locq2: Location quotient

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

Calculating the location quotient (a.k.a. Hoover-Balassa quotient) for a given number of I industries and J regions

Usage

1
2
locq2(e_ij, industry.id, region.id, LQ.norm = "none", 
LQ.output = "mat", na.rm = TRUE)

Arguments

e_ij

a vector with the employment of industry i in region j

industry.id

a vector containing the IDs of the industries i

region.id

a vector containing the IDs of the regions j

LQ.norm

Type of normalization of the location quotients: no normalization (default: LQ.norm = "none"), z values (LQ.norm = "OG") or z values of logged location quotients (LQ.norm = "T")

LQ.output

Type of output: matrix (default: CI.output = "mat") or data frame (CI.output = "df")

na.rm

logical argument that indicates whether NA values should be excluded before computing results

Details

The location quotient is a simple measure for the concentration of an industry (i) in a region (j) and is also the mathematical basis for other related indicators in regional economics (e.g. gini.conc()). The function returns the value LQ which is equal to 1 if the concentration of the regarded industry is exactly the same as the over-all concentration (that means, it is proportionally represented in region j). If the value of LQ is smaller (bigger) than 1, the industry is underrepresented (overrepresented). The function checks the input values for errors (i.e. if employment in a region is bigger than over-all employment).

Two types of normalization are available: z values of the location quotients (O'Donoghue/Gleave 2004) or z values of logged location quotients (Tian 2013).

Value

A matrix or data frame containing IxJ values of LQ

Author(s)

Thomas Wieland

References

Farhauer, O./Kroell, A. (2014): “Standorttheorien: Regional- und Stadtoekonomik in Theorie und Praxis”. Wiesbaden : Springer.

Hoen A.R./Oosterhaven, J. (2006): “On the measure of comparative advantage”. In: The Annals of Regional Science, 40, 3, p. 677-691.

Nakamura, R./Morrison Paul, C. J. (2009): “Measuring agglomeration”. In: Capello, R./Nijkamp, P. (eds.): Handbook of Regional Growth and Development Theories. Cheltenham: Elgar. p. 305-328.

O'Donoghue, D./Gleave, B. (2004): “A Note on Methods for Measuring Industrial Agglomeration”. In: Regional Studies, 38, 4, p. 419-427.

Tian, Z. (2013): “Measuring agglomeration using the standardized location quotient with a bootstrap method”. In: Journal of Regional Analysis and Policy, 43, 2, p. 186-197.

See Also

litzenberger, gini.conc, gini.spec, locq, hoover, ellison.a, ellison.a2, ellison.c, ellison.c2

Examples

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data (G.regions.industries)

lqs <- locq2(e_ij = G.regions.industries$emp_all, 
G.regions.industries$ind_code, G.regions.industries$region_code, 
LQ.output = "df")
# output as data frame

lqs_sort <- lqs[order(lqs$LQ, decreasing = TRUE),]
# Sort decreasing by size of LQ

lqs_sort[1:5,]

