Figures and tables in Comparative analysis of different techniques to impute expenditures into an income data set

Abstract

Income and budget data seldom are measured in the same dataset. In order to make simulations that need both, one requires a reliable procedure to merge an income and a budget survey into one combined dataset. This paper contains the comparison and evaluation of five different techniques to impute expenditures into income datasets: parametric estimation of Engel curves, nonparametric estimation, both constrained and unconstrained matching using a distance function and grade correspondence. After a detailed description of the methods as well as a comparison of the main pros and cons, their effectiveness is tested upon an artificially split data file. In general, the parametric and non-parametric estimation seem to yield the best results, generating imputed values that are closest to the observed values for the budget shares.

This article contains 17 tables.

Tables

Table 1. RMSE per method and per expenditure category

RMSE	FOOD, NON-ALCOHOLIC BEVERAGES	ALCOHOLIC BEVERAGES	TOBACCO	CLOTHING AND FOOTWEAR	HOME FUELS AND ELECTRICITY	RENTS	HOUSEHOLD SERVICES	HEALTH	PRIVATE TRANSPORT
Parametric	0.1597	0.0284	0.0249	0.0632	0.0790	0.2113	0.1538	0.0830	0.1156
Kernel	0.1607	0.0286	0.0252	0.0637	0.0817	0.2220	0.1529	0.0836	0.1137
Distance	0.2231	0.0382	0.0338	0.2074	0.1324	0.3567	0.1938	0.1309	0.2232
Constrained	0.2242	0.0394	0.0348	0.2048	0.1813	0.3556	0.1980	0.1336	0.2396
Grade Corr.	0.4926	0.2005	0.0684	0.2314	0.1812	0.4314	0.3804	0.2247	0.3722
RMSE	PUBLIC TRANSPORT	COMMUNI-CATION	RECREATION AND CULTURE	EDUCATION	RESTAURANTS AND HOTELS	OTHER GOODS AND SERVICES	DURABLES	SAVINGS	AVERAGE	WEIGHTED AVERAGE
Parametric	0.0415	0.0897	0.1259	0.0155	0.1241	0.1464	0.2818	0.8323	0.1431	0.2274
Kernel	0.0430	0.0896	0.1279	0.0157	0.1229	0.1470	0.2826	0.8288	0.1439	0.2278
Distance	0.0461	0.1023	0.1994	0.0239	0.1900	0.2115	0.4133	1.5169	0.2357	0.3819
Constrained	0.0477	0.1024	0.1977	0.0231	0.1788	0.2370	0.3939	1.5244	0.2398	0.3865
Grade Corr.	0.0497	0.0690	0.1574	0.0300	0.3155	7.2507	0.4445	11.024	1.2180	2.2701

Table 2. P-values for the Statistical Tests (Kolmogorov Smirnov, Sign Test, Signed Rank Test) for Food & Non-alcoholic Beverages by Income decile

