Popular in Economics

Central Monetary Authorities

Macroeconomic modelling of CBDC: a critical review

European Central Bank Ulrich Bindseil

Central Monetary Authorities

Financing Private Credit

Federal Reserve Bank of New York Nina Boyarchenko

Economics

Failing Banks

Massachusetts Institute of Technology Emil Verner

Economic History

Golden Fetters

UC Berkeley Barry Eichengreen

Economic Inequalities

Visions of Inequality

City University of New York Branko Milanovic

Economics

School Finance Equalization Increases Intergenerational Mobility

Yale University Barbara Biasi

Economics

Olivier Blanchard on U.S. Pandemic-Era Inflation

Peterson Institute for International Economics Olivier Blanchard

An Introduction to Econometric Theory

View more insights in Social Sciences - Economics - Econometrics

View more figures from University of Exeter

View the page of James Davidson

Read the Book

Next in Econometrics

xtevent: Estimation and Visualization in the Linear Panel Event-Study Design

Simon Freyaldenhoven | Federal Reserve Bank of Philadelphia

Efficient Likelihood Evaluation of State-Space Representations

David DeJong | University of Pittsburgh

James Davidson discusses some of the mathematical foundations underling econometric methods.

Image courtesy of interviewee. February 21, 2024

Log-in or Sign-up to Faculti
Currently viewing this subject insight as a guest. You have insight(s) remaining for this month. Login to view 8000+ figures on the platform.

Generating Workspace...

Export as PDF

This video video discusses the complexities and challenges associated with applying classical statistical models, particularly in the field of economics. It highlights the importance of applied mathematics for economists conducting empirical work, focusing on concepts such as sampling distributions and the assumptions inherent in statistical models.

The author critiques the classical progression model, noting that it is often taught despite its limitations, particularly in the context of economic data, which does not always adhere to the model's assumptions. Issues such as autocorrelation and multicollinearity in time series data are addressed, explaining how these factors violate the assumptions of independence used in classical statistics.

This video video emphasizes the importance of being honest with students about the applicability of statistical models in economics, advocating for a deeper understanding of data randomness and the necessity of employing more realistic assumptions. Additionally, it touches upon the challenges of heteroscedasticity in data and suggests ways to mitigate such issues in analysis.

Overall, the text expresses a need for a more comprehensive and realistic teaching approach in economics and statistics, acknowledging that although simplified models might be useful for teaching purposes, they may not accurately represent the complexities of real-world data analysis.

Language:

Export as PDF

X-TIMESTAMP-MAP=LOCAL:00:00:00.000,MPEGTS:90000

1
00:00:00.575 --> 00:00:02.505
Well, it's, it's applied mathematics,

2
00:00:02.725 --> 00:00:06.345
but it's, things that are of interest to economists

3
00:00:06.925 --> 00:00:09.025
or let's say particularly economists who want

4
00:00:09.025 --> 00:00:10.985
to do empirical work and, and work with data

5
00:00:11.165 --> 00:00:12.705
and test hypotheses

6
00:00:12.765 --> 00:00:16.865
and all that kind of thing, which it is assumed that,

7
00:00:16.925 --> 00:00:19.585
the university trained economists should know.

8
00:00:19.685 --> 00:00:22.865
So most people have to go through a, a course of this type,

9
00:00:23.325 --> 00:00:24.985
more or less technical.

10
00:00:25.285 --> 00:00:28.625
Um, my book is on the more technical side, deliberately,

11
00:00:28.655 --> 00:00:31.625
it's aimed as at, for,

12
00:00:32.855 --> 00:00:35.705
more mathematically inclined students if you, if you will.

13
00:00:36.255 --> 00:00:38.265
It's, it's a, it's an important idea,

14
00:00:38.705 --> 00:00:40.025
this sampling distribution.

15
00:00:40.885 --> 00:00:44.585
And I think that it has to do in many cases, really

16
00:00:44.585 --> 00:00:48.515
with the thought experiment, you have to, the,

17
00:00:48.735 --> 00:00:50.715
the investigator has to say to himself,

18
00:00:50.865 --> 00:00:53.595
I've got a sample here, which I collected by.

19
00:00:53.595 --> 00:00:55.115
It might be even be a time series,

20
00:00:55.295 --> 00:00:56.755
or it might be a sample survey,

21
00:00:56.975 --> 00:00:58.875
or might be a bit of panel data.

