The Marginal Product of Capital: New Facts and Interpretation

Transcription

1 The Marginal Product of Capital: New Facts and Interpretation Julia Faltermeier Universitat Pompeu Fabra October 11, 2017 Universitat Pompeu Fabra Julia Faltermeier 1

2 Convergence in aggregate MPKs across countries Mean-reversion Fall in dispersion Annual Growth Rate of MPK (%) NLD IND CHN LKA CHE SEN BOL ECU AUS CAN TZA NOR COL DEUUSA ZAF CYP CMRCRI CIV NZL TUN MEX URY ISR FIN MYS FRA AUT GBR SWE HND DNK BFA ITA KOR JAM PRT ESP JPN GRC KEN PER ARG PHL MLT IRL MAR CHL HKG SGP THA BRA TUR EGY PAN GTM Avg. MPK PRY JORTWN Standard Deviation of MPK Year Notes: (a) Geometric growth rate and MPK at the beginning of the sample are calculated relative to the world. The OLS coefficient is , significant at the 1% level. (b) The standard deviation of MPKs reduces on average by.0005 each year. Universitat Pompeu Fabra Julia Faltermeier 2

3 No correlation with capital inflows Capital Inflows and Changes in MPKs Capital Inflows (relative to initial output) PRY JOR GRC JAM ESP IRL NZL AUS CYP MLT PRT HND BFA GBR USA PAN TUR CRI GTM COL FRA ITA SENTZA KEN LKA BRA URY MEXTUN EGY DNK ECU CAN JPN CMR ARG HKG KOR CIV MAR PHL THA AUT ISR FIN CHLCHE NLD TWN DEU BOL SWE MYS CHN NOR SGP ZAF IND PER Change in MPK Universitat Pompeu Fabra Julia Faltermeier 3

4 What drives the convergence in MPKs? 1. New Facts Convergence in MPKs Pos. correlation with capital shares Neg. correlation with capital-labor ratio No correlation with capital inflows Increase in North-South trade Universitat Pompeu Fabra Julia Faltermeier 4

5 What drives the convergence in MPKs? 1. New Facts Convergence in MPKs Pos. correlation with capital shares Neg. correlation with capital-labor ratio No correlation with capital inflows Increase in North-South trade 2. Interpretation: Trade integration leads to convergence Multi-country, dynamic Heckscher-Ohlin-Krugman model with costly trade Two channels: Sectoral reallocation Aggregate savings Universitat Pompeu Fabra Julia Faltermeier 5

6 What drives the convergence in MPKs? 1. New Facts Convergence in MPKs Pos. correlation with capital shares Neg. correlation with capital-labor ratio No correlation with capital inflows Increase in North-South trade 2. Interpretation: Trade integration leads to convergence Multi-country, dynamic Heckscher-Ohlin-Krugman model with costly trade Two channels: Sectoral reallocation Aggregate savings 3. Quantification Universitat Pompeu Fabra Julia Faltermeier 6

7 Literature Efficiency of capital allocation Caselli & Feyrer (2007) Heathcote & Perri (2013) Chirinko & Mallick(2008), Lowe et al. (2012) David et al. (2014), Monge-Naranjo et al. (2015) Allocation puzzle Gourinchas & Jeanne (2013), Aizenmann et al. (2007), Alfaro et al. (2014) International Trade Romalis (2004), Zymek (2015), Fadinger (2011) Cuñat & Maffezzoli (2007), Alvarez and Lucas (2007), Acemoglu & Ventura (2002) Labor share & CES Karabarbounis & Neiman (2014), Elsby et al. (2013), Antràs (2004) Universitat Pompeu Fabra Julia Faltermeier 7

8 How do I measure the MPK? Following Caselli & Feyrer: Return to capital c,t = (1 α Lc,t α Nc,t ) PY c,t Y t,i P K c,t K c,t }{{} MPK Four adjustments: 1. Natural capital 2. Relative prices 3. Depreciation rate 4. Capital gain (future price of capital goods) Convergence Return + (1 δ c,t ) P K c,t+1 P Kc,t }{{} Capital gain Universitat Pompeu Fabra Julia Faltermeier 8

