Estimating the effect of exchange rate changes on total exports

Transcription

1 Estimating the effect of exchange rate changes on total exports 1 Thierry Mayer (Science Po, Banque de France) and Walter Steingress (Bank of Canada) BIS Workshop 1 The views expressed in this paper are those of the authors and do not necessarily reflect those of the Banque de France, the Eurosystem or the Bank of Canada.

2 Main question How to estimate the response of aggregate exports to exchange rate changes? Standard approach: Real Effective Exchange Rate (REER) regression (McGuirk (1986)) d ln E it = β 1 d ln REER it + β 2 ω nit d ln X nt + e it (1) n =i

3 Main question How to estimate the response of aggregate exports to exchange rate changes? Standard approach: Real Effective Exchange Rate (REER) regression (McGuirk (1986)) d ln E it = β 1 d ln REER it + β 2 ω nit d ln X nt + e it (1) n =i Can we reconnect this macro-level REER regressions with micro-level foundations of bilateral trade (i.e. gravity)?

4 What we do 1 We re-visit the theoretical foundations of macro-level Real Effective Exchange Rate (REER) regression

5 What we do 1 We re-visit the theoretical foundations of macro-level Real Effective Exchange Rate (REER) regression 2 We calibrate a standard gravity model to quantify estimation biases in different models used in marco-level applied work

6 What we do 1 We re-visit the theoretical foundations of macro-level Real Effective Exchange Rate (REER) regression 2 We calibrate a standard gravity model to quantify estimation biases in different models used in marco-level applied work 3 Can our new REER regression explain differences in elasticties estimated from bilateral and aggregate data?

7 Main results Structural gravity models with a unique elasticity of substitution permit aggregation from the bilateral level without bias. Simulations show the main sources of bias in specifications used in applied work: 1 Functional form assumptions 2 Omitted variables 3 Differences in the weighting scheme Estimation biases in the exchange rate elasticity appear to be a minor concern. Bias seems to be mainly on the demand elasticity

8 Literature Theoretical foundations of Real Effective Exchange Rate (REER) Armington (1969), McGuirk (1986), Chinn (2006), Bayoumi et al. (2013), Patel et al. (2017), Bems Johnson (2017) Bayoumi et al. (2005), Klau Fung (2006), Bennett Zarnic (2009), Schmitz et al. (2011), Barnett et al. (2016) Empirical macroeconomic literature on exchange rate and demand elasticities : Orcutt (1950), Houthakker Magee (1969), Goldstein et al. (1985), Spilimbergo Vamvakidis (2003), Freund Pierola (2012), Imbs Méjean (2015), Bussiere et al. (2014), Ahmed et al. (2016) Campa Goldberg (2005), Vigfusson et al. (2009), Bussière et al. (2014) Gravity literature and exchange rate Anderson Vesselovsky Yotov (2016)

9 Theoretical framework (Dekle, Eaton and Korum (2007)) Total exports of country i in international currency E i = X ni = π ni X n n =i n =i X n... total expenditure of importer n, π ni... expenditure share of n on goods from i

10 Theoretical framework (Dekle, Eaton and Korum (2007)) Total exports of country i in international currency E i = X ni = π ni X n n =i n =i X n... total expenditure of importer n, π ni... expenditure share of n on goods from i With CES preferences π ni = (r ip ni ) θ (r n P n ) θ r n... nominal exchange rate of n, P n... price index in local currency, θ... trade elasticity P ni = P ii τ ni... producer price of exporter i (P ii ), trade costs (τ ni )

11 Counterfactual analysis: change in total exports Exact hat notation (ACR (2012)) X ni X ni X ni X ni... bilateral trade after the change Change in total exports Ê i = ω ni π ni X n = ω ni n =i n =i ( ˆr i P ii ) θ ( ˆr n P n ) θ X n ω ni X ni /E i denotes the export share

12 Macro-level Real Exchange Rate (RER) regression Taking logs, the aggregate exchange rate regression: ln Ê i = θ ln RERi + ln n =i X n ω ni ( ) θ (2) ˆr n P n where the real exchange rate (RER i ) is defined as: ln RERi = ln ˆr i P ii (3) No aggregation bias... if equation (2) is run

13 Which regressions do people run? McGuirk (1986) derives the standard aggregate exchange rate regression: 1 Start from changes in bilateral trade flows: ˆX ni = ˆπ ni ˆX n Use functional form of trade shares and take log : ( ) ˆr ln ˆX ni = θ ln i P ii + ln ˆX n ˆr n ˆP n

