What do Exporters Know?

Transcription

1 What do Exporters Know? Michael J. Dickstein Eduardo Morales NYU Stern Princeton University September 12, 2016

2 Mr. Siegel In 2003, Mr. Siegel started Orb Audio, a maker of home theater systems. When the value of the dollar dropped in 2008, Mr. Siegel started to pay for country-specific internet ads and web pages aimed at consumers in England, Australia, Finland, and Canada. In 2010, 10 percent of Orb Audio s business was in Finland. According to Mr. Siegel, the big volume of exports to Finland can be explained because two years ago someone bought his speakers and wrote a nice review in an internet forum. (information taken from NYT 04/22/2010)

3 There are Many Mr. Siegels In 2014, approximately 300,000 firms sold in foreign markets (U.S. Census). Firms entry decision into export markets explains approximately 70% of the cross-country variation in aggregate US exports (Bernard et al., 2009). When taking such decision, potential exporters face considerable uncertainty. Firms enter a market if the expected value of exporting is positive. Firms choice will depend on expectations about the future evolution of their own productivity, exchange rates, trade policy, political stability in foreign countries, etc. Many other firm decisions depend on expectations about future payoffs: developing a new product (Bernard et al., 2010; Bilbiie et al., 2012). depends on expectations about future demand. investing in R&D (Aw et al., 2011). depends on expectations about success of research activity. importing (Blaum et al., 2014, Antràs et al., 2014)

4 In this paper Focus on exporters foreign markets participation decision. Estimate export fixed costs for several countries. Compute the predicted effect on export participation and aggregate exports of a counterfactual reduction in export fixed costs. Similar exercises in Roberts and Tybout (1997), Das et al. (2007), Arkolakis (2010), Cherkashin et al. (2010), Moxnes (2010), Eaton et al. (2011), Arkolakis (2013), Ruhl and Willis (2014). This previous literature assumes that the researcher has perfect knowledge of the content of firms information sets at the time of deciding whether to enter a foreign market. We relax this assumption in the context of a very simple partial equilibrium two-period model of export participation. Additionally, test content of exporters information sets. We also generalize our procedure to: (a) dynamic binary choice models à la Das et al. (2007); (b) sample selection models à la Heckman (1979).

5 In this paper First, we show that the estimates of export fixed costs are very sensitive to the assumptions researchers impose on agents information sets. Estimates of export entry costs (in thousands of 2000 USD): Exporters Information Argentina U.S. Japan Perfect Foresight , ,621.4 Dist. + Lag. Sales + Lag. Exports ,069,4 Assumptions on information sets are important for counterfactual predictions. Effect on aggregate exports of decreasing export entry costs by 40%: Exporters Information Argentina U.S. Japan Perfect Foresight 45.9% 201.5% 214.9% Dist. + Lag. Sales + Lag. Exports 36.1% 38.5% 226.3%

6 In this paper Second, we use two types of moment inequalities, (1) odds-based inequalities and (2) revealed-preference, that allow for partial knowledge of exporters information sets. Estimates of export entry costs: Exporters Information Argentina U.S. Japan At least (79.1, (181.3, (309.2, Dist. + Lag. Sales + Lag. Exports 104.1) 243.6) 420.5) Bounds on counterfactual predictions computed under the same assumptions needed for estimation: researcher observes a subset of firms information sets. Effect on aggregate exports of decreasing export entry costs by 40%: Exporters Information Argentina U.S. Japan At least (15.0%, (20.5%, (435.2%, Dist. + Lag. Sales + Lag. Exports 17.4%) 29.8%) 520.8%)

7 In this paper Third, we use our inequalities to learn about exporters true information sets. We can test the null hypothesis that a set of variables observed by the researcher is a subset of the information set of the exporters. { } exporters at least know dist. H 0 : p-value: = 0.14/ lag. sales + lag. exports { } H 0 : perfect foresight p-value: = 0.005/0.005 We will try to answer questions like Do large firms have more information than small firms? Do previous exporters have more information than non-exporters? Do all firms have more information about countries that are popular export destinations relative to less popular ones?

8 Literature on Inference with Unobserved Expectations Manski (2002) shows that preference parameters and unobserved expectations are not separately identified from the distribution of choices alone. Rosen and Willis (1979), Manski (1991), and Ahn and Manski (1993) propose a solution that relies on assuming that agents are rational; form expectations conditioning on a set of variables that are fully observed by the researcher. The revealed-preference inequalities in Pakes (2010) allow firms expectations to depend on variables that are unobserved to the researcher. However, in the specific case of binary choice models, agents preferences must not be affected by individual and choice-specific structural errors. The standard approach in binary choice models (e.g. logit, probit) is to assume that these structural errors follow a known parametric distribution. Our inequalities allow to estimate a probit (or logit) model whose index function includes expectations that depend on information sets that are only partly observed by the researcher.

9 Overview Benchmark Model. Data. Measurement of Export Revenues. Estimation with Full Knowledge of Exporters Information Sets. Estimation with Partial Knowledge of Exporters Information Sets. Testing Content of Firms Information Sets. Counterfactuals with Partial Knowledge of Exporters Information Sets. Dynamic Model Selection Model Conclusions

10 MODEL

11 Theoretical Model: Summary Single-agent partial equilibrium model. Two-period model. First period: firms decide whether to export to each possible destination market; if they export, they must pay export fixed costs; entry decision depends on expectations about potential export revenue upon entry and expectations are rational firms information set used to predict export revenues is left unspecified. Second period: firms observe the realized demand in each destination and their realized productivity, determine their optimal price in each market in which they have decided to enter, and obtain export profits. No discounting between periods.

12 Demand Every firm faces an isoelastic demand in every country, ijt Y jt P 1 η jt x ijt = p η where p ijt is the price set by i in j at t, Y jt is the total expenditure, and P jt is the ideal price index P jt = [ ] 1 1 η p 1 η ijt di, i A jt where A jt denotes the set of all firms selling in j at t. Trivial to allow also for demand shifters that vary at the jt level and common for all firms in the same country of origin. Constant elasticity of demand: η. In an extension, allow η to vary across countries.,

13 Supply Every firm is the single world producer of a variety. Market structure: monopolistic competition in every destination country. Constant marginal production cost: c it. If a firm exports a positive amount to j, it must pay two additional costs: iceberg trade costs τ ijt fixed costs f ijt In dynamic extension, allow also for sunk entry costs s ijt.

