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Econ 240C

Econ 240C. Power 17. Outline. The Law of One Price. Law of One Price: Outline. Definition: slides 5-6 Applied to wheat trade: slides: slides 7-9 Time Series Notation: slides 10 - 11 Data and Traces: slides 12-14 Show that Import Price, DNSPJ, is Evolutionary: slides 15-16

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Econ 240C

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  1. Econ 240C Power 17

  2. Outline • The Law of One Price

  3. Law of One Price: Outline • Definition: slides 5-6 • Applied to wheat trade: slides: slides 7-9 • Time Series Notation: slides 10 - 11 • Data and Traces: slides 12-14 • Show that Import Price, DNSPJ, is Evolutionary: slides 15-16 • Show that Import Price Minus Sum of Export Price (-1) + Freight Rate (-2) is stationary: slides 18 - 26

  4. Outline Cont. • Show that logs of import & export prices are evolutionary of order one: slides 27- 36 • Show that log of price ratio is stationary: slides 37- 49 • Speed of convergence: slides 50 - 54 • Cointegration: slides 55 - • Long run equilibrium relationship between log of import price and log of export price (with freight and lags): slides 56 - 57 • VAR speed of adjustment model: slide 58-60

  5. The Law of One Price • The New Palgrave Dictionary of Money and Finance • Next slide

  6. The Law of One Price • This law is an immediate consequence of the absence of arbitrage and, like the absence of arbitrage, follows from individual rationality. Departures from the no arbitrage condition imply that there are profit opportunities. These arise because it would be profitable for arbitrageurs to buy good i in the country in which it is cheaper and transport it to the country in which it is more expensive, and in doing so, profit in trade.

  7. Commodity Trade Issues • Well defined product: World Wheat Statistics • # 2 Dark Northern Spring 14% • Western White • Hard Winter • Transport costs • US: export • Pacific Ports • Gulf Ports

  8. Prices in $/metric ton • Import price notation: DNSJ is Japanese import price in $/metric ton for Dark Northern Spring wheat • Export price notation: DNSG is export price for Dark Northern Spring from a Gulf Port; DNSP is export price for Dark Northern Spring from a Pacific Port • Lagged one month because commodity arbitrage takes time

  9. Transport Cost in $/Metric Ton • Freight rates are forward prices and are lagged two months

  10. Time Series • Import Price: DNSJ • Export Price (lagged one) Plus Freight (lagged two): DNSGT • Logarithm of Price Ratio: ln [DNSJ/DNSGT] = lnDNSJ – lnDNSGT denoted lnratiodnsgjt = ln[1 + ∆/DNSGT] ~ ∆/DNSGT, the fractional price differential, where ∆ = DNSJ – DNSGT, and can be positive or negative

  11. Time Series • Is the log of the export price evolutionary, of order one? • Ln DNSJ = lndnsj • Is the log of the import price evolutionary, of order one? • Ln DNSGT = lndnsgt • Is their difference stationary, of order zero, ie. are they cointegrated? • i.e. Is the log price ratio ( the fractional price differential) stationary? • Ln{DNSJ/DNSGT] =lnratiodnsjgt

  12. Data

  13. Table Three: Pacific DNS • Log of Ratio of Import Price to Pacific Export Price (lag 1) Plus Pacific Freight (lag2) • Stationary • No unit root • AR (1) Model: root 0.54, normal residual • Log of Import Price and Log of Pacific Export Price (lag 1) Plus Pacific Freight (lag 2) • Cointegrated • VEC: one lag • Rank: 1, 1, 1, 1, 2 • Data: no trend; Integrating Equation: Intercept, no trend, rank one, 1%

  14. Correlogram of Import Price, DNSJ

  15. Unit Root Test

  16. Dark Northern Spring Japan • Export Price is Evolutionary • The Import Price Minus the Sum of the Export Price (-1) + Freight Rate (-2) is Stationary • So the Import Price and the Export Price Never Wander Off from each other, i.e. they are cointegrated

  17. Histogram

  18. Correlogram

  19. Unit Root Test

  20. ARONE Model

  21. Diagnostics

  22. Correlogram of Residuals

  23. Correlogram of Residuals Squared

  24. ARCH-LM Test

  25. Show that Logs of Prices Are Evolutionary

  26. Conclude • Log of Import Price, lndnsj, is evolutionary

  27. Conclude • Both the log of the import price and the log of the Pacific export price (lagged one) plus the Pacific Freight Rate (lagged two) are evolutionary, of order one. • To be of order one, not higher, their differences should be stationary, i.e. of order zero. • Unit root tests show this is the case

  28. Log of Price Ratio

  29. Conclusions • Log of ratio of import price to the export price (lagged one) plus freight rate (lagged two) is stationary and is modeled as an autoregressive process of the first order with mean zero and root 0.54

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