14 Which regressions do people run? McGuirk (1986) derives the standard aggregate exchange rate regression: 1 Start from changes in bilateral trade flows: ˆX ni = ˆπ ni ˆX n Use functional form of trade shares and take log : ( ) ˆr ln ˆX ni = θ ln i P ii + ln ˆX n ˆr n ˆP n 2 Sum the bilateral changes across all importers ) ˆr i P ii ˆr k ˆP kk ( ln Ê i = θ ω ni π nk ln n =i k =i using the fact that ln ˆP n = K k=1 π nk ln ( ˆrk ˆrn ˆP kk ) + ω ni ln ˆX n n =i

15 Double-weighted REER à la McGuirk (1986) Standard aggregate exchange rate regression ln Ê i = θ ln REERi + ω ni ln ˆX n (4) n =i ln REER i is the double-weighted Real Effective Exchange Rate ( ) ˆr ln REERi = ω ni π nk ln i P ii n =i k =i ˆr k ˆP kk (5) i ˆp 1 β i ) of exporter i relative to other exporter price ( changes ( ˆP kk ) times the changes in the bilateral exchange rate ˆri ˆr k ). Changes in the unit cost of production ( P ii = ŵ β

16 Comparing Structural Gravity and McGuirk (1986) We can re-write the REER equation of McGuirk: ln Ê i = ( ) θ ln RERi ω ni ln ( ) θ ˆP n ˆr n } n =i {{ } θ ln REERi + ω ni ln ˆX n k =i and compare with gravity ( ) X n ln Ê i = θ ln RERi + ln ω ni ( ) θ n =i ˆP n ˆr n by Jensen s inequality: ln n =i ω ni ( ) X n ( ) θ ω ni ln ˆX n ω ni ln ( ) θ ˆP n ˆr n ˆP n ˆr n n =i n =i Larger exchange rate shocks will induce larger bias.

17 Simulation - Dekle, Eaton and Kortum (2007) approach Goal of simulation: How large is aggregation bias? Data from Dekle, Eaton and Kortum (2007) Trade and GDP data for 39 countries + ROW in the year 2004 Calibration: trade elasticity θ = 4 Simulation: One country receives a random exchange rate shocks. Repeat 100 times with different exchange rate shocks for all 39 countries.

18 Quantifying the bias: nominal exchange rate shock ( ˆr i ) Partial equilibrium (wages are fixed, good prices adjust) ( ) Changes : RER i = r i and X i = 1 p 1 β i

19 Quantifying the bias: nominal exchange rate shock ( ˆr i ) Partial equilibrium (wages are fixed, good prices adjust) ( ) Changes : RER i = r i and X i = 1 p 1 β i General equilibrium (wages and prices adjust) Goods market clearing condition for given trade deficit (D i ) ˆr i ŵ i Y i + D i = n ( π ni ( l π nl ˆr i ŵ β i ˆr l ŵ β l ˆp 1 β ) θ i ˆp 1 β l ) θ ( ˆr nŵ n Y n + D n ). (6) ( ) Changes : RER i = r i ŵ β i p 1 β i and X n = ˆr n ŵ n Y n + D n Hypothesis : the deficit is fixed in international currency units

20 Simulation 5 specifications to evaluate the aggregation bias: 1 Baseline (exact hat algebra) produces unbiased estimates 2 Gold medal mistake omitting the unobserved Multilateral Resistance Term (MRT) 3 Approximation via log changes 4 REER à la McGuirk (1986) 5 Log approximation with IMF weights this is the standard method used in applied empirical work

21 Exchange Rate Regression in specification 1 Specification 1: Baseline (exact hat algebra) ln Ê i = β 1 RER ln RERi + β 1 X ln ω ni n =i X n ( ) β 1 RER ˆr n P n + ɛ i This is the Structural Gravity model implied regression that results in unbiased estimates for the exchange rate elasticity ( β 1 RER = 4) and the demand elasticity ( β 1 X = 1).

22 Exchange Rate Regression in specification 2 Specification 2: Gold Medal mistake: omitting the Multilateral Resistance Term (MRT) ln Ê i = β 2 RER ln RERi + β 2 X ln ω ni X n + ɛ i n =i This regression evaluates the bias when omitting the Multilateral Resistance Term ((r n P n ) θ ) from the theory implied exchange rate equation in specification 1.

23 Exchange Rate Regression in specification 3 Specification 3: Approximation via log changes ln Ê i = β 3 RER ln RERi + β 3 X ω ni n =i ln ˆX n ( ) β 3 RER ln ˆr n P n + ɛ i Motivation: one might be tempted to approximate the baseline regression with changes in logs rather than the log of the change.