22
00:00:58.875 --> 00:01:00.775
Something like that says,

23
00:01:01.315 --> 00:01:04.335
how do I interpret this from a statistical point of view?

24
00:01:04.445 --> 00:01:05.695
What does it, what does it mean?

25
00:01:06.035 --> 00:01:07.495
So you have to imagine

26
00:01:08.085 --> 00:01:11.415
that it's a drawing from a distribution, a distribution

27
00:01:11.415 --> 00:01:15.535
of many such samples, which you can independently draw from.

28
00:01:15.755 --> 00:01:17.895
And often, this is of course, how the world works.

29
00:01:18.045 --> 00:01:21.215
That, that if you, if you, if you look at a sample of,

30
00:01:21.555 --> 00:01:24.655
of households, typically somebody will have gone

31
00:01:24.655 --> 00:01:27.775
to the trouble of, of making a random drawing of, of,

32
00:01:28.275 --> 00:01:29.895
of postal codes

33
00:01:29.895 --> 00:01:31.695
or something of that kind and picking them out.

34
00:01:32.515 --> 00:01:34.135
Uh, so, but sometimes this is,

35
00:01:34.135 --> 00:01:35.415
this is, this is more theoretical.

36
00:01:35.735 --> 00:01:39.655
I mean, I, or, or it's basically it's a fiction.

37
00:01:40.395 --> 00:01:43.415
Uh, if you are thinking of a time series of,

38
00:01:43.415 --> 00:01:46.495
stock price, well, that just happened once in the world.

39
00:01:46.565 --> 00:01:48.335
It's not gonna happen again in the same way.

40
00:01:48.915 --> 00:01:52.215
Um, so except in a, in a parallel universe,

41
00:01:52.275 --> 00:01:55.095
if you like your quantum theory, that that way, then,

42
00:01:55.355 --> 00:01:57.295
you know, it could be like that.

43
00:01:57.995 --> 00:02:00.055
So that's what a sample distribution is.

44
00:02:00.115 --> 00:02:03.055
Of course, we could still describe it by making some,

45
00:02:03.365 --> 00:02:04.615
some assumptions more

46
00:02:04.615 --> 00:02:06.495
or less sensible, in order

47
00:02:06.495 --> 00:02:07.855
to describe this distribution.

48
00:02:08.555 --> 00:02:11.975
And then we can begin to interpret our drawing

49
00:02:12.235 --> 00:02:16.255
and how we understand the randomness in, in the dataset

50
00:02:16.255 --> 00:02:17.335
that we actually possess.

51
00:02:17.815 --> 00:02:20.015
I do take this quite seriously in my book,

52
00:02:20.015 --> 00:02:21.135
because of course, the,

53
00:02:21.155 --> 00:02:23.975
the classical progression model is a nice bit of nonsense.

54
00:02:24.515 --> 00:02:29.255
Um, it sets some assumptions, that,

55
00:02:29.275 --> 00:02:32.615
really don't hold, at least for economic data.

56
00:02:32.645 --> 00:02:35.775
They hold in, in, in, in, in certain situations.

57
00:02:36.195 --> 00:02:40.615
Uh, experimental science, you can imagine setting some,

58
00:02:40.765 --> 00:02:43.055
some parameters of an experiment then observing

59
00:02:43.055 --> 00:02:44.175
the outcome of the experiment.

60
00:02:44.175 --> 00:02:45.935
But economics is by

61
00:02:45.935 --> 00:02:48.215
and large, non-experimental in character.

62
00:02:48.315 --> 00:02:50.295
So, so that really doesn't work.

63
00:02:50.915 --> 00:02:54.415
Um, nonetheless, it's taught to generations

64
00:02:54.435 --> 00:02:55.455
of undergraduates,

65
00:02:55.595 --> 00:02:58.815
and I've never heard of any single one that's ever said,

66
00:02:58.945 --> 00:03:01.565
please, sir, this emperor has no clothes.

67
00:03:01.595 --> 00:03:05.365
This makes no sense, you know, which clearly shows

68
00:03:05.365 --> 00:03:08.725
that people don't understand the other topics that they're,

69
00:03:08.955 --> 00:03:10.565
that they're taught now.