14 Information Set When deciding whether to export to market j in period t, firm i knows: fixed costs of exporting f ijt ; additionally, an information set J ijt that will help i predict export revenues. The set J ijt includes any variable that helps i predict either demand conditions in market j or its marginal cost of selling to j (Y jt, P jt ) τ ijt c it. As an example, J ijt might include lagged values of these variables, information on the number of competitors operating in market j (A jt ) or on their productivity (p i jt, for i i), tariffs, demand conditions in j affecting all potential exporters from the same country, etc.

15 Expected Revenue Conditional on Exporting Conditional on entering destination market j, firm i obtains revenue Assume that r ijt = [ η η 1 ] 1 η τ ijt c it Y jt. P jt E i [τ 1 η ijt c it, J ijt ] = E i [τ 1 η jt c it, J ijt ]. More generally, the effect of any firm-destination-year specific shock on export revenues is assumed to be: (a) unpredictable to firms when deciding on export entry; (b) uncorrelated with firms variable production costs; and (c) mean zero. In an extension, we relax this mean independence assumption and allow for firm-destination-year specific shocks that are unobserved to the researcher but observed to firms when deciding on their export destinations.

16 Expected Profits Conditional on Exporting The export profits that i would obtain in j if it were to export to t are and model fixed export costs as with π ijt = η 1 r ijt f ijt, f ijt = β 0 + β 1 dist j + ν ijt, ν ijt (J ijt, dist j ) N(0, σ 2 ). In words, unobserved heterogeneity in fixed costs is assumed to be normally distributed and independent of both the observed (to the researcher) determinants of fixed export costs (f ijt ) and of those determinants of export revenues known to firms when deciding on their export destinations (J ijt ). In an extension, we assume f ijt = β j + ν ijt instead.

17 Decision to Export Assuming firms have rational expectations, firm i exports to j at t if E[π ijt J ijt, f ijt ] 0. Therefore, d ijt = 1{η 1 E[r ijt J ijt ] β 0 β 1 dist j ν ijt 0}, and the probability that i exports to j conditional on (J ijt, dist j ) is P(d ijt = 1 J ijt, dist j ) = Φ ( σ 1( η 1 )) E[r ijt J ijt ] β 0 β 1 dist j. Not a simple probit because E[r ijt J ijt ] is unobserved. Generally both r ijt and J ijt are unobserved. Parameters to estimate θ (β 0, β 1, σ). Use η = 5 as normalization by scale.

18 DATA

19 Data Sources Data sources and variables used in the analysis: Chilean customs database: dummy for positive exports: d ijt, firm-country specific exports: r ijt, aggregate exports: R jt = i r ijt, Chilean industrial survey: CEPII: domestic sales: r iht = r it j r ijt, physical distance to Chile: dist j. Unbalanced panel of firms for the sample period: Sectors: manufacture of chemicals and chemical products; food products.

20 MEASUREMENT OF EXPORT REVENUES

21 Measurement of Export Revenues Only difficulty to estimate θ is that firms expectations on revenue, are unobserved. E[r ijt J ijt ], No matter which assumptions we impose on the content of the information set J ijt, dealing with the unobserved firms expectations requires constructing a measure r obs ijt of the potential export revenues r ijt. This measure need not be perfect. However, the difference between rijt obs firms true information set: and r ijt must be mean independent of E[r obs ijt J ijt ] = E[r ijt J ijt ].

22 Measurement of Export Revenues How can we construct r obs ijt in our setting? Export revenue r ijt is unobserved for firms that do not export, so rijt obs directly observed in the data for every firm, country and year. If we had assumed that τ ijt = τ jt, then our model predicts that is not r ijt = r iht R jt with R hjt = d i R jtr i ht, hjt i =1 and, given that r iht, R hjt and R jt are all observed, we could construct r obs ijt r iht R hjt R jt.

23 Measurement of Export Revenues Given the expression for actual export revenue implied by our model, and the assumption that we can rewrite Therefore, we use r ijt = [ η η 1 ] 1 η τ ijt c it Y jt, P jt E i [τ 1 η ijt c it, J ijt ] = E i [τ 1 η jt c it, J ijt ], r ijt = α jt r iht + e ijt, with E i [e ijt r iht, J ijt ] = 0. r obs ijt ˆα jt r iht. Given E i [e ijt r iht, J ijt ] = 0, it holds that E[ˆα jt r iht J ijt ] = E[r ijt J ijt ].

24 Market-year Revenue Shifters: Chemicals αjt ARG URY PRY BOL PER BRA ECU COL PAN VEN CRI SLV GTM DOM MEX USA ESP AUS GBR ITA JPN ˆα jt < 0.1 for all destinations and years. ˆα jt relatively larger for Brasil, Mexico, Japan, Spain and US.

25 Country-year Revenue Shifters: Food αjt ARG URG BOL PER BRA ECU COL PAN VEN CRI MEX USA CAN NZL ESP AUS FRA GBR BEL ITA NLD DEU DNK IDN SGP SRI MAL IND JPN PHL THA KOR CHN ˆα jt < 0.1 for most destinations and years. ˆα jt relatively larger for US, Japan, Singapore, Mexico, and Spain.

26 ESTIMATION CONDITIONAL ON FULL KNOWLEDGE OF EXPORTERS INFORMATION SETS

27 Assuming an Information Set The model above does not specify the content of the information set J ijt. These information sets are generally unobservable in standard trade datasets. Under the assumption that J obs ijt = J ijt, the export probability conditional on (Jijt obs, dist j ) is P(d ijt = 1 J obs ijt and one can estimate E[r obs ijt, dist j ) = Φ ( σ 1( η 1 E[rijt obs Jijt obs )) ] β 0 β 1 dist j, Jijt obs ] non-parametrically and θ using ML. The ML estimator is asymptotically unbiased if and only if the researcher has a perfect proxy for firms unobserved expectations; i.e. E[rijt obs Jijt obs ] = E[r ijt J ijt ].