Example output

Location quotients 
I = 17 industries, J = 16 regions 

    j_region i_industry         LQ
1         BB     WZ08-B 2.53143635
2         BB     WZ08-C 0.68572315
3         BB     WZ08-D 1.17364755
4         BB     WZ08-E 1.79456845
5         BB     WZ08-F 1.59977784
6         BB     WZ08-G 0.95501272
7         BB     WZ08-H 1.32127936
8         BB     WZ08-I 1.03794255
9         BB     WZ08-J 0.56258760
10        BB     WZ08-K 0.65293292
11        BB     WZ08-L 1.10888462
12        BB     WZ08-M 0.73662381
13        BB     WZ08-N 1.25713010
14        BB     WZ08-P 0.90529762
15        BB     WZ08-Q 1.15404231
16        BB     WZ08-R 1.06569453
17        BB     WZ08-S 1.14093733
18        BE     WZ08-B 0.04030901
19        BE     WZ08-C 0.37224900
20        BE     WZ08-D 0.46721079
21        BE     WZ08-E 1.30128835
22        BE     WZ08-F 0.77160121
23        BE     WZ08-G 0.83133221
24        BE     WZ08-H 0.87982228
25        BE     WZ08-I 1.35561299
26        BE     WZ08-J 1.78334039
27        BE     WZ08-K 0.76630600
28        BE     WZ08-L 2.13220960
29        BE     WZ08-M 1.39880205
30        BE     WZ08-N 1.24261162
31        BE     WZ08-P 1.38842157
32        BE     WZ08-Q 1.09329902
33        BE     WZ08-R 2.55595102
34        BE     WZ08-S 1.32596177
35        BW     WZ08-B 0.66079495
36        BW     WZ08-C 1.39686522
37        BW     WZ08-D 1.08619881
38        BW     WZ08-E 0.58965258
39        BW     WZ08-F 0.90700957
40        BW     WZ08-G 0.94925233
41        BW     WZ08-H 0.81896663
42        BW     WZ08-I 0.91329490
43        BW     WZ08-J 1.03161136
44        BW     WZ08-K 0.93299299
45        BW     WZ08-L 0.73100144
46        BW     WZ08-M 1.03371385
47        BW     WZ08-N 0.79770538
48        BW     WZ08-P 0.96492895
49        BW     WZ08-Q 0.86952412
50        BW     WZ08-R 0.85181917
51        BW     WZ08-S 0.86268292
52        BY     WZ08-B 0.80780543
53        BY     WZ08-C 1.19027848
54        BY     WZ08-D 0.83437836
55        BY     WZ08-E 0.71373881
56        BY     WZ08-F 1.02804094
57        BY     WZ08-G 0.98798257
58        BY     WZ08-H 0.86641628
59        BY     WZ08-I 1.03908860
60        BY     WZ08-J 1.15507644
61        BY     WZ08-K 1.10588903
62        BY     WZ08-L 0.86338941
63        BY     WZ08-M 1.02659931
64        BY     WZ08-N 0.84869706
65        BY     WZ08-P 0.92522447
66        BY     WZ08-Q 0.90796789
67        BY     WZ08-R 0.82205402
68        BY     WZ08-S 0.90921251
69        HB     WZ08-B 0.00000000
70        HB     WZ08-C 0.78635701
71        HB     WZ08-D 0.91797184
72        HB     WZ08-E 1.23932277
73        HB     WZ08-F 0.62129234
74        HB     WZ08-G 0.90131925
75        HB     WZ08-H 1.76928155
76        HB     WZ08-I 0.99043082
77        HB     WZ08-J 1.05771072
78        HB     WZ08-K 0.78251782
79        HB     WZ08-L 1.32547228
80        HB     WZ08-M 1.12025321
81        HB     WZ08-N 1.29381608
82        HB     WZ08-P 1.05631685
83        HB     WZ08-Q 0.95448911
84        HB     WZ08-R 1.31966131
85        HB     WZ08-S 1.13966158
86        HE     WZ08-B 0.37357729
87        HE     WZ08-C 0.85803520
88        HE     WZ08-D 0.96279546
89        HE     WZ08-E 0.85322034
90        HE     WZ08-F 0.89276813
91        HE     WZ08-G 1.00063206
