Econometrics in STATA: multiple population linear regression model

textbook attached

https://www.sea-stat.com/wp-content/uploads/2020/0…

obs wage educ exper tenure nonwhite female married numdep smsa northcen south west
1
3.1
11
2
0
0
1
0
2
1
0
0
1
2 3.24
12
22
2
0
1
1
3
1
0
0
1
3
3
11
2
0
0
0
0
2
0
0
0
1
4
6
8
44
28
0
0
1
0
1
0
0
1
5
5.3
12
7
2
0
0
1
1
0
0
0
1
6 8.75
16
9
8
0
0
1
0
1
0
0
1
7 11.25
18
15
7
0
0
0
0
1
0
0
1
8
5
12
5
3
0
1
0
0
1
0
0
1
9
3.6
12
26
4
0
1
0
2
1
0
0
1
10 18.18
17
22
21
0
0
1
0
1
0
0
1
11 6.25
16
8
2
0
1
0
0
1
0
0
1
12 8.13
13
3
0
0
1
0
0
1
0
0
1
13 8.77
12
15
0
0
0
1
2
1
0
0
1
14
5.5
12
18
3
0
0
0
0
1
0
0
1
15 22.2
12
31
15
0
0
1
1
1
0
0
1
16 17.33
16
14
0
0
0
1
1
1
0
0
1
17
7.5
12
10
0
0
1
1
0
1
0
0
1
18 10.63
13
16
10
0
1
0
0
1
0
0
1
19
3.6
12
13
0
0
1
1
3
1
0
0
1
20
4.5
12
36
6
0
1
1
0
1
0
0
1
21 6.88
12
11
4
0
1
0
0
1
0
0
1
22 8.48
12
29
13
0
0
1
3
1
0
0
1
23 6.33
16
9
9
0
1
0
0
1
0
0
1
24 0.53
12
3
1
0
1
0
0
1
0
0
1
25
6
11
37
8
1
1
0
0
1
0
0
1
26 9.56
16
3
3
1
0
1
1
1
0
0
1
27 7.78
16
11
10
0
0
1
1
1
0
0
1
28 12.5
16
31
0
0
0
1
0
1
0
0
1
29 12.5
15
30
0
0
0
1
2
1
0
0
1
30 3.25
8
9
1
0
1
1
2
1
0
0
1
31
13
14
23
5
0
0
1
2
1
0
0
1
32
4.5
14
2
5
0
1
0
2
1
0
0
1
33 9.68
13
16
16
0
1
0
0
1
0
0
1
34
5
12
7
3
0
1
0
0
1
0
0
1
35 4.68
12
3
0
0
1
0
0
1
0
0
1
36 4.27
16
22
4
1
1
1
1
1
0
0
1
37 6.15
12
15
6
1
1
1
1
1
0
0
1
38 3.51
4
39
15
0
0
1
5
1
0
0
1
39
3
14
3
3
0
1
1
0
1
0
0
1
40 6.25
12
11
0
0
1
0
0
1
0
0
1
41 7.81
12
3
0
0
1
1
0
1
0
0
1
42
10
12
20
5
1
1
1
4
1
0
0
1
43
4.5
14
16
0
0
1
1
1
1
0
0
1
44
4
11
45
12
0
1
1
0
1
0
0
1
45 6.38
13
11
4
0
1
0
0
1
0
0
1
46 13.7
15
20
13
0
0
1
2
1
0
0
1
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
1.67
2.93
3.65
2.9
1.63
8.6
5
6
2.5
3.25
3.4
10
21.63
4.38
11.71
12.39
6.25
3.71
7.78
19.98
6.25
10
5.71
2
5.71
13.08
4.91
2.91
3.75
11.9
4
3.1
8.45
7.14
4.5
4.65
2.9
6.67
3.5
3.26
3.25
8
9.85
7.5
5.91
11.76
3
10
12
14
12
12
16
12
12
12
15
16
8
18
16
13
14
10
10
14
14
16
12
16
12
16
17
12
12
12
13
12
12
12
18
9
16
10
12
12
12
12
12
8
12
12
14
12
1
36
9
15
18
3
15
7
2
3
1
13
8
7
40
42
36
13
9
26
7
25
10
3
3
17
17
20
7
24
28
2
19
13
22
3
4
7
6
13
14
14
40
11
14
40
1
0
2
2
1
0
2
5
7
0
0
1
0
8
0
20
5
8
0
3
23
4
3
5
2
0
2
8
34
0
19
0
1
13
0
5
1
0
5
2
3
0
4
24
7
6
39
0
0
0
0
0
0
0
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0
0
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1
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1
1
1
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1
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1
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1
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1
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1
1
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1
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1
1
1
1
0
0
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1
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1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
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1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
1
0
2
2
0
1
0
2
1
1
0
0
0
0
0
0
4
0
2
3
3
1
4
0
3
2
2
0
2
1
1
4
2
4
0
1
0
1
1
1
1
2
1
2
0
2
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
94 4.81
95
6.5
96
4
97
3.5
98 13.16
99 4.25
100
3.5
101 5.13
102 3.75
103
4.5
104 7.63
105
15
106 6.85
107 13.33
108 6.67
109 2.53
110
9.8
111 3.37
112 24.98
113
5.4
114 6.11
115
4.2
116 3.75
117
3.5
118 3.64
119
3.8
120
3
121
5
122 4.63
123
3
124
3.2
