Lecture 3: Producer-Level Analysis; French Firms

Transcription

1 Lecture 3: Producer-Level Analysis; French Firms Samuel Kortum April 13, 2007

2 An Anatomy of International Trade Joint project with Jonathan Eaton and Francis Kramarz.

3 Technologies Countries: i =1,...N. Goods: j =[0,J]. Technologies: Z i (j) is the efficiency in i of producing j. Model efficiencies as random variables: Pr[Z i (j) z] =e (T i/j)z θ. Let J, measure of goods produced with efficiency greater than z is m i (z) = lim J[1 J e (T i/j)z θ ]=Ti z θ

4 Costs Cost of inputs in country i is w i ; iceberg costs of delivery to n are d ni. Measure of goods that country i can supply to n at cost less than c µ ni (c) =m i (w i d ni /c) =T i (w i d ni ) θ c θ. Measure of goods that the world can supply to n at cost less than c where Φ n = P N i=1 T i (w i d ni ) θ. µ n (c) = X N i=1 µ ni(c) =Φ n c θ,

5 Demand Expenditure on good j in country n à pn (j)! 1 σ X n X n (j) =α n (j) P n The α n (j): random demand shock, E[α n (j) Z(j)] = 1. Define e θ = θ/(σ 1) and restrict e θ>1.

6 Entry Fixed cost of selling good j in country n is E n (j) =E n ε n (j). Ratio η n (j) =α n (j)/ε n (j): random entry shock, E[η n (j) Z(j)] = 1. Entry shock applies to producers from every i. The vector (α n (j),η n (j)) drawn from a density f(α, η).

7 Market Structure A firm in i owns technology Z i (j) for producing good j. If firm supplies j to country n, actsasamonopolist. Sets price p n (j) = σ σ 1 C n(j). Gross profit X n (j)/σ, soentersiff X n (j)/σ E n ε n (j). Cost threshold: enter if C n (j) c n (η), withη n (j) =α n (j)/ε n (j)..

8 Overview of the Elements A Country: technology T i,wagew i, geography d ni,sizex n,andentry cost E n. A Good: market-specific demandα n (j) and entry shock η n (j). A Firm: location i, goodj, andefficiency Z i (j). Technology Z i (j) isthebackboneofthefirm.

9 Empirical Strategy Thesourcecountryi is always France. Observe behavior of French firms in many different markets n. Take market size X n and French sales X nf as given. Derive implications for moments calculated from French firms. Check model s consistency with these predicted moments.

10 Moments Mean exports to country n: E[X nf (j) n] = eθ eθ 1 E[α n (j)η n (j) eθ 1 ] E[η n (j) eθ σe n. ] Number of French firms exporting to n: J nf = X nf /E[X nf (j) n]. Mean sales in France of those exporting to n: E[X FF (j) n] = eθ eθ 1 E[α F (j)η n (j) e θ 1 ] E[η n (j) eθ ] Ã! 1/ e θ JnF σe F. J FF

11 The Cadaver: French Manufacturers, 1986 Merge administrative records on each firm with customs data on its exports, by country.

12 The Cadaver: French Manufacturers, 1986 Merge administrative records on each firm with customs data on its exports, by country. Overall 230,000 firms and 113 countries.

13 The Cadaver: French Manufacturers, 1986 Merge administrative records on each firm with customs data on its exports, by country. Overall 230,000 firms and 113 countries. Combine with aggregate data on the size of each country s market

14 The Cadaver: French Manufacturers, 1986 Merge administrative records on each firm with customs data on its exports, by country. Overall 230,000 firms and 113 countries. Combine with aggregate data on the size of each country s market... and France s share of it.

15 What Can We Learn? A new crop of trade models have emerged, built on:

16 What Can We Learn? A new crop of trade models have emerged, built on: specific form of heterogeneity in producer efficiency.

17 What Can We Learn? A new crop of trade models have emerged, built on: specific form of heterogeneity in producer efficiency. iceberg trade costs.

18 What Can We Learn? A new crop of trade models have emerged, built on: specific form of heterogeneity in producer efficiency. iceberg trade costs. fixed costs of entering markets.