70
00:03:11.245 --> 00:03:13.725
I mean, the reason, of course, that we do this,

71
00:03:13.725 --> 00:03:16.565
by the way, the, you know, the peculiarity of the,

72
00:03:16.565 --> 00:03:19.765
of the assumptions is this idea of the fixed progressor

73
00:03:20.325 --> 00:03:24.805
that when you draw this, this sample, every time you do it,

74
00:03:24.805 --> 00:03:26.645
you get a new dependent variable.

75
00:03:26.785 --> 00:03:30.005
But the X is on the other side. They're always the same.

76
00:03:30.725 --> 00:03:32.505
That's the assumption that you have to make.

77
00:03:32.505 --> 00:03:34.985
And of course, it makes no sense, so that if you,

78
00:03:34.985 --> 00:03:37.985
if you draw a sample of some economic behavior,

79
00:03:37.985 --> 00:03:41.225
everything is new, you know, the, the income

80
00:03:41.225 --> 00:03:45.385
of the consumer, the, the expenditures of the consumer,

81
00:03:45.685 --> 00:03:47.785
you know, because the consumer is drawn randomly

82
00:03:47.845 --> 00:03:50.185
and all his characteristics or her characteristics.

83
00:03:50.975 --> 00:03:53.635
So that's the problem with it, is that it's not really,

84
00:03:53.825 --> 00:03:55.155
it's, it is not real.

85
00:03:55.495 --> 00:03:57.355
Why do we teach it to undergraduates?

86
00:03:57.355 --> 00:04:01.515
Because basically it involves statistical concepts, which,

87
00:04:02.045 --> 00:04:05.955
which are conveyable without too much advanced theory.

88
00:04:06.215 --> 00:04:10.475
And as I expl try to explain in my, in my little book,

89
00:04:10.865 --> 00:04:11.915
this is reasonable

90
00:04:11.945 --> 00:04:14.915
because if you just extend

91
00:04:14.935 --> 00:04:17.235
to those more realistic assumptions,

92
00:04:17.265 --> 00:04:19.915
letting the data be fully random, for example,

93
00:04:20.455 --> 00:04:22.915
but tell some stories about it, then

94
00:04:23.495 --> 00:04:27.555
the properties which you prove vigorously under the,

95
00:04:27.555 --> 00:04:31.235
classical progression model are I'll sort of roughly, right?

96
00:04:31.495 --> 00:04:34.955
You know, and then as a fallback, there's acetic theory,

97
00:04:34.965 --> 00:04:37.595
which says that if you've got a big enough sample,

98
00:04:38.665 --> 00:04:40.525
the world looks pretty much like

99
00:04:40.525 --> 00:04:41.685
the classical progression model.

100
00:04:41.825 --> 00:04:43.125
Not exactly, but,

101
00:04:43.425 --> 00:04:45.565
but the same sort of conclusions can be drawn.

102
00:04:45.585 --> 00:04:47.245
So, so there are various get outs.

103
00:04:47.745 --> 00:04:50.435
So basically, this is why it's a sad paradox.

104
00:04:50.495 --> 00:04:52.315
You, you teach these things to students

105
00:04:52.545 --> 00:04:56.315
because you believe that this, it can be explained in the,

106
00:04:56.335 --> 00:04:58.675
in the framework of a, of a 10 week course

107
00:04:59.135 --> 00:05:00.955
to non mathematical people,

108
00:05:01.365 --> 00:05:03.395
which most economists of course are.

109
00:05:04.365 --> 00:05:06.385
Um, so, you know, we get by, but,

110
00:05:06.405 --> 00:05:08.425
but I think it should, it's always good to be honest

111
00:05:08.485 --> 00:05:10.585
to students and tell them what they're teaching them.

112
00:05:10.925 --> 00:05:12.905
And that's what I, that's what I've always tried

113
00:05:12.905 --> 00:05:14.665
to do, for better or worse.

114
00:05:15.135 --> 00:05:16.545
Well, the ga markoff theorem,

115
00:05:16.545 --> 00:05:19.185
because is the thing that everybody, has

116
00:05:19.185 --> 00:05:21.025
to remember about, and they think,

117
00:05:21.025 --> 00:05:22.345
but these two pals, Gauss

118
00:05:22.345 --> 00:05:25.585
and Markov, he said, no, actually one died in the same year.

119
00:05:25.585 --> 00:05:28.145
The other was born. So they weren't really well connected,

120
00:05:28.685 --> 00:05:30.265
but they did work on the same kind

121
00:05:30.265 --> 00:05:31.865
of things, wonderful people.

