How to conduct the NLSUR

[Gidion Adirinekso]

I am a new user of STATA. I hope somebody give me a light.

Right now, I am trying to estimate system equations with nonlinear in parameters using NLSUR.
Here, I attached the system equations, the stata command and the result.

The Command in Stata

nlsur ( Rc = {s=0.5}*{τ=2.5}*(({δ=0.12}+{theta=0.616})/({δ=0.12}+{s=0.5}*{theta=0.616}))*Nc - {τ=2.5}*xkab) ( Rcu = {s=0.5}*{τ=2.5}*Nc + {s=0.5}*{τ=2.5}*xkab) (Lc = ({s=0.5}*{theta=0.616}/({δ=0.12}+{s=0.5}*{theta=0.616}))*N - ({s=0.5}*{theta=0.616}/({δ=0.12}+{s=0.5}*{theta=0.616}))*Lr) ( jcurban= (({r=0.1}+{δ=0.12}+{β=0.2}*{s=0.5}*{theta=0.616}) / (1-{β=0.2}*({r=0.1}+{δ=0.12}))*({fsc=0.15}*{r=0.1}+{f sc=0.15}*{δ=0.12}) + ({s=0.5}*{theta=0.616}*{τ=2.5}-{s=0.5}*{theta=0.616}*{s=0.5}*{τ=2.5})/({δ=0.12}+{s=0.5}*{theta=0.616})*N - ({s=0.5}*{theta=0.616}*{τ=2.5}-{s=0.5}*{theta=0.616}*{s=0.5}*{τ=2.5})/({δ=0.12}+{s=0.5}*{theta=0.616})*Lr)) (wc=((({β=0.2}*{r=0.1}+{β=0.2}*{δ=0.12}+{β=0.2}*{s =0.5}*{theta=0.616})*({fsc=0.01}*({r=0.1}+{δ=0.12} ))) / (({r=0.1}+{δ=0.12}-{β=0.2}*{r=0.1}-{β=0.2}*{δ=0.12})*{theta=0.616}))+(({r=0.1}+({β=0. 2}*({r=0.1}+{s=0.5}*{theta=0.616}+{δ=0.12}))) + ({δ=0.12}*{τ=2.5}-{δ=0.12}*{s=0.5}*{τ=2.5})) / ({r=0.1}+{δ=0.12}+{β=0.2}*{s=0.5}*{theta=0.616})*( ( {s=0.5}*{theta=0.616})/({δ=0.12}+{s=0.5}*{theta=0.616}))*N-(({r=0.1}+({β=0.2}*({r=0.1}+{s=0.5}*{theta=0.616}+ {δ=0.12}))) + ({δ=0.12}*{τ=2.5}-{δ=0.12}*{s=0.5}*{τ=2.5})) / ({r=0.1}+{δ=0.12}+{β=0.2}*{s=0.5}*{theta=0.616})*( ( {s=0.5}*{theta=0.616})/({δ=0.12}+{s=0.5}*{theta=0.616}))*Lr)

The Result:

Calculating NLS estimates...
Iteration 0: Residual SS = 1.41e+16
Iteration 1: Residual SS = 1.37e+16
Iteration 2: Residual SS = 1.37e+16
Iteration 3: Residual SS = 1.37e+16
Iteration 4: Residual SS = 1.37e+16
Iteration 5: Residual SS = 1.37e+16
Iteration 6: Residual SS = 1.37e+16
Iteration 7: Residual SS = 1.37e+16
Iteration 8: Residual SS = 1.37e+16
Iteration 9: Residual SS = 1.37e+16
Iteration 10: Residual SS = 1.37e+16
Iteration 11: Residual SS = 1.37e+16
Iteration 12: Residual SS = 1.37e+16
Iteration 13: Residual SS = 1.37e+16
Calculating FGNLS estimates...
Iteration 0: Scaled RSS = 2457.553
Iteration 1: Scaled RSS = 2437.816
Iteration 2: Scaled RSS = 2435.802
Iteration 3: Scaled RSS = 2435.8
Iteration 4: Scaled RSS = 2435.8