92        HE     WZ08-H 1.22087276
93        HE     WZ08-I 0.95713387
94        HE     WZ08-J 1.14070777
95        HE     WZ08-K 1.67105825
96        HE     WZ08-L 1.11329390
97        HE     WZ08-M 1.14577703
98        HE     WZ08-N 1.05259119
99        HE     WZ08-P 1.00852066
100       HE     WZ08-Q 0.89806801
101       HE     WZ08-R 0.86514510
102       HE     WZ08-S 1.05281844
103       HH     WZ08-B 0.60293882
104       HH     WZ08-C 0.47819341
105       HH     WZ08-D 0.43328697
106       HH     WZ08-E 1.14420055
107       HH     WZ08-F 0.54321632
108       HH     WZ08-G 1.06543149
109       HH     WZ08-H 1.49586101
110       HH     WZ08-I 1.06340664
111       HH     WZ08-J 1.92669126
112       HH     WZ08-K 1.51750779
113       HH     WZ08-L 1.58718383
114       HH     WZ08-M 1.62939131
115       HH     WZ08-N 1.25306076
116       HH     WZ08-P 0.94227395
117       HH     WZ08-Q 0.85646040
118       HH     WZ08-R 1.49145640
119       HH     WZ08-S 0.80551283
120       MV     WZ08-B 0.62357963
121       MV     WZ08-C 0.62301559
122       MV     WZ08-D 1.01188381
123       MV     WZ08-E 1.56422569
124       MV     WZ08-F 1.27165366
125       MV     WZ08-G 0.94853768
126       MV     WZ08-H 1.12437316
127       MV     WZ08-I 1.75746375
128       MV     WZ08-J 0.47514730
129       MV     WZ08-K 0.53839001
130       MV     WZ08-L 1.30340736
131       MV     WZ08-M 0.68975714
132       MV     WZ08-N 1.24843530
133       MV     WZ08-P 0.99662284
134       MV     WZ08-Q 1.28931677
135       MV     WZ08-R 1.05006851
136       MV     WZ08-S 1.11581843
137       NI     WZ08-B 1.49870856
138       NI     WZ08-C 0.95124382
139       NI     WZ08-D 0.99327187
140       NI     WZ08-E 1.06454974
141       NI     WZ08-F 1.09697556
142       NI     WZ08-G 1.07589772
143       NI     WZ08-H 1.04091430
144       NI     WZ08-I 1.02271964
145       NI     WZ08-J 0.67163761
146       NI     WZ08-K 0.91084562
147       NI     WZ08-L 0.80402696
148       NI     WZ08-M 0.86930264
149       NI     WZ08-N 0.96751474
150       NI     WZ08-P 1.08880536
151       NI     WZ08-Q 1.07284116
152       NI     WZ08-R 0.92045858
153       NI     WZ08-S 0.99654505
154       NW     WZ08-B 1.45957668
155       NW     WZ08-C 0.93123247
156       NW     WZ08-D 1.21397404
157       NW     WZ08-E 1.04083563
158       NW     WZ08-F 0.87355060
159       NW     WZ08-G 1.06121904
160       NW     WZ08-H 0.99612245
161       NW     WZ08-I 0.87502053
162       NW     WZ08-J 0.98306093
163       NW     WZ08-K 1.02057979
164       NW     WZ08-L 0.99281610
165       NW     WZ08-M 1.03665894
166       NW     WZ08-N 1.06598926
167       NW     WZ08-P 0.98463506
168       NW     WZ08-Q 1.05956484
169       NW     WZ08-R 0.96115392
170       NW     WZ08-S 1.02835714
171       RP     WZ08-B 1.03712355
172       RP     WZ08-C 1.08226777
173       RP     WZ08-D 0.93496794
174       RP     WZ08-E 0.98868603
175       RP     WZ08-F 1.11348854
176       RP     WZ08-G 1.01112743
177       RP     WZ08-H 0.96339718
178       RP     WZ08-I 1.11212635
179       RP     WZ08-J 0.81220576
180       RP     WZ08-K 0.88792918
181       RP     WZ08-L 0.77744999
182       RP     WZ08-M 0.77645583
183       RP     WZ08-N 0.80261808
184       RP     WZ08-P 1.09761779
185       RP     WZ08-Q 1.04184599
