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Spatial 2SLS¶
This notebook contains the PySAL/spreg code for Chapter 7 - Spatial 2SLS
in: Modern Spatial Econometrics in Practice: A Guide to GeoDa, GeoDaSpace and PySAL.
by: Luc Anselin and Sergio J. Rey.
[1]:
%load_ext watermark
%watermark
Last updated: 2021-01-03T11:26:48.607797-05:00
Python implementation: CPython
Python version : 3.8.6
IPython version : 7.19.0
Compiler : Clang 11.0.0
OS : Darwin
Release : 20.2.0
Machine : x86_64
Processor : i386
CPU cores : 8
Architecture: 64bit
[2]:
import numpy
import libpysal
import spreg
%watermark -w
%watermark -iv
Watermark: 2.1.0
spreg : 1.2.0.post1
libpysal: 4.3.0
numpy : 1.19.4
Data¶
[3]:
libpysal.examples.explain("baltim")
baltim
======
Baltimore house sales prices and hedonics, 1978.
----------------------------------------------------------------
* baltim.dbf: attribute data. (k=17)
* baltim.shp: Point shapefile. (n=211)
* baltim.shx: spatial index.
* baltim.tri.k12.kwt: kernel weights using a triangular kernel with 12 nearest neighbors in KWT format.
* baltim_k4.gwt: nearest neighbor weights (4nn) in GWT format.
* baltim_q.gal: queen contiguity weights in GAL format.
* baltimore.geojson: spatial weights in geojson format.
Source: Dubin, Robin A. (1992). Spatial autocorrelation and neighborhood quality. Regional Science and Urban Economics 22(3), 433-452.
[4]:
# Read Baltimore data
db = libpysal.io.open(libpysal.examples.get_path("baltim.dbf"), "r")
ds_name = "baltim.dbf"
# Read dependent variable
y_name = "PRICE"
y = numpy.array(db.by_col(y_name)).T
y = y[:, numpy.newaxis]
# Read exogenous variables
x_names = ["NROOM", "NBATH", "PATIO", "FIREPL", "AC", "GAR", "AGE", "LOTSZ", "SQFT"]
x = numpy.array([db.by_col(var) for var in x_names]).T
[5]:
# Read spatial data
ww = libpysal.io.open(libpysal.examples.get_path("baltim_q.gal"))
w = ww.read()
ww.close()
w_name = "baltim_q.gal"
w.transform = "r"
Basic Spatial 2SLS¶
The model to estimate is:
\[y = \rho Wy + X \beta + \epsilon\]
where you use \(WX\) as instruments of \(Wy\).
[6]:
model = spreg.GM_Lag(
y,
x,
w=w,
name_y=y_name,
name_x=x_names,
name_w="baltim_q",
name_ds="baltim"
)
print(model.summary)
REGRESSION
----------
SUMMARY OF OUTPUT: SPATIAL TWO STAGE LEAST SQUARES
--------------------------------------------------
Data set : baltim
Weights matrix : baltim_q
Dependent Variable : PRICE Number of Observations: 211
Mean dependent var : 44.3072 Number of Variables : 11
S.D. dependent var : 23.6061 Degrees of Freedom : 200
Pseudo R-squared : 0.7278
Spatial Pseudo R-squared: 0.6928
------------------------------------------------------------------------------------
Variable Coefficient Std.Error z-Statistic Probability
------------------------------------------------------------------------------------
CONSTANT -2.5762742 5.5210355 -0.4666288 0.6407655
NROOM 0.9440746 1.0609697 0.8898224 0.3735612
NBATH 5.5981348 1.7376725 3.2216283 0.0012746
PATIO 5.8424768 2.7435166 2.1295577 0.0332081
FIREPL 6.4579185 2.4238370 2.6643369 0.0077140
AC 5.4871926 2.3450930 2.3398614 0.0192909
GAR 4.3565951 1.6955478 2.5694321 0.0101865
AGE -0.0730060 0.0523546 -1.3944510 0.1631814
LOTSZ 0.0579765 0.0149534 3.8771359 0.0001057
SQFT 0.0395330 0.1638055 0.2413409 0.8092909
W_PRICE 0.5823313 0.0721387 8.0723813 0.0000000
------------------------------------------------------------------------------------
Instrumented: W_PRICE
Instruments: W_AC, W_AGE, W_FIREPL, W_GAR, W_LOTSZ, W_NBATH, W_NROOM,
W_PATIO, W_SQFT
================================ END OF REPORT =====================================
Second order spatial lags¶
You can also use \([WX, W^2X]\) as instruments of \(Wy\).