9 Evidence across countries OLS Regression for Avg. Return Explanatory variable Slope coefficient Constant R 2 Obs Avg. Y L 0.011* 0.041*** (0.054) (0.000) Avg. K L 0.013*** 0.045*** (0.004) (0.000) Avg. Capital Share 0.426*** (0.000) (0.182) Notes: * p < 0.1, ** p < 0.05, *** p < 0.01; p-values in parentheses. Averages are computed over the deviation from the cross-country mean weighted by capital. By Year Y/L By Year K/L Comparison Caselli & Feyrer Universitat Pompeu Fabra Julia Faltermeier 9

10 Evidence over time Channels of convergence Capital accumulation Sectoral Reallocation IND IND Growth rate of MPK KEN SEN COL MEX NLD BOL CHE LKA ECU PER AUS CAN TZA ARG CMR NOR USA CRICYP ZAF DEU CIV PHL NZL ISRURY TUR TUN FIN MYS FRA AUT HND SWE PAN GBR MLT SGP GTM BFA IRL DNK ITA THA KOR JAM PRT MAR CHL ESP GRC JPN HKG JOR BRA PRY CHN TWN EGY Growth rate of K/L Growth rate of MPK BOL PRY CHL BRA SEN CHE ECU EGY TZA ARG ZAF NOR AUS CAN COLCRI CYP CMR CIV PHL USADEU URY ISR NZL TUN TUR MEX MYS FIN FRA AUT GBR HND SGP MLT SWE PAN GTM IRL BFA DNK THA ITA JAM HKG JOR KEN MAR PRT GRC ESP TWN JPN CHN PER NLD LKA KOR Growth rate of Capital Share Notes: Geometric growth rates are calculated relative to the world. (a) OLS coefficient of is significant at the 1% level. (b) OLS coefficient of.587 is significant at the 1% level. Universitat Pompeu Fabra Julia Faltermeier 10

11 Additional Facts North-South Trade has increased Evidence No capital inflows to high MPK economies Evidence Universitat Pompeu Fabra Julia Faltermeier 11

12 Model description Set-up World of N c countries Labor and capital as factors ( of production ) Country c defined by β, A L, A K, L, {τ c,c } N c c =1 Consumption Overlapping generations model Closed international financial markets Production Two intermediates - labor & capital-intensive Tradable inputs with monopolistc competition Universitat Pompeu Fabra Julia Faltermeier 12

13 Consumers Set-up max U c,t = (C c,t) 1 ρ (C + c,t+1 ) 1 ρ β c C c,t,c c,t+1 1 ρ 1 ρ s.t. budget constraints: P c,t C c,t = w c,t s c,t P c,t+1 C c,t+1 = ( rc,t+1 P c,t + (1 δ) P c,t+1 P c,t ) s c,t Universitat Pompeu Fabra Julia Faltermeier 13

14 Consumers Optimal Savings decision Aggregate savings determine next period s capital stock: where K c,t+1 = s c,t P c,t L c,t s c,t = β 1 ρc w c,t β 1 ρc + ( rc,t+1 P c,t+1 + (1 δ) ) ρ 1 ρ Universitat Pompeu Fabra Julia Faltermeier 14

15 Producers Three stages of production B Final c,t = ( ) Pc,t K 1 σ + P L 1 σ 1 σ 1 c,t Universitat Pompeu Fabra Julia Faltermeier 15

16 Producers Three stages of production B Final c,t = B Assembly c,t (i) = ( ) Pc,t K 1 σ + P L 1 σ 1 σ 1 c,t ( ) 1 Ni 0 p c,t(ω i ) 1 ɛ 1 ɛ dω i Universitat Pompeu Fabra Julia Faltermeier 16

