> ## iterated SUR estimation
> fitsur <- systemfit("SUR", system, labels, data=kmenta, maxit=100 )
> print( fitsur )

systemfit results 
method: iterated SUR 

convergence achieved after 35 iterations

        N DF     SSR     MSE    RMSE       R2   Adj R2
demand 20 17 105.389 6.19935 2.48985 0.606925 0.560681
supply 20 16 146.061 9.12884 3.02140 0.455227 0.353082

The covariance matrix of the residuals used for estimation
        demand  supply
demand 6.19907 7.49338
supply 7.49338 9.12855

The covariance matrix of the residuals
        demand  supply
demand 6.19935 7.49367
supply 7.49367 9.12884

The correlations of the residuals
         demand   supply
demand 1.000000 0.996125
supply 0.996125 1.000000

The determinant of the residual covariance matrix: 0.437694
OLS R-squared value of the system: 0.531076
McElroy's R-squared value for the system: 0.832629

SUR estimates for demand  (equation 1 )
Model Formula: q ~ p + d

             Estimate Std. Error   t value Pr(>|t|)    
(Intercept) 97.516307   9.663008 10.091713        0 ***
p           -0.143687    0.09971  -1.44104  0.16774    
d             0.18202   0.022572  8.064129        0 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 2.489849 on 17 degrees of freedom
Number of observations: 20 Degrees of Freedom: 17 
SSR: 105.388914 MSE: 6.199348 Root MSE: 2.489849 
Multiple R-Squared: 0.606925 Adjusted R-Squared: 0.560681 


SUR estimates for supply  (equation 2 )
Model Formula: q ~ p + f + a

             Estimate Std. Error  t value Pr(>|t|)    
(Intercept) 77.900537   12.12427 6.425173    8e-06 ***
p            0.105094   0.117246 0.896349 0.383355    
f             0.10841   0.020513 5.284965  7.4e-05 ***
a            0.191543   0.032047 5.976971  1.9e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 3.021397 on 16 degrees of freedom
Number of observations: 20 Degrees of Freedom: 16 
SSR: 146.06139 MSE: 9.128837 Root MSE: 3.021397 
Multiple R-Squared: 0.455227 Adjusted R-Squared: 0.353082 

> 
> ## 2SLS estimation
> inst <- ~ d + f + a
> fit2sls <- systemfit( "2SLS", system, labels, inst, kmenta )
> print( fit2sls )

systemfit results 
method: 2SLS 

        N DF     SSR     MSE    RMSE       R2   Adj R2
demand 20 17 65.7291 3.86642 1.96632 0.754847 0.726005
supply 20 16 96.6332 6.03958 2.45756 0.639582 0.572004

The covariance matrix of the residuals
        demand  supply
demand 3.86642 4.35744
supply 4.35744 6.03958

The correlations of the residuals
         demand   supply
demand 1.000000 0.901724
supply 0.901724 1.000000

The determinant of the residual covariance matrix: 4.36424
OLS R-squared value of the system: 0.697214

2SLS estimates for demand  (equation 1 )
Model Formula: q ~ p + d
Instruments: ~d + f + a

             Estimate Std. Error   t value Pr(>|t|)    
(Intercept) 94.633304   7.920838 11.947385        0 ***
p           -0.243557   0.096484 -2.524313 0.021832   *
d            0.313992   0.046944  6.688695    4e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.966321 on 17 degrees of freedom
Number of observations: 20 Degrees of Freedom: 17 
SSR: 65.729088 MSE: 3.866417 Root MSE: 1.966321 
Multiple R-Squared: 0.754847 Adjusted R-Squared: 0.726005 


2SLS estimates for supply  (equation 2 )
Model Formula: q ~ p + f + a
Instruments: ~d + f + a

             Estimate Std. Error  t value Pr(>|t|)    
(Intercept) 49.532442  12.010526 4.124086 0.000795 ***
p            0.240076   0.099934 2.402347 0.028785   *
f            0.255606    0.04725 5.409637  5.8e-05 ***
a            0.252924   0.099655 2.537996 0.021929   *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 2.457555 on 16 degrees of freedom
Number of observations: 20 Degrees of Freedom: 16 
SSR: 96.633244 MSE: 6.039578 Root MSE: 2.457555 
Multiple R-Squared: 0.639582 Adjusted R-Squared: 0.572004 

