Information Globalization, Risk Sharing and International Trade

Transcription

1 Information Globalization, Risk Sharing and International Trade Isaac Baley, Laura Veldkamp, and Michael Waugh New York University Fall 214 Baley, Veldkamp, Waugh (NYU) Information and Trade Fall / 24

2 Overview Motivation Puzzle: low level of cross-country trade. - Trade frictions: tariffs, transportation, distribution, language - Information frictions: search frictions, unknown quality But if international trade < domestic trade, home agents must know something foreigners do not (asymmetry). Question: Do asymmetric information frictions about aggregate conditions explain low trade? Baley, Veldkamp, Waugh (NYU) Information and Trade Fall / 24

3 Overview This paper Two-country, two-good, endowment economy (standard Armington). One new ingredient: Asymmetric information - Agents know home endowment, noisy signals about foreign endowment. - Relative price (P foreign good /P home good ) is uncertain. Exporting is risky. Results: Information globalization (reductions in signal noise). Reduces risk-sharing Reduces trade share Increases expected utility Baley, Veldkamp, Waugh (NYU) Information and Trade Fall / 24

4 Overview What s New About This? Information about match-specific variables (no asymmetry) Allen (213), Petropoulou (211), Rauch Watson (24), Eaton et.al. (211) Why is domestic trade is so much higher? Information about aggregate conditions Steinwender (214) Does partial eqbm logic extend to general eqbm? This paper: Information asymmetry in general equilibrium. Uncertainty about what others know (asymmetric info) affects relative prices. Reverses PE effect on trade. Baley, Veldkamp, Waugh (NYU) Information and Trade Fall / 24

5 Overview Key Ideas Information inhibits risk-sharing (Hirschleifer 79) Example: Two independent lotteries. Maximum risk-sharing = maximum trade. risk-sharing trade Unlike financial market, less info more risky activity. Because of 2 goods. Hedge risk by exporting more. Effect works through second-order beliefs. Takeaways 1 The equilibrium effects of information frictions are important. 2 We should look for other information asymmetries. Baley, Veldkamp, Waugh (NYU) Information and Trade Fall / 24

6 Model Environment Environment (standard part) 1 period, 2 countries (x and y), a continuum of agents in each. Preferences: Risk neutral on CES composite consumption [ E (cx θ + cy θ ) 1/θ], θ (, 1) Individual endowments: - country x firm: z x units of good x, ln z x N (µ x, σx) 2 - country y firm: z y units of good y, ln z y N (µ y, σy 2 ) Aggregate shocks: µ x N (m x, s 2 x ), µ y N (m y, s 2 y ) Budget sets: agents take price q (units of x per y) as given [ ] in country x : c x [, z x t x ], c y, tx q in country y : c y [, z y t y ], c x [, t y q] Budgets imply: (i) no resale, (ii) t, c, and (iii) no financial markets. Baley, Veldkamp, Waugh (NYU) Information and Trade Fall / 24

7 Model Environment Timing and Information Structure (new part) 1 Observe own z and domestic µ. All parameters known. 2 Receive noisy signal about µ abroad (common signal): x country: m y = µ y + η y, η y N(, s y 2 ) y country: m x = µ x + η x, η x N(, s x 2 ) 3 Choose exports t before observing q Forecast price 4 International market clears at q. 5 Consumption is realized. Baley, Veldkamp, Waugh (NYU) Information and Trade Fall / 24

8 Model Environment Forecasting international price To forecast price q, a firm forms 1st & 2nd order beliefs (suffic stats): 1 What are my beliefs about foreign productivity? µ y I x N ( ) ˆm y, ŝy 2 ˆm y = s 2 y m y + s y 2 s 2 y + s 2 y m y, ŝy 2 = s 2 y 1 + s y 2 2 What are my ( beliefs ) about foreign beliefs about my productivity? ˆm x I x N ˆm x, ŝx 2, ˆm x = s 2 x m x + s 2 s 2 x x + s 2 x µ x, ŝ 2 x = (s 2 x s 2 x + s 2 x ) 2 Baley, Veldkamp, Waugh (NYU) Information and Trade Fall / 24

9 Model Environment Equilibrium An equilibrium is export policy: t x (z x, µ x, ˆm y ) and t y (z y, µ y, ˆm x ) beliefs {F (µ y I x ), F ( ˆm x I x )} and {F (µ x I y ), F ( ˆm y I y )} price function q(µ x, µ y, ˆm x, ˆm y ) 1 Given beliefs and price function, exports maximize utility. 2 Price q clears the international market. Solution: Details µ+ σ2 2 Policy : t = zψ(µ, ˆm) = T = e }{{} Price : q = T x = e µx µy (σ 2 x σ2 y ) Ψ T y }{{} Ψ relative fundamentals aggregate endowment Ψ(µ, ˆm) }{{} trade share Baley, Veldkamp, Waugh (NYU) Information and Trade Fall / 24