122
00:05:31.865 --> 00:05:33.865
They both were, it's a,

123
00:05:33.975 --> 00:05:37.545
it's a result which is proved rigorously under the framework

124
00:05:37.545 --> 00:05:38.985
of the classical progression model.

125
00:05:39.605 --> 00:05:42.745
And it says that lease squares is a good thing to do.

126
00:05:43.605 --> 00:05:47.945
Um, provided you can show that these squares is unbiased,

127
00:05:47.945 --> 00:05:51.065
which it is under the classical aggression model, then Gauss

128
00:05:51.065 --> 00:05:54.465
and markoff tell you jointly that your

129
00:05:55.015 --> 00:05:56.705
estimator will have the minimum

130
00:05:57.405 --> 00:06:00.125
Possible variance in the,

131
00:06:00.425 --> 00:06:02.605
and we've gotta be careful here what we mean by that.

132
00:06:02.605 --> 00:06:04.805
Because in a fixed sample, which is

133
00:06:04.805 --> 00:06:07.605
what we're talking about, but obviously a repeated sample,

134
00:06:08.025 --> 00:06:10.925
technically, so we're discussing the distribution

135
00:06:10.925 --> 00:06:15.885
of our estimator under, repeated sampling,

136
00:06:15.915 --> 00:06:17.965
then it's, it's going to be efficient.

137
00:06:17.965 --> 00:06:19.405
That's, that's the technical term.

138
00:06:19.505 --> 00:06:21.725
We, we say it's, it's, it's the, so,

139
00:06:21.785 --> 00:06:24.365
so we say it's best in the class of linear,

140
00:06:24.405 --> 00:06:26.325
I didn't mention, that's

141
00:06:26.325 --> 00:06:28.805
of course talking about Lee Squares best in the class

142
00:06:28.825 --> 00:06:31.245
of linear, unbiased estimators.

143
00:06:31.555 --> 00:06:33.565
Blue is what we teach the students,

144
00:06:34.025 --> 00:06:36.085
and that's what the gas Markle Theum says.

145
00:06:36.425 --> 00:06:39.205
So the gas markle theorem, once again, not entirely true,

146
00:06:40.065 --> 00:06:43.885
but as true as we might wish, is

147
00:06:43.885 --> 00:06:47.525
what one can say auto correlation is the property

148
00:06:47.595 --> 00:06:50.645
that regression disturbances are related.

149
00:06:50.905 --> 00:06:53.245
Our correlated, you know, they move together.

150
00:06:53.245 --> 00:06:55.725
They're not an independent drawing, which is what you want.

151
00:06:55.745 --> 00:06:58.925
That's, that's what the, the gas progression model says

152
00:06:58.925 --> 00:07:01.445
that your disturbances are independently drawn.

153
00:07:01.905 --> 00:07:05.845
And, and so if that's not true, then of course the,

154
00:07:06.185 --> 00:07:10.045
for example, the gas markoff, the, no longer,

155
00:07:10.065 --> 00:07:11.165
no longer applies.

156
00:07:11.825 --> 00:07:15.125
Um, and, also your,

157
00:07:15.785 --> 00:07:18.325
if you are doing inference yourt statistics will be,

158
00:07:18.325 --> 00:07:20.045
will be biased and things like that.

159
00:07:21.245 --> 00:07:23.905
Um, the trouble with this is

160
00:07:24.015 --> 00:07:26.345
that when do you encounter order correlation?

161
00:07:26.345 --> 00:07:27.665
Usually in time series,

162
00:07:27.665 --> 00:07:29.745
because then there's an ordering to the data,

163
00:07:30.035 --> 00:07:32.985
which makes it sensible to, to believe

164
00:07:33.015 --> 00:07:34.545
that there may be a relationship

165
00:07:34.545 --> 00:07:37.145
between successive observations, you know,

166
00:07:37.145 --> 00:07:40.585
because they come in, in,

167
00:07:40.985 --> 00:07:42.145
adjacent periods of time.

168
00:07:42.325 --> 00:07:45.425
So you tend to get auto correlation in the context

169
00:07:45.445 --> 00:07:46.665
of time series.

170
00:07:47.485 --> 00:07:50.945
But of course, time series violate the assumptions

171
00:07:50.945 --> 00:07:52.665
of the classical progression model with

172
00:07:52.665 --> 00:07:53.905
or without auto correlation.