> 
> ## 2SLS estimation with different instruments in each equation
> inst1 <- ~ d + f
> inst2 <- ~ d + f + a
> instlist <- list( inst1, inst2 )
> fit2sls2 <- systemfit( "2SLS", system, labels, instlist, kmenta )
> print( fit2sls2 )

systemfit results 
method: 2SLS 

        N DF     SSR     MSE    RMSE       R2   Adj R2
demand 20 17 67.4466 3.96745 1.99185 0.748441 0.718846
supply 20 16 96.6332 6.03958 2.45756 0.639582 0.572004

The covariance matrix of the residuals
        demand  supply
demand 3.96744 3.83562
supply 3.83562 6.03958

The correlations of the residuals
         demand   supply
demand 1.000000 0.783569
supply 0.783569 1.000000

The determinant of the residual covariance matrix: 9.24969
OLS R-squared value of the system: 0.694011

2SLS estimates for demand  (equation 1 )
Model Formula: q ~ p + d
Instruments: ~d + f

              Estimate Std. Error  t value Pr(>|t|)    
(Intercept) 106.789358  11.143545 9.583069        0 ***
p            -0.411599   0.144845 -2.84166 0.011271   *
d             0.361681   0.056406 6.412096    6e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.991845 on 17 degrees of freedom
Number of observations: 20 Degrees of Freedom: 17 
SSR: 67.446561 MSE: 3.967445 Root MSE: 1.991845 
Multiple R-Squared: 0.748441 Adjusted R-Squared: 0.718846 


2SLS estimates for supply  (equation 2 )
Model Formula: q ~ p + f + a
Instruments: ~d + f + a

             Estimate Std. Error  t value Pr(>|t|)    
(Intercept) 49.532442  12.010526 4.124086 0.000795 ***
p            0.240076   0.099934 2.402347 0.028785   *
f            0.255606    0.04725 5.409637  5.8e-05 ***
a            0.252924   0.099655 2.537996 0.021929   *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 2.457555 on 16 degrees of freedom
Number of observations: 20 Degrees of Freedom: 16 
SSR: 96.633244 MSE: 6.039578 Root MSE: 2.457555 
Multiple R-Squared: 0.639582 Adjusted R-Squared: 0.572004 

> 
> ## 3SLS estimation with GMM-3SLS formula
> inst <- ~ d + f + a
> fit3sls <- systemfit( "3SLS", system, labels, inst, kmenta, formula3sls="GMM" )
> print( fit3sls )

systemfit results 
method: 3SLS 

        N DF      SSR     MSE    RMSE       R2   Adj R2
demand 20 17  65.7291 3.86642 1.96632 0.754847 0.726005
supply 20 16 107.9138 6.74461 2.59704 0.597508 0.522041

The covariance matrix of the residuals used for estimation
        demand  supply
demand 3.86642 4.35744
supply 4.35744 6.03958

The covariance matrix of the residuals
        demand  supply
demand 3.86642 5.00443
supply 5.00443 6.74461

The correlations of the residuals
        demand  supply
demand 1.00000 0.97999
supply 0.97999 1.00000

The determinant of the residual covariance matrix: 1.03320
OLS R-squared value of the system: 0.676177
McElroy's R-squared value for the system: 0.786468

3SLS estimates for demand  (equation 1 )
Model Formula: q ~ p + d
Instruments: ~d + f + a

             Estimate Std. Error   t value Pr(>|t|)    
(Intercept) 94.633304   7.920838 11.947385        0 ***
p           -0.243557   0.096484 -2.524313 0.021832   *
d            0.313992   0.046944  6.688695    4e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.966321 on 17 degrees of freedom
Number of observations: 20 Degrees of Freedom: 17 
SSR: 65.729088 MSE: 3.866417 Root MSE: 1.966321 
Multiple R-Squared: 0.754847 Adjusted R-Squared: 0.726005 