FGNLS regression
---------------------------------------------------------------------
Equation | Obs Parms RMSE R-sq Constant
----------------+----------------------------------------------------
1 Rc | 492 4 3494019 0.2344* (none)
2 Rcu | 492 2 3959116 0.1811* (none)
3 Lc | 492 3 64264.35 0.9049* (none)
4 jcurban | 492 7 58396.85 0.6779 r
5 wc | 492 7 187692.6 -0.0248 fsc
---------------------------------------------------------------------
* Uncentered R-sq

------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
/s | .8927031 .0072136 123.75 0.000 .8785646 .9068415
/t | 4.651894 .309321 15.04 0.000 4.045636 5.258152
/d | 4.214471 1.323854 3.18 0.001 1.619764 6.809177
/theta | 2.216726 .7013804 3.16 0.002 .8420457 3.591406
/r | -3.906808 1.240583 -3.15 0.002 -6.338305 -1.475311
/ß | .9887485 .000669 1478.02 0.000 .9874374 .9900597
/fsc | 2956.139 . . . . .
------------------------------------------------------------------------------




My Questions are::

1. If I want to know the relationship between variables, It was right what I’ve done?
2. If the step is yes, how to make an interpretation in every equation ?
3. If the step is wrong, please give me the light how to conduct rightly to estimate non linear in parameters of system equations.

Thank You.
Best Regard
Gidion

[Emad Shehata]

Nonlinear system of equations or any nonlinear function must has an economic meaning.
Check the name of your model and then look for how to calculate marginal effects and elasticities.

[Jorge Eduardo Perez Perez]

Gidion.

I'm afraid your questions are too broad to give you a meaningful answer. We can not know whether what you're doing is "right" or "wrong" without knowing what you're trying to achieve.

You should check the advice given in the FAQ on how to ask questions on Statalist. I'd be happy to answer specific questions after you tell us exactly what you're looking for.
http://www.stata.com/support/faqs/re...statalist-faq/

[Gidion Adirinekso]

Dear Emad Shehata and Jorge Eduardo Perez Perez.

Thank you for your advices, and I will explain generally about the model:.

About the economic meaning. I try to test is there any relationship between land rent differentials (between urban and rural) to urban labor market (major issues) and also urban land market (minor issues). In Urban labor market I am trying to know how land rent differentials cause job creation and wages in urban labor market. In urban land rent, I want to know how land rent differentials cause land rent for employee and unemployee in urban area. Actually, I want to modify Zenou model and test impirically. Theoritical background of this research was inspiring by Harris-Todaro Model of migration, but I will see from another side using Zenou's model. I hope this will make it clear.

Questions:
1. Am I right to do what Emad Shehata suggestion ? I attached below the command and the results
2. If then, on the process stata give message : Maximum number of iterations exceeded. How should I do ?

This is more complete and technically I have done:

The Equations (for clear letter, please look at attachment)
Rc(x)=sτ [ (δ+θ^c) / (δ+sθ^c) ]*N^c - τx
R_U^c (x)=s.τ (N^c - x)
L^(C*)= (s〖θ^c〗^(*1-μ))/(δ+s〖θ^(c*)〗^(1-μ) ) (N-L^(R*) )
w_L^C=(1-β)(r+δ)(1-s)τ/(r+δ+βs ̅〖θ^C〗^(1-μ) ) L^(C*) +β(r+δ+s ̅〖θ^C〗^(1-μ) )/(r+δ+βs ̅〖θ^C〗^(1-μ) ) y^(C*)
y^(C*)=(r+δ+βs ̅〖θ^C〗^(1-μ))/(1-β)(r+δ) γ(r+δ)/〖θ^C〗^(-μ) + (s〖θ^c〗^(1-μ) (1-s)τ)/(δ+s〖θ^c〗^(1-μ) ) (N-L^(R*) )



The Variables:
The Variables: R_L^(c*) (x)=Urban Land Rent for worker , N^c=Total Population in urban area, x=xkab=distance from cbd , R_U^c (x)=urban land rent for unemployment, N=total population , L^R=number of working labor in rural, w_L^C=wages in urban , L^(C*)=number of working labor in urban , y^(C*)=job creation in urban

The parameters: s=searc effort of labor to find job τ=commuter cost of worker, δ=job destroying rate , 〖θ^c=theta〗^ =market tightness in urban labor market , r=discount rate , β=bargaining power of labor , μ=cobb douglas coef between 0-1, γ=fsc=firm search cost, x=distance from CBD


