Results. Two-step GMM estimates of simultaneous equations. Dependent variable: Disease.

From left to right, the number of control variables increases in a stepwise fashion. The IVs for income are the variables that are in the income equation (listed in the corresponding columns in Table 4) but not in the disease equation here. Robust standard errors are presented in parentheses next to their corresponding coefficient estimates. First-stage F-test indicates strength of IVs if there is only one endogenous variable (income). If there are multiple endogenous variables (income and spatially lagged disease), Shea's Partial R2 indicates strength of IVs [75]. The institutions variable is not included as an IV for income and therefore 4b and 3b are identical. Bold indicates significance at the 10% level. n = 139.IVVariable is instrumented.JBased on Hansen's J statistic.aUnits×10−2.*p≤0.10.**p≤0.05.***p≤0.01.

从左至右，控制变量的数量呈阶梯式递增。收入的工具变量（Instrumental Variables，IVs）指纳入收入方程（见表4对应列）但未纳入本次疾病方程的变量。各系数估计值旁的括号内标注了稳健标准误。当仅存在单个内生变量（收入）时，第一阶段F检验可用于衡量工具变量的强度。当存在多个内生变量（收入与空间滞后疾病变量）时，采用谢亚部分R²（Shea's Partial R²）衡量工具变量的强度[75]。制度变量未被纳入收入的工具变量集合，因此模型4b与模型3b完全一致。字体加粗代表在10%的显著性水平下显著。观测样本量n=139。工具变量已通过工具变量法处理内生性问题。J检验：基于汉森J统计量。注a：单位为×10⁻²。* 表示p≤0.10，** 表示p≤0.05，*** 表示p≤0.01。