3SLS estimates for supply  (equation 2 )
Model Formula: q ~ p + f + a
Instruments: ~d + f + a

             Estimate Std. Error  t value Pr(>|t|)    
(Intercept) 52.197204  11.893372 4.388764 0.000458 ***
p            0.228589   0.099673 2.293388 0.035706   *
f            0.228158   0.043994 5.186139    9e-05 ***
a            0.361138   0.072889 4.954608 0.000143 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 2.597039 on 16 degrees of freedom
Number of observations: 20 Degrees of Freedom: 16 
SSR: 107.913821 MSE: 6.744614 Root MSE: 2.597039 
Multiple R-Squared: 0.597508 Adjusted R-Squared: 0.522041 

> 
> 
> 
> cleanEx(); ..nameEx <- "vcov.systemfit"
> 
> ### * vcov.systemfit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: vcov.systemfit
> ### Title: Variance covariance matrix of coefficients
> ### Aliases: vcov.systemfit
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Not run: library( systemfit )
> 
> data( kmenta )
> attach( kmenta )
> demand <- q ~ p + d
> supply <- q ~ p + f + a
> labels <- list( "demand", "supply" )
> system <- list( demand, supply )
> 
> ## perform OLS on each of the equations in the system
> fitols <- systemfit( "OLS", system, labels )
> 
> ## print the coefficients
> vcov( fitols )
            (Intercept)            p            d                          
(Intercept) 56.54080696 -0.594801461  0.032162194   0.0000000  0.0000000000
p           -0.59480146  0.008222392 -0.002333464   0.0000000  0.0000000000
d            0.03216219 -0.002333464  0.002063143   0.0000000  0.0000000000
             0.00000000  0.000000000  0.000000000 131.3983031 -0.9874997306
             0.00000000  0.000000000  0.000000000  -0.9874997  0.0090029614
             0.00000000  0.000000000  0.000000000  -0.3043609  0.0008439930
             0.00000000  0.000000000  0.000000000  -0.2791832  0.0005220243
                                      
(Intercept)  0.000000000  0.0000000000
p            0.000000000  0.0000000000
d            0.000000000  0.0000000000
            -0.304360904 -0.2791832170
             0.000843993  0.0005220243
             0.002133318  0.0013155895
             0.001315589  0.0095097150
> 
> 
> 
> cleanEx(); ..nameEx <- "vcov.systemfit.equation"
> 
> ### * vcov.systemfit.equation
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: vcov.systemfit.equation
> ### Title: Variance covariance matrix of coefficients
> ### Aliases: vcov.systemfit.equation
> ### Keywords: models
> 
> ### ** Examples
> 
> ## Not run: library( systemfit )
> 
> data( kmenta )
> attach( kmenta )
> demand <- q ~ p + d
> supply <- q ~ p + f + a
> labels <- list( "demand", "supply" )
> system <- list( demand, supply )
> 
> ## perform OLS on each of the equations in the system
> fitols <- systemfit( "OLS", system, labels )
> 
> ## print the coefficients of the first equation
> vcov( fitols$eq[[1]] )
            (Intercept)            p            d
(Intercept) 56.54080696 -0.594801461  0.032162194
p           -0.59480146  0.008222392 -0.002333464
d            0.03216219 -0.002333464  0.002063143
> 
> ## print the coefficients of the second equation
> vcov( fitols$eq[[2]] )
                                                     
 131.3983031 -0.9874997306 -0.304360904 -0.2791832170
  -0.9874997  0.0090029614  0.000843993  0.0005220243
  -0.3043609  0.0008439930  0.002133318  0.0013155895
  -0.2791832  0.0005220243  0.001315589  0.0095097150
> 
> 
> 
> ### * <FOOTER>
> ###
> cat("Time elapsed: ", proc.time() - get("ptime", env = .CheckExEnv),"\n")
Time elapsed:  68.56 26.85 95.87 0 0 
> grDevices::dev.off()
null device 
          1 
> ###
> ### Local variables: ***
> ### mode: outline-minor ***
> ### outline-regexp: "\\(> \\)?### [*]+" ***
> ### End: ***
> quit('no')