Real Exchange Rates and Primary Commodity Prices

Transcription

1 Real Exchange Rates and Primary Commodity Prices João Ayres Inter-American Development Bank Constantino Hevia Universidad Torcuato Di Tella Juan Pablo Nicolini FRB Minneapolis and Universidad Torcuato Di Tella CEBRA September 28th, 2017

2 This is a data paper. We show that an important fraction of the volatility of RER between Japan, UK and Germany against the US can be accounted for by shocks that affect a few PCP. Why writing a paper about it? RER disconnect puzzle for these RER. (Engel (1999) and Betts and Kehoe (2004)) 1. RER unrelated to fundamentals. 2. Very volatile. 3. Very persistent. Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 1 / 51

3 The puzzle is not present in Small Open Economies that specialize in the production of one primary commodity. Betts and Kehoe (2004), Chen and Rogoff (2003) and Hevia and Nicolini (2013), Ricci, Milessi-Ferreti and Lee (2013). RER responds to exogenous movements in PCP. Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 2 / 51

4 The relationship is also present for some Large economies like Brazil. We explore this relationship for pairs of Large Developed economies: Japan, UK, Germany against the US. Is the dichotomy in the literature that stresses PC for SOE, but ignores them for LDE justified? Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 3 / 51

5 Why PCP? The top 10 commodities account for 18% of world trade in 2012 (12% in 1990). Only the direct measure. Primary commodities are at the bottom of the production structure. They are traded in competitive markets, where the law of one price holds. Very volatile and persistent. Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 4 / 51

6 Potential mechanism: Movements in PCP change costs. Assume input-output matrices of the two countries are different enough. Then, PCP changes affect final good prices asymmetrically: the RER ought to change. Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 5 / 51

7 Plan Discuss the empirical strategy. For US and UK, we analyze r USA,UK t ( ) P USA t = ln Pt UK S t = β p X t,usa + v t. (1) 1. Endogeneity problems. 2. Selection of commodities. 3. Time varying coefficients. Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 6 / 51

8 Plan Descriptive statistics. Regressions (levels and four year differences) and focus on R 2. Alternative way to select commodities. Out-of-sample fit. Monte-Carlo simulations. Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 7 / 51

9 Plan A model that illustrates a mechanism. A model-based exercise. Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 8 / 51

10 Endogeneity problems PCP are very likely correlated with the RER between these four big economies. No hope to get consistent estimators of parameters. Our focus is on R 2. Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 9 / 51

11 How much of the variability of the RER can be accounted for by shocks that affect a set of PCP? According to theory the RER and PCP are determined simultaneously. Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 10 / 51

12 Let ξ t R n be a vector representing the state of the economy. In equilibrium r USA,UK t = f (ξ t ), (2) p X,USA t = g(ξ t ). Using a linear approximation r USA,UK t = θ ξ t, (3) p X,USA t = Ωξ t, Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 11 / 51

13 Consider the projection Using can write Proj(r USA,UK t p X t,usa ) = β p X t,usa. β = (θ Ω )(ΩΩ ) 1. p X,USA t = Ωξ t, r USA,UK t = β Ωξ t + (θ β Ω)ξ t. (4) The underlying (implicit) assumption in much of the literature on bilateral RER between developed countries is that β Ωξ t, can be safely ignored. Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 12 / 51

14 Let state variables be divided in two sets as ξ t = [ξ 1t ξ 2t ], so that rt USA,UK = θ 1ξ 1t + θ 2ξ 2t p X t,usa = Ω 1 ξ 1t + Ω 2 ξ 2t. A sufficient condition for the R 2 of the regression to be zero is thus θ 1 = 0 and Ω 2 = 0 Implies an equilibrium with a block-recursive structure. Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 13 / 51

15 Selection of commodities We chose the 10 most traded commodities in 1990, for which we have data from We run the regression with those commodities. We select the 4 (tried also 5 and 3) with highest t-stats. Run the regression again with only those 4 PCP. Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 14 / 51