28 Bias when J ijt J obs ijt Bias when the assumed information set Jijt obs is too large. Formally, distribution of J ijt conditional on Jijt obs is degenerate. Perfect foresight is a special case: E[r ijt J obs ijt ] = r ijt. For the sake of isolating the impact that assumptions imposed on J ijt have on parameter estimates, let s assume that r ijt is observed. In this case, the difference between the true agents expectation and the researchers proxy for it is equal to the expectational error that firms make when forecasting their export revenue upon entry: ε ijt = E[r ijt J obs ijt ] E[r ijt J ijt ] with ε ijt r ijt E[r ijt J ijt ] Assuming rational expectations implies cov(ε ijt, r ijt ) > 0. Therefore, wrongly assuming perfect foresight is equivalent to introducing classical measurement error in firms expectations cov(ε ijt,e[r ijt J obs ijt ]) > 0.

29 Bias when J ijt J obs ijt Understanding bias due to wrongly assuming perfect foresight is equivalent to understanding bias due to classical measurement error in probit models. Using proof in Yatchew and Griliches (1985), we can show that: if agent s true expectations are normally distributed E[r ijt J ijt ] N(0, σ 2 e ), and the expectational error is normal conditional on agents information sets ε ijt J ijt N(0, σ 2 ε), then there is an upward bias in the estimates of β 0, β 1 and σ. Bias increases in σ 2 ε/σ 2 e. Deviations from normality in the distribution of expectations or errors will alter the exact formula for the bias. However, our simulations show that the ML estimator always overestimates fixed export costs.

30 Bias when J ijt J obs ijt Table: Bias under Perfect Foresight Model Distribution of Distribution of Upward Bias Upward Bias E[r ijt J ijt ] ε ijt in β 0 in σ 1 N(0, 1) N(0, 0.25) 31% 34% 2 N(0, 1) N(0, 0.5) 49% 55% 3 N(0, 1) N(0, 1) 124% 138% 4 t 2 t 2 241% 300% 5 t 5 t 5 131% 153% 6 t 20 t % 141% 7 t 50 t % 140% 8 log-normal(0, 1) log-normal(0, 1) 274% 246% 9 log-normal(0, 1) log-normal(0, 1) 197% 342% More generally, impact of assuming an information set that is too large is to overestimate fixed export costs

31 Bias when J obs ijt J ijt The assumed information set J obs ijt Formally, distribution of J obs ijt is too small. conditional on J ijt is degenerate. In this case, the difference between the true agents expectation and the researchers proxy for it is mean independent of this researchers proxy. Defining then ξ ijt E[r ijt J obs ijt ] E[r ijt J ijt ], cov(ξ ijt,e[r ijt J obs ijt ]) = 0. If ξ ijt is normally distributed and fully independent of Jijt obs (so that the probit functional form structure is preserved), then the ML estimates of β 0 and β 1 are consistent and only the estimates of σ are biased upwards. Parameters β 0 and β 1 will also be biased if ξ ijt is not normally distributed.

32 Bias when Assumed Information Set is too Small Table: Bias when Information Set is too Small Model Distribution of Distribution of Upward Bias Upward Bias E[r ijt J ijt ] ξ ijt in β 0 in σ 1 N(0, 1) N(0, 0.25) 0.2% 1% 2 N(0, 1) N(0, 0.5) 0.2% 3% 3 N(0, 1) N(0, 1) 0.1% 11% 4 t 2 t 2 1.5% 32% 5 t 5 t 5 0.1% 17% 6 t 20 t % 12% 7 t 50 t % 12% 8 log-normal(0, 1) log-normal(0, 1) 20.1% 24% 9 log-normal(0, 1) log-normal(0, 1) -28.2% 14%

33 Empirical Application In our model, E[r ijt J ijt ] = E[α jt r iht J ijt ], and, therefore, firms use the information set J ijt to predict α jt r iht. Two alternative extreme assumptions on the content of firms information sets that point identify the fixed costs parameters θ are: 1 Perfect foresight. Assume J obs ijt such that E[α jt r iht J obs ijt ] = α jt r iht. 2 Minimal information set. Assume J obs ijt such that J obs ijt (r iht 1, R jt 1, dist j ).

34 Average Fixed Export Costs - Chemicals Country-specific fixed export costs under perfect foresight (in thousands of 2000 USD) Argentina U.S. Japan , ,621.4 (766.6, 969.3) (1,453.7, 1,836.3) (2,309.0, 2,933.8) Country-specific fixed export costs under minimal information set (in thousands of 2000 USD): Argentina U.S. Japan ,069.4 (323.4, 373.9) (620.6, 715.5) (989.2, 1,149.6) Perfect foresight estimates of fixed export costs are around 2.5 times as large as the minimal information set ones.

35 Average Fixed Export Costs - Food Country-specific fixed export costs under perfect foresight (in thousands of 2000 USD) Argentina U.S. Japan 2, , ,395.1 (1,878.4, 2,220.2) (2,019.2, 2,385.8) (2,211.8, 2,578.4) Country-specific fixed export costs under minimal information set (in thousands of 2000 USD): Argentina U.S. Japan 1, , ,482.4 (1,189.4, 1,358.4) (1,277.1, 1,455.5) (1,383.8, 1,581.0) Perfect foresight estimates of fixed export costs are around 1.6 times as large as the minimal information ones.

36 ESTIMATION CONDITIONAL ON PARTIAL KNOWLEDGE OF EXPORTERS INFORMATION SETS

37 Exporters Information Sets are Partially Observed It is generally hard to observe everything included in agents information sets. It is generally feasible to observe a subset of their content. No matter which information sets J ijt potential exporters truly have, these are likely to include: lagged own domestic sales: r iht 1, lagged aggregate exports from home country to each destination: R jt 1, distance from home country: dist j. Under the assumption that firms information sets are only partially observed, the model parameters are only partially identified. We use two types of moment inequalities, odds-based moment inequalities, revealed-preference moment inequalities, that allow to estimate the model parameters under the assumption that the researcher only observes part of firms information sets.