The Command in Stata

nlsur ( Rc = {s=0.5}*{τ=2.5}*(({δ=0.12}+{theta=0.616})/({δ=0.12}+{s=0.5}*{theta=0.616}))*Nc - {τ=2.5}*xkab) ( Rcu = {s=0.5}*{τ=2.5}*Nc + {s=0.5}*{τ=2.5}*xkab) (Lc = ({s=0.5}*{theta=0.616}/({δ=0.12}+{s=0.5}*{theta=0.616}))*N - ({s=0.5}*{theta=0.616}/({δ=0.12}+{s=0.5}*{theta=0.616}))*Lr) ( jcurban= (({r=0.1}+{δ=0.12}+{β=0.2}*{s=0.5}*{theta=0.616}) / (1-{β=0.2}*({r=0.1}+{δ=0.12}))*({fsc=0.15}*{r=0.1}+{f sc=0.15}*{δ=0.12}) + ({s=0.5}*{theta=0.616}*{τ=2.5}-{s=0.5}*{theta=0.616}*{s=0.5}*{τ=2.5})/({δ=0.12}+{s=0.5}*{theta=0.616})*N - ({s=0.5}*{theta=0.616}*{τ=2.5}-{s=0.5}*{theta=0.616}*{s=0.5}*{τ=2.5})/({δ=0.12}+{s=0.5}*{theta=0.616})*Lr)) (wc=((({β=0.2}*{r=0.1}+{β=0.2}*{δ=0.12}+{β=0.2}*{s =0.5}*{theta=0.616})*({fsc=0.01}*({r=0.1}+{δ=0.12} ))) / (({r=0.1}+{δ=0.12}-{β=0.2}*{r=0.1}-{β=0.2}*{δ=0.12})*{theta=0.616}))+(({r=0.1}+({β=0. 2}*({r=0.1}+{s=0.5}*{theta=0.616}+{δ=0.12}))) + ({δ=0.12}*{τ=2.5}-{δ=0.12}*{s=0.5}*{τ=2.5})) / ({r=0.1}+{δ=0.12}+{β=0.2}*{s=0.5}*{theta=0.616})*( ( {s=0.5}*{theta=0.616})/({δ=0.12}+{s=0.5}*{theta=0.616}))*N-(({r=0.1}+({β=0.2}*({r=0.1}+{s=0.5}*{theta=0.616}+ {δ=0.12}))) + ({δ=0.12}*{τ=2.5}-{δ=0.12}*{s=0.5}*{τ=2.5})) / ({r=0.1}+{δ=0.12}+{β=0.2}*{s=0.5}*{theta=0.616})*( ( {s=0.5}*{theta=0.616})/({δ=0.12}+{s=0.5}*{theta=0.616}))*Lr)

The Result:

Calculating NLS estimates...
Iteration 0: Residual SS = 1.41e+16
Iteration 1: Residual SS = 1.37e+16
Iteration 2: Residual SS = 1.37e+16
Iteration 3: Residual SS = 1.37e+16
Iteration 4: Residual SS = 1.37e+16
Iteration 5: Residual SS = 1.37e+16
Iteration 6: Residual SS = 1.37e+16
Iteration 7: Residual SS = 1.37e+16
Iteration 8: Residual SS = 1.37e+16
Iteration 9: Residual SS = 1.37e+16
Iteration 10: Residual SS = 1.37e+16
Iteration 11: Residual SS = 1.37e+16
Iteration 12: Residual SS = 1.37e+16
Iteration 13: Residual SS = 1.37e+16
Calculating FGNLS estimates...
Iteration 0: Scaled RSS = 2457.553
Iteration 1: Scaled RSS = 2437.816
Iteration 2: Scaled RSS = 2435.802
Iteration 3: Scaled RSS = 2435.8
Iteration 4: Scaled RSS = 2435.8

FGNLS regression
---------------------------------------------------------------------
Equation | Obs Parms RMSE R-sq Constant
----------------+----------------------------------------------------
1 Rc | 492 4 3494019 0.2344* (none)
2 Rcu | 492 2 3959116 0.1811* (none)
3 Lc | 492 3 64264.35 0.9049* (none)
4 jcurban | 492 7 58396.85 0.6779 r
5 wc | 492 7 187692.6 -0.0248 fsc
---------------------------------------------------------------------
* Uncentered R-sq