173
00:07:54.125 --> 00:07:55.625
So, so if you're thinking,

174
00:07:55.905 --> 00:07:59.585
although it's taught to students, not mine, I might say,

175
00:08:00.005 --> 00:08:03.665
but, pretty often as something to look out

176
00:08:03.805 --> 00:08:06.265
for in the world of the classical progression model,

177
00:08:06.485 --> 00:08:09.345
the truth is that, that it doesn't really apply.

178
00:08:10.245 --> 00:08:12.985
Um, it's, it's a more advanced topic than,

179
00:08:13.055 --> 00:08:14.425
than you really can think.

180
00:08:14.925 --> 00:08:17.425
Um, but then of course, what we have

181
00:08:17.425 --> 00:08:19.905
to face is the students are very often given practical

182
00:08:20.465 --> 00:08:21.945
exercises on time series.

183
00:08:22.415 --> 00:08:24.385
This is, this is, this is a fairly, of course,

184
00:08:24.385 --> 00:08:27.105
time service data are not difficult to, to find.

185
00:08:27.165 --> 00:08:30.425
You just pull 'em out of the blue book and, and, and, and,

186
00:08:30.565 --> 00:08:31.785
and, and, and so on.

187
00:08:32.285 --> 00:08:36.465
So very easy to give students practical exercises using time

188
00:08:36.465 --> 00:08:40.265
series, even though the, the theory

189
00:08:40.265 --> 00:08:42.465
that they've been taught doesn't really work.

190
00:08:42.805 --> 00:08:45.185
But you know, that's all right off all,

191
00:08:45.185 --> 00:08:46.265
they're only undergraduates.

192
00:08:46.265 --> 00:08:49.865
So, so, so we expect a little,

193
00:08:50.005 --> 00:08:52.465
inconsistencies in what we tell them, but,

194
00:08:52.765 --> 00:08:54.665
but, I don't, you know, but, but,

195
00:08:55.025 --> 00:08:56.285
but the truth is out there.

196
00:08:56.425 --> 00:08:59.485
So, I don't think it's a big issue really.

197
00:08:59.705 --> 00:09:01.045
But anyway, that's what I have

198
00:09:01.045 --> 00:09:04.645
to say rather extensively about all the correlation is

199
00:09:04.675 --> 00:09:06.745
that it's,

200
00:09:07.135 --> 00:09:09.505
it's a problem which you are going to encounter.

201
00:09:09.505 --> 00:09:12.145
However, there's one other thing to say is that dealing

202
00:09:12.145 --> 00:09:16.185
with it, traditionally there have been various fixes

203
00:09:16.205 --> 00:09:18.905
for auto correlation, which are best avoided

204
00:09:18.905 --> 00:09:21.385
because they can make things worse rather than better.

205
00:09:21.765 --> 00:09:24.705
Uh, but that's another story to go into, which makes

206
00:09:24.925 --> 00:09:27.225
for an interesting exercise for this,

207
00:09:27.225 --> 00:09:28.425
for, you know, for students.

208
00:09:29.175 --> 00:09:30.955
Um, but I have to say that

209
00:09:30.955 --> 00:09:33.355
because my book is, is Elementary,

210
00:09:34.015 --> 00:09:36.435
it says nothing about disorder correlation at all.

211
00:09:36.535 --> 00:09:38.475
It doesn't, doesn't deal with time series

212
00:09:38.475 --> 00:09:41.395
because it, it tries to keep everything on a realistic,

213
00:09:41.895 --> 00:09:43.115
even keel.

214
00:09:44.175 --> 00:09:46.075
Now, you also mentioned multiline.

215
00:09:46.295 --> 00:09:48.995
That's the other multi-syllable word that we have to teach.

216
00:09:49.695 --> 00:09:52.115
Um, it just says the data are no good.

217
00:09:53.455 --> 00:09:55.515
So, you know, I don't think you should take it too seriously

218
00:09:55.575 --> 00:09:57.435
or maybe that your model is no good

219
00:09:57.435 --> 00:10:01.075
because you've, you've piled more explanatory variables into

220
00:10:01.075 --> 00:10:03.235
it than it can really cope with,

221
00:10:03.235 --> 00:10:05.195
because they're basically telling you, you know,

222
00:10:05.195 --> 00:10:08.875
it's the same data, it's the same information process in

223
00:10:08.875 --> 00:10:10.875
different ways, and you get, that's what you,

224
00:10:11.095 --> 00:10:12.395
how you get co linearity.

