Inference for the neighbourhood inequality index

Figures & data

Figure 1. Scaling and zonation effects on neighbourhood inequality.

Figure 2. Neighbourhood inequality in Chicago, IL, 2014, versus two counterfactual distributions.

Note: Author analysis of US Census and American Community Survey (ACS) data. Confidence intervals are at the 95% level. (a) NI(F₀, d) - NI(F₁, d), (b) NI(F₀, d) - NI(F², d).

Table 1. Monte Carlo simulations of the size and power of dominance tests for NI curves that are based on the NI index SE approximations.

	Distance cut-offs (miles)									# Rejected	Rejected	Weak	Strong
	0.4	0.7	1	1.4	1.7	2	3	5	12
$n$	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)
(A) Size comparisons for the true null $H_0^3:NI(y_{0,r}^n,d)=NI(y_{1,r}^n,d),\mathrm{\forall }d$
1000	.	0.00	.	0.24	.	0.19	0.16	0.03	0.01	1.1	0.46	0.60	0.00
2000	0.00	0.00	0.32	0.22	0.23	0.19	0.10	0.08	0.00	2.4	0.62	0.53	0.00
5000	0.00	0.00	0.33	0.15	0.17	0.09	0.01	0.01	0.00	1.1	0.52	0.47	0.00
8000	0.00	0.00	0.22	0.06	0.09	0.06	0.05	0.01	0.00	0.8	0.38	0.53	0.00
(B) Power comparisons for the true alternative $H_a^3:NI(y_{0,r}^n,d)\ge NI(y_{2,r}^n,d),\mathrm{\forall }d$
1000	.	0.00	.	0.29	.	0.31	0.19	0.09	0.03	1.7	0.60	0.92	0.00
2000	0.00	0.00	0.40	0.31	0.44	0.26	0.13	0.08	0.00	3.3	0.85	0.88	0.00
5000	0.00	0.00	0.55	0.28	0.49	0.24	0.12	0.09	0.03	4.3	0.81	0.98	0.00
8000	0.00	0.05	0.57	0.34	0.53	0.32	0.30	0.22	0.15	8.7	0.82	0.99	0.00

Figure 3. Trends in neighbourhood inequality in Chicago, IL.

Note: Author analysis of US Census and American Community Survey (ACS) data. Confidence intervals are at the 95% level.

Table 2. P-values for the null hypothesis of the type $H_0^1:NI\left(y_t,d\right)=G\left(y_t\right)$ and $H_0^2:NI\left(y_t,d\right)=NI\left(y_t,0.4\right)$, with $t=1980,1990,2000,2014$ and $G\left(y_{1980}\right)=0.434$, $G\left(y_{1990}\right)=0.461$, $G\left(y_{2000}\right)=0.473$, $G\left(y_{2014}\right)=0.486$.

Years	Distance $d$ (miles)
2–7	0.4	1	2	3	5	12
(A) p-values for $H_0^1$
1980	0.000	0.000	0.000	0.000	0.004	0.160
1990	0.000	0.000	0.000	0.000	0.000	0.003
2000	0.000	0.000	0.000	0.000	0.001	0.070
2014	0.000	0.000	0.000	0.000	0.002	0.108
(B) p-values for $H_0^2$
1980	.	0.493	0.454	0.396	0.239	0.067
	0	0.000	0.001	0.003	0.009	0.020
1990	.	0.357	0.122	0.046	0.020	0.002
	0	0.004	0.014	0.020	0.025	0.039
2000	.	0.311	0.410	0.461	0.239	0.060
	0	−0.008	−0.004	0.002	0.012	0.027
2014	.	0.467	0.465	0.390	0.269	0.071
	0	−0.001	0.002	0.005	0.011	0.027

Note: Differences in levels of the neighborhood inequality (NI) index are shown in italics.