10 Model Environment Parameter Choice Results will be theoretical and numerical. For numerical results, Table: Summary of Model Parameters Parameter m x = m y σ x = σ y s x = s y θ Value Eliminate asymmetry in fundamentals, only asymmetry is from info. Mean of aggregate log endowment is 1. Elasticity of substitution is 1/(1 θ) = 4. Variance s matters relative to signal precision. We vary signal precision. Results are averages over many simulations. Parameters Baley, Veldkamp, Waugh (NYU) Information and Trade Fall / 24

11 Results Results Overview Information globalization: Vary precision s 2. (symmetric changes) Main result: Information globalization reduces trade. Three parts to the explanation: 1 Trade Coordination: Information Corr[T x, T y ] 2 Risk sharing: Corr[C, C ], Corr[C x, C y ] 3 Trade flows: export share E[Ψ/(1 Ψ)]. Volume E[T ] ambiguous. At the end: welfare and the role of elasticity. Baley, Veldkamp, Waugh (NYU) Information and Trade Fall / 24

12 Results Result 1: Information coordination Proposition In a neighborhood around perfect information, increasing the precision of both countries signals s 2 reduces var(ψ Ψ ). Ex: With perfect info, Ψ = 1 Ψ. Co-linearity var(ψ Ψ ) =. Coordination motive: When other country exports more, relative price of your good rises, more incentive for you to export. Export choice: max Ψ ( z xe (1 Ψ) θ + ( Ψ q ) ) θ 1/θ (µx, ˆm y ) More foreign exports enters as lower q. Raises benefit of exporting Ψ. Baley, Veldkamp, Waugh (NYU) Information and Trade Fall / 24

13 Results Result 1: Information coordination Without information, coordination is impossible. 1 Exports Correlation Horizontal axis is log signal precision. Vertical axis is corr(t x, T y ). Baley, Veldkamp, Waugh (NYU) Information and Trade Fall / 24

14 Results Result 2: Information risk-sharing Recall that information facilitates coordination. Next: Coordination prevents prices from fluctuating enough to share risk. Proposition Take the home country s export policy as given by fixing the distribution of T x. If foreign firms coordinate more (var(t y T x ) falls), then var(1/q) decreases. Relative price is q = T x /T y. When T x and T y move proportionately, q stays constant. Like a sticky price. But price changes are central to risk-sharing. High prices compensate for low endowment & v-versa. Baley, Veldkamp, Waugh (NYU) Information and Trade Fall / 24

15 Results Result 2: Information risk-sharing.2 Utility Correlation Consumption correlation measures risk-sharing. Ex: with perfect risk-sharing All endowments are split proportionately: T x = αµ x, T y = (1 α)µ y. Exports are uncorrelated: corr(t x, T y ) = because endowments (µ x and µ y ) are uncorrelated. But consumption is perfectly correlated: corr(c, C ) = 1. Baley, Veldkamp, Waugh (NYU) Information and Trade Fall / 24

16 Results Result 3: Information trade Recall that information price variance. Next result proves that lower price variance reduces trade (holding mean price and covariance with consumption fixed). Proposition Holding fixed cov(c 1 θ, q θ )/E[C 1 θ ], a mean-preserving decrease in var(1/q) increases the trade share Ψ/(1 Ψ). Why? b/c exports are a convex function of price. Baley, Veldkamp, Waugh (NYU) Information and Trade Fall / 24

17 Results Result 3: Information trade low info Relative price of foreign good q high info Export share q θ low info high info low info average export share high info average export share Home endowment µ x Home endowment µ x Information flattens the price function (sticky price). Exports are convex function of that relative price. Convexity is hedging risk of low foreign consumption (c y ). Lower price variance lower average trade. Baley, Veldkamp, Waugh (NYU) Information and Trade Fall / 24

18 Results Result 3: Information trade Trade Share = Exports/Consumption Doubling precision can halve the trade share (near s 2 = 1). Baley, Veldkamp, Waugh (NYU) Information and Trade Fall / 24

19 Results Key Mechanism: 2nd-order beliefs Fix beliefs about other country s precision (2nd order inactive). Increase true signal precision (1st order active). Trade does not fall. Export/consumption Info globalization Both beliefs active 2nd order inactive Both beliefs inactive Baley, Veldkamp, Waugh (NYU) Information and Trade Fall / 24