16 Time varying coefficients Constants in linearization depend on equilibrium you are approximating around. Production, imports and exports of commodities change over time. Run the regressions for 4 sub-periods. Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 15 / 51

17 Results Monthly data from 1960 to We start by showing moments of RER and PCP Both for the whole period and for sub-periods. In levels and in 4-year differences Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 16 / 51

18 Table: Volatilities of real exchange rates and primary commodity prices (a) LEVEL Real Exchange Rates US-UK US-DEU US-JPN Average across commodities Simple Trade weighted (b) 4-YEAR DIFFERENCES Real Exchange Rates US-UK US-DEU US-JPN Average across commodities Simple Trade weighted

19 Figure: 10-years rolling volatilities of real exchange rates and commodity prices (United Kingdom) COMMODITIES RER - UNITED KINGDOM 0.3 VOLATILITY

20 Figure: 10-years rolling volatilities of real exchange rates and commodity prices (Germany) COMMODITIES RER - GERMANY 0.3 VOLATILITY

21 Figure: 10-years rolling volatilities of real exchange rates and commodity prices (Japan) COMMODITIES RER - JAPAN 0.3 VOLATILITY

22 Autocorrelation for 4-year differences between 0.95 an 0.98 for the 3 RER and the 10 PCP. The simple correlations are high. Tables with the R 2 follow. Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 21 / 51

23 Table: Regressions in 4-year differences with 10 commodities - R United Kingdom Germany Japan Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 22 / 51

24 Table: Regressions in 4-year differences with 4 commodities (best-fit) - R United Kingdom Germany Japan Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 23 / 51

25 Figure: Real exchange rates and fitted values, in 4-year differences with 4 commodities, best fit, , United Kingdom LOG OF REAL EXCHANGE RATE (RER) data fitted values, ρ = Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 24 / 51

26 Figure: Real exchange rates and fitted values, in 4-year differences with 4 commodities, best fit, , Germany LOG OF REAL EXCHANGE RATE (RER) data fitted values, ρ = Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 25 / 51

27 Figure: Real exchange rates and fitted values, in 4-year differences with 4 commodities, best fit, , Japan 0.6 data fitted values, ρ = 0.7 LOG OF REAL EXCHANGE RATE (RER) Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 26 / 51

28 Robustness Exercises Now we perform an out-of-sample exercise. Run the regression from Jan-1960 to Dec Choose the 4 commodities with the highest t-stats. Use data for those 4 PCP from Jan-1973 to Jan T, and the estimated coefficients, to fit value of the RER. Compare with data. Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 27 / 51

29 Figure: Out-of-sample fit 6 months ahead, with 4 best-fit commodities,united Kingdom 0.6 data fitted values, ρ = 0.45 LOG OF REAL EXCHANGE RATE (RER) Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 28 / 51

30 Figure: Out-of-sample fit 6 months ahead, with 4 best-fit commodities, Germany LOG OF REAL EXCHANGE RATE (RER) data fitted values, ρ = Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 29 / 51

31 Figure: Out-of-sample fit 6 months ahead, with 4 best-fit commodities, Japan LOG OF REAL EXCHANGE RATE (RER) data fitted values, ρ = Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 30 / 51

32 Figure: Out-of-sample fit, 4 best-fit commodities, correlations as a function of r (months ahead) 1 CORRELATION (ACTUAL VS FITTED) UNITED KINGDOM GERMANY JAPAN PERIODS AHEAD (MONTHS) Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 31 / 51

33 Are the results spurious? Estimate time series process for each RER Estimate a VAR for the 10 PCP Simulate series using orthogonal shocks and reproduce our regressions. The R 2 0 as the sample size goes to. Get samples of size 660 and compute the distribution of the R 2. Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 32 / 51

34 Figure: Small sample distribution of the R 2 over the period , with 4 best-fit commodities, United Kingdom R 2 Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 33 / 51

35 Figure: Small sample distribution of the R 2 over the period , with 4 best-fit commodities, Germany R 2 Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 34 / 51