	INCOME DECILE 1	INCOME DECILE 2	INCOME DECILE 3	INCOME DECILE 4	INCOME DECILE 5	INCOME DECILE 6	INCOME DECILE 7	INCOME DECILE 8	INCOME DECILE 9	INCOME DECILE 10
KOLM. SMIRNOV P-VALUE
Parametric	0.000	0.000	0.000	0.000	0.000	0.000	0.045	0.002	0.213	0.003
Kernel	0.000	0.000	0.000	0.000	0.000	0.000	0.001	0.000	0.071	0.058
Distance	0.019	0.937	0.226	0.524	0.640	0.536	0.084	0.019	0.572	0.408
Constrained	0.008	0.624	0.444	0.977	0.405	0.849	0.002	0.605	0.572	0.304
Grade Corr.	0.000	0.000	0.000	0.002	0.022	0.569	0.009	0.013	0.000	0.000
SIGN TEST P-VALUE
Parametric	0.0001	0.0000	0.0074	0.3093	0.3068	0.4292	0.7453	0.8685	0.2816	0.0055
Kernel	0.0913	0.0016	0.0172	0.0109	0.1252	0.0397	0.0511	0.0311	0.1615	0.3181
Distance	0.0073	0.3239	0.1974	0.4767	0.9186	0.1876	0.3297	0.0174	0.1061	0.3181
Constrained	0.0006	0.5540	0.6918	1.0000	0.2609	0.8744	0.0092	0.1674	0.1615	0.3748
Grade Corr.	0.0000	0.0000	0.0003	0.1201	0.7616	0.6435	1.0000	0.1725	0.0000	0.0000
SIGNED RANK TEST P-VALUE
Parametric	0.0086	0.0000	0.0206	0.9100	0.6720	0.5854	0.4199	0.9981	0.7140	0.0118
Kernel	0.7695	0.0092	0.0775	0.3235	0.0927	0.2790	0.0871	0.0355	0.2895	0.2565
Distance	0.0012	0.3908	0.3347	0.4168	0.8198	0.1974	0.3532	0.0812	0.4333	0.1810
Constrained	0.0001	0.9497	0.2668	0.9551	0.2932	0.9222	0.0019	0.3668	0.0741	0.0764
Grade Corr.	0.0000	0.0000	0.0000	0.0009	0.4365	0.6466	0.6104	0.0185	0.0000	0.0000

Table 3. P-values for the Statistical Tests (Kolmogorov Smirnov, Sign Test, Signed Rank Test) for Clothing & Footwear by Income decile

	INCOME DECILE 1	INCOME DECILE 2	INCOME DECILE 3	INCOME DECILE 4	INCOME DECILE 5	INCOME DECILE 6	INCOME DECILE 7	INCOME DECILE 8	INCOME DECILE 9	INCOME DECILE 10
KOLM. SMIRNOV P-VALUE
Parametric	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Kernel	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Distance	0.228	0.451	0.101	0.049	0.703	0.792	0.102	0.605	0.152	0.598
Constrained	0.547	0.307	0.500	0.771	0.309	0.665	0.440	0.863	0.447	0.532
Grade Corr.	0.006	0.067	0.021	0.010	0.240	0.260	0.152	0.754	0.000	0.000
SIGN TEST P-VALUE
Parametric	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0002	0.0000
Kernel	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0002	0.0000
Distance	0.0742	0.1581	0.3233	0.1746	0.9178	0.9145	0.3254	1.0000	0.7869	0.7393
Constrained	0.9171	0.0386	0.2559	0.2521	0.3768	0.7488	0.8265	0.8664	0.5882	0.5044
Grade Corr.	0.0205	0.1301	0.0807	0.0057	0.9589	0.6399	0.1910	0.9562	0.0157	0.0000
SIGNED RANK TEST P-VALUE
Parametric	0.0001	0.0001	0.0000	0.0000	0.0048	0.0003	0.0658	0.0056	0.0158	0.0001
Kernel	0.0006	0.0024	0.0000	0.0000	0.0204	0.0000	0.0120	0.0004	0.0047	0.0017
Distance	0.5840	0.3338	0.2254	0.0556	0.6569	0.9276	0.0646	0.5447	0.5943	0.5390
Constrained	0.7142	0.0521	0.1738	0.3413	0.2139	0.8735	0.2613	0.5648	0.5366	0.4289
Grade Corr.	0.0192	0.0345	0.0113	0.0007	0.3995	0.2746	0.1999	0.8189	0.0012	0.0000

Table 4. P-values for the Statistical Tests (Kolmogorov Smirnov, Sign Test, Signed Rank Test) for Private Transport by Income decile