20 Results Trade share vs. total exports Decrease in share E[Ψ/(1 Ψ)] and non-monotonic effect on volume E[T ]..62 Export Fraction 1.74 Exports E(Ψ).56 E(T) Precision 1.62 Precision Baley, Veldkamp, Waugh (NYU) Information and Trade Fall / 24

21 Results Non-monotonic effect on volume E[T ] How can volume rise while share falls? σ2 µ+ - Since T = e 2 Ψ = f Ψ: E[T ] = E [f ] E[Ψ] +C [f, Ψ] Covariance comes from coordination: As s 2 rises, good shocks at home can be better anticipated abroad: f x T x = ˆmx E[q I y ] T y Foreign response is better anticipated at home, inducing more exports: T y = ˆm x E[q I x ] T x Uncertainty Baley, Veldkamp, Waugh (NYU) Information and Trade Fall / 24

22 Results Information increases welfare Information globalization increases average utility, but also increases utility volatility. 5.4 Utility 1.18 Utility Volatility Trade correlation balanced consumption bundles. Balance increases utility. Baley, Veldkamp, Waugh (NYU) Information and Trade Fall / 24

23 Results The Role of Elasticity alization 2 Info globalization Export/Consumption τ Elasticity of substitution does not change the direction of the info effect on trade. For low elasticity (blue line = 1.1, almost Cobb-Dgls) trade shares nearly constant. For medium (pink =1.25) and high (black=4) elasticity, trade share is more sensitive to information. Baley, Veldkamp, Waugh (NYU) Information and Trade Fall / 24

24 Conclusion Conclusion Asymmetric information frictions don t look at all like iceberg costs. Why does better information reduce trade? It allows us to coordinate exports more, which makes the relative price sticky. Mathematically: Export share is a convex function of relative price, so less variation in relative price makes export share fall. Economically: Sticky prices share less risk. Less risk sharing less trade. What frictions might inhibit cross-border trade? Firm-specific info? Maybe equilibrium effects are weaker. Delegation and monitoring frictions? Why don t countries share more risk? b/c they know too much. Baley, Veldkamp, Waugh (NYU) Information and Trade Fall / 24

25 Additional material Additional material Baley, Veldkamp, Waugh (NYU) Information and Trade Fall

26 Additional material How does uncertainty change with information? Uncertainty about foreign shocks decreases with signal precision. Uncertainty about foreign beliefs increases, then decreases. 5 log(variances) 1 log(precisions) Signal Posterior Second Order back Baley, Veldkamp, Waugh (NYU) Information and Trade Fall

27 Additional material Parameters Model parameters Parameter m x = m y σ x = σ y s x = s y θ Value Solve fixed point problem (Ψ, Ψ, q). Simulate independent random draws of productivity and signal noise. Compute unconditional moments. back Baley, Veldkamp, Waugh (NYU) Information and Trade Fall

28 Additional material Balanced consumption Utility components A second order approximation to E[C] around (E[C x], E[C y ]) yields: ( ) θ ( ) θ (1 θ) C E[Cx] E[Cy ] C + (2(1 + Corr[C x, C y ])CV[C x]cv[c y ] 2 C C }{{} balance (CV[C x] + CV[C y ]) 2 ) }{{} volatility E(C) E(C x ) E(C y ) CV(C x ) CV(C y ) Corr(C x, C y ) Baley, Veldkamp, Waugh (NYU) Information and Trade Fall

29 Additional material Characterization (1/2) Optimal exports: Every firm exports the same fraction of their endowment t(z, µ x, ˆm y ) = zψ(µ x, ˆm y ), t(z, µ x, ˆm y ) = zγ(µ x, ˆm y ) Aggregate exports T x (µ x, ˆm y ) = z x Ψ(µ x, ˆm y )df (z x µ x ) = e µx σ2 x Ψ(µx, ˆm y ) = f x Ψ(µ x, ˆm y ) T y (µ y, ˆm x ) = z y Γ(µ y, ˆm x )df (z y µ y ) = e µy σ2 y Γ(µy, ˆm x ) = f y Γ(µ y, ˆm x ) Equilibrium relative price q(µ x, µ y, ˆm x, ˆm y ) = f (µ x, µ y ) Ψ(µ x, ˆm y ) Γ(µ y, ˆm x ) where f (µ x, µ y ) exp[(µ x µ y ) + 1/2(σ 2 x σ 2 y )] is relative fundamentals. Baley, Veldkamp, Waugh (NYU) Information and Trade Fall