38 Odds-Based Moment Inequalities If Z ijt J ijt, then [ M ob (Z ijt ; θ ) = E ml ob (d ijt, rijt obs, dist j ; θ ) m ob u (d ijt, r obs ijt, dist j ; θ ) ] Z ijt 0, with m ob l m ob 1 Φ ( σ ( )) 1 η 1 rijt obs β 0 β 1 dist j ( ) = d ijt Φ ( σ 1( )) η 1 rijt obs (1 d ijt ), β 0 β 1 dist j u ( ) = (1 d ijt ) Φ ( σ 1( )) η 1 rijt obs β 0 β 1 dist j 1 Φ ( σ 1( )) η 1 rijt obs d ijt, β 0 β 1 dist j with r obs ijt = ˆα jt r iht. We denote M ob ( ) as the conditional odds-based moment inequalities.

39 Odds-Based Moment Inequalities - Proof for m ob l ( ) From model, E[1{η 1 E[r ijt J ijt ] β 0 β 1 dist j ν ijt 0} d ijt J ijt, dist j ] 0. Given assumptions on firm-country-year specific revenue shocks, E[1{η 1 E[α jt r iht J ijt ] β 0 β 1 dist j ν ijt 0} d ijt J ijt, dist j ] 0. Given distributional assumption on ν ijt, E[Φ(σ 1 (η 1 E[α jt r iht J ijt ] β 0 β 1 dist j )) d ijt J ijt, dist j ] 0. Doing simple algebra, E[d ijt 1 Φ(σ 1 (η 1 E[α jt r iht J ijt ] β 0 β 1 dist j )) Φ(σ 1 (η 1 E[α jt r iht J ijt ] β 0 β 1 dist j )) (1 d ijt ) J ijt, dist j ] 0.

40 Odds-Based Moment Inequalities - Proof for m ob l ( ) Given rational expectations assumption and convexity of Φ( )/(1 Φ( )), E[d ijt 1 Φ(σ 1 (η 1 α jt r iht β 0 β 1 dist j )) Φ(σ 1 (η 1 α jt r iht β 0 β 1 dist j )) Given properties of ˆα jt and convexity of Φ( )/(1 Φ( )), E[d ijt 1 Φ(σ 1 (η 1 ˆα jt r iht β 0 β 1 dist j )) Φ(σ 1 (η 1 ˆα jt r iht β 0 β 1 dist j )) (1 d ijt ) J ijt, dist j ] 0. (1 d ijt ) J ijt, dist j ] 0, Given assumption that Z ijt J ijt and Law of Iterated Expectations E[d ijt 1 Φ(σ 1 (η 1 ˆα jt r iht β 0 β 1 dist j )) Φ(σ 1 (η 1 ˆα jt r iht β 0 β 1 dist j )) Identical process for m ob u ( ) but starting from (1 d ijt ) Z ijt ] 0. E[d ijt 1{η 1 E[r ijt J ijt ] β 0 β 1 dist j ν ijt 0} J ijt, dist j ] 0.

41 Revealed-Preference Moment Inequalities If Z ijt J ijt, then with [ M r (Z ijt ; θ ) = E m r l ( ) = (1 d ijt ) ( η 1 r obs ijt m r l (d ijt, r obs ijt, dist j ; θ ) m r u(d ijt, r obs ijt, dist j ; θ ) ] Z ijt 0, ) β 0 β 1dist j + dijt σ φ( σ 1 (η 1 rijt obs β 0 β 1dist j ) ) Φ ( σ 1 (η 1 rijt obs β 0 β 1dist j ) ) ijt β 0 β 1dist j ) ) mu( ) r ( = d ijt η 1 rijt obs ) β 0 β 1dist j + (1 dijt )σ φ( σ 1 (η 1 r obs with r obs ijt = ˆα jt r iht. 1 Φ ( σ 1 (η 1 r obs ijt β 0 β 1dist j ) ) We denote M r ( ) as the conditional revealed-preference moment inequalities.

42 Revealed-Preference Moment Inequalities - Proof for m r u( ) From model, E[d ijt (η 1 E[r ijt J ijt ] β 0 β 1 dist j ν ijt ) J ijt, dist j ] 0. Given assumptions on firm-country-year specific revenue shocks, E[d ijt (η 1 E[α jt r iht J ijt ] β 0 β 1 dist j ν ijt ) J ijt, dist j ] 0. Given distributional assumption on ν ijt, E[d ijt ( η 1 E[α jt r iht J ijt ] β 0 β 1 dist j ) + (1 d ijt )σ φ( σ 1 (η 1 E[α jt r iht J ijt ] β 0 β 1 dist j ) ) 1 Φ ( σ 1 (η 1 E[α jt r iht J ijt ] β 0 β 1 dist j ) ) J ijt, dist j ] 0.

43 Revealed-Preference Moment Inequalities - Proof for m r u( ) Given rational expectations assumption and convexity of φ( )/(1 Φ( )), E[d ijt ( η 1 α jt r iht β 0 β 1 dist j ) + (1 d ijt )σ φ( σ 1 (η 1 α jt r iht β 0 β 1 dist j ) ) 1 Φ ( σ 1 (η 1 α jt r iht β 0 β 1 dist j ) ) J ijt, dist j ] 0. Given properties of ˆα jt, convexity of φ( )/(1 Φ( )), Z ijt J ijt, and LIE E[d ijt ( η 1 ˆα jt r iht β 0 β 1 dist j ) + (1 d ijt )σ φ( σ 1 (η 1 ˆα jt r iht β 0 β 1 dist j ) ) 1 Φ ( σ 1 (η 1 ˆα jt r iht β 0 β 1 dist j ) ) Z ijt] 0. Identical process for ml r ( ) but starting from E[(1 d ijt )( (η 1 E[r ijt J ijt ] β 0 β 1 dist j ν ijt )) J ijt, dist j ] 0.

44 Inference Procedure We combine the odds-based and revealed-preference moment inequalities to compute a single confidence set. The resulting confidence set is tighter that if we had used only the odds-based inequalities or only the revealed-preference inequalities. To compute the confidence set for the true parameter θ, we apply the procedure in Andrews and Soares (2010) with the Modified Method of Moments (MMM) test statistic. To compute the critical value, we use a Generalized Moment Selection (GMS) method and the Bayesian Information Criterion (BIC) constant κ ln(sample size), to compute the measure of slackness of the moment inequalities. We base inference on a finite set of unconditional moment inequalities. In spite of the loss of information this entails, the resulting confidence set is still sufficiently tight to yield economically meaningful results.

