Table 3

Obtaining a joint preferred specification for social care, healthcare and public health expenditure by combining full specifications with forward selection (second-stage results) (created by the authors)

Variables(1)(2)(3)(4)
All causesAll causesAll causesAll causes
2013/2014 PB/GSS/PH spend2013/2014 PB/GSS/PH spend2013/2014 PB/GSS/PH spend2013/2014 PB/GSS/PH spend
SYLLR 2013/2014/2015SYLLR 2013/2014/2015SYLLR 2013/2014/2015SYLLR 2013/2014/2015
Outcome modelOutcome modelOutcome modelOutcome model
Instrument PB/GSS/PH spendInstrument PB/GSS/PH spendInstrument PB/GSS/PH spendInstrument PB/GSS/PH spend
WeightedWeightedWeightedWeighted
IV second stageIV second stageIV second stageIV second stage
Parsimonious specificationSpecification_2Specification_3Specification_4
11 instruments7 instruments5 instruments4 instruments
Public health expenditure per person−0.051
(0.039)
−0.043
(0.047)
−0.060
(0.044)
−0.099**
(0.045)
CCG (PB) healthcare spend per person−0.862***
(0.223)
−0.461
(0.313)
−0.637*
(0.369)
−0.693**
(0.333)
Social service (GSS) spend per person−0.206
(0.133)
−0.469***
(0.161)
−0.370*
(0.205)
−0.471**
(0.237)
% population aged 16–74 that are permanently sick0.649***
(0.046)
0.651***
(0.054)
0.672***
(0.052)
0.528***
(0.073)
% population providing unpaid care−0.381***
(0.086)
−0.388***
(0.096)
−0.400***
(0.097)
−0.143
(0.118)
% population in white ethnic group0.163***
(0.042)
0.195***
(0.043)
0.180***
(0.046)
0.299***
(0.078)
Older adult: social service need per person0.416***
(0.143)
Constant13.352***
(1.733)
10.204***
(2.389)
11.655***
(2.873)
12.245***
(2.546)
Observations150150150150
Endogeneity test statistic10.64417.68621.10023.214
Endogeneity p value0.0140.0010.0000.000
Hansen-Sargan test statistic25.69010.4322.1730.080
Hansen-Sargan p value0.0010.0340.3370.778
Pesaran-Taylor reset statistic0.0520.3720.0800.001
Pesaran-Taylor p value0.8200.5420.7770.972
SW_PB F-statistic5.9776.8337.87813.534
SW_PB p value0.0000.0000.0000.000
SW_GSS F-statistic4.9395.5216.1359.722
SW_GSS p value0.0000.0000.0010.000
SW_PH F-statistic18.45122.09230.94446.946
SW_PH p value0.0000.0000.0000.000
  • Robust SEs in parentheses.

  • ***p<0.01, **p<0.05, *p<0.1.

  • CCG, Clinical Commissioning Group; PH, public health; SW, Sanderson-Windmeijer.