	INCOME DECILE 1	INCOME DECILE 2	INCOME DECILE 3	INCOME DECILE 4	INCOME DECILE 5	INCOME DECILE 6	INCOME DECILE 7	INCOME DECILE 8	INCOME DECILE 9	INCOME DECILE 10
KOLM. SMIRNOV P-VALUE
Parametric	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Kernel	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Distance	0.001	0.028	0.393	0.710	0.405	0.024	0.244	0.264	0.152	0.259
Constrained	0.000	0.123	0.982	0.361	0.230	0.082	0.207	0.359	0.883	0.800
Grade Corr.	0.000	0.001	0.056	0.603	0.832	0.115	0.071	0.430	0.032	0.001
SIGN TEST P-VALUE
Parametric	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
Kernel	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
Distance	0.0071	0.0286	0.0895	0.6435	0.6426	0.0793	0.3566	0.2687	0.6276	0.6573
Constrained	0.0134	0.0750	0.1793	0.2801	0.7580	0.0173	0.7043	0.2941	0.1178	0.7393
Grade Corr.	0.0001	0.0080	0.0997	0.1885	0.4136	0.0382	0.0177	0.4783	0.4214	0.0071
SIGNED RANK TEST P-VALUE
Parametric	0.0000	0.0000	0.0000	0.0068	0.0005	0.0000	0.1635	0.0150	0.0093	0.0002
Kernel	0.0000	0.0000	0.0000	0.0001	0.0000	0.0000	0.0505	0.0124	0.0070	0.0374
Distance	0.0365	0.0278	0.2695	0.7604	0.6489	0.0135	0.1925	0.0949	0.2934	0.8728
Constrained	0.0243	0.0652	0.4758	0.2550	0.9930	0.0270	0.5431	0.1092	0.1507	0.9040
Grade Corr.	0.0000	0.0003	0.0989	0.3547	0.3325	0.0104	0.0463	0.2263	0.2372	0.0005

Table 5. P-values for the Statistical Tests (Kolmogorov Smirnov, Sign Test, Signed Rank Test) for Saving by Income decile

	INCOME DECILE 1	INCOME DECILE 2	INCOME DECILE 3	INCOME DECILE 4	INCOME DECILE 5	INCOME DECILE 6	INCOME DECILE 7	INCOME DECILE 8	INCOME DECILE 9	INCOME DECILE 10
KOLM. SMIRNOV P-VALUE
Parametric	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Kernel	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Distance	0.722	0.050	0.226	0.771	0.405	0.234	0.018	0.673	0.829	0.011
Constrained	0.920	0.199	0.982	0.977	0.640	0.418	0.630	0.912	0.508	0.030
Grade Corr.	0.040	0.247	0.067	0.078	0.027	0.003	0.213	0.053	0.000	0.000
SIGN TEST P-VALUE
Parametric	0.0000	0.0000	0.0000	0.0044	0.0000	0.0000	0.1590	0.0001	0.0002	0.0000
Kernel	0.0000	0.0000	0.0000	0.0005	0.0000	0.0000	0.0171	0.0000	0.0001	0.0000
Distance	0.3892	0.0607	0.4278	0.7604	1.0000	0.3703	0.1041	0.6193	0.5904	0.1491
Constrained	0.1037	0.0102	0.3723	0.4767	0.5398	0.8744	0.5882	0.2040	0.5183	0.0959
Grade Corr.	1.0000	0.3562	0.4961	0.2925	0.3118	0.1357	0.7467	0.0560	0.3084	0.0000
SIGNED RANK TEST P-VALUE
Parametric	0.0000	0.0000	0.0010	0.0084	0.0010	0.0155	0.9880	0.0011	0.0264	0.0000
Kernel	0.0001	0.0000	0.0048	0.0010	0.0003	0.0001	0.1471	0.0000	0.0146	0.0000
Distance	0.8222	0.0934	0.4229	0.9461	0.3304	0.2561	0.0876	0.6433	0.8904	0.0281
Constrained	0.5855	0.0650	0.6691	0.6501	0.8823	0.9395	0.3458	0.4177	0.3587	0.0085
Grade Corr.	0.9726	0.6301	0.1146	0.0371	0.0456	0.4947	0.3127	0.1129	0.2783	0.0000