45 Average Fixed Export Costs Average fixed export costs (95% confidence interval): Sector Argentina U.S. Japan Chemicals (79.1, 104.1) (181,3, 243,6) (309,2, 420,5) Food (175.6, 270.1) (227.3, 308.9) (269.1, 361.0) Average fixed export costs (relative to perfect foresight case): Argentina U.S. Japan Chemicals (9.1%, 11.9%) (11.0%, 14.8%) (11.8%, 16.3%) Food (8.6%, 13.1%) (10.3%, 14.0%) (11.2%, 15.0%) Average fixed export costs (relative to minimal information set): Argentina U.S. Japan Chemicals (22.7%, 29.8%) (27.1%, 36.4%) (28.9%, 39.3%) Food (13.8%, 21.2%) (16.6%, 22.6%) (18.1%, 24.3%)

46 Average Fixed Export Costs Figure: Chemicals ARG BOL BRA ECUCOL CRI DOM MEX USA ESP AUS ITA JPN

47 Average Fixed Export Costs Figure: Food ARG BOLBRA COL CRI MEX USA NZL ESP FRA DNK IDN SGP JPN KORCHN

48 Distribution of Fixed Export Costs Figure: United States d1 d2 d3 d4 d5 d6 d7 d8 d9 (a) Chemicals d1 d2 d3 d4 d5 d6 d7 d8 d9 (b) Food All estimation procedures generate similar estimates for the lowest quantiles. Smallest quantiles need not necessarily correspond to actual exporters. The whole distribution matters for counterfactuals.

49 Country-specific Average Fixed Export Costs Figure: Chemicals ARG BOL BRA COL CRI DOM MEX USA ESP AUS ITA JPN Average fixed export costs are computed here as country fixed effects. Moment inequality confidence set becomes very large for far away countries.

50 Country-specific Average Fixed Export Cost Figure: Food BOL BRA COL CRI MEX NZL ESP FRA DNK IDN SGP JPN KORCHN Average fixed export costs are computed here as country fixed effects. Food sector has larger number of actual and potential exporters. Both ML estimates remain above confidence set for nearly all countries.

51 TESTING CONTENT OF FIRMS INFORMATION SETS

52 Testing Content of Firms Information Sets Given a set of unconditional moment inequalities, Bugni et al. (2015) describe a procedure to test the null hypothesis that there exists at least one value of the parameter vector θ consistent with all inequalities. This is a test of joint validity of all the inequalities used for identification. Each moment inequality is implied by: (a) the assumptions embedded in our theoretical model; (b) the assumption that the corresponding Z ijt J ijt. Therefore, rejecting the null could mean that either our theoretical model is inconsistent with the data or our vector of instruments Z ijt is invalid. To address this issue, we perform multiple hypothesis tests in which we only vary the vector Z ijt. We will find that our model is compatible with the data when combined with the assumption that Z ijt J ijt only for some specific vectors Z ijt. Ideally, we would like to have a test that determines valid and invalid moments among a large set of them: as far as we know, such a test does not exist for moment inequality settings.

53 Testing Content of Firms Information Sets Intuitively, our test is therefore just a test of validity of moments. When we reject that a vector Z ijt is in the information set J ijt for a given subset of firms, countries or years, this is because E[ε ijt Z ijt ] 0, ε ijt r ijt E[r ijt J ijt ], for that subset of firms, countries and years. In words, we reject the null that Z ijt is in the information set of a subset of firms, countries or years only if Z ijt is not mean independent of the expectational error that these firms make for those countries and years. We therefore pre-test for the relevance of all instruments Z ijt whose validity we want to test i.e. we show that they have predictive power for r ijt.

54 Test of Instrument Relevance Table: Instrument Relevance for ˆα jt r iht Chemicals Food Covariates (1) (2) (3) (4) R jt a a a a (20.7) (11.1) (28.2) (15.7) r iht a a a a (16.0) (16.1) (33.2) (33.3) dist j a a a a (23.9) (12.8) (10.5) (5.40) α jt a a (5.14) (8.86) Firms All All All All Countries All All All All Num. Obs. 44,037 44,037 84,975 84,975 R

55 Test of Instrument Validity Table: Validity of Z ijt as Instrument Set of Firms Set of Export Vector Tested Chemicals Food Destinations Z ijt p-value p-value All All (dist j, r iht 1, R jt 1 ) All All α jt r iht Large Popular (dist j, r iht 1, R jt 1, α jt 1 ) Large Unpopular (dist j, r iht 1, R jt 1, α jt 1 ) Small Popular (dist j, r iht 1, R jt 1, α jt 1 ) Small Unpopular (dist j, r iht 1, R jt 1, α jt 1 ) Small & Exporter t 1 All (dist j, r iht 1, R jt 1, α jt 1 ) Small & Non-Exporter t 1 All (dist j, r iht 1, R jt 1, α jt 1 ) Large & Non-exporter t 1 All (dist j, r iht 1, R jt 1, α jt 1 ) Large & Exporter t 1 All (dist j, r iht 1, R jt 1, α jt 1 )

56 What did we Learn about Exporters Information Sets? We can reject that firms have perfect foresight. We cannot reject that potential exporters know, at least, their own lagged domestic sales, lagged Chilean exports and distance to each potential destination market. Large firms have relevant information about potential export revenues that small firms do not have. There is no evidence that: firms have information about destination markets that have been popular in the past that they do not have for nonpopular markets. Learning from other exporters? previous exporters have more information that previously non-exporting firms: Learning from previous export experience? We are not testing for the impact of exporting on productivity or for learning about firm-destination idiosyncratic demand.