36 Figure: Small sample distribution of the R 2 over the period , with 4 best-fit commodities, Japan R 2 Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 35 / 51

37 Figure: Fitted correlations and bootstrap bands under the null hypothesis of orthogonality, with 4 best-fit commodities, United Kingdom CORRELATION (FITTED VS BOOTSTRAPPED) % bands (bootstrap) median (bootstrap) fitted PERIODS AHEAD (MONTHS) Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 36 / 51

38 Figure: Fitted correlations and bootstrap bands under the null hypothesis of orthogonality, with 4 best-fit commodities, Germany CORRELATION (FITTED VS BOOTSTRAPPED) % bands (bootstrap) median (bootstrap) fitted PERIODS AHEAD (MONTHS) Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 37 / 51

39 Figure: Fitted correlations and bootstrap bands under the null hypothesis of orthogonality, with 4 best-fit commodities, Japan CORRELATION (FITTED VS BOOTSTRAPPED) % bands (bootstrap) median (bootstrap) fitted PERIODS AHEAD (MONTHS) Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 38 / 51

40 Model Imagine a world with many countries, which have different technologies and different endowments. We will describe the environment for country i. (for simplicity, we omit superscript i for the moment) Preferences E 0 β t U(C t ), t=0 where C t represents consumption of a non-traded final good (think of many!). Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 39 / 51

41 All we exploit from the model comes from its production structure. We use Cobb-Douglas, for simplicity. Let Y t = C t = Z y t (n y t ) α (q t ) 1 α where q t is a domestic, intermediate good Q t = Z q t [n q t ] βn [x t ] βx [m t ] βm. Technology to produce the primary commodity x t, X t = Z h t [n x t ] η E 1 η The primary commodity m t must be imported. Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 40 / 51

42 The marginal cost of the final good can be expressed as But so Taking logs, P q t P t = κy Z y t P t = κy Z y t (W t ) α (P q t ) 1 α. = κq Zt h [W t ] βn [Pt x ] βx [Pt m ] βm, (W t ) α ( κq Zt h [W t ] βn [Pt x ] βx [Pt m ] βm ) 1 α ln P t = ln κy Zt y +(α+(1 α)β n ) ln W t +(1 α)(ln κq Zt h +β x ln Pt x +β m ln Pt m ) Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 41 / 51

43 From the cost minimization conditions of the primary commodity sector, we have [ ] E 1 η W t = Pt x ηzt h Using this to replace the wage above ln P t = ln κy Z y t + (α + (1 α)β n ) ln ηzt h [ ] E +(α + (1 α)β n ) (1 η) ln + (1 α) ln κq Z h t n x t +(1 α)β m ln P m t + (α + (1 α)β n + (1 α)β x ) ln P x t Note that (1 α)β m + α + (1 α)β n + (1 α)β x = 1. n x t Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 42 / 51

44 If we collect productivity shocks and labor input in a single term Z t, ln P t = (1 α)β m ln P m t + (α + (1 α)β n + (1 α)β x ) ln P x t + Z t Not a unique representation in economy with many goods. Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 43 / 51

45 In general, then, we can write the solution for the price level in the US as where ln P US t = k + N h=1 N h=1 a US h ln PUS (h) t + Z US t a US h = 1, Similarly, for a different country we have ln P t = k + N ã h ln P t (h) + Z t. h=1 Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 44 / 51

46 The law of one price Pt US (h) S t = P t (h), where S t is the nominal exchange rate. Then so ln PUS t S t = P t ln P t ln S t = k + ( k k ) N 1 + h=1 N h=1 ã h ln Pt US (h) + Z t ( ) ( ah US ã h ln Pt US (h) + Zt US Z ) t. This regression equation is used in the empirical section. Key: ( a US h ã h ) 0. Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 45 / 51

47 We now select the 4 commodities with the largest trade share in the USA There are sizeable differences in the amounts traded with the other three countries, specially for Germany and Japan. Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 46 / 51

