Entry, Trade Costs and International Business Cycles Roberto Fattal and Jose Lopez UCLA SED Meetings July 10th 2010 Entry, Trade Costs and International Business Cycles SED Meetings July 10th 2010 1 / 17
Goals of the Paper Trend in International Trade Literature to write models with Heterogeneous Firms, Entry and Exit of Establishments and Fixed Costs of Exporting. Long run analysis Are these important margins to consider when studying International Business Cycles? This paper provides a quantitative analysis of the role of 1) entry and 2) fixed costs of exporting in an international business cycle model with heterogeneous firms. Our work is close to Ghironi-Melitz (2005) (which lacks both capital and endogenous labor) and Alessandria and Choi (2007) (which has no entry) Entry, Trade Costs and International Business Cycles SED Meetings July 10th 2010 2 / 17
Preview of Results Adding these two margins is not innocuous, it has implications for the volatility of aggregate variables, in particular for Investment, Exports and Trade Balance. The model has a better fit of second moments than the standard BKK In addition, the model delivers a negative correlation between RER and Ratio of Consumption (Backus-Smith), under some assumptions about the measurement of the CPI. Entry, Trade Costs and International Business Cycles SED Meetings July 10th 2010 3 / 17
Technology and Problem of the Firms Final Good Sector (competitive) 2 R I 4 y ω2ωt t(ω) I θ ρ 1 (θ 1) θ 1 ρ R θ dg + ω2ωx,t yx,t y t (ω) = y x,t(ω) = pt (ω) θ PD,t P t P t θ (θ 1) θ 1 (ω) θ dg θ p x,t (ω) θ P X,t P t P t θ ρ Y t ρ Y t Intermediate Goods Sector (monopolistic competition) y(ω) = Zω [k(ω)] α [l(ω)] 1 ρ(ω) = θ θ 1 MC p(ω) ρ x (ω) = Q 1 θ θ 1 τmc p(ω) r α w 1 α 1 MC p (ω) = α 1 α Zω α ρ 1 ρ 3 5 ρ ρ 1 Entry, Trade Costs and International Business Cycles SED Meetings July 10th 2010 4 / 17
Exporting decision, Entry and Exit Profits from export sales are h 1 θ Qt PX,t θ ρ θ ρ d x = x,t (ω)i P Y w t t t Z t f x if firm ω exports 0 otherwise Export cutoff ω x,t = inf fω : d x,t (ω) > 0g Entrants pay sunk entry cost (fe) in units of effective labor. Productivity is drawn from G(ω). Exit is exogenous, and occurs with probability δ Free Entry Condition: w f e Z = ṽ t = E t Law of Motion of firms: s=t+1 [β(1 δ)] s t Uc (C s, l s ) γ ds U c (C t, l t ) N D,t = (1 δ) (N D,t 1 + N e,t 1 ) Entry, Trade Costs and International Business Cycles SED Meetings July 10th 2010 5 / 17
The Problem of the Representative Household Household s in each country solve : max E o t=0 β t 2 C µ t 4 (1 l t) 1 µ 3 5 1 γ 1 γ C t + K t+1 + ϕ t+1 ṽ t (N D,t + N e,t ) + B t+1 = (1 + r B t )B t + (r k t + 1 δ k )K t + ( d t + ṽ t )ϕ t N D,t + w t l t Our benchmark results refer to the case of international bond trading Entry, Trade Costs and International Business Cycles SED Meetings July 10th 2010 6 / 17
Two Approaches to Measure the Price Indices Model Based Price Index: h P t = N D,t ( p t ) 1 θ + Nx,t p x,t 1 i 1 θ 1 θ Cleaning it from Variety Effect: P t = ND,t N t ( p t ) 1 θ + N x,t N t 1 p x,t 1 θ 1 θ where N t = N d,t + N x,t The RER without variety effect is: 2 Q = P ND,t P = N 4 t ( p t ) 1 θ + N x,t N t N D,t N t ( p t ) 1 θ + N x,t N t ( p x,t ) 1 p x,t 1 Look also at model with fixed Expenditure Shares. θ θ 3 5 1 1 θ Entry, Trade Costs and International Business Cycles SED Meetings July 10th 2010 7 / 17
Calibration Standard Parameters β, γ, µ Usual in RBC literature α, δ K ρ Z, ρ Z, ρ Z,Z Stochastic process from BKK Microlevel Parameters δ 0.025 Exogenous death rate τ 1.3 Iceberg costs θ = ρ 3.8 Elasticity of Substitution κ 3.4 Shape parameter Pareto Distribution (1 β(1 δ)) f x /f e 0.235 β(1 δ) Match N X /N D = 21% Entry, Trade Costs and International Business Cycles SED Meetings July 10th 2010 8 / 17