57 COUNTERFACTUALS UNDER PARTIAL KNOWLEDGE OF EXPORTERS INFORMATION SETS

58 Counterfactuals in Incomplete Models The model presented above is incomplete, in the sense that it does not fully specify firms information sets. However, the restrictions embedded in it, combined with the assumption that we observe a vector Z ijt such that Z ijt J ijt, are enough to generate bounds on the export probability P(d ijt = 1 J ijt, dist j ) = Φ ( σ 1( η 1 E[r ijt J ijt ] β 0 β 1 dist j )), for any given value of the parameter vector (β 0, β 1, σ). This allows to compute export probabilities in counterfactual scenarios.

59 Counterfactuals - Chemicals Effect of a 40% reduction in fixed export costs. Predicted growth in number of exporters: Argentina U.S. Japan Moment Ineq. (43.1%, 47.1%) (443.5%, 533.5%) (83.3%, 111.9%) Perfect foresight 51.6% 201.9% 632.7% Min. Info. Set 53.5% 135.8% 755.1% Predicted growth in total exports: Argentina U.S. Japan Moment Ineq. (15.0%, 17.4%) (435.2%, 520.8%) (20.5%, 29.8%) Perfect Foresight 45.9% 201.5% 214.9% Min. Info. Set 36.1% 38.5% 226.3%

60 Counterfactuals - Food Effect of a 40% reduction in fixed export costs. Predicted growth in number of exporters: Argentina U.S. Japan Moment Ineq. (127.4%, 204.2%) (35.5%, 41.6%) (57.6%, 71.8%) Perfect foresight 123.4% 90.9% 90.9% Min. Info. Set 126.1% 79.2% 79.2% Predicted growth in total exports: Argentina U.S. Japan Moment Ineq. (52.5%, 92.3%) (3.5%, 4.5%) (20.5%, 29.8%) Perfect Foresight 117.6% 24.9% 24.9% Min. Info. Set 106.8% 19.4% 19.4%

61 Counterfactuals and Information Sets For a given predicted growth in number of exporters, perfect foresight assumption will always predict maximum growth in volume of exports. Intuition: Perfect foresight selects as entrants those firms that ex post should have entered; i.e. firms that ex post make positive net export profits. Except for ν ijt, those firms with higher ex post gross profits in a country j correspond to those firms with higher ex post export revenues in j. Given that ν ijt is distributed independently from any determinant of export revenues, perfect foresight selects as entrants those firms that, on average, will have higher ex post export revenues. Notice that the overall effect predicted by the perfect foresight model might still be smaller than that predicted by the minimal information set model.

62 DYNAMICS

63 Dynamics Modify benchmark model and assume that firms must pay sunk export costs to new destinations. We model sunk export costs as π ijt = η 1 j r ijt f ijt (1 d ijt 1 )s ijt. s ijt = γ 0 + γ 1 dist j, and assume information sets evolve independently of past export decisions Export dummy therefore becomes J ijt+1 J ijt, d ijt J ijt+1 J ijt. d ijt = 1{η 1 E[r ijt J ijt ] β 0 β 1dist j (1 d ijt 1 )(γ 0 + γ 1dist j ) ν ijt + δe[v (J ijt+1, f ijt+1, s ijt+1, d ijt = 1) V (J ijt+1, f ijt+1, s ijt+1, d ijt = 0) J ijt, f ijt, s ijt ] 0} The parameter to estimate is θ D (β 0, β 1, σ, γ 0, γ 1).

64 Dynamics Export decision now depends on firms expectations of both static revenues r ijt and the difference in the value function depending on whether firm i exported to j in period t. We discussed before how we can find a measure of r ijt. Finding a measure of the difference in value functions V ( ) is impossible: V ( ) at t + 1 depends on the observed choice at t + 1, d ijt+1, which is a function of the observed choice at t, d ijt. Therefore, even if firms were to only take into account profits at periods t and t + 1 when making a decision at t, we can, at best, only find a measure of either V (, d ijt = 1) or V (, d ijt = 0). Adjusting the Euler approach in Morales et al. (2015) to the presence of the normal shocks ν ijt, we can find bounds on θ D without having to find a measure of the difference in value functions.

65 Fixed and Sunk Costs Estimates - Chemicals Table: Average fixed and sunk export costs Chemicals Estimator Cost Argentina Japan United States Benchmark Fixed [79.1, 104.1] [309.2, 420.5] [181.3, 243.6] Dynamics Fixed [55.8, 109.3] [853.3, 1,670.0] [409.2, 800.8] Sunk [384,2, 734,3] [5,874.4, 11,224.5] [2,816.6, 5,382.7] Sunk costs are significantly larger than average fixed export costs. Both fixed and sunk costs increase significantly with distance. Bounds on fixed costs estimates in dynamic model are wider: reflects difficulty to separately identify fixed and sunk costs. Fixed costs in dynamic model are larger, specially for further away countries. Effect of accounting for difference in value functions.

66 SELECTION ON EXPORT REVENUE SHOCKS

67 Selection on Export Revenue Shocks Benchmark model assumes that we can rewrite export revenues as We assume here that r ijt = α jt r iht + e ijt, with E i [e ijt r iht, J ijt ] = 0. r ijt = (α 0 + α 1 R jt )r iht + ξ ijt d ijt = 1{η 1 E[α jt r iht J ijt ] β 0 β 1 dist j (ν ijt + η 1 ξ ijt ) 0}. and impose the following distributional assumption ( ) (( ) ( ξ ijt (J 0 σξ jt, dist j ) N 2 σ ξν, 0 σ ξν σ 2 ν ijt )). If one additionally assumes perfect foresight, the resulting model corresponds exactly to the Heckman (1979) selection model.

68 Selection Model Estimates - Chemicals Table: Average fixed export costs Chemicals Estimator Cost Argentina Japan United States Benchmark Fixed [79.1, 104.1] [309.2, 420.5] [181.3, 243.6] Selection Fixed [67.7, 135.1] [1,033.9, 2,064.3] [495.8, 989.9] Bounds on fixed costs estimates in selection model are wider: uncertainty in α jt gets translated into uncertainty in α jt. Fixed costs in selection model are larger, specially for further away countries. cov(α jt, ξ ijt d ijt = 1) < 0 in the selected sample = downward bias in the α jt if we ignore selection correction; downward bias in α jt implies upward bias in σ 1 ; upward bias in σ 1 implies downward bias in β 0 and β 1.