225
00:10:13.015 --> 00:10:16.515
The, the x's in your equation are,

226
00:10:17.095 --> 00:10:19.075
are too closely related to one another.

227
00:10:19.255 --> 00:10:22.635
And this means that a matrix, you want to invert,

228
00:10:22.675 --> 00:10:24.595
I won't go into those technicalities too much,

229
00:10:24.655 --> 00:10:29.595
but, are, may, may fail to be invertible or,

230
00:10:29.975 --> 00:10:33.755
or your standard errors become, unacceptably large

231
00:10:33.775 --> 00:10:35.475
and horrible things like that happen.

232
00:10:36.015 --> 00:10:38.875
Um, but it basically means either you are using the data in

233
00:10:38.875 --> 00:10:41.275
the wrong way, which means your model is no good,

234
00:10:41.695 --> 00:10:43.435
or it means that the data are no good

235
00:10:43.495 --> 00:10:46.835
and you've gotta, you know, extend your sample in some way.

236
00:10:47.335 --> 00:10:49.915
Uh, but, but it's not, but, but,

237
00:10:49.915 --> 00:10:51.595
but there is no simple fix for it.

238
00:10:52.585 --> 00:10:56.285
Hetero elasticity, which is the third one you mentioned,

239
00:10:56.745 --> 00:10:57.925
is a little more interesting

240
00:10:57.925 --> 00:11:00.045
because you, you can realistically get

241
00:11:00.045 --> 00:11:01.445
that in the classical progression model

242
00:11:01.445 --> 00:11:03.885
because it's something that could apply,

243
00:11:04.025 --> 00:11:06.165
in a cross section, which basically is,

244
00:11:06.345 --> 00:11:08.765
is when all the data have the same time,

245
00:11:09.065 --> 00:11:11.125
but they're, they're for different, different agents

246
00:11:11.125 --> 00:11:13.645
or different objects, over that time.

247
00:11:14.225 --> 00:11:16.725
So supposing you're looking at a cross section of firms,

248
00:11:17.595 --> 00:11:19.325
well, you may have some very big firms

249
00:11:19.425 --> 00:11:23.205
and some little corner shops in the same sample, and, and,

250
00:11:23.305 --> 00:11:27.805
and you are really mixing, two different types of types

251
00:11:27.865 --> 00:11:30.205
of agent who aren't really comparable.

252
00:11:30.825 --> 00:11:35.045
And so, if some of them have, you know,

253
00:11:35.135 --> 00:11:37.405
their profits measured in, in billions

254
00:11:37.405 --> 00:11:39.925
and others have their profits measured in hundreds

255
00:11:39.925 --> 00:11:44.085
or thousands, this poses a problem

256
00:11:44.195 --> 00:11:48.085
because the, the,

257
00:11:48.585 --> 00:11:51.525
the residuals for these different observations may have very

258
00:11:51.525 --> 00:11:53.540
different variances, is what it it comes down to.

259
00:11:53.540 --> 00:11:54.965
So, so it's a part

260
00:11:54.965 --> 00:11:57.085
of the classical progression model assumptions is

261
00:11:57.085 --> 00:12:00.405
that all the variances of your observations are the same

262
00:12:00.475 --> 00:12:03.685
that they, there are, they're a homogeneous collection.

263
00:12:04.525 --> 00:12:05.985
So there are ways to fix this.

264
00:12:06.165 --> 00:12:08.625
For example, you would, you would not look at profits,

265
00:12:08.625 --> 00:12:10.705
you would look at profits as a percentage of revenue,

266
00:12:10.885 --> 00:12:13.785
and then you get something which will be easily comparable

267
00:12:13.785 --> 00:12:16.745
between the big agent and the small agent.

268
00:12:17.165 --> 00:12:19.985
So, you know, that, that's just, so, so

269
00:12:19.985 --> 00:12:23.025
that's something which it is useful to discuss,

270
00:12:23.295 --> 00:12:24.625
with, with, with students.

271
00:12:24.645 --> 00:12:27.065
And you can do sometimes do something about it.

272
00:12:27.205 --> 00:12:28.385
But, but,

273
00:12:29.045 --> 00:12:32.065
you may need more sophisticated methods, unfortunately.