125 3.91
126 6.43
127 5.48
128
1.5
129
2.9
130
5
131 8.92
132
5
133 3.52
134
2.9
135
4.5
136 2.25
137
5
138
10
139 3.75
140
10
12
12
9
13
12
14
12
15
12
12
12
14
15
12
12
12
17
11
18
12
14
14
10
14
12
15
8
16
14
15
12
18
16
10
8
10
11
18
15
12
11
12
12
14
16
2
14
2
4
19
1
34
5
3
6
14
35
8
7
11
14
35
46
7
45
29
6
15
33
15
5
7
6
33
2
4
1
29
17
17
36
31
23
13
3
15
48
6
12
5
19
9
39
28
0
1
1
0
22
2
0
6
0
12
4
7
3
11
10
0
0
12
25
3
0
16
0
0
2
1
12
1
0
0
0
3
3
3
30
2
1
3
0
1
0
0
0
5
3
13
11
0
0
0
0
0
0
0
0
0
0
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1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
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1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
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0
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1
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1
0
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1
1
1
0
1
0
1
1
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0
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1
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1
0
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1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
2
0
0
3
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
1
3
0
2
0
1
2
2
0
0
2
0
0
0
0
1
3
2
4
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
10.95
7.9
4.72
5.84
3.83
3.2
2
4.5
11.55
2.14
2.38
3.75
5.52
6.5
3.1
10
6.63
10
2.31
6.88
2.83
3.13
8
4.5
8.65
2
4.75
6.25
6
15.38
14.58
12.5
5.25
2.17
7.14
6.22
9
10
5.77
4
8.75
6.53
7.6
5
5
21.86
8.64
16
12
12
13
12
15
10
12
16
13
9
12
13
12
12
14
16
16
9
18
10
10
13
12
18
13
12
13
13
13
18
12
12
13
12
12
12
14
10
12
16
16
12
14
12
12
12
23
2
15
5
18
2
3
31
20
34
5
11
31
8
2
18
3
3
4
4
1
1
28
47
13
2
48
6
8
25
13
8
19
1
43
19
11
43
44
22
3
3
41
5
14
24
28
20
0
1
0
2
2
0
4
5
15
0
0
3
5
2
5
0
2
1
4
0
0
5
4
1
6
2
5
0
21
7
1
10
4
5
9
5
4
3
11
2
2
11
0
11
16
8
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
1
4
0
0
1
3
2
5
3
3
0
5
1
0
0
1
2
0
0
5
0
4
1
1
0
0
0
0
1
2
2
0
0
2
1
0
1
0
0
0
2
1
0
0
0
0
3
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
188
3.3
189 4.44
190 4.55
191
3.5
192 6.25
193 3.85
194 6.18
195 2.91
196 6.25
197 6.25
198 9.05
199
10
200 11.11
201 6.88
202 8.75
203
10
204 3.05
205
3
206
5.8
207
4.1
208
8
209 6.15
210
2.7
211 2.75
212
3
213
3
214 7.36
215
7.5
216
3.5
217
8.1
218 3.75
219 3.25
220 5.83
221
3.5
222 3.33
223
4
224
3.5
225 6.25
226 2.95
227 5.71
228
3
229 22.86
230
9
231 8.33
232
3
233 5.75
234 6.76
12
12
12
12
16
16
14
11
16
12
12
17
12
12
16
8
12
12
12
16
12
12
9
13
16
14
8
14
13
12
18
9
8
8
12
14
12
16
8
13
9
16
12
15
11
14
12
25
3
11
7
9
5
9
1
2
13
10
5
30
31
1
9
10
38
19
5
26
35
2
1
19
3
36
29
1
38
1
29
36
4
45
22
20
5
15
10
3
16
38
33
2
6
19
8
0
0
6
2
0
3
0
1
0
2
3
8
19
2
0
0
0
6
0
2
12
0
2
10
2
24
24
2
3
2
0
15
0
4
3
4
0
2
2
0
7
1
26
0
5
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
3
0
0
3
0
0
3
0
0
2
0
2
0
1
0
1
1
0
0
3
1
3
1
1
1
0
3
0
0
2
0
1
0
0
2
0
1
0
0
2
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
235
10
236
3
237
3.5
238 3.25
239
4
240 2.92
241 3.06
242
3.2
243 4.75
244
3
245 18.16
246
3.5
247 4.11
248 1.96
249 4.29
250
3
251 6.45
252
5.2
253
4.5
254 3.88
255 3.45
256 10.91
257
4.1
258
3
259
5.9
260
18
261
4
262
3
263 3.55
264
3
265 8.75
266
2.9
267 6.26
268
3.5
269
4.6
270
6
271 2.89
272 5.58
273
4
274
6
275
4.5
276 2.92
277 4.33
278 18.89
279 4.28
280 4.57
281 6.25
12
12
18
12
12
12
12
12
12
14
16
12
14
11
12
10
12
6
13
