  Endogeneity bias and instrument variable validation have always been
important topics in statistics and econometrics. In the era of big data, such
issues typically combine with dimensionality issues and, hence, require even
more attention. In this paper, we merge two well-known tools from machine
learning and biostatistics---variable selection algorithms and probablistic
graphs---to estimate house prices and the corresponding causal structure using
2010 data on Sydney. The estimation uses a 200-gigabyte ultrahigh dimensional
database consisting of local school data, GIS information, census data, house
characteristics and other socio-economic records. Using "big data", we show
that it is possible to perform a data-driven instrument selection efficiently
and purge out the invalid instruments. Our approach improves the sparsity of
variable selection, stability and robustness in the presence of high
dimensionality, complicated causal structures and the consequent
multicollinearity, and recovers a sparse and intuitive causal structure. The
approach also reveals an efficiency and effectiveness in endogeneity detection,
instrument validation, weak instrument pruning and the selection of valid
instruments. From the perspective of machine learning, the estimation results
both align with and confirms the facts of Sydney house market, the classical
economic theories and the previous findings of simultaneous equations modeling.
Moreover, the estimation results are consistent with and supported by classical
econometric tools such as two-stage least square regression and different
instrument tests. All the code may be found at
\url{https://github.com/isaac2math/solar_graph_learning}.