------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
/s | .8927031 .0072136 123.75 0.000 .8785646 .9068415
/t | 4.651894 .309321 15.04 0.000 4.045636 5.258152
/d | 4.214471 1.323854 3.18 0.001 1.619764 6.809177
/theta | 2.216726 .7013804 3.16 0.002 .8420457 3.591406
/r | -3.906808 1.240583 -3.15 0.002 -6.338305 -1.475311
/ß | .9887485 .000669 1478.02 0.000 .9874374 .9900597
/fsc | 2956.139 . . . . .
------------------------------------------------------------------------------

Questions:

1. If I want to know the relationship between variables, It was right what I’ve done?
2. If the step is yes, how to make an interpretation in every equation ?
3. If the step is wrong, please give me the light how to conduct rightly to estimate non linear in parameters of system equations.

New Step Follow the Emad Shehata’s suggestion

Command:nlcom
%one by one equation%
Eq: Rc
nlcom ((_b[/b0]*_b[/b1])*((_b[/b2]+_b[/b3])/(_b[/b2]+_b[/b0])*_b[/b3])) (_b[/b1])
Eq: Ru
nlcom (_b[/b0]*_b[/b1]) (-_b[/b0]*_b[/b1])
Eq: Lc
nlcom (_b[/b0]*_b[/b3]/(_b[/b2]+_b[/b0]*_b[/b3]))(-_b[/b0]*_b[/b3]/(_b[/b2]+_b[/b0]*_b[/b3]))
Eq: Jcurban
nlcom (((_b[/b5]+_b[/b2]+_b[/b4]*_b[/b0]*_b[/b3]) / (1-_b[/b4]*(_b[/b5]+_b[/b2])))*((_b[/b6]*_b[/b5]+_b[/b6]*_b[/b2]) /_b[/b11]))(((_b[/b0]*_b[/b3]*_b[/b1])-(_b[/b0]*_b[/b3]*_b[/b0]*_b[/b1]))/(_b[/b2]+_b[/b0]*_b[/b3])) (-((_b[/b0]*_b[/b3]*_b[/b1])-(_b[/b0]*_b[/b3]*_b[/b0]*_b[/b1]))/(_b[/b2]+_b[/b0]*_b[/b3]))

Eq: Wc
nlcom ((_b[/b4] *_b[/b5] +_b[/b4]*_b[/b2]+_b[/b4]*_b[/b0]*_b[/b3])*(_b[/b6]*(_b[/b5]+_b[/b2])) / (_b[/b5]+_b[/b2]-_b[/b4]*_b[/b5]_b[/b4]*_b[/b2]*_b[/b3]))(((_b[/b5]+_b[/b4]*(_b[/b5]+_b[/b0]
*_b[/b3]+_b[/b2]))+ (_b[/b2] *_b[/b1])*(1-_b[/b0])) / (_b[/b5]+_b[/b2]+_b[/b4]*_b[/b0]
*_b[/b3]))*(( _b[/b0]*_b[/b3])/(_b[/b2]+_b[/b0]*_b[/b3]))(-((_b[/b5]+_b[/b4]*(_b[/b5]
+_b[/b0]*_b[/b3]+_b[/b2]))+ (_b[/b2] *_b[/b1])*(1-_b[/b0])) / (_b[/b5]+_b[/b2]+_b[/b4]*_b[/b0]
*_b[/b3]))*(( _b[/b0]*_b[/b3])/(_b[/b2]+_b[/b0]*_b[/b3]))
(((_b[/r]+_b[/ß]*(_b[/r]+_b[/s]*_b[/T1µ]+_b[/d]))+ (_b[/d] *_b[/t])*(1-_b[/s])) /(_b[/r]+_b[/d]+_b[/ß]*_b[/s]*_b[/T1µ]))*(( _b[/s]*_b[/T1µ])/(_b[/d]+_b[/s]*_b[/T1µ]))
(-((_b[/r]+_b[/ß]*(_b[/r]+_b[/s]*_b[/T1µ]+_b[/d]))+ (_b[/d] *_b[/t])*(1-_b[/s])) / (_b[/r]+_b[/d]+_b[/ß]*_b[/s]*_b[/T1µ]))*(( _b[/s]*_b[/T1µ])/(_b[/d]+_b[/s]*_b[/T1µ]))

