by Ajay Agrawal
quality of its chief scientist and hence fi rms are also indexed by q. A higher-
Artifi cial Intelligence and International Trade 473
quality scientist produces a better search engine. A fi rm engages in activity a
that increases advertising revenues r( a) where r > 0. Let p( q) be the propor-a
tion of consumers who choose fi rm q’s search engine. It is natural to assume
that p > 0 that is, a better scientist produces a more desirable search engine.
q
The fi rm’s profi t before payments to the scientist is ( a,q) = p( q) r( a) – c( a) where c( a) is the cost of the fi rm’s ad- generating activity. In this model the fi rm is essentially the scientist, but we can delink the two by assuming that
the scientist is paid with stock options and so receives a fraction (1 – ) of
the profi ts. It is straightforward to show that profi t ( a,q) is supermodular in ( a, q). This implies positive assortative matching; fi rms with better scientists engage in more ad- generating activity. This means that fi rms with better
scientists will also have more users ( p > 0), more revenues [∂ r( a( q) ,q) / ∂ q q
> 0], and higher profi ts [∂( a( q) ,q)/∂ q > 0]. Putting these together, better scientists anchor bigger and more profi table fi rms.7
To place this model into an international- trade setting, we assume that
there are multiple countries, a second constant- returns- to-scale industry
(clothing), and no international migration of scientists or workers. Because
there are profi ts in the search engine industry, policies that expand that
industry generate higher profi ts. This is the foundation of strategic trade
policy. In its simplest form, if there are supernormal profi ts then tariff s and other trade policies can be used to shift profi ts away from the foreign country
and to the domestic country.
Strategic trade policy was fi rst developed by Brander and Spencer (1981)
and variants of it have appeared in many of the models discussed below.
Unfortunately, the case for strategic trade policy is not as clear as it might
seem. Its biggest logical problem is the assumption of positive profi ts: if
there is free entry, then entry will continue until profi ts are driven to zero.8
This means that any government policy that encourages entry of fi rms or
training of scientists will be off set by ineffi
cient entry of fi rms or scientists.
Put simply, strategic trade policies only work if there are profi ts, but with free
entry there are no profi ts (see Eaton and Grossman 1986). The conclusion
we draw from this is that the model needs enriching before it can be used to
justify trade policy.
Before enriching the model, we note that there are two other compelling
7. The fi rst- order condition for advertising activities is = ( pr – c ) = 0. We a
a
a
assume that the second- order condition is satisfi ed: < 0. Supermodularity is given aa
by ∂2( a,q) / ∂ a∂ q = p r > 0. The result that advertising activity levels a( q) are increas-q a
ing in q comes from diff erentiating the fi rst- order condition: p r + a = 0 or a =
q a
aa
q
q
– p r / > 0. The result that average revenues p( q) r( a) are increasing in q follows from q a
aa
∂ p( q) r( a( q)) / ∂ q = p r + pr a > 0. The result that profi ts ( a( q) ,q) are increasing in q follows q
a q
from ∂( a,q)/∂ q = a + p r( a) = p r( a) > 0 where we have used the fi rst- order condi-a
q
q
q
tion ( = 0).
a
8. Free entry implies that ex ante profi ts are zero. Of course, ex post profi ts (operating profi ts of survivors) are always positive; otherwise, survivors would exit.
474 Avi Goldfarb and Daniel Trefl er
reasons for being skeptical about the effi
cacy of strategic trade policy. First,
such policies set up political economy incentives for fi rms to capture the
regulatory process used to determine the amount and form of government
handouts. Second, the logic of strategic trade policy fails if there is retalia-
tion on the part of the foreign government. Retaliation generates a trade war
in which both countries lose. Artifi cial intelligence meets all the conditions
that Busch (2001) identifi es as likely to lead to a trade war. We now turn to
enriching our model.
Superstar Scientists.9 Strategic trade policies are more compelling in set-
tings where scale and/or knowledge creation and diff usion are prevalent. To
this end we follow section 19.2 in assuming that there are economies of scale
in data. This will cause the market to be dominated by a small number of
search engine fi rms; that is, it will turn our model into something that looks
like a superstar model. To be more precise, it is a little diff erent from standard
superstar models that make assumptions on the demand side (Rosen 1981).
The superstar assumptions here are on the supply side.
Modifying our model slightly, we introduce scale in data by assuming that
the share of consumers choosing a search engine ( p( q)) is increasing at an increasing rate ( p > 0);10 p > 0 implies that profi ts and scientist earnings qq
qq
increase at an increasing rate, that is, they are convex in q.11 This, in turn, implies that the distribution of fi rm size becomes highly skewed toward large
fi rms. It also implies that the shareholders of large fi rms will make spec-
tacular earnings, that is, the 1 percent will pull away from the rest of society.