69 CONCLUSION

70 Conclusion Many binary choice decisions depend on agents expectations of variables entering their payoff functions. Agents expectations are generally unobservable to the econometrician. Standard estimation approaches require strong assumptions on the content of agents information sets. We introduce a new estimation procedure that allows both for: partial observability by the researcher of agents information sets; individual and choice-specific structural errors (i.e. payoff-relevant variables that are observed by the agent and not by the econometrician). We show that the misspecification of agents information sets may have large consequences for the estimates of structural models and, therefore, also for the model predictions for any counterfactual exercise of interest.

71 What do Exporters Know? Michael J. Dickstein Stanford University and NBER Eduardo Morales Princeton University and NBER June 23, 2015 Abstract Much of the variation in international trade volume is driven by firms extensive margin decision to participate in export markets. To understand this decision and predict the sensitivity of export flows to changes in trade costs, we estimate a standard model of firms export participation. In choosing whether to export, firms weigh the fixed costs of exporting against the forecasted profits from serving a foreign market. We show that the estimated parameters and counterfactual predictions from the model depend heavily on how the researcher specifies firms expectations over these profits. We therefore develop a novel moment inequality approach with weaker assumptions on firms expectations. Our approach introduces a new set of moment inequalities odds-based inequalities and applies the revealed preference inequalities introduced in Pakes (2010) to a new setting. We use data from Chilean exporters to show that, relative to methods that require specifying firms information sets, our approach generates estimates of fixed export costs that are 65-85% smaller. Counterfactual reductions in fixed costs generate gains in export participation that are 30% smaller, on average, than those predicted by existing approaches. Keywords: export participation, demand under uncertainty, discrete choice methods, moment inequalities We thank Tim Bresnahan, Lorenzo Caliendo, Jan De Loecker, Dave Donaldson, Liran Einav, Alon Eizenberg, Guido Imbens, Ariel Pakes, Esteban Rossi-Hansberg, James Tybout and seminar participants at the CEPR-JIE conference on Applied Industrial Organization, Dartmouth College, LMU, the NBER ITI meeting, Pennsylvania State University, Princeton University, the Stanford/Berkeley IO Fest, Stanford University, UCLA, University of Virginia, and Wharton School for helpful suggestions. All errors are our own. mjd@stanford.edu, ecmorale@princeton.edu.

72 1 Introduction In 2013, approximately 300,000 US firms chose to export to foreign markets. 1 The decision of these firms to sell abroad drives much of the variation in trade volume from the US. 2 Thus, to predict how aggregate exports may change with lower trade costs, exchange rate movements, or other policy or market fluctuations, researchers need to understand firms extensive margin decisions to participate in export markets. A large literature in international trade focuses on modeling firms export decisions. 3 Empirical analyses of these decisions, however, face a serious data obstacle: the decision to export depends on a firm s expectations of the profits it will earn when serving a foreign market, which the researcher rarely observes. Absent direct data on firms expectations, researchers must impose assumptions on how firms form these expectations. For example, researchers commonly assume firms expectations are rational and depend on a set of variables observed in the data. The precise specification of agents information, however, can importantly influence the overall measurement, as Manski (1993, 2004), and Cunha and Heckman (2007) show in the context of evaluating the returns to schooling. In the export setting, the assumptions on expectations may affect both the estimates of the costs firms incur when exporting and predictions of how firms will respond to counterfactual changes in these trade costs. In this paper, we first document that estimates of the parameters underlying firms export decisions depend heavily on how researchers specify the firm s expectations. We compare the predictions of a standard model in the international trade literature (Melitz, 2003; Helpman et al., 2008) under two different sets of assumptions on how exporters form their expectations: the perfect foresight case, under which firms perfectly predict their profits when exporting, and a limited information specification in which firms only use a specific observed set of variables to predict their own export profits. Under each assumption on firms information, we recover values for the fixed costs of exporting and predict changes in exports across markets in reaction to a policy that reduces these fixed costs by 40%. Finding important differences in the predictions from the two models, we then develop a new empirical model of export participation that places fewer restrictions on firms expectations. Under our new approach, firms may gather different signals about their productivity relative to competitors, or about the evolution of exchange rates, trade policy, political stability abroad, and foreign demand; we do not require the researcher to have full knowledge of each exporter s information set. Instead, the researcher need only specify a subset of the variables that agents use to form their expectations about their profits conditional on exporting. The 1 Department of Commerce (2015) 2 According to Bernard et al. (2010), approximately 70% of the cross-sectional variation in exports comes from firms entering a market rather than changing their export volume 3 See for example Das et al. (2007), Arkolakis (2010), Moxnes (2010), Eaton et al. (2011), Ruhl and Willis (2014), Arkolakis et al. (2014a), and Cherkashin et al. (2015). A recent literature also focuses on the decisions of importers; e.g. Antràs et al. (2014). 1

73 researcher must observe this subset, but need not observe any remaining variables that affect the firm s expectations. The set of unobserved variables may vary flexibly across firms, markets, and years. In contrast, standard estimation approaches require the researcher to fully specify and observe all variables in exporters information sets. The trade-off from specifying only a subset of the firm s information is that we can only partially identify the true parameters of interest. To do so, we develop a new type of moment inequality, which we label the odds-based inequality, and combine it with inequalities based on revealed preference. 4 Using these inequalities, our empirical burden is twofold. First, we must show that placing fewer assumptions on expectations matters both for the estimates of the parameters of the exporter s problem and for the predictions of export flows under counterfactual trade policy. Second, our robust approach must generate bounds on the model s parameters and on predicted exports that are small enough to be informative. We perform our empirical analysis in the context of a standard partial equilibrium, two period model of export participation. 5 We estimate this model using data on Chilean exporters in two industrial sectors, the manufacture of chemicals and food products. We proceed in three steps. First, we demonstrate the sensitivity of both the estimated fixed costs of exporting and the predictions of firms export participation to assumptions the researcher imposes on firms profit forecasts. Specifically, using maximum likelihood methods, we estimate a perfect foresight model under which firms predict perfectly the revenues they will earn upon entry. Under this assumption, for example, we find export costs in the chemicals sector from Chile to Argentina, Japan, and United States to equal $894,000, $2.8 million, and $1.7 million, respectively. We compare these estimates to an alternative approach, developed in Willis and Rosen (1979), Manski (1991) and Ahn and Manski (1993), in which we assume that firms expectations are rational and specify that firms form their expectations using only three variables: distance to the export market, aggregate exports from Chile to that market in the prior year, and the firm s own productivity from the prior year. The estimated fixed costs of exporting under this limited information approach are approximately 20-30% lower than those found under the perfect foresight assumption, in both the chemicals and food sector. That the fixed cost estimates differ under perfect foresight and the limited information approach reflects a possible bias in the estimation. Both the limited information procedure and the perfect foresight approach require the researcher to specify precisely the content of the agent s information set. If firms actually employ a different set of variables either 4 A growing empirical literature employs moment inequalities derived from revealed preference arguments, including Ho (2009), Crawford and Yurukoglu (2012), Ho and Pakes (2014), Eizenberg (2014), Wollman (2014), and Morales et al. (2015). This work generally follows the methodology developed in Pakes (2010) and Pakes et al. (2015); our revealed preference inequalities apply this methodology in a new setting with a distinct error structure. 5 By combining the insights in this paper with the Euler s perturbation method introduced in Morales et al. (2015), we could similarly perform our analysis in the context of a fully dynamic export participation model à la Das et al. (2007). 2