274
00:12:32.245 --> 00:12:33.905
And then, and, and,

275
00:12:33.905 --> 00:12:36.705
and then you are involved in, non-linearities,

276
00:12:36.805 --> 00:12:40.225
you'll need asso theory to interpret what you've done and,

277
00:12:40.285 --> 00:12:41.585
and so on and so on.

278
00:12:41.725 --> 00:12:42.905
So, not so easy.

Understanding Sampling Distributions in Economics

00:00:00 - Well, it's, it's applied mathematics, but it's, things that are of interest to economists or let's say particularly economists who want to do empirical work and, and work with data and test hypotheses and all that kind of thing, which it is assumed that, the university trained economists should know. So most people have to go through a, a course of this type, more or less technical. my book is on the more technical side, deliberately, it's aimed as at, for,
00:00:36 - It's, it's a, it's an important idea, this sampling distribution. And I think that it has to do in many cases, really with the thought experiment, you have to, the, the investigator has to say to himself, I've got a sample here, which I collected by. It might be even be a time series, or it might be a sample survey, or might be a bit of panel data. Something like that says, how do I interpret this from a statistical point of view?
00:01:06 - So you have to imagine that it's a drawing from a distribution, a distribution of many such samples, which you can independently draw from. And often, this is of course, how the world works. That, that if you, if you, if you look at a sample of, of households, typically somebody will have gone to the trouble of, of making a random drawing of, of, of postal codes or something of that kind and picking them out. so, but sometimes this is, this is, this is more theoretical.
00:01:40 - if you are thinking of a time series of, stock price, well, that just happened once in the world. It's not gonna happen again in the same way. so except in a, in a parallel universe, if you like your quantum theory, that that way, then, you know, it could be like that. So that's what a sample distribution is. Of course, we could still describe it by making some, some assumptions more or less sensible, in order
00:02:08 - And then we can begin to interpret our drawing and how we understand the randomness in, in the dataset that we actually possess. I do take this quite seriously in my book, because of course, the, the classical progression model is a nice bit of nonsense. it sets some assumptions, that, really don't hold, at least for economic data. They hold in, in, in, in, in certain situations. experimental science, you can imagine setting some,
00:02:43 - the outcome of the experiment. But economics is by and large, non-experimental in character. So, so that really doesn't work. nonetheless, it's taught to generations of undergraduates, and I've never heard of any single one that's ever said, please, sir, this emperor has no clothes. This makes no sense, you know, which clearly shows that people don't understand the other topics that they're, that they're taught now.

Challenges of Teaching Classical Statistical Assumptions

00:03:13 - by the way, the, you know, the peculiarity of the, of the assumptions is this idea of the fixed progressor that when you draw this, this sample, every time you do it, you get a new dependent variable. But the X is on the other side. They're always the same. That's the assumption that you have to make. And of course, it makes no sense, so that if you, if you draw a sample of some economic behavior, everything is new, you know, the, the income of the consumer, the, the expenditures of the consumer,
00:03:47 - and all his characteristics or her characteristics. So that's the problem with it, is that it's not really, it's, it is not real. Why do we teach it to undergraduates? Because basically it involves statistical concepts, which, which are conveyable without too much advanced theory. And as I expl try to explain in my, in my little book, this is reasonable because if you just extend to those more realistic assumptions,
00:04:20 - but tell some stories about it, then the properties which you prove vigorously under the, classical progression model are I'll sort of roughly, right? You know, and then as a fallback, there's acetic theory, which says that if you've got a big enough sample, the world looks pretty much like the classical progression model. Not exactly, but, but the same sort of conclusions can be drawn. So, so there are various get outs.
00:04:50 - You, you teach these things to students because you believe that this, it can be explained in the, in the framework of a, of a 10 week course to non mathematical people, which most economists of course are. so, you know, we get by, but, but I think it should, it's always good to be honest to students and tell them what they're teaching them. And that's what I, that's what I've always tried to do, for better or worse. Well, the ga markoff theorem, because is the thing that everybody, has
00:05:21 - but these two pals, Gauss and Markov, he said, no, actually one died in the same year. The other was born. So they weren't really well connected, but they did work on the same kind of things, wonderful people. They both were, it's a, it's a result which is proved rigorously under the framework of the classical progression model. And it says that lease squares is a good thing to do. provided you can show that these squares is unbiased, which it is under the classical aggression model, then Gauss
00:05:55 - estimator will have the minimum Possible variance in the, and we've gotta be careful here what we mean by that. Because in a fixed sample, which is what we're talking about, but obviously a repeated sample, technically, so we're discussing the distribution of our estimator under, repeated sampling, then it's, it's going to be efficient. That's, that's the technical term. We, we say it's, it's, it's the, so,