%Simultanously Command%
nlcom ((_b[/b0]*_b[/b1])*((_b[/b2]+_b[/b3])/(_b[/b2]+_b[/b0])*_b[/b3])) (_b[/b1]) (_b[/b0]*_b[/b1]) (-_b[/b0]*_b[/b1]) (_b[/b0]*_b[/b3]/(_b[/b2]+_b[/b0]*_b[/b3]))(-_b[/b0]*_b[/b3]/(_b[/b2]+_b[/b0]*_b[/b3])) (((_b[/b5]+_b[/b2]+_b[/b4]*_b[/b0]*_b[/b3]) / (1-_b[/b4]*(_b[/b5]+_b[/b2])))*((_b[/b6]*_b[/b5]+_b[/b6]*_b[/b2]) /_b[/b11]))
(((_b[/b0]*_b[/b3]*_b[/b1])-(_b[/b0]*_b[/b3]*_b[/b0]*_b[/b1]))/(_b[/b2]+_b[/b0]*_b[/b3])) (-((_b[/b0]*_b[/b3]*_b[/b1])-(_b[/b0]*_b[/b3]*_b[/b0]*_b[/b1]))/(_b[/b2]+_b[/b0]*_b[/b3]))
((_b[/b4] *_b[/b5] +_b[/b4]*_b[/b2]+_b[/b4]*_b[/b0]*_b[/b3])*(_b[/b6]*(_b[/b5]+_b[/b2])) / (_b[/b5]+_b[/b2]-_b[/b4]*_b[/b5]_b[/b4]*_b[/b2]*_b[/b3]))(((_b[/b5]+_b[/b4]*(_b[/b5]+_b[/b0]
*_b[/b3]+_b[/b2]))+ (_b[/b2] *_b[/b1])*(1-_b[/b0])) / (_b[/b5]+_b[/b2]+_b[/b4]*_b[/b0]
*_b[/b3]))*(( _b[/b0]*_b[/b3])/(_b[/b2]+_b[/b0]*_b[/b3]))(-((_b[/b5]+_b[/b4]*(_b[/b5]
+_b[/b0]*_b[/b3]+_b[/b2]))+ (_b[/b2] *_b[/b1])*(1-_b[/b0])) / (_b[/b5]+_b[/b2]+_b[/b4]*_b[/b0]
*_b[/b3]))*(( _b[/b0]*_b[/b3])/(_b[/b2]+_b[/b0]*_b[/b3]))
(((_b[/r]+_b[/ß]*(_b[/r]+_b[/s]*_b[/T1µ]+_b[/d]))+ (_b[/d] *_b[/t])*(1-_b[/s])) /(_b[/r]+_b[/d]+_b[/ß]*_b[/s]*_b[/T1µ]))*(( _b[/s]*_b[/T1µ])/(_b[/d]+_b[/s]*_b[/T1µ]))
(-((_b[/r]+_b[/ß]*(_b[/r]+_b[/s]*_b[/T1µ]+_b[/d]))+ (_b[/d] *_b[/t])*(1-_b[/s])) / (_b[/r]+_b[/d]+_b[/ß]*_b[/s]*_b[/T1µ]))*(( _b[/s]*_b[/T1µ])/(_b[/d]+_b[/s]*_b[/T1µ]))
The Result
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_nl_1 | .0056013 .0003659 15.31 0.000 .0048843 .0063184
_nl_2 | 4.648134 .3089781 15.04 0.000 4.042548 5.25372
_nl_3 | 4.140423 .3068229 13.49 0.000 3.539061 4.741785
_nl_4 | -4.140423 .3068229 -13.49 0.000 -4.741785 -3.539061
_nl_5 | .31955 .00465 68.72 0.000 .3104361 .3286639
_nl_6 | -.31955 .00465 -68.72 0.000 -.3286639 -.3104361
_nl_7 | -.0003123 .0001464 -2.13 0.033 -.0005992 -.0000254
_nl_8 | .162239 .0041954 38.67 0.000 .1540162 .1704618
_nl_9 | -.162239 .0041954 -38.67 0.000 -.1704618 -.1540162
_nl_10 | -8.429482 2.243205 -3.76 0.000 -12.82608 -4.032882
_nl_11 | .064887 .0159501 4.07 0.000 .0336254 .0961486
_nl_12 | -.064887 .0159501 -4.07 0.000 -.0961486 -.0336254
------------------------------------------------------------------------------

Thank U