19 What Can We Learn? A new crop of trade models have emerged, built on: specific form of heterogeneity in producer efficiency. iceberg trade costs. fixed costs of entering markets. Use detailed French data to test the structure of these new models.

20 What Can We Learn? A new crop of trade models have emerged, built on: specific form of heterogeneity in producer efficiency. iceberg trade costs. fixed costs of entering markets. Use detailed French data to test the structure of these new models. Are they on the right track?

21 What Do We Learn? These new models do very well (they were, after all, inspired by findings of Bernard and Jensen as well as Tybout).

22 What Do We Learn? These new models do very well (they were, after all, inspired by findings of Bernard and Jensen as well as Tybout). Take Monopolistic Competition model of Melitz (2003)

23 What Do We Learn? These new models do very well (they were, after all, inspired by findings of Bernard and Jensen as well as Tybout). Take Monopolistic Competition model of Melitz (2003)... using formulation of Chaney (2006), and add some noise.

24 What Do We Learn? These new models do very well (they were, after all, inspired by findings of Bernard and Jensen as well as Tybout). Take Monopolistic Competition model of Melitz (2003)... using formulation of Chaney (2006), and add some noise. Or, take Ricardian model of BEJK (2003), add fixed entry costs and noise.

25 What Do We Learn? These new models do very well (they were, after all, inspired by findings of Bernard and Jensen as well as Tybout). Take Monopolistic Competition model of Melitz (2003)... using formulation of Chaney (2006), and add some noise. Or, take Ricardian model of BEJK (2003), add fixed entry costs and noise. Tell this story through a set of empirical regularities: targets for theories.

26 What Do We Learn? These new models do very well (they were, after all, inspired by findings of Bernard and Jensen as well as Tybout). Take Monopolistic Competition model of Melitz (2003)... using formulation of Chaney (2006), and add some noise. Or, take Ricardian model of BEJK (2003), add fixed entry costs and noise. Tell this story through a set of empirical regularities: targets for theories. It can all be distilled into Three Basic Facts.

27 Fact I: Large Markets Attract More Entrants

28 : Entry of French Firms and Market Size French firms entering market market size ($ billions)

29 : Entry of French Firms and Market Size FRA French firms entering market SIE BEL SWI GER ITA UNK NET SPA USA CAMOR PORDEN AUT SWE CAN COT ALG TUN GRENOR JAP SEN ISRSAU FIN IRE HOK AUL TOG SIN SOU BEN EGY NIGMAL BUK KUW CEN MAD TURYUG IND MAS ZAI BRA JOR NZE TAI KOR HUN MAU CHI VEN MEX ARG SYR NIA PAK MAY THA IRQ CZE USR CHA ANG OMA COL INO CHN URU BUL KEN PANPHI PER RWA ROM GEE BUR ECU IRN LIY PAR SRISUD ETH DOMZIM CUB MOZ COS GUA GHA LIB TRIBAN ZAM TAN JAM HON BOL ELS NIC VIE SOM PAP MAW ALB UGA NEP AFG market size ($ billions)

30 : Entry (relative to market share) and Market Size estimate of firms entering market (thousands) market size ($ billions)

31 : Entry (relative to market share) and Market Size estimate of firms entering market (thousands) SIE GER AUL UNK SWI CHN BRA AUT TAI GEE ITA FRA DENBEL NET SPA NZE BUL NOR CZE FIN ROM SWE YUG ISR SOU ARG MEXKOR IND MAY IRE GRE VIE HOK HUN VEN CHIPOR SINSAU CUB TUR IRN COL ALG EGY ZIM SUD ECU CAM COT PER INO ALB MOR TAN COS PAN SYRPHI TRI URU PAK TUN BUK SEN GUA ETH ELS DOM JORKUW THA SRI BOLPAR HON JAM ZAI IRQ PAP OMA BAN NIA TOG ANG SOM MAS LIY CHA MAL KEN RWA BEN MAD NEP UGA NIC BUR NIG MOZ CEN ZAMGHA LIB MAU AFG MAW market size ($ billions) CAN JAP USR USA

32 Elaboration of Fact I Larger markets do attract more entrants.

33 Elaboration of Fact I Larger markets do attract more entrants. Need to condition on market share to correct for geography effects.