The Role of Entry Degree of entry irrelevant for quantities, but important for relative prices. If there is no entry, aggregate quantities are too volatile, second moments resemble standard BKK. Entry, Trade Costs and International Business Cycles SED Meetings July 10th 2010 9 / 17
The Volatility of Entry Define entry Cost be: ˆf e = f e + γ e [exp (N D,t N D ) 1]. Entry, Trade Costs and International Business Cycles SED Meetings July 10th 2010 10 / 17
Changing the fraction of exporting firms: Quantities have little sensitivity to Share of Exporters, but important for relative prices If all firms export, the model with just entry, delivers the usual positive correlation consumption ratio and RER Entry, Trade Costs and International Business Cycles SED Meetings July 10th 2010 11 / 17
The Volatility of the Fraction of Exporting Firms Entry, Trade Costs and International Business Cycles SED Meetings July 10th 2010 12 / 17
Conclusion Regarding quantities, entry and the export margin combine to keep aggregate volatilities close to the data. In this result is crucial that Entry and Investment behave as substitutes for consumption smoothing. In the BKK, the usual feature introduced to reduce volatility is ad-hoc adjustments to investment. Entry and the export margin can help to explain the negative correlation of the Consumption Ratio and RER, under the assumption that CPI captures changes in the set of goods. Complementarity Result: both extensive margins have to be present for the model to deliver novel results. Entry, Trade Costs and International Business Cycles SED Meetings July 10th 2010 13 / 17
International Business Cycles: The Model vs The Data Data Benchmark GM(replic) BKK(replic) Volatilities (% Std Dev) Gdp 1.67 1.44 0.94 1.42 Trade Balance/Gdp 0.45 0.40 0.12 0.64 Standard Deviation relative to Gdp Number of Firms 0.48 0.28 0.29 Number of Exporters 0.80 0.85 Entry 3.77 3.78 3.86 International Correlations Gdp 0.58 0.01 0.42 0.10 Consumption 0.36 0.79 0.96 0.79 Investment 0.30 0.86 0.70 Hours Worked 0.42 0.58 0.54 Other Correlations Ratio Cons vs RER 0.35 0.87 0.60 0.76 Ratio Cons vs TOE 0.97 0.45 0.76 Entry, Trade Costs and International Business Cycles SED Meetings July 10th 2010 14 / 17
The Role of the Financial Structure. Financial Structure Data Complete Markets Bond Financial Aut. Volatilities (% Std Dev) Gdp 1.67 1.52 1.44 1.42 Exports 3.94 1.89 1.17 0.75 Trade Balance/Gdp 0.45 0.75 0.40 0.00 Std Dev relative to Gdp Consumption 0.81 0.48 0.52 0.54 Investment 2.84 3.83 2.45 1.11 Hours Worked 0.66 0.71 0.62 0.61 Number of Firms 0.48 0.31 0.28 0.28 Number of Exporters 1.22 0.80 0.51 Entry 3.77 4.10 3.78 3.70 International Correlations Gdp 0.58 0.09 0.01 0.05 Consumption 0.36 0.92 0.79 0.74 Investment 0.30 0.95 0.86 0.32 Hours Worked 0.42 0.71 0.58 0.55 Other Correlations Ratio Cons vs RER 0.35 0.66 0.87 0.56 Ratio Cons vs TOE 0.13 0.97 0.87 Ratio Cons vs TOT 0.74 0.49 0.08 0.91 Entry, Trade Costs and International Business Cycles SED Meetings July 10th 2010 15 / 17
Log-Lineal Equation of the RER ~Q = (2s D 1) TOE (1 s D ) ~ω x,t ~ω x,t + 1 θ 1 ND N D + N x s D N D,t N x,t N D,t Nx,t Entry, Trade Costs and International Business Cycles SED Meetings July 10th 2010 16 / 17
The expression for the ratio of Trade Balance to GDP: " TB GDP = EX 1 GDP Nx Q θ (TOE) 1 θ Y N x Y where the ratio of exports to GDP is given by: ω # θ 1 x ω x EX GDP = 1 θ 1 ω ω x τ θ 1 Q θ Y N d Y N x + 1 Entry, Trade Costs and International Business Cycles SED Meetings July 10th 2010 17 / 17