12
10
12
14
13
12
18
12
12
12
12
12
8
13
13
14
12
10
16
12
16
12
14
18
17
13
14
15
29
2
3
4
10
4
14
15
19
17
29
2
5
38
3
47
7
47
23
12
11
25
6
3
14
13
9
1
6
11
47
49
37
2
7
22
8
1
43
2
2
1
1
26
1
37
12
0
0
1
0
1
0
10
5
0
0
7
0
0
3
0
0
6
13
2
3
0
23
0
1
7
0
0
0
0
1
44
6
17
0
0
8
0
1
6
2
1
3
0
20
1
7
4
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
2
0
0
0
0
1
3
1
3
4
1
2
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
2
0
0
2
2
0
2
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
282 2.95
283 8.75
284
8.5
285 3.75
286 3.15
287
5
288 6.46
289
2
290 4.79
291 5.78
292 3.18
293 4.68
294
4.1
295 2.91
296
6
297
3.6
298 3.95
299
7
300
3
301 6.08
302 8.63
303
3
304 3.75
305
2.9
306
3
307 6.25
308
3.5
309
3
310 3.24
311 8.02
312 3.33
313 5.25
314 6.25
315
3.5
316 2.95
317
3
318 4.69
319 3.73
320
4
321
4
322
2.9
323 3.05
324 5.05
325 13.95
326 18.16
327 6.25
328 5.25
14
12
8
12
12
8
12
9
12
16
12
16
12
12
13
10
6
12
12
16
12
8
12
6
4
11
11
7
12
18
12
16
12
14
12
10
10
9
10
12
12
12
10
16
16
16
12
41
24
38
18
26
45
27
2
41
11
5
3
3
4
21
34
49
6
26
9
23
33
5
49
48
35
23
26
16
23
36
4
10
18
3
7
7
33
34
8
17
2
5
41
35
11
4
23
1
26
0
1
2
0
0
8
4
0
1
2
0
13
26
6
5
9
0
9
2
2
7
0
31
2
1
0
3
8
0
0
2
1
0
7
2
12
0
1
0
0
16
28
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
4
0
0
3
3
0
2
0
0
0
0
4
0
6
1
0
0
1
0
1
0
0
0
2
3
2
1
1
0
3
1
1
2
0
1
0
2
2
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
329 4.79
330 3.35
331
3
332 8.43
333
5.7
334 11.98
335
3.5
336 4.24
337
7
338
6
339 12.22
340
4.5
341
3
342
2.9
343
15
344
4
345 5.25
346
4
347
3.3
348 5.05
349 3.58
350
5
351 4.57
352 12.5
353 3.45
354 4.63
355
10
356 2.92
357 4.51
358
6.5
359
7.5
360 3.54
361
4.2
362 3.51
363
4.5
364 3.35
365 2.91
366 5.25
367 4.05
368 3.75
369
3.4
370
3
371 6.29
372 2.54
373
4.5
374 3.13
375 6.36
12
7
8
16
16
18
13
10
16
14
16
12
9
11
11
12
11
12
12
12
12
14
14
18
12
12
12
11
12
17
16
13
13
12
14
14
11
10
8
14
12
10
17
9
12
12
14
12
35
33
8
2
8
29
14
26
11
10
13
23
1
35
5
13
22
21
19
13
15
3
6
6
16
31
1
5
3
11
6
11
7
5
5
2
44
44
13
26
2
10
2
35
6
8
3
0
0
6
0
10
1
5
3
3
2
0
20
2
31
2
11
3
9
0
0
5
0
2
5
1
2
0
2
0
0
7
3
2
0
4
2
7
25
0
15
1
3
0
0
5
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
3
1
1
0
0
2
0
1
1
2
0
0
2
2
0
0
2
3
2
3
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
3
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
376 4.68
377
6.8
378 8.53
379 4.17
380 3.75
381 11.1
382 3.26
383 9.13
384
4.5
385
3
386 8.75
387 4.14
388 2.87
389 3.35
390 6.08
391
3
392
4.2
393
5.6
394
10
395 12.5
396 3.76
397
3.1
398 4.29
399 10.92
400
7.5
401 4.05
402 4.65
403
5
404
2.9
405
8
406 8.43
407 2.92
408 6.25
409 6.25
410 5.11
411
4
412 4.44
413 6.88
414 5.43
415
3
416
2.9
417 6.25
418 4.34
419 3.25
420 7.26
421 6.35
422 5.63
16
12
10
0
14
15
16
12
11
11
12
13
12
13
16
15
16
15
12
18
6
6
12
12
16
9
12
11
10
12
8
9
17
16
11
10
8
13
14
13
11
7
16
12
13
14
16
1
14
14
22
8
1
15
14
37
1
4
29
45
22
42
9
8
31
24
16
6
14
47
34
6
7
27
24
18
12
27
49
4
24
3
2
29
34
10
5
2
39
5
14
8
10
2
0
10
6
10
4
4
5
12
10
1
4
0
8
0
10
0
0
15
24
5
0
0
25
5
2
4
2
5
0
3
3
0
0
2
0
0
11
21
3
0
0
21
2
2
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
2
0
0
0
2
2
3
2
1
0
0
0
2
0
0
1
2
0
1
4
5
2
0
1
1
3
0
2
1
3
0
0
2
0
1
3
0
1
1
2
0
0
2
0
2
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
1
1
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424
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426
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427 12.5
428 2.88