34 Elaboration of Fact I Larger markets do attract more entrants. Need to condition on market share to correct for geography effects. Doing so, the French data point is not far off the line.

35 Elaboration of Fact I Larger markets do attract more entrants. Need to condition on market share to correct for geography effects. Doing so, the French data point is not far off the line. Number of exporters rises less than in proportion to market size (elasticity 2/3).

36 Elaboration of Fact I Larger markets do attract more entrants. Need to condition on market share to correct for geography effects. Doing so, the French data point is not far off the line. Number of exporters rises less than in proportion to market size (elasticity 2/3). Thus, average exports per firms rises with market size (elasticity 1/3).

37 Fact II: Large Firms Enter Markets That Others Don t

38 : Size in France and Popularity Ranking of the Market average sales in French market ($ millions) popularity of market penetrated

39 : Size in France and Popularity Ranking of the Market average sales in French market ($ millions) FRA BEL BOL MAW UGA SOM ZAM ELS JAM SIE ALB GUA COS GHA LIB HON VIE NIC AFG DOM SUD ETH BAN ROM GEE LIY SRI ZIMPAP TAN PER KEN ECU MOZ IRN BUR CUB PAR TRI NEP COL USR BUL ANG URU RWA ARGSYR JORNIA CZE HUN MEX PAN MAU EGY TUR YUG MAL CHA BUKNIG IRE TOG BEN CEN MADMAS ZAI VEN CHI PAK CHN IRQ INOPHI OMA THA MAY BRA KUW IND KOR TAI NZE SIN SOU POR DEN GRE FIN NOR SWE AUT MOR ALG TUN SEN SAU AUL ISR HOK COT CAM JAP CAN NET SPA ITAUNK USA GER SWI popularity of market penetrated

40 : Size in France and Number Entering the Market 1000 average sales in French market ($ millions) firms selling to the nth most popular market

41 : Size in France and Number Entering the Market 1000 average sales in French market ($ millions) UGA MAW BOL SOM ALBSIE JAM ELS ZAM AFG NIC VIEGUA HON GHA LIB COS PAP BAN DOM ZIM ETH TANMOZSUD SRI TRIPAR LIY CUB BUR ECUPER GEE ROM KEN NEP IRN RWA PHI URU BUL PAN ANG OMA COL CHN INO USR CZE IRQ PAK NIA MAY SYR MEX THA MAU CHI JOR VEN HUN ARG CHA MAS NZE KOR BRA MAD ZAI MAL TAI CEN YUG TUR NIG IND BUK EGY BEN KUW TOG SOU SIN IRE HOK AUL ISR SAU FIN SEN NOR GRE TUN JAP ALG COT POR DEN MOR CAM SWE AUT CAN SPA USA NET UNK ITA SWI GER BEL FRA firms selling to the nth most popular market

42 : Size in France and Number Entering Multiple Markets

43 : Size in France and Number Entering Multiple Markets 1000 average sales in French market ($ millions) firms selling to k or more markets

44 Elaboration of Fact II Performance in export markets highly correlated with performance at home.

45 Elaboration of Fact II Performance in export markets highly correlated with performance at home. Measure how common it is for a firm to export to a particular market.

46 Elaboration of Fact II Performance in export markets highly correlated with performance at home. Measure how common it is for a firm to export to a particular market. Measure how common it is for a firm to export to many markets.

47 Elaboration of Fact II Performance in export markets highly correlated with performance at home. Measure how common it is for a firm to export to a particular market. Measure how common it is for a firm to export to many markets. Firms that are uncommon exporters, in either sense, tend to be big in France.

48 Elaboration of Fact II Performance in export markets highly correlated with performance at home. Measure how common it is for a firm to export to a particular market. Measure how common it is for a firm to export to many markets. Firms that are uncommon exporters, in either sense, tend to be big in France. The relationships are strikingly linear on a log-log scale.

49 Fact III: Size Distribution of Firms, Same across Markets In foreign markets we only observe size via the export sales of French firms.

50 Fact III: Size Distribution of Firms, Same across Markets In foreign markets we only observe size via the export sales of French firms. Can t literally be the same distribution since mean exports increases in market size.