24 Exchange Rate Regression in specification 4 Specification 4: REER à la McGuirk (1986) ln Ê i = β 4 RER ln REERi + β 4 X ω ni ln ˆX n + ɛ i k =i The main difference with the baseline specification 1 is: we use the Real Effective Exchange Rate (REER) rather than the (RER) in the baseline specification

25 Exchange Rate Regression in specification 5 Specification 5: log approximation with IMF weights ln Ê i = β 5 RER ln REER IMF i + β 5 X ω ni ln Xˆ n + ɛ i k =i The difference with specification 4 is that we use the IMF weighting scheme in constructing the Real Effective Exchange Rate. This is the standard method used in applied empirical work Note: IMF weights differ from the theoretical implied weights used in specification 4. IMF

26 General equilibrium regression results Baseline REER McGuirk GM mistake d ln approx. IMF weights (ideal-reer) (real-reer) (1) (2) (3) (4) (5) Exchange rate Mean Bias Std dev MSE 1/ Foreign demand Mean Bias Std dev MSE 1/ Notes: The sample consists of 39 countries and each country receives 100 random exchange rate shocks. The total number of estimated exchange rate and demand elasticities is 3900 for each of the 5 different specifciations. Significant bias in both elasticities in all specifications. MTI

27 Summary of simulation results On average, bias in demand and exchange rate elasticity are small. The size of the bias depends on the magnitude and the type of the exchange rate shock here. Bias does not depend on the level of the trade elasticity (θ) Results with θ = 0.8 here. Model does not perfectly explain bilateral flows. Assume stochastic trade costs, see here. Biases are amplified (bias in exchange rate elasticity is close to 1%, in demand elasticity is close to 20%)

28 Empirical part Do ideal-reer regressions reduce the difference between bilateral and aggregate elasticities? construct empirical counterparts of the 5 regression specifications above. We use annual bilateral trade flows of 25 countries over the period RER is Nominal Exchange Rate deflated by CPI. REER is BIS Narrow REER deflated by the CPI. Foreign Demand is nominal GDP from Penn World Table. Bilateral trade flows from CEPII.

29 Empirical regressions We run exchange rate regressions at different level of aggregation Bilateral Regression: ln E nit = α 0 α 1 ln RER nit + α 2 ln X nt + e nit Aggregate Regression: the same 5 regression specifications as in the simulation Test: do exchange rate elasticities and demand elasticities differ? in pooled and country-specific sample

30 Empirical estimates of pooled regressions Bilateral Aggregate Baseline GM mistake d ln app. McGuirk IMF (1) (2) (3) (4) (5) (6) Exchange rate Point estimate Std. error (0.024) (0.06) (0.059) (0.057) (0.066) (0.067) Foreign demand Point estimate Std. error. (0.019) (0.106) (0.076) (0.096) (0.038) (0.042) Observations R Notes: The sample consists of 25 countries over the period No significant differences between bilateral and aggregate elasticities when using ideal-reer (baseline). significant differences in all other specifications

31 Empirical estimates of country-by-country regressions Aggregate versus Bilateral Exchange Rate Elasticities Baseline specification (ideal-reer) for aggregate estimates Aggregate versus Bilateral Demand Elasticities Baseline specification (ideal-reer) for aggregate estimates Bilateral RER Elasticity CAN AUS SWE SGP USA IRL ESP MEX NED DNK NZL ITA AUT FIN PRT GRC GBR FRA JPN CHE DEU BEL HKG KOR NOR Bilateral Foreign Demand Elasticity GRC FIN SWE AUSNZL AUT ITA BEL ESP GBR PRT CHE DEU NOR NED DNK FRA IRL MEX USA KOR SGP HKG JPN CAN Aggregate ideal-reer Elasticity Aggregate Foreign Demand Elasticity Red line corresponds to 45 degree line; Red line corresponds to 45 degree line; Blue line is best linear fit with 95 perc. confidence interval Blue line is best linear fit with 95 perc. confidence interval