In this setting we expect that a small number of large fi rms will capture
most of the world market for search engines. Further, these fi rms will be
hugely profi table. We have in mind a situation like that found empirically
in the search engine market. The top fi ve leaders are (billions of monthly
visitors in parentheses): Google (1.8), Bing (0.5), Yahoo (0.5), Baidu (0.5),
and Ask (0.3).12 If the Chinese government subsidizes Baidu or excludes
Google from China, then Baidu captures a larger share of the market. This
generates higher profi ts and higher earnings for shareholders within China,
making China better off both absolutely and relatively to the United States.
Depending on the details of the model, the United States may or may not
be absolutely worse off .
This example is very similar to the mid- 1980s discussions about commer-
cial jet production. At a time when it was understood that there was room for
only two players in the industry (Boeing and McDonnell Douglas were the
leaders), the European Union (EU) heavily subsidized Airbus and ultimately
9. To our knowledge there are no superstar- and- trade models beyond Manasse and Turrini (2001), which deals with trade and wage inequality.
10. This is an ad hoc assumption, but to the extent that it has the fl avor of scale economies, we will see less ad hoc variants in the models reviewed below.
11. From a previous footnote, ∂( a( q) ,q)/∂ q = p r( a). Hence ∂2( a( q) ,q)/∂ q 2 = p r + p r a > 0.
q
qq
q a q
12. Source: http:// www .ebizmba .com/ articles/ search- engines, July, 2017.
Artifi cial Intelligence and International Trade 475
forced McDonnell Douglas to exit. These EU subsidies were enormous, but
may nevertheless have
been valuable for EU taxpayers.13
Our superstars model provides a more compelling case for government
intervention because scale in data acts as a natural barrier to entry that pre-
vents the free- entry condition from off setting the impacts of government
policies. Thus, the government can benefi cially subsidize the education of
AI scientists and/or subsidize the entry of fi rms, for example, by off ering
tax breaks, subsidies, expertise, incubators, and so forth. This establishes
that scale economies and the supernormal profi ts they sometimes imply
strengthen the case for strategic trade policy.
There is, however, one more assumption we have made that is essential to
the argument for strategic trade policy, namely, that there are no interna-
tional knowledge spillovers. In the extreme, if all the knowledge created, for
example, by Canadian scientists, moved freely to the United States or China,
then a Canadian subsidy would help the world, but would not diff erentially
help Canada. This establishes the critical role of knowledge diff usion (in
addition to scale) for thinking about government policies that promote AI.
Empirics. What do we know about superstar eff ects empirically? Nothing
from the trade literature. We know that superstars matter for the rate and
direction of innovation in academic research. We know that universities
have played a key role in developing AI expertise and that a small number
of university- affi
liated chief scientists have played a key role in developing
new technologies. We also have some evidence of a knowledge externality.
Azoulay, Graff Zivin, and Wang (2010) show that the death of a superstar
scientist in a fi eld slows progress in the research area of the superstar. The
fi eld suff ers as scientists associated with the deceased superstar produce less
research. While Azoulay, Graff Zivin, and Wang do not consider AI, their
work points to the existence of knowledge spillovers that are local rather
than global.
Inequality. This discussion has not had much to say about inequality.
In our superstars model, industrial policy and strategic trade policies are
successful precisely because they promote large and highly profi table fi rms.
We know that these fi rms account for an increasing share of total economic
activity and that they are likely major contributors both to falling labor
shares (Autor et al. 2017) and to rising top- end inequality. Thus, the policies
being supported by our model do not lead to broad- based prosperity. This
cannot be ignored.
Extensions. While the above model of AI science superstars is useful, it
13. The subsidies have continued unabated for over four decades. In 2016, the World Trade Organization (WTO) found that WTO- noncompliant EU subsidies were $10 billion. This does not include the WTO- compliant subsidies. Likewise, the WTO found comparable numbers
for WTO- noncompliant US subsidies of Boeing. See Busch (2001) for a history. This raises the possibility that subsidies that are intended to get a fi rm “on its feet” become permanent, which is yet another reason to be skeptical about strategic trade policies.
476 Avi Goldfarb and Daniel Trefl er
has a number of other problems. It is beyond the scope of this chapter to
resolve these problems through additional modeling. Instead, we highlight
each problem and review the related international trade and growth litera-
tures in order to provide insights into how the model might be improved and
what the implications of these improvements are for thinking about trade
and trade policy. The problems we cover are the following.
1. The scale assumption p > 0 is ad hoc. In subsection B below, we con-
qq
sider scale returns that are external to the fi rm and show that the form of
the scale returns matters for policy.