48 Table: Share of imports and exports in each country (% average in ) United States United Kingdom Germany Japan imp. exp. imp. exp. imp. exp. imp. exp. Petroleum Fish Timber Gold Meat Maize Aluminium Wheat Copper Cotton SUM Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 47 / 51

49 Table: R 2 using 4 commodities with largest US-trade share, Number of Commodities 10 4 (best-fit) 4 (largest US-trade share) United Kingdom Germany Japan Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 48 / 51

50 Conclusions A simplifying - and somehow unfair - summary of the literature on exchange rates is that it has evolved according to a certain dichotomy. The role of trade in primary commodities has been explicitly modeled in studying developing economies. But models used to analyze large developed economies focuses on trade in differentiated final products exclusively and ignore trade in primary commodities. Maybe they should not... Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 49 / 51

51 APPENDIX Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 50 / 51

52 Table: Unit root tests (p-values) Real Exchange Rates Level 3-years diff. 4-years diff. 5-years diff. US-UK US-DEU US-JPN Commodities Oil Fish Meat Aluminium Copper Gold Wheat Maize Timber Cotton

53 Table: Correlations ( ) Oil Fish Meat Alum. Copper Gold Wheat Maize Timber Cotton RER US-UK US-DEU US-JPN Commodities Oil 1.00 Fish Meat Alum Copper Gold Wheat Maize Timber Cotton

54 Table: Bootstrap distributions of the R 2 under the null hypothesis of orthogonality, with 4 best-fit commodities Percentiles distribution of R 2 ˆR 2 Median Pr(R 2 ˆR 2 ) United Kingdom Germany Japan

55 Table: Share of imports and exports in each country (% average in ) United States United Kingdom Germany Japan imp. exp. imp. exp. imp. exp. imp. exp. Petroleum Fish Meat Aluminium Copper Gold Wheat Maize Timber Cotton SUM Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 54 / 51

56 Table: Regressions in 4-year differences, selecting 3 commodities - R United Kingdom Germany Japan Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 55 / 51

57 Table: Regressors from previous sub-period, selecting 3 commodities - R United Kingdom Germany Japan Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 56 / 51

58 Table: Regression coefficients, in 4-year differences - United Kingdom Oil Fish Meat Aluminium Copper Gold Wheat Maize Timber Cotton Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 57 / 51

59 Table: Regression coefficients, in 4-year differences - Germany Oil Fish Meat Aluminum Copper Gold Wheat Maize Timber Cotton Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 58 / 51

60 Table: Regression coefficients, in 4-year differences - Japan Oil Fish Meat Aluminium Copper Gold Wheat Maize Timber Cotton Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 59 / 51

61 Table: Bootstrap distributions of R 2 under the null hypothesis of orthogonality, with 4 com. (largest US-trade share) in 4-year diff Percentiles distribution of R 2 ˆR 2 Median Pr(R 2 ˆR 2 ) United Kingdom Germany Japan Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 60 / 51

62 Figure: Fitted correlations and bootstrap bands under the null hypothesis of orthogonality, with 4 commodities (largest US-trade share), United Kingdom 1 CORREL (FITTED VS BOOTSTRAP) % bands (bootstrap) median (bootstrap) fitted PERIODS AHEAD (MONTHS) Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 61 / 51

63 Figure: Fitted correlations and bootstrap bands under the null hypothesis of orthogonality, with 4 commodities (largest US-trade share), Germany 1 CORREL (FITTED VS BOOTSTRAP) % bands (bootstrap) median (bootstrap) fitted PERIODS AHEAD (MONTHS) Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 62 / 51

64 Figure: Fitted correlations and bootstrap bands under the null hypothesis of orthogonality, with 4 commodities (largest US-trade share), Japan 1 CORREL (FITTED VS BOOTSTRAP) % bands (bootstrap) median (bootstrap) fitted PERIODS AHEAD (MONTHS) Ayres, Hevia, Nicolini (2017) Real Exchange Rates and Primary Commodity Prices 63 / 51