51 Fact III: Size Distribution of Firms, Same across Markets In foreign markets we only observe size via the export sales of French firms. Can t literally be the same distribution since mean exports increases in market size. Need to scale percentiles of exports by the country-level mean.

52 Fact III: Size Distribution of Firms, Same across Markets In foreign markets we only observe size via the export sales of French firms. Can t literally be the same distribution since mean exports increases in market size. Need to scale percentiles of exports by the country-level mean. Thus 10 (vertical axis) means ten times the mean.

53 Fact III: Size Distribution of Firms, Same across Markets In foreign markets we only observe size via the export sales of French firms. Can t literally be the same distribution since mean exports increases in market size. Need to scale percentiles of exports by the country-level mean. Thus 10 (vertical axis) means ten times the mean. Moving right (horizontal axis) means heading through the distribution to smaller firms.

54 : Distribution of French Sales in France percentile / mean p

55 : Distribution of French Exports to Germany percentile / mean p

56 : Distribution of French Exports to Ireland percentile / mean p

57 : Distribution of French Exports to the United Kingdom percentile / mean p Di t ib ti f F h Fi ' E t t th U it d Ki d

58 : Distribution of French Exports to the United States percentile / mean p

59 Elaboration of Fact III Characteristic shape.

60 Elaboration of Fact III Characteristic shape. Linear for large firms.

61 Elaboration of Fact III Characteristic shape. Linear for large firms. But, then many really small firms that break the linearity.

62 Interpretation of the Three Facts Fact I suggests firm heterogeneity so that only a minority of firms enter a particular market.

63 Interpretation of the Three Facts Fact I suggests firm heterogeneity so that only a minority of firms enter a particular market. Also, suggest an entry cost that only more efficient firms are willing to pay.

64 Interpretation of the Three Facts Fact I suggests firm heterogeneity so that only a minority of firms enter a particular market. Also, suggest an entry cost that only more efficient firms are willing to pay. In a large market firms can more easily cover this entry cost.

65 Interpretation of the Three Facts Fact I suggests firm heterogeneity so that only a minority of firms enter a particular market. Also, suggest an entry cost that only more efficient firms are willing to pay. In a large market firms can more easily cover this entry cost. If the entry cost rises modestly with market size, explain why mean exports rise.

66 Interpretation of the Three Facts Fact II suggests firm-level heterogeneity in efficiency, carrying over to wherever it sells.

67 Interpretation of the Three Facts Fact II suggests firm-level heterogeneity in efficiency, carrying over to wherever it sells. Firm efficiency connects entry decisions and how much the firm sells.

68 Interpretation of the Three Facts Fact II suggests firm-level heterogeneity in efficiency, carrying over to wherever it sells. Firm efficiency connects entry decisions and how much the firm sells. The log linearity in Fact II is indicative of a Pareto distribution of efficiency.

69 Interpretation of the Three Facts Fact II suggests firm-level heterogeneity in efficiency, carrying over to wherever it sells. Firm efficiency connects entry decisions and how much the firm sells. The log linearity in Fact II is indicative of a Pareto distribution of efficiency. Fact III is consistent with a Pareto distribution: country invariance and linearity at the upper end.

70 Interpretation of the Three Facts Fact II suggests firm-level heterogeneity in efficiency, carrying over to wherever it sells. Firm efficiency connects entry decisions and how much the firm sells. The log linearity in Fact II is indicative of a Pareto distribution of efficiency. Fact III is consistent with a Pareto distribution: country invariance and linearity at the upper end. Nonlinearity in Fact III suggests noise so that some firms enter even though they are not that great.

71 Conclusion Its an exciting time to be working in international trade.

72 Conclusion Its an exciting time to be working in international trade. There are a bunch of new theories and a real explosion of evidence.

73 Conclusion Its an exciting time to be working in international trade. There are a bunch of new theories and a real explosion of evidence. At a basic level, models and data are speaking to each other.

74 Conclusion Its an exciting time to be working in international trade. There are a bunch of new theories and a real explosion of evidence. At a basic level, models and data are speaking to each other. With this ongoing communication, we will get better and better quantitative models to use for policy analysis.