186       RP     WZ08-R 0.84980529
187       RP     WZ08-S 1.16588522
188       SH     WZ08-B 0.50781453
189       SH     WZ08-C 0.70825132
190       SH     WZ08-D 1.12486850
191       SH     WZ08-E 1.07075848
192       SH     WZ08-F 1.10434491
193       SH     WZ08-G 1.24561001
194       SH     WZ08-H 1.01125569
195       SH     WZ08-I 1.24839661
196       SH     WZ08-J 0.74969253
197       SH     WZ08-K 0.83551779
198       SH     WZ08-L 1.19805526
199       SH     WZ08-M 0.79054982
200       SH     WZ08-N 0.97278705
201       SH     WZ08-P 0.95402623
202       SH     WZ08-Q 1.16622898
203       SH     WZ08-R 1.04187941
204       SH     WZ08-S 1.14551776
205       SL     WZ08-B 0.28262836
206       SL     WZ08-C 1.17528104
207       SL     WZ08-D 1.14655390
208       SL     WZ08-E 0.95555809
209       SL     WZ08-F 0.90168578
210       SL     WZ08-G 1.03709014
211       SL     WZ08-H 0.88510466
212       SL     WZ08-I 0.91118767
213       SL     WZ08-J 0.71335872
214       SL     WZ08-K 1.00829835
215       SL     WZ08-L 0.70188161
216       SL     WZ08-M 0.80607528
217       SL     WZ08-N 1.07517490
218       SL     WZ08-P 0.91478745
219       SL     WZ08-Q 1.07609694
220       SL     WZ08-R 0.76312628
221       SL     WZ08-S 0.88407410
222       SN     WZ08-B 1.27461722
223       SN     WZ08-C 0.98674167
224       SN     WZ08-D 1.06370934
225       SN     WZ08-E 1.44574860
226       SN     WZ08-F 1.37942858
227       SN     WZ08-G 0.87877390
228       SN     WZ08-H 1.04766884
229       SN     WZ08-I 0.94963696
230       SN     WZ08-J 0.77177039
231       SN     WZ08-K 0.66207187
232       SN     WZ08-L 1.13954218
233       SN     WZ08-M 0.84593173
234       SN     WZ08-N 1.16564671
235       SN     WZ08-P 0.96585901
236       SN     WZ08-Q 1.04755952
237       SN     WZ08-R 1.14191353
238       SN     WZ08-S 0.97747264
239       ST     WZ08-B 2.46543307
240       ST     WZ08-C 0.92971721
241       ST     WZ08-D 1.26427871
242       ST     WZ08-E 1.82518528
243       ST     WZ08-F 1.41047238
244       ST     WZ08-G 0.91725978
245       ST     WZ08-H 1.20124302
246       ST     WZ08-I 0.90205821
247       ST     WZ08-J 0.48743444
248       ST     WZ08-K 0.61339328
249       ST     WZ08-L 1.01116936
250       ST     WZ08-M 0.66273010
251       ST     WZ08-N 1.27965475
252       ST     WZ08-P 0.97989325
253       ST     WZ08-Q 1.14016799
254       ST     WZ08-R 0.83292947
255       ST     WZ08-S 0.92573968
256       TH     WZ08-B 0.71406370
257       TH     WZ08-C 1.18498975
258       TH     WZ08-D 0.86075784
259       TH     WZ08-E 1.60429355
260       TH     WZ08-F 1.34810048
261       TH     WZ08-G 0.86611841
262       TH     WZ08-H 0.89449072
263       TH     WZ08-I 0.86442567
264       TH     WZ08-J 0.68691767
265       TH     WZ08-K 0.63163471
266       TH     WZ08-L 0.85118961
267       TH     WZ08-M 0.68143391
268       TH     WZ08-N 1.10932507
269       TH     WZ08-P 0.97105764
270       TH     WZ08-Q 1.06286017
271       TH     WZ08-R 0.85829191
272       TH     WZ08-S 1.09231373
    j_region i_industry       LQ
33        BE     WZ08-R 2.555951
1         BB     WZ08-B 2.531436
239       ST     WZ08-B 2.465433
28        BE     WZ08-L 2.132210
111       HH     WZ08-J 1.926691

REAT documentation built on Sept. 5, 2021, 5:18 p.m.