74 more information or less to predict their potential export profits, the estimates of the model parameters will generally be biased. Thus, our second key step is to employ our new types of moments inequalities to partially identify the exporter s fixed costs under weaker assumptions. Here, we again assume that firms know the distance to the export market, the aggregate exports to that market in the prior year, and their own productivity from the prior year. However, unlike the limited information approach described earlier, the inequalities we define do not restrict firms to use only these three variables when forecasting their potential export profits. We require only that firms know at least these variables. We chose this set of three variables in our specification because they are contained either in firms own balance sheets or in official government statistics. It seems reasonable, therefore, to assume all firms might know at least these variables. We can, however, go further and test the null hypothesis that the potential exporters information sets satisfy this minimal requirement. Specifically, conditional on the model, we use the specification test suggested in Andrews and Soares (2010) to test our assumption that these three variables are in the firm s information set. 6 Under the traditional maximum likelihood methods, we estimate the fixed costs for exports from Chile to Argentina, for example, to equal $594,000 or $894,000 in the chemicals sector, depending on the specification of the information set. Using our inequalities approach, we find much lower fixed costs, between approximately $270,000 and $298,000 in the chemicals sector. This range is small enough to be informative for policy. In addition, in model specification tests using data from both the chemicals and food sectors, we cannot reject the null hypothesis that exporters know at least distance, lagged productivity, and lagged aggregate exports when making their export decisions. To address further the question of what do exporters know?, we repeat this test under the same model and data, but placing one additional variable in the firm s information set. In this alternative, we assume the firm also knows the productivity of other firms that export to each destination country. Repeating the test, we now reject the null that firms knew this information when making their export decision at the 4% level in the chemicals sector and the 1% level in the food sector. Similarly, we can also reject the assumption of perfect foresight at any generally used significance level. Finally, as a third key step, we conduct counterfactuals using our inequalities, imposing the same minimal requirements on firms information sets as we imposed in estimation. Our counterfactual predictions are also set-identified. We provide bounds that indicate how firms would respond to a counterfactual policy that reduces the fixed costs of exporting by 40%. Starting with the approaches that require explicit assumptions on the exact content of each firm s information set, we find that the results differ substantially with these assumptions. For example, compared to predictions under perfect foresight, the predicted export participation under the alternative procedure that assumes firms know only distance, lagged aggregate 6 Alternative specification tests for partially identified models defined by moment inequalities have been provided in Romano and Shaikh (2008), Andrews and Guggenberger (2009), and Bugni et al. (2015). 3

75 exports and lagged productivity is 3% and 20% higher for Argentina and Japan and 12% lower for the United States, in the chemicals sector. Comparing the predictions from these two models to those computed using our moment inequalities, in the latter we predict gains in export participation from counterfactual reductions in fixed costs that are 30% smaller on average, depending upon the destination market and manufacturing sector. We illustrate our contribution using the exporter s problem. Our approach, however, provides a robust methodology to estimate the parameters of many decisions in economics that depend on agents forecasts of key variables. For example, when a firm develops a new product, it must form expectations of the likely future demand (Bernard et al., 2010; Bilbiie et al., 2012; Arkolakis et al., 2014b). To determine whether to invest in research and development projects, the firm must form expectations about the success of the research activity (Aw et al., 2011). On the consumer side, Greenstone et al. (2014) examine the enlistment of soldiers in the US Army; the decision to reenlist depends on the soldiers expectations about the riskiness of the task assigned. Similarly, a retiree s decision to purchase a private annuity (Ameriks et al., 2015) depends on her expectations about life expectancy. In education, the decision to attend college crucially depends on potential students expectations about the difference in lifetime earnings with and without a college education (Freeman, 1971; Willis and Rosen, 1979; Manski and Wise, 1983). In these settings, even without direct elicitation of agent s preferences (Manski, 2004), our approach can recover bounds on the economic primitives of the agent s problem without imposing strong assumptions on agents expectations. We proceed in this paper by first describing our model of firm exports in Section 2, building up to an expression for firms export participation decisions. In Sections 3 and 4 we describe our data, empirical setting, and three alternative empirical models. We first outline the maximum likelihood procedures that require the researcher to have full knowledge of agents information sets. We then introduce our moment inequality estimator and discuss how to build these inequalities as well as conduct counterfactuals with possibly set-identified parameters and with only partial knowledge of agents information sets. In Section 5, we compare the parameter estimates resulting from the alternative empirical models. In Section 6, we use our inequality approach to predict the effect on export participation and export volume from a reduction in fixed export costs. Section 8 concludes. 2 Export Model We begin with a model of a firm s export decisions. All firms located in country h may choose to sell in every export market j. We index the firms located in h and active at period t by i = 1,..., N t. 7 We index the potential destination countries by j = 1,..., J. We model firms export decisions using a two-period model. In the first period, firms choose 7 For ease of notation, we will eliminate the subindex for the country of origin h. 4