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430
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432
4.5
433
10
434 3.81
435
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436 9.42
437 6.33
438
4
439
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440
20
441 11.25
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3.5
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444 14.38
445 6.36
446 3.55
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4.5
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452 3.25
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1.5
454
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456
2.9
457 3.29
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460
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461 4.08
462 3.75
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3
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475
4.5
476 17.5
477 8.18
478 9.09
479 11.82
480 3.25
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4.5
483 3.71
484
6.5
485
2.9
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487 2.23
488
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489 8.33
490
2.9
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492 4.55
493 3.28
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496 3.15
497 12.5
498 5.15
499 3.13
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505 17.71
506 6.25
507
2.6
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512 4.38
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514 4.95
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1. wage
2. educ
3. exper
4. tenure
5. nonwhite
6. female
7. married
8. numdep
9. smsa
10. northcen
11. south
12. west
13. construc
14. ndurman
15. trcommpu
16. trade
17. services
18. profserv
19. profocc
20. clerocc
21. servocc
average hourly earnings
years of education
years potential experience
years with current employer
=1 if nonwhite
=1 if female
=1 if married
number of dependents
=1 if live in SMSA
=1 if live in north central U.S
=1 if live in southern region
=1 if live in western region
=1 if work in construc. indus.
=1 if in nondur. manuf. indus.
=1 if in trans, commun, pub ut
=1 if in wholesale or retail
=1 if in services indus.
=1 if in prof. serv. indus.
=1 if in profess. occupation
=1 if in clerical occupation
=1 if in service occupation
1 wage
2 educ
3 exper
4 tenure
5 nonwhite
6 female
7 married
8 numdep
9 smsa
10 northcen
11 south
12 west
13 construc
14 ndurman
15 trcommpu
16 trade
17 services
18 profserv
19 profocc
20 clerocc
21 servocc
22 lwage
23 expersq
24 tenursq
average hourly earnings
years of education
years potential experience
years with current employer
=1 if nonwhite
=1 if female
=1 if married
number of dependents
=1 if live in SMSA
=1 if live in north central U.S
=1 if live in southern region
=1 if live in western region
=1 if work in construc. indus.
=1 if in nondur. manuf. indus.
=1 if in trans, commun, pub ut
=1 if in wholesale or retail
=1 if in services indus.
=1 if in prof. serv. indus.
=1 if in profess. occupation
=1 if in clerical occupation
=1 if in service occupation
log(wage)
exper^2
tenure^2
Q#1: [50 Points] Consider the following Population Linear Regression Function (PLRF):
Y = Bo + BiXi + B2X2i+ B3X3i + BaXi + B5 Xsiti
(1)
where, Y₁ = average hourly earnings/wage in $, X₁ = years of education, X₂ = years of potential experience,
X3 = years with current employer (tenure), X₁ = 1 if female, X5 = 1 if nonwhite, and u₁ = the usual error
term of the model.