Table A1. P-values for Food & Non-alcoholic Beverages by Age of Reference Person

	AGE < 30	30 <= AGE < 50	50 <= AGE < 65	65 <= AGE
KOLM. SMIRNOV P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.000 0.000 0.040 0.049 0.005	0.000 0.000 0.975 0.774 0.000	0.000 0.000 0.143 0.737 0.000	0.000 0.000 0.408 0.886 0.001
SIGN TEST P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.0000 0.0000 0.0419 0.0324 0.0241	0.0290 0.0001 0.4176 0.3010 0.8906	0.0000 0.0050 0.2738 0.8884 0.6175	0.9159 0.0843 0.8053 0.9159 0.2359
SIGNED RANK TEST P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.0000 0.0000 0.0094 0.0120 0.0016	0.4845 0.0181 0.9159 0.5883 0.0211	0.0007 0.0324 0.7293 0.7856 0.0045	0.5176 0.5517 0.9754 0.7631 0.0176

Table A2. P-values for Food and Non-alcoholic Beverages by Professional Status

	(SELF-) EMPLOYED	UNEMPLOYED	(EARLY) RETIRED	OTHER
KOLM. SMIRNOV P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.000 0.000 0.407 0.772 0.000	0.000 0.000 0.087 0.033 0.000	0.000 0.000 0.036 0.017 0.001	0.003 0.003 0.000 0.002 0.008
SIGN TEST P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.0011 0.0001 0.1775 0.5839 0.2880	0.3409 0.1440 0.2276 0.0042 0.1033	0.0000 0.0000 0.0086 0.0016 0.5616	0.0639 0.2480 0.0639 0.0370 0.6530
SIGNED RANK TEST P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.0297 0.0049 0.9349 0.4898 0.0003	0.0216 0.0026 0.0608 0.0087 0.0025	0.0000 0.0000 0.0051 0.0021 0.0407	0.0151 0.0296 0.0057 0.0160 0.0619

Table A3. P-values for Foods and Non-alcoholic Beverages by Household Type

	SINGLE WITHOUT CHILDREN	SINGLE WITH CHILDREN	COHABITING WITHOUT CHILDREN	COHABITING WITH CHILDREN
KOLM. SMIRNOV P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.000 0.000 0.365 0.781 0.000	0.019 0.008 0.180 0.424 0.152	0.000 0.000 0.393 0.601 0.000	0.000 0.000 0.056 0.784 0.000
SIGN TEST P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.0000 0.0000 0.6006 0.8752 0.0000	0.8439 0.6937 0.0756 0.4307 0.8482	0.0000 0.0111 0.4393 0.0400 0.0000	0.0000 0.0000 0.0873 0.7434 0.0000
SIGNED RANK TEST P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.0000 0.0000 0.9581 0.9793 0.0000	0.9659 0.7772 0.1487 0.3869 0.6513	0.0000 0.0000 0.8952 0.0580 0.0000	0.0000 0.0000 0.4990 0.8262 0.0000

Table A4. P-values for Clothing and Footwear by Age of Reference Person

	AGE < 30	30 <= AGE < 50	50 <= AGE < 65	65 <= AGE
KOLM. SMIRNOV P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.000 0.000 0.060 0.246 0.513	0.000 0.000 0.266 0.606 0.467	0.000 0.000 0.027 0.440 0.021	0.000 0.000 0.445 0.280 0.292
SIGNTEST P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.0000 0.0000 0.6225 0.5109 0.6676	0.0000 0.0000 0.6440 0.3863 0.9104	0.0000 0.0000 0.0966 0.4384 0.8883	0.0000 0.0000 0.9132 0.5614 0.9432
SIGNED RANK TEST P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.0000 0.0000 0.5804 0.3702 0.4759	0.0000 0.0000 0.4255 0.5941 0.3834	0.0000 0.0000 0.0816 0.6191 0.1766	0.0006 0.0014 0.3289 0.1008 0.6787