17 Producers Three stages of production B Final c,t = B Assembly c,t (i) = p c,t (ω i ) = ( ) Pc,t K 1 σ + P L 1 σ 1 σ 1 c,t ( Ni ɛ ɛ 1 τ c, c 1 ɛ ) 1 0 p c,t(ω i ) 1 ɛ dω i ( ) zi ( r c,t A K c,t w c,t A L c,t ) 1 zi Universitat Pompeu Fabra Julia Faltermeier 17

18 Producers Three stages of production B Final c,t = B Assembly c,t (i) = p c,t (ω i ) = ( ) Pc,t K 1 σ + P L 1 σ 1 σ 1 c,t ( Ni ɛ ɛ 1 τ c, c 1 ɛ ) 1 0 p c,t(ω i ) 1 ɛ dω i ( ) zi ( r c,t A K c,t w c,t A L c,t ) 1 zi Assume z = 1 in K-sector & z = 0 in L-sector Universitat Pompeu Fabra Julia Faltermeier 18

19 Market clearing Factor market clearing gives: N K,t = 1 f ɛ c n K c,t = AK c,t K c,t Goods market clearing requires: ( r c,t A K c,t ) ɛ C c τ 1 ɛ c,c A K c,tk c,t (1) ( ) 1 A K c,tk c,t (2) c ( P K c,t) ɛ Q K c,t = (ɛ 1) 1 ɛ ɛ ɛ f (3) Universitat Pompeu Fabra Julia Faltermeier 19

20 Steady state Combined with market clearing conditions and a normalization, steady state depends on following system of N c equations: K c = β 1 ρc + ( r c P c β 1 ρc ) ρ 1 + (1 δ) ρ wc Pc L c (4) Details: What determines K? Pure HO Properties Universitat Pompeu Fabra Julia Faltermeier 20

21 A pure Heckscher Ohlin Model ɛ, f 0 Collapse input and intermediate stage of production Three groups: North, South and Autarky sort depending on export-sector (r c, w c ) = (A K c p K W, τal cp L W ) if c N (τa K c p K W, AL cp L W ) if c S Universitat Pompeu Fabra Julia Faltermeier 21

22 Market clearing (I) Aggregate price level: ( ( ) 1 σ ( ) ) 1 1 σ P N,t = pw K + τpw L 1 σ ( ( ) 1 σ ( ) ) 1 1 σ P S,t = τpw K + pw L 1 σ Market clearing world prices: ( p K W,t p L W,t ) σ = ( PN,t P S,t ) 1 σ c S A L cl c + τ σ c N A L cl c c N A K c K c + τ σ ( PN P S ) 1 σ c S A K c K c Universitat Pompeu Fabra Julia Faltermeier 22

23 Market clearing (II) k South ( p L W τp K W ) σ < k Autarky < ( τp L W p K W ) σ k North Universitat Pompeu Fabra Julia Faltermeier 23

24 Properties of Pure HO model 1. Capital-abundant countries have lower MPKs Details 2. Reduction in trade cost leads to convergence in MPKs Details 3. Positive correlation between MPKs and capital-shares Details 4. Positive correlation between changes in MPKs and changes in capital-shares Details 5. Negative correlation between changes in MPKs and capital-labor ratios Details Universitat Pompeu Fabra Julia Faltermeier 24

25 Property 1 & 2 1. Capital-abundant countries have lower MPKs 2. Reduction in trade cost leads to convergence in MPKs r N P N rs P S = AK N A K S ( (p K W ) 1 σ + τ 1 σ ( p L W ) 1 σ ) 1 σ 1 ( (p K W ) 1 σ + τ σ 1 ( p L W ) 1 σ ) 1 σ 1 < 1 Back Universitat Pompeu Fabra Julia Faltermeier 25

26 Short comings: Only North-South trade Same conditional factor prices within block Move in and out of autarky as endowments change No decreasing returns Universitat Pompeu Fabra Julia Faltermeier 26