[7]:
# using second order spatial lags for the instruments, set w_lags = 2
model2 = spreg.GM_Lag(
y,
x,
w=w,
w_lags=2,
name_y=y_name,
name_x=x_names,
name_w="baltim_q",
name_ds="baltim"
)
print(model2.summary)
REGRESSION
----------
SUMMARY OF OUTPUT: SPATIAL TWO STAGE LEAST SQUARES
--------------------------------------------------
Data set : baltim
Weights matrix : baltim_q
Dependent Variable : PRICE Number of Observations: 211
Mean dependent var : 44.3072 Number of Variables : 11
S.D. dependent var : 23.6061 Degrees of Freedom : 200
Pseudo R-squared : 0.7276
Spatial Pseudo R-squared: 0.6915
------------------------------------------------------------------------------------
Variable Coefficient Std.Error z-Statistic Probability
------------------------------------------------------------------------------------
CONSTANT -2.8867580 5.4563344 -0.5290654 0.5967601
NROOM 0.9527428 1.0613055 0.8977083 0.3693411
NBATH 5.5975309 1.7386698 3.2194330 0.0012844
PATIO 5.7884989 2.7409866 2.1118304 0.0347010
FIREPL 6.4012808 2.4201110 2.6450360 0.0081682
AC 5.4587589 2.3451078 2.3277220 0.0199269
GAR 4.3440361 1.6961624 2.5610969 0.0104342
AGE -0.0713188 0.0521742 -1.3669353 0.1716456
LOTSZ 0.0575329 0.0149111 3.8583943 0.0001141
SQFT 0.0377524 0.1638248 0.2304438 0.8177470
W_PRICE 0.5893267 0.0695101 8.4782886 0.0000000
------------------------------------------------------------------------------------
Instrumented: W_PRICE
Instruments: W2_AC, W2_AGE, W2_FIREPL, W2_GAR, W2_LOTSZ, W2_NBATH, W2_NROOM,
W2_PATIO, W2_SQFT, W_AC, W_AGE, W_FIREPL, W_GAR, W_LOTSZ,
W_NBATH, W_NROOM, W_PATIO, W_SQFT
================================ END OF REPORT =====================================
Spatial Diagnostics¶
[8]:
model = spreg.GM_Lag(
y,
x,
w=w,
spat_diag=True,
name_y=y_name,
name_x=x_names,
name_w="baltim_q",
name_ds="baltim"
)
print(model.summary)
REGRESSION
----------
SUMMARY OF OUTPUT: SPATIAL TWO STAGE LEAST SQUARES
--------------------------------------------------
Data set : baltim
Weights matrix : baltim_q
Dependent Variable : PRICE Number of Observations: 211
Mean dependent var : 44.3072 Number of Variables : 11
S.D. dependent var : 23.6061 Degrees of Freedom : 200
Pseudo R-squared : 0.7278
Spatial Pseudo R-squared: 0.6928
------------------------------------------------------------------------------------
Variable Coefficient Std.Error z-Statistic Probability
------------------------------------------------------------------------------------
CONSTANT -2.5762742 5.5210355 -0.4666288 0.6407655
NROOM 0.9440746 1.0609697 0.8898224 0.3735612
NBATH 5.5981348 1.7376725 3.2216283 0.0012746
PATIO 5.8424768 2.7435166 2.1295577 0.0332081
FIREPL 6.4579185 2.4238370 2.6643369 0.0077140
AC 5.4871926 2.3450930 2.3398614 0.0192909
GAR 4.3565951 1.6955478 2.5694321 0.0101865
AGE -0.0730060 0.0523546 -1.3944510 0.1631814
LOTSZ 0.0579765 0.0149534 3.8771359 0.0001057
SQFT 0.0395330 0.1638055 0.2413409 0.8092909
W_PRICE 0.5823313 0.0721387 8.0723813 0.0000000
------------------------------------------------------------------------------------
Instrumented: W_PRICE
Instruments: W_AC, W_AGE, W_FIREPL, W_GAR, W_LOTSZ, W_NBATH, W_NROOM,
W_PATIO, W_SQFT
DIAGNOSTICS FOR SPATIAL DEPENDENCE
TEST MI/DF VALUE PROB
Anselin-Kelejian Test 1 5.234 0.0221
================================ END OF REPORT =====================================
White Standard Errors¶
[9]:
model = spreg.GM_Lag(
y,
x,
w=w,
robust="white",
spat_diag=True,
name_y=y_name,
name_x=x_names,
name_w="baltim_q",
name_ds="baltim"
)
print(model.summary)
REGRESSION
----------
SUMMARY OF OUTPUT: SPATIAL TWO STAGE LEAST SQUARES
--------------------------------------------------
Data set : baltim
Weights matrix : baltim_q
Dependent Variable : PRICE Number of Observations: 211
Mean dependent var : 44.3072 Number of Variables : 11
S.D. dependent var : 23.6061 Degrees of Freedom : 200
Pseudo R-squared : 0.7278
Spatial Pseudo R-squared: 0.6928
White Standard Errors
------------------------------------------------------------------------------------
Variable Coefficient Std.Error z-Statistic Probability
------------------------------------------------------------------------------------
CONSTANT -2.5762742 7.0147591 -0.3672648 0.7134215
NROOM 0.9440746 1.4002856 0.6742015 0.5001832
NBATH 5.5981348 2.1605285 2.5910951 0.0095671
PATIO 5.8424768 2.9445656 1.9841558 0.0472385
FIREPL 6.4579185 2.4500195 2.6358641 0.0083923
AC 5.4871926 2.6021469 2.1087175 0.0349690
GAR 4.3565951 2.2070747 1.9739228 0.0483905
AGE -0.0730060 0.0976079 -0.7479516 0.4544894
LOTSZ 0.0579765 0.0237454 2.4415887 0.0146228
SQFT 0.0395330 0.2355809 0.1678105 0.8667323
W_PRICE 0.5823313 0.1325884 4.3920220 0.0000112
------------------------------------------------------------------------------------
Instrumented: W_PRICE
Instruments: W_AC, W_AGE, W_FIREPL, W_GAR, W_LOTSZ, W_NBATH, W_NROOM,
W_PATIO, W_SQFT
DIAGNOSTICS FOR SPATIAL DEPENDENCE
TEST MI/DF VALUE PROB
Anselin-Kelejian Test 1 5.234 0.0221
================================ END OF REPORT =====================================