Research at Intersection of Trade and IO. Interest in heterogeneous impact of trade policy (some firms win, others lose, perhaps in same industry)

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1 Research at Intersection of Trade and IO Countries don t export, plant s export Interest in heterogeneous impact of trade policy (some firms win, others lose, perhaps in same industry) (Whatcountriesa Get skewed distrib- Closely related to size distribution stuff. firm sells to, analogous to how big it is. utions... These models relate size distribution of plants to industry parameters, like transportation cost. Then used to talk about micro data, like whether plants export or not.

2 Eaton Kortum Like Dornbusch, Fischer, Samuelson, Ricardian trade with continuum of goods [0 1] () efficiency in producing good in country is labor cost in country Unit cost to produce in is ()

3 iceberg cost cost of to. =1. 1, 6= Perfect competition () = Ã ()!

4 Price of good in country () =min{ 1 (); =1 } Consumers purchase individual goods in amounts () to maximize = " Z 1 () 1 0 # 1

5 Technology () random variable drawn a certain way to make everying work out really easily Frechet (also called Type II extreme value) () = is a country specific. Bigger get better productivity draws governs extent of Ricardian comparative advantage. Bigger less variability log has standard deviation (6)

6 Country presents country with a distribution of prices () = Pr( ) =1 ( ) = 1 ( ) Lowest price will be less than, unless each source s price is greater than. So () =Pr( ) is () = 1 = 1 Y = 1 Φ (1 ()) =1 Y ( ) =1

7 for Φ = X =1 ( ) Price parameter Φ. If =1,thenΦ the same everywhere. =1, =, 6=, theφ = Probability that country provides a good at the lowest price in country is = = Z Y 0 6= Z Y 0 6= [1 ] () ( ) ()

8 = Z 0 Y 6= = ( ) Z ( ) h ( ) 1i ( ) 0 Y ( ) h 1i = ( ) Z ³ P ( ) h 1i 0 = ( ) Z Φ h 1i = ( ) 1 Φ Φ = ( ) Φ 0 0 Conditional distribution of price paid (condition upon country oforigin)issameasunconditioned, (). That is: () = 1 Z 0 Π 6= (1 ()) ()

9 holds for each. The RHS is distribution of costs conditioned upon actually buying. Now the denominator is the probability of buying from. With () wearelookingattheprobability costislessthanorequalto. So on the right side, we want to integrate over every at and get the probability of that event (this is (), combined with the event that all other locations have a higher cost. So... Z 1 Π 6= (1 ()) () (1) 0 = 1 Z Π 6= 0 1 = 1 = 1 Z 0 Φ = 1 Φ 1 Φ Φ 0 1 Φ

10 = 1 Φ = (). Can calculate a price index for the CES objective function 1+ = Φ 1 = Γ( +1 1(1 ) )

11 Alvarez Lucas have this cleaner... Think of this as starting with an exponential. Suppose have avariable draw from exponential. Let say get two draws, from 1 and 2. () = () = 1 Consider a new variable 12 =min{ 1 2 }What is distribution of this. Call this (). Probability that 1 and 2 are both above is 1 2 = ( 1+ 2 ).

12 Trade Flows Average expenditure per good does not vary by source Fraction of s expenditure on goods from country = = ( ) Φ = ( ) P =1 ( ) Looking like a gravity equation. Try to get it closer. Exporter s total sales = = X =1 X =1 = X =1 ( ) Φ

13 So the distribution is () =1 ( 1+ 2 ). So now suppose we set = 1. Now take the min from draws. Then the distribution of this variable is () =1 Finally, for our cost, let s just let it be (****Check****) = 1 When get bigger, the cost distribution is compressed. So then the distribution of is () =1 0

14 Or Remember that = = X =1 Φ P =1 Φ = Φ 1 = Φ = P =1 ³ So = Φ

15 = = P ³ =1 P =1 ³ Fixing denominator, sales enter with unit elasticity. So fixing denominator, looks like a standard gravivity model where ln = (distance) + ln +ln

16 Geography Trade and Prices = = ( ) Φ ( ) = Φ Ã! Φ Φ Look at symmetric case =, =, =, then = Can see that decreases in. As increases, dispersion decreases, so can t offset transportation costs Look at figure 1

17

18 Note identification problem: versus Could follow strategies like Hummels to estimate directly. But physical transportation costs only part of transportation costs To identify, bring in more data

19 Price Data retail price data for 19 countries for 50 manufacturered products. So =150 () =ln () ln () Calculate ln ( )=mean (). (Tricky step) To get at, () bounded above by ln and bound attained for goods that imports from. Every country imports from every other. (Note here the strong assumption comes in that transportation cost is the same for each good.

20 Take second highest vlue of across commodities to obtain ameasureofln = max 2 { ()} P 50 =1 [ ()] 50 ln Ã! So have a price measure exp, Look at figure Table II and Figure 2. estimate of. Get slope of 8.28, an

21

22

23 AER piece Look at facts in paper. Extension of the model. Each country gets two draws rather than one, rather than one of same thing. Then Bertrand competition. Let () be the cost of supplier rank to from () = Ã ()! Thelowestcostis 1 () =min { 1 ()}

24 The lowest cost can t charge more than then the second lowest cost 2 () =min ( 2 () min 6= { 1()} ) But won t want to charge more than a markup = () =min{ 2 () 1 ()} 1. So Distribution of 1 2 in any country ( 1 2 ) = Pr( ) = h ³ i 2

25 Results 1. Probability country exports to is = ( ) Φ Conditional distribution of costs (given sell) same for all countries, everything at extensive margin Get distribution of prices with truncation Get exact price index, formula has same shape as before = Φ 1 (but has a new definition) =

26 Implications for Productivity, Exporting, and Size Productivity, value of output divided by input where actual markup. (here at least) (1 + ) =1+ So actually a measure of markup Markup is drawn from Pareto truncated at monopoly markup () = 1,1 = 1 Have a distribution of ( ( 1 ) = 1 1 = 1, 1 1

27 So higher, higher (stochastically dominant sense)

28 Efficiency in Exporting Selling at home need 1 () 1 () for all 6= Selling some other market 1 () 1 () for all 6= Higher hurdle (have triangle inequality) Plants export more likely to have higher measured efficiency Compare with Melitz model. Suppose two countries and a fixed cost to export. Suppose have parameter that leads

29 to multiplicative scaling up of profits. (Or, whatever...). Let be fixed cost to export. Then profits are (where is profits in market when =1) Will export if no export : export : + 0 ˆ =

30 Efficiency and Size Why would exporting plants have higher domestic sales? (First, ifwejustaskaboutallsales,easy,ifexport,shouldbebigger for one obvious reason, make it harder. Why if export, do you sell more locally?) 1, then easy, efficient, then lower price to sell more 1. Tricky. More efficient, on average have more efficient rivals, so sell more, but then revenues...

31

32 Number of Industries percentage of plants in the industry that export

33 percentage of plants < >4.00 ratio of labor productivity Nonexporters Exporters

34 percentage of plants < >4.00 ratio of labor productivity Nonexporters Exporters

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