27 Full model A K N K N A K S K S = ( ( ˆp σ ( i τ 1 ɛ ˆp ɛ σ ) ) ɛ 1 P σ N Y N ɛ σ i P σ τ 1 ɛ ( ˆp ɛ σ S Y S i ( ( (1 ˆp ɛ i τ 1 ɛ ) ɛ σ ɛ 1 ˆp ɛ i ˆp σ ɛ 1 i τ1 ɛ) ɛ σ τ 1 ɛ) ) PN σ Y ɛ 1 ) N ɛ σ (τ) 1 ɛ P σ S Y S where ˆp K = r N rs A K S A K N and ˆp L = w N A L S w S A L N. Universitat Pompeu Fabra Julia Faltermeier 27

28 Quantitative Exercise Baseline Match Output and bilateral imports with A L and τ i,j (asymmetric) ɛ 1 = 14 - trade elasticity/ determines inc. returns to scale σ < 1 & A K chosen to match US elasticity between K and L and capital share fixed cost assumed equal across countries Counterfactual Exercises What would have happened to returns in 1970 if the trade cost had been as low as 2000? What would have happened to returns in 1970 if the distribution of capital had been like the 2000s? Universitat Pompeu Fabra Julia Faltermeier 28

29 Model Fit 1970 Universitat Pompeu Fabra Julia Faltermeier 29

30 Model Fit 2000 Universitat Pompeu Fabra Julia Faltermeier 30

31 Sources of convergence Universitat Pompeu Fabra Julia Faltermeier 31

32 Counterfactual exercise Universitat Pompeu Fabra Julia Faltermeier 32

33 Quantify contribution Index = 1 i MPK cf MPK i MPK cf Only fall in tau - index = Only change in endowment - index = Universitat Pompeu Fabra Julia Faltermeier 33

34 Conclusion 1. New facts on the aggregate MPK - convergence and its channels 2. Trade integration as an important driver is consistent with the data 3. Quantify contribution of fall in trade cost as 30 % Equalized MPKs are the result of sectoral reallocation and (domestic) changes in factor endowments and do not indicate the absence of international financial frictions Universitat Pompeu Fabra Julia Faltermeier 34

35 Thank you!

36 Appendix Universitat Pompeu Fabra Julia Faltermeier 36

37 Conditions for a high steady-state capital In the absence of trade costs when input prices are equalized, the steady state capital is higher for patient countries whose capital-productivity is not too high, such that: ( ( ) 1 ) ( ( ) βc ρ 1 (1 δ) kc β 1 + r 1 ) βc ρ 1 c A K P β A K c c A K c < 0 for ρ < 1 k > 1 if: β c β c > 0 for ρ = 1 ( c ( ) 1 ) ( ( ) 1 ) βc ρ 1 βc ρ 1 (1 δ) β 1 c β A K c c A K c > 0 for ρ > 1 + r A K P Back Universitat Pompeu Fabra Julia Faltermeier 37

38 Property 3 Positive correlation between MPKs and capital-shares r N K N < r SK S P N Q N P S Q S QN K S QN K D }{{} >1 < QK S S QS K D }{{} <1 P 1 σ N τ σ 1 P 1 σ S Necessary condition for the North to have a lower capital-share: P 1 σ N > 1 τ σ 1 P 1 σ S ( τ 2) 1 σ > 1 Back Universitat Pompeu Fabra Julia Faltermeier 38

39 Property 4 Positive correlation between changes in MPKs and changes in capital-shares Sc K r c Kc = w c L c + r c Kc = 1 + P c r c ( 1 ( ) 1 ( ) ρ + β ρ rc 1 ρ rc 1 ρ c + (1 δ) P c P c ) ρ 1 ρ 1 Back Universitat Pompeu Fabra Julia Faltermeier 39