2. In our model, there is no knowledge creation within fi rms and no
knowledge diff usion across fi rms and borders. In subsection C below, we
review endogenous growth models and show that the form of knowledge
diff usion, whether it is local or global, matters for policy.
3. Our model ignores the geography of the industry and so does not speak
to economic geography and “supercluster” policies. We review the economic
geography literature in subsection D below.
4. In section E below we discuss the implications for supercluster policies.
19.3.2 Increasing Returns to Scale External
to the Firm—A Basic Trade Model
We start with a simple trade model featuring economies of scale whose
geographic scope is variable, that is, regional, national, or international.
The model captures the core insights of richer models developed by Ethier
(1982), Markusen (1981), and Helpman (1984), along with more recent
developments by Grossman and Rossi- Hansberg (2010, 2012).
Firm i produces a homogeneous good using a production function
q = Q F( L , K ),
i
i
i
where L is employment of labor, K is employment of capital, F displays i
i
constant returns to scale, Q is industry output ( Q = Σ q ), and 0 < < 1; i i
Q is like a Solow residual in that it controls productivity. The idea is that a fi rm’s productivity depends on the output of all fi rms.14 If Q is world output of the industry, then productivity Q is common to all fi rms internationally and scale has no implications for comparative advantage. On the other
hand if Q is national output of the industry, then the country with the larger output Q will have higher productivity Q and hence will capture the entire world market.
Artifi cial intelligence as an industry has a technology that lies some-
where between national returns to scale ( Q is national output) and inter-
national returns to scale ( Q is international output). With national returns
14. Each fi rm ignores the impact of its output decision on Q so that returns to scale can be treated as external to the fi rm.
Artifi cial Intelligence and International Trade 477
to scale, a government policy such as tariff s or production subsidies that
increases domestic output will increase national welfare because the policy
raises average productivity at home and also drive exports. Whether it helps
or hurts the foreign country depends on a number of factors such as the
strength of the scale returns (the size of a) and the size of the countries
(Helpman 1984). Most important, the domestic benefi ts of industrial and
trade policies depend on the geographic extent of scale, that is, how much
of it is national versus international.
Whether scale operates at the national or international level is not easy
to assess and has not been attempted for AI. For the DRAM market in
the 1980s, Irwin and Klenow (1994) show that external economies of scale
were entirely international rather than national. Other evidence that AI
economies are international is the fact that AI algorithms have been dis-
seminated internationally via scientifi c journals and teaching, and research
and development (R&D)- based AI knowledge has diff used internationally
via imitation and reverse engineering. On the other hand, the colocation of
AI researchers in Silicon Valley and a handful of other technology hubs is
suggestive of natio
nal and even subnational returns to scale. Azoulay, Graff
Zivin, and Wang (2010) also suggests the existence of subnational returns
to scale. Clearly, more research is needed on the extent of national versus
international returns to scale in AI.
19.3.3 Knowledge Creation and Diff usion: Endogenous Growth
In the previous section, scale was external to the fi rm and, relatedly, fi rms
did no research. We now introduce fi rm- level research. Conveniently, some
of the key implications of fi rm- level innovation are similar to those from the
previous section, namely, that trade policy depends in large part on the ex-
tent to which knowledge spillovers are national or international. To see this,
we review the main endogenous growth models that feature international
trade. These are Grossman and Helpman (1989, 1990, 1991), Rivera- Batiz
and Romer (1991), and Aghion and Howitt (2009, ch. 15). In these models,
fi rms conduct costly R&D and there is an externality that aff ects these costs.
The dominant model in the trade literature features quality ladders (Gross-
man and Helpman 1991) featuring vertical (quality) diff erentiation. The
highest- quality fi rm takes the entire market and earns profi ts.15
Innovation improves the quality of the frontier fi rm by a constant pro-
portion . At date t > 0, let n( t) be the number of quality improvements during the time interval (0, t) so that the frontier quality is n( t). Firms invest
an amount r in R&D and this generates an endogenous probability p( r) of becoming the quality leader (with quality n( t)+1).
A key feature of the R&D process is an externality: innovators stand
15. Ex post profi ts are needed in order to justify R&D expenses. However, these models have a free- entry condition that drives ex ante profi ts to zero.
478 Avi Goldfarb and Daniel Trefl er
on the shoulders of giants in the sense that they improve on the frontier
level of quality. Had they improved on their own quality, there would be
no externality. A two- sector, two- country quality ladder model appears in
Grossman and Helpman (1991). Grossman and Helpman assume that there
is a standard constant- returns- to-scale sector and a quality sector.16
Another popular approach is Romer’s (1990) expanding- varieties model.
Final goods producers combine varieties of intermediates using a constant