For this question, use the WAGE data set that you used in PS #2. Here is the description of the variables in
the dataset for your consumption. We might be using this data set for the coming problem sets too.
Obs:
526
1. wage
2. educ
3. exper
4. tenure
5. nonwhite
6. female
7. married
8. numdep
9. smsa
10. northcen
11. south
12. west
13.
construc
14. ndurman
15.
trcommpu
16. trade
17.
services
18. profserv
19. profocc
20. clerocc
21.
servOCC
22. lwage
23. expersq
24. tenursq
average hourly earnings
years of education
years potential experience
years with current employer
=1 if nonwhite
=1 if female
=1 if married
number of dependents
=1 if live in SMSA
=1 if live in north central U.S.
=1 if live in southern region
=1 if live in western region
=1 if work in construc. Indus.
=1 if in nondur. Manuf. Indus.
=1 if in trans, commun, pub ut
1 if in wholesale or retail
=1 if in services indus.
=1 if in prof. serv. Indus.
=1 if in profess. Occupation
=1 if in clerical occupation
=1 if in service occupation
log (wage)
exper^2
tenure^2
(a) [9 Points] Consider the following restricted version of equation (1) Y₁ = ẞo + ẞ₁×₁i + B2X2i + U₁.
Suppose that X2 is omitted from the model by the researcher. For X2 to cause omitted variable bias
(OVB), what conditions should it satisfy? Show mathematically that the OLS estimator ẞ₁ is biased
if X2 is omitted from the model.
(b) [8 Points] Run a regression of Y₁ = В₁ + ß4×4 + u₁ and interpret the slope coefficient ẞ4. (Hint:
X4 is a binary explanatory variable.)
(c) [9 Points] First generate a dummy variable D; such that D₁ = 1 if male and D₁ = 0 if female. Then
run a regression of Y₁ = B₁ + B₁×₁ + ẞ4×4 + B6D₁ + u₁. What do you notice in the result? Explain
why? Show mathematically that if X and D₂ are related, this result is inevitable.
(d) [8 Point] Run, first, a simple regression of Y₂ = ßo + B₁×₁ + u₁ then Y₁ = Po + B₁₁ + ß₂X₂ + U₁.
Explain what happened to B₁ (before and after) and why it happened.
(e) [8 Points] Now run the full model (1), using both homoscedastic-only and heteroskedasticity-
robust standard errors, and interpret and compare the results of both regressions. Why do we care
about heteroskedasticity problem that might exist in the data?
(f) [8 Point] Based on the regression result of the later (i.e., heteroskedasticity-robust standard
errors), conduct the following hypothesis testing:
i.
Ho: B0 vs H₁: B₁ 0 where i = 1, 2, …, 5
ii.
Ho: B₁ = B2 B3 = ß₁ = ẞ5 = 0 vs H₁: At least one ẞ₁ = 0Q#3: [20 points] Allcott and Gentzkow (2017) conducted an online survey of US adults regarding fake
news after the 2016 presidential election. In their survey, they showed survey respondents news headlines
about the 2016 election and asked about whether the news headlines were true or false. Some of the news
headlines were fake and others were true. Their dependent variable Y; takes value 1 if survey respondent
i correctly identifies whether the headline is true or false, value 0.5 if respondent is “not sure”, and value
0 otherwise. Suppose that one conducts a similar survey and obtains the following regression result:
Ŷi
-2
= 0.65 + 0.012College + 0.015ln(Daily media time) + 0.003Age, R² = 0.14, n = 828,
(0.02) (0.004)
(0.003)
(0.001)
where College is a binary indicator that equals 1 if a survey respondent is college graduate and 0 otherwise,
In(Daily media time) is the logarithm of daily time consuming media, and Age is age in years.
(a) [5 points] Suppose that you would like to test that people with higher education have more accurate
beliefs about news at the 1% level. State your null hypothesis precisely and report your test result.
[2 points]
(b)
[5 points] The estimated coefficient for In(Daily media time) is significantly positive. Interpret this
result. Explain why this is plausible. [2 points]
(c) [5 points] Even if Age is omitted, there will be little concern about the omitted variable bias problem.
Do you agree? Explain briefly. [3 points]
(d) [5 points] Suppose that you now conjecture that Republicans may have different beliefs about news
than Democrats. Assume that there are three groups in the data: Democrats, Republicans and
Independents. How would you change the specification of the linear regression model by adding or
subtracting regressors? Explain briefly. [3 points]