Table A5. P-values for Clothing and Footwear by Professional Status

	(SELF-) EMPLOYED	UNEMPLOYED	(EARLY) RETIRED	OTHER
KOLM. SMIRNOV P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.000 0.000 0.292 0.772 0.009	0.000 0.000 0.418 0.167 0.439	0.000 0.000 0.040 0.569 0.830	0.000 0.000 0.328 0.732 0.762
SIGN TEST P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.0000 0.0000 0.1116 0.5905 0.7841	0.0002 0.0000 0.7870 0.3074 0.9474	0.0000 0.0000 0.3112 0.6233 0.9047	0.0106 0.0106 0.9022 1.0000 0.9050
SIGNED RANK TEST P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.0000 0.0000 0.2560 0.8673 0.0694	0.2529 0.1388 0.8363 0.2142 0.5889	0.0000 0.0000 0.2228 0.9046 0.8375	0.1108 0.2108 0.7173 0.8845 0.8468

Table A6. P-values for Clothing and Footwear by Household Type

	SINGLE WITHOUT CHILDREN	SINGLE WITH CHILDREN	COHABITING WITHOUT CHILDREN	COHABITING WITH CHILDREN
KOLM. SMIRNOV P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.000 0.000 0.111 0.562 0.000	0.000 0.000 0.424 0.245 0.576	0.000 0.000 0.507 0.689 0.001	0.000 0.000 0.980 0.923 0.000
SIGN TEST P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.0000 0.0000 0.4529 0.9111 0.0000	0.1145 0.0482 0.2276 0.1933 0.2853	0.0000 0.0000 0.9784 0.8290 0.0090	0.0000 0.0000 0.2743 0.8267 0.0000
SIGNED RANK TEST P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.0000 0.0000 0.6935 0.8083 0.0000	0.5362 0.6380 0.3204 0.1432 0.5147	0.0000 0.0000 0.8651 0.9476 0.0771	0.0005 0.0004 0.7866 0.8488 0.0000

Table A7. P-values for Private Transport by Age of Reference Person

	AGE < 30	30 <= AGE < 50	50 <= AGE < 65	65 <= AGE
KOLM. SMIRNOV P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.000 0.000 0.803 0.179 0.117	0.000 0.000 0.208 0.888 0.437	0.000 0.000 0.027 0.024 0.078	0.000 0.000 0.184 0.253 0.321
SIGN TEST P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.0000 0.0000 1.0000 0.1707 0.0123	0.0000 0.0000 0.7100 0.5658 0.7783	0.0000 0.0000 0.2313 0.2922 0.0526	0.0000 0.0000 0.9139 0.4492 0.5238
SIGNED RANK TEST P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.0000 0.0000 0.7543 0.0849 0.0064	0.0000 0.0000 0.5907 0.5879 0.7072	0.0000 0.0000 0.1387 0.1294 0.0205	0.0140 0.0107 0.3946 0.1398 0.3618

Table A8. P-values for Private Transport by Professional Status

	(SELF-) EMPLOYED	UNEMPLOYED	(EARLY) RETIRED	OTHER
KOLM. SMIRNOV P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.000 0.000 0.292 0.698 0.711	0.000 0.000 0.418 0.863 0.003	0.000 0.000 0.071 0.017 0.057	0.000 0.000 0.732 0.234 0.262
SIGN TEST P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.0000 0.0000 0.9831 0.4439 0.8337	0.0000 0.0000 0.1704 0.6797 0.0037	0.0000 0.0000 0.6200 0.2659 0.0736	0.0805 0.0021 0.3916 0.1048 0.3742
SIGNED RANK TEST P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.0000 0.0000 0.5281 0.2410 0.6898	0.0018 0.0004 0.2536 0.9629 0.0017	0.0000 0.0000 0.2885 0.0380 0.0074	0.2079 0.1102 0.2036 0.1353 0.3010