32 Empirical estimates of country-by-country regressions Aggregate versus Bilateral Exchange Rate Elasticities Baseline specification (ideal-reer) for aggregate estimates Aggregate versus Bilateral Demand Elasticities Baseline specification (ideal-reer) for aggregate estimates Bilateral RER Elasticity CAN AUS SWE SGP USA IRL ESP MEX NED DNK NZL ITA AUT FIN PRT GRC GBR FRA JPN CHE DEU BEL HKG KOR NOR Bilateral Foreign Demand Elasticity GRC FIN SWE AUSNZL AUT ITA BEL ESP GBR PRT CHE DEU NOR NED DNK FRA IRL MEX USA KOR SGP HKG JPN CAN Aggregate ideal-reer Elasticity Aggregate Foreign Demand Elasticity Red line corresponds to 45 degree line; Red line corresponds to 45 degree line; Blue line is best linear fit with 95 perc. confidence interval Blue line is best linear fit with 95 perc. confidence interval Aggregate versus Bilateral Demand Elasticities REER McGuirk specification (real-reer) for aggregate estimates Aggregate versus Bilateral Demand Elasticities REER McGuirk specification (real-reer) for aggregate estimates Bilateral RER Elasticity IRL NED ESP AUTDNK ITA MEX NZL AUS DEU FIN GRC PRT GBR CHEJPNFRA BEL HKG KOR NORSWE SGP USA CAN Aggregate real-reer Elasticity Red line corresponds to 45 degree line; Blue line is best linear fit with 95 perc. confidence interval Bilateral Foreign Demand Elasticity CAN KOR FIN USAGRC HKG JPN NZL SWE AUS ESP GBR DEU ITA BEL AUT PRT SGP NEDNOR DNKCHE FRA MEX IRL Aggregate Foreign Demand Elasticity Red line corresponds to 45 degree line; Blue line is best linear fit with 95 perc. confidence interval

33 Conclusion We reconnect macro-level Real Effective Exchange Rate (REER) regressions with micro-founded bilateral trade equations (gravity) with unique elasticity of substitution aggregation without bias possible We quantify estimation biases of specifciations used in empirical macro-literautre. bias for exchange rate and demand elasticity can be significant (up to 20%) Our empirical evidence confirms analytical (simulated) results. our ideal-reer reduces differences between aggregate and bilateral elasticities Policy institutions may revisit their projection models...

34 Appendix

35 EER calculated by policy institutions (IMF) Effective Exchange Rate (EER) based on McGuirk (1986) ( ) ri P ln REER i = TW ik ln i r k =i k P k where: TW ik = n =i ω ni π nk IMF calculate weights for the effect on production (not exports) where ψ ni = X ni N k=1 X ki These weights are normalized to 1 TWik IMF N = ψ ni π nk n=1 includes the home market share TWik IMF N n=1 = ψ ni π nk N n=1 ψ ni (1 π ni ) which leads to a bias in export equations. Back

36 Partial equilibrium regression results Baseline REER McGuirk GM mistake d ln approx. IMF weights ( ideal-reer ) ( real-reer ) (1) (2) (3) (4) (5) Exchange rate Mean Bias Std dev MSE 1/ Foreign demand Mean Bias Std dev MSE 1/ Notes: The sample consists of 39 countries and each country receives 100 random exchange rate shocks. The total number of estimated exchange rate and demand elasticities is 3900 for each of the 5 different specifciations. Small significant bias in exchange rate elasticities. Back

37 GETI regression results with stochastic trade costs Baseline REER McGuirk GM mistake d ln approx. IMF weights (ideal-reer) (real-reer) (1) (2) (3) (4) (5) Exchange rate Mean Bias Std dev MSE 1/ Foreign demand Mean Bias Std dev MSE 1/ Notes: The sample consists of 39 countries and each country receives 100 random exchange rate shocks. The total number of estimated exchange rate and demand elasticities is 3900 for each of the 5 different specifciations. Significant bias in both elasticities in all specifications. Bias in demand elasticity larger than in exchange rate elasticity. Back

38 GETI regression results with θ = 0.8 Baseline REER McGuirk GM mistake d ln approx. IMF weights (ideal-reer) (real-reer) (1) (2) (3) (4) (5) Exchange rate Mean Bias Std dev MSE 1/ Foreign demand Mean Bias Std dev MSE 1/ Notes: The sample consists of 39 countries and each country receives 100 random exchange rate shocks. The total number of estimated exchange rate and demand elasticities is 3900 for each of the 5 different specifciations. Significant bias in both elasticities in all specifications. Bias in demand elasticity larger than in exchange rate elasticity. Back

39 Bias in exchange rate and demand elasticity in MTI Plot the magnitude of the exchange rate shock against the estimated elasticities in the IMF specification Bias depends on economic size.

40 Bias in exchange rate and demand elasticity in GETI Plot the magnitude of the exchange rate shock against the estimated elasticities in the IMF specification Bias depends on remoteness. Back