Challenges of Teaching Regression Analysis

00:06:24 - I didn't mention, that's of course talking about Lee Squares best in the class of linear, unbiased estimators. Blue is what we teach the students, and that's what the gas Markle Theum says. So the gas markle theorem, once again, not entirely true, but as true as we might wish, is what one can say auto correlation is the property that regression disturbances are related. Our correlated, you know, they move together.
00:06:55 - That's, that's what the, the gas progression model says that your disturbances are independently drawn. And, and so if that's not true, then of course the, for example, the gas markoff, the, no longer, no longer applies. and, also your, if you are doing inference yourt statistics will be, will be biased and things like that. the trouble with this is
00:07:26 - Usually in time series, because then there's an ordering to the data, which makes it sensible to, to believe that there may be a relationship between successive observations, you know, because they come in, in, adjacent periods of time. So you tend to get auto correlation in the context of time series. But of course, time series violate the assumptions of the classical progression model with or without auto correlation.
00:07:55 - although it's taught to students, not mine, I might say, but, pretty often as something to look out for in the world of the classical progression model, the truth is that, that it doesn't really apply. it's, it's a more advanced topic than, than you really can think. but then of course, what we have to face is the students are very often given practical exercises on time series. This is, this is, this is a fairly, of course,
00:08:27 - You just pull 'em out of the blue book and, and, and, and, and, and, and so on. So very easy to give students practical exercises using time series, even though the, the theory that they've been taught doesn't really work. But you know, that's all right off all, they're only undergraduates. So, so, so we expect a little, inconsistencies in what we tell them, but, but, I don't, you know, but, but,
00:08:56 - So, I don't think it's a big issue really. But anyway, that's what I have to say rather extensively about all the correlation is that it's, it's a problem which you are going to encounter. However, there's one other thing to say is that dealing with it, traditionally there have been various fixes for auto correlation, which are best avoided because they can make things worse rather than better. but that's another story to go into, which makes for an interesting exercise for this,

Challenges in Economic Data Analysis and Teaching

00:09:29 - but I have to say that because my book is, is Elementary, it says nothing about disorder correlation at all. It doesn't, doesn't deal with time series because it, it tries to keep everything on a realistic, even keel. Now, you also mentioned multiline. That's the other multi-syllable word that we have to teach. it just says the data are no good. So, you know, I don't think you should take it too seriously or maybe that your model is no good
00:10:01 - it than it can really cope with, because they're basically telling you, you know, it's the same data, it's the same information process in different ways, and you get, that's what you, how you get co linearity. The, the x's in your equation are, are too closely related to one another. And this means that a matrix, you want to invert, I won't go into those technicalities too much, but, are, may, may fail to be invertible or,
00:10:33 - and horrible things like that happen. but it basically means either you are using the data in the wrong way, which means your model is no good, or it means that the data are no good and you've gotta, you know, extend your sample in some way. but, but it's not, but, but, but there is no simple fix for it. Hetero elasticity, which is the third one you mentioned, is a little more interesting because you, you can realistically get
00:11:01 - because it's something that could apply, in a cross section, which basically is, is when all the data have the same time, but they're, they're for different, different agents or different objects, over that time. So supposing you're looking at a cross section of firms, well, you may have some very big firms and some little corner shops in the same sample, and, and, and you are really mixing, two different types of types of agent who aren't really comparable.
00:11:35 - their profits measured in, in billions and others have their profits measured in hundreds or thousands, this poses a problem because the, the, the residuals for these different observations may have very different variances, is what it it comes down to. So, so it's a part of the classical progression model assumptions is that all the variances of your observations are the same that they, there are, they're a homogeneous collection.
00:12:06 - For example, you would, you would not look at profits, you would look at profits as a percentage of revenue, and then you get something which will be easily comparable between the big agent and the small agent. So, you know, that, that's just, so, so that's something which it is useful to discuss, with, with, with students. And you can do sometimes do something about it. But, but, you may need more sophisticated methods, unfortunately. And then, and, and, and then you are involved in, non-linearities,