Table A9. P-values for Private Transport by Household Type

	SINGLE WITHOUT CHILDREN	SINGLE WITH CHILDREN	COHABITING WITHOUT CHILDREN	COHABITING WITH CHILDREN
KOLM. SMIRNOV P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.000 0.000 0.022 0.042 0.000	0.000 0.000 0.130 0.959 0.576	0.000 0.000 0.091 0.919 0.001	0.000 0.000 0.221 0.404 0.030
SIGN TEST P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.0000 0.0000 0.3470 0.1562 0.0000	0.0176 0.0015 0.0375 0.4752 0.7688	0.0000 0.0000 0.1241 0.2821 0.0049	0.0000 0.0000 0.2141 1.0000 0.0101
SIGNED RANK TEST P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.0000 0.0000 0.4570 0.1728 0.0000	0.1487 0.0527 0.0383 0.6356 0.7509	0.0000 0.0000 0.1483 0.5067 0.0022	0.0000 0.0000 0.4078 0.8123 0.0141

Table A10. P-values for Saving by Age of Reference Person

	AGE < 30	30 <= AGE < 50	50 <= AGE < 65	65 <= AGE
KOLM. SMIRNOV P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.000 0.000 0.021 0.006 0.000	0.000 0.000 0.416 0.476 0.381	0.000 0.000 0.703 0.383 0.008	0.000 0.000 0.853 0.694 0.016
SIGN TEST P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.0000 0.0000 0.1060 0.0105 0.0814	0.0000 0.0000 0.1242 0.1242 0.0990	0.0000 0.0000 0.6334 0.7153 0.2439	0.0001 0.0000 0.6984 0.4179 0.7804
SIGNED RANK TEST P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.0000 0.0000 0.0473 0.0031 0.0033	0.0000 0.0000 0.2626 0.2073 0.9675	0.0000 0.0000 0.5934 0.9326 0.7188	0.0097 0.0022 0.9932 0.4939 0.1205

Table A11. P-values for Saving by Professional Status

	(SELF-) EMPLOYED	UNEMPLOYED	(EARLY) RETIRED	OTHER
KOLM. SMIRNOV P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.000 0.000 0.571 0.698 0.000	0.000 0.000 0.167 0.719 0.048	0.000 0.000 0.005 0.000 0.001	0.328 0.072 0.162 0.046 0.361
SIGN TEST P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.0000 0.0000 0.6131 0.8331 0.9834	0.0359 0.0488 0.1823 0.1122 0.2880	0.0000 0.0000 0.0007 0.0002 0.0014	0.8176 0.8176 0.2480 0.0639 1.0000
SIGNED RANK TEST P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.0000 0.0000 0.6747 0.6992 0.0311	0.2288 0.3944 0.5829 0.5988 0.5618	0.0000 0.0000 0.0035 0.0001 0.0055	0.7038 0.8534 0.2225 0.0559 0.5543

Table A12. P-values for Saving by Household Type

	SINGLE WITHOUT CHILDREN	SINGLE WITH CHILDREN	COHABITING WITHOUT CHILDREN	COHABITING WITH CHILDREN
KOLM. SMIRNOV P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.000 0.000 0.070 0.202 0.000	0.019 0.012 0.326 0.424 0.697	0.000 0.000 0.091 0.991 0.001	0.000 0.000 0.001 0.139 0.000
SIGN TEST P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.0000 0.0000 0.3734 0.2285 0.0090	0.1145 0.0482 0.4307 1.0000 0.8482	0.0000 0.0000 0.2742 0.7693 0.0238	0.0000 0.0000 0.0454 0.2030 0.0000
SIGNED RANK TEST P-VALUE
Parametric Kernel Distance Constrained Grade Corr.	0.0000 0.0000 0.3145 0.2334 0.0003	0.6009 0.4572 0.6833 0.7697 0.1839	0.0017 0.0000 0.4703 0.5726 0.2573	0.0000 0.0000 0.0598 0.4227 0.0000