40 Trade growth Level of Trade Share of Trade Trade measured as Total Exports (bn USD) Share of Total Exports (%) Year Year NN Trade SS Trade NN Trade SS Trade NS-SN Trade NS-SN Trade Notes: Total trade is calculated as the sum of the value of exports of goods as reported the IMF Direction of Trade statistics (DOTS) of the 60 countries in the sample. The sample captures 70% of world exports. The division into North and South follows the IMF classification into Advanced and Developing Economies. Back Universitat Pompeu Fabra Julia Faltermeier 40

41 No correlation with capital inflows Capital Inflows and Changes in MPKs Capital Inflows (relative to initial output) PRY JOR GRC JAM ESP IRL NZL AUS CYP MLT PRT HND BFA GBR USA PAN TUR CRI GTM COL FRA ITA SENTZA KEN LKA BRA URY MEXTUN EGY DNK ECU CAN JPN CMR ARG HKG KOR CIV MAR PHL THA AUT ISR FIN CHLCHE NLD TWN DEU BOL SWE MYS CHN NOR SGP ZAF IND PER Change in MPK Back Universitat Pompeu Fabra Julia Faltermeier 41

42 Convergence in return as well as both components Mean-reversion Fall in dispersion Annual Growth Rate of Return (%) LKA CHN COL URY BOL USA AUS CRI NZL CAN KOR HND IND MLT TZA PER EGY ARG ISR SEN ECU ZAF NOR MYS SWE JPN CHE MEX BFA TUN FRA FIN AUT DEU CYP NLD ITA JAM IRL KEN DNK PRT GBR ESP CIV GRC PAN THA CHL CMR MAR BRA PHL SGP TUR GTM HKG JOR PRY TWN Avg. Return Standard Deviation of Return (3-Year MA of Capital Gain) Year Notes: (a) Geometric growth rates and return at the beginning of the sample are calculated relative to the world. OLS coefficient of significant at the 1% level. A level of MPK twice the world MPK is associated with a percentage points lower growth rate (b) The standard deviation in the return reduces on average by each year or.021 over the whole sample. Back Universitat Pompeu Fabra Julia Faltermeier 42

43 How do my results differ from Caselli & Feyrer? Variation with new data is about 2 higher Poor countries are disproportionately affected 75% due to better data on labor share and natural resources, 24% due to rel. prices No significant corr. with income for both samples Difference between measures by income (1996) Difference between PWT 9.0 and CF CIV BOL EGY PAN PER ECU CRI CHL IRL PHL NZL URY MARMEX ZAFTUN PRY MYS SGP KOR JOR SWEITA GRC ISR JPN GBR LKA FRA CHE CANUSA FINAUS JAM ESP DNK AUT PRT NLDNOR COL Log Real GDP per worker Back Universitat Pompeu Fabra Julia Faltermeier 43

44 Growth decomposition Which margin of adjustment drives convergence? 3/4 of reduction relative to MPK W is explained by reduction in Y K - which is driven by increase in K L 1/4 of reduction relative to MPK W comes from adjustments in the capital share Rel. price has no explanatory power Universitat Pompeu Fabra Julia Faltermeier 44

45 Fact 1: Convergence - Return to capital α PY P K Y K + (1 δ) PK t+1 P K t Percentile difference 90th - 10th percentile of Return (3-Year MA of Capital Gain) year Universitat Pompeu Fabra Julia Faltermeier 45

46 S.D. of capital gain (3-y moving average) (1 δ) PK t+1 P K t Standard Deviation of Capital Gain (3-Year MA) Year Universitat Pompeu Fabra Julia Faltermeier 46

47 World return World MPK Real World Return World MPK - weighted by capital stock Year Real World Return - weighted by capital stock Year Universitat Pompeu Fabra Julia Faltermeier 47

48 Correlation with GDP per worker over time Correlation log(gdp p.w.) with 95% CI Year Back Universitat Pompeu Fabra Julia Faltermeier 48

49 Correlation with Capital per worker over time Correlation log(k/l) with 95% CI Year Back Universitat Pompeu Fabra Julia Faltermeier 49