30 Additional material Characterization (2/2) Optimal fraction of exports depends on what agents believe will be the fraction of output that others will export. ( ) θ 1/θ Ψ(µ x, ˆm y ) = arg max (1 Ψ) θ Ψ + df (µ y I x )df ( ˆm x I x ) (1 + τ)q(µ x, µ y, ˆm x, ˆm y ) ( ) θ 1/θ Γ(µ y, ˆm x ) = arg max (1 Ψ) θ Ψq(µx, µ y, ˆm x, ˆm y ) + (1 + τ) Ψ(µx, ˆmy ) q(µ x, µ y, ˆm x, ˆm y ) = f (µ x, µ y ) Γ(µ y, ˆm x ) df (µ y I x )df ( ˆm x I x ) Fixed point problem: Ψ = g 1 (I x, q) Γ = g 2 (I y, q) q = f Ψ Γ back Baley, Veldkamp, Waugh (NYU) Information and Trade Fall 214 3

31 Additional material Information decreases trade but increases utility and risk. Exports Endowment No info Noisy signals Full info s 2 = s 2 = 2 s 2 = (.26) (.24) (.22) Total Exports (.66) (1.9) (1.37) Relative Price of y (1.36) (.79) (.42) Utility (1.13) (1.15) (1.16) Averages (dispersion) across simulations. Total endowment in each country: average 4.48 (5.79). Baley, Veldkamp, Waugh (NYU) Information and Trade Fall

32 Additional material Mechanisms Trade flows with both frictions (same scale) E(Ψ).4 1 E(T) Baley, Veldkamp, Waugh (NYU) Information and Trade Fall

33 Additional material Mechanisms Coordination with both frictions (same scale) Corr(Ψ, Ψ * ) Corr(T x,t y * ) Corr(f,Ψ) Baley, Veldkamp, Waugh (NYU) Information and Trade Fall

34 Additional material Mechanisms Risk sharing with both frictions (same scale) Corr(C, C*).7 Corr(fx/fy, q).7.7 CV(q) Baley, Veldkamp, Waugh (NYU) Information and Trade Fall

35 Additional material Mechanisms Utility components with both frictions (same scale) E(C) 5 4 E(C x ) E(C y ) CV(C x ) CV(C y ) Corr(C x, C y ) Baley, Veldkamp, Waugh (NYU) Information and Trade Fall

36 Additional material Mechanisms Trade flows with both frictions (individual scales) E(Ψ) E(T) Baley, Veldkamp, Waugh (NYU) Information and Trade Fall

37 Additional material Mechanisms Coordination with both frictions (individual scales) Corr(Ψ, Ψ * ) Corr(T x,t y * ) Corr(f,Ψ) Baley, Veldkamp, Waugh (NYU) Information and Trade Fall

38 Additional material Mechanisms Risk sharing with both frictions (individual scales) Corr(C, C*).195 Corr(fx/fy, q).74.3 CV(q) Baley, Veldkamp, Waugh (NYU) Information and Trade Fall

39 Additional material Mechanisms Utility components with both frictions (individual scales) E(C) E(C x ) E(C y ) CV(C x ) CV(C y ) Corr(C x, C y ) Baley, Veldkamp, Waugh (NYU) Information and Trade Fall

40 2) Risk sharing Trade liberalization Trade liberalization increases risk sharing Utility correlation rises: Corr[C, C ]. Prices allow shocks to be transmitted, good hedge. Consumptions reflect iid endowments. Corr(C, C ).2 Corr(f x/f y, q).71.4 CV (q) Corr(C x, C y) Baley, Veldkamp, Waugh (NYU) Information and Trade Fall 214 4

41 2) Risk sharing Information globalization Information globalization decreases risk sharing Utility correlation falls: Corr[C, C ]. Terms of trade are a less effective to hedge against productivity shocks. (?,?). Corr(C, C ).22 Corr(f x/f y, q) CV (q) Corr(C x, C y) Baley, Veldkamp, Waugh (NYU) Information and Trade Fall

42 3) Welfare Trade liberalization Trade liberalization increases welfare Trade liberalization increases utility E[C] and decreases its volatility. Expected Utility 5.4 Volatility of Utility 1.32 Consumptions of X and Y.5 E(C) CV(C) Corr(C x,c y ) Baley, Veldkamp, Waugh (NYU) Information and Trade Fall

43 3) Welfare Information globalization Information globalization increases welfare Utility E[C] and its volatility increase. Expected Utility Volatility of Utility Consumptions of X and Y.2.15 E(C) CV(C) Corr(C x,c y ) Baley, Veldkamp, Waugh (NYU) Information and Trade Fall