Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University LECTURES 8 & 9: PURCHASING POWER PARITY (PPP) EMPIRICAL TESTS OF PPP Motivating questions: How integrated are goods markets internationally? How rapidly do prices adjust?

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University PPP: ALTERNATIVE DEFINTIONS Absolute PPP P ≡ the absolute price of a basket of goods in local currency, not just an index ( from P enn W orld T ables or World Bank’s I ntl. C omparison P rogram.), i.e., the ratio of purchasing powers. Q=1, where real exchange rate Q In logs, e = p - p*.

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University PPP: ALTERNATIVE DEFINTIONS (continued) Relative PPP CPI ≡ is a price index, expressed relative to an arbitrary base year e.g., “CPI 2000 ≡ 100.0” ( from national agencies ). or. Q is constant (at ). In logs, Δe = Δ cpi – Δ cpi* (relative to some base year). Annual depreciation = π - π*.

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University PPP: EMPIRICAL QUESTIONS Does PPP hold: in the short run?in the long run? What is the test’s “statistical power”? What is the estimated speed of adjustment to the LR? Are PPP deviations: related to variation in nominal exchange rates? - Can one infer causality? - Is Var(q) related to currency regimes? related to geography? - To distance? To borders? Does the Law of One Price hold better in some sectors than others? - Commodities vs. Manufactures & Services - Tradables vs. Nontradables - Imports (Is there full pass-through?)

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University PPP in a sense holds well in hyperinflations: The cumulative change in E corresponds to the cumulative change in CPI.

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University MODERN PPP TEST SPECIFICATION: the real exchange rate as an autoregressive process (random walk, or unit root) (full adjustment to PPP) (gradual adjustment to PPP). Common finding in tests of 1980s: can’t reject H 0. True problem: Insufficient power in the tests, due to insufficient data. Since 1990, studies have sought more data. where u t ≡ random disturbance with E(u t ) = 0.

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University With 100 or 200 years of data it is not hard to reject random walk, i.e., to detect regression to the mean. qtqt

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University Studies with long time series: Time Period Estmtd. Speed of Adjustment Half-life (years) JF (1990) Updated WTP (2007) (s.e.=.05).124 Abuaf & Jorion (1990) Lothian & M. Taylor (1996) 2 centuries 3-5 Alan Taylor (2002) 19 currencies (s.e.=.01) 3.4 – 4.1 Cross-country Number of panel data studies: countries Frankel & Rose (1995) Wei & Parsley (1998) Choi, Mark & Sul (2004)

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University Taylor spliced together 100+ years of data for 20 currencies: One lesson: reversion to LR

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University Three useful kinds of empirical evidence: The pattern of movement in real exchange rates: band or threshold RW trend AR. Effects of exchange rate regime on variability in Q. Tests of Law of One Price for narrowly defined goods. PPP clearly fails in the short run. What is H Alt ? Sticky prices? How can we tell?

Four patterns of deviation from PPP and their likely origins: a)Band <= barriers to trade b)Random walk <= shifts in terms of trade c)Trend <= Balassa- Samuelson effect d)Autoregression <= sticky prices. Band Random Walk TrendAutoregression Q ≡

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University Var(e t ) and Var (q t ) are correlated. Is it coincidence? No, it can’t be: Every time a regime switch raises variability of nominal exchange rates, it also raises variability of real exchange rates. · Pre- and post-1973 (Fig. 19.4) · Inter-war period (Eichengreen 1988 ): float vs fix · Post-war regimes (Mussa 1986 ): - Canadian float in the 1950s - Ireland regime changes (see appendix table) · A century of PPP ( Alan Taylor 2002 ): Gold standard Interwar Bretton Woods Float

When nominal exchange rate variability (¥/$) went up with floating, real exchange rate variability went up in tandem. Coincidence? Figure 19.4 Nominal & real exchange rates both became more volatile after

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University The final nail in the coffin: Exchange rate variability across a century of regimes Variability of real exchange rate Variability of nominal exchange rate Again, each time a more flexible regime raises nominal variability, it raises real variability too Each observation is a country-regime. (Adapted from A.Taylor, 2002 )

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University Appendix: Early test of PPP that I do not recommend: (e.g., Jacob Frenkel pioneering 1976 German hyperinflation test) Claim: H 0 holds well in hyperinflation. But: Conceptual problems: - Where does u t come from? Purely transitory variation in q t ? - What is the H Alt ? Technically, p t -p* t may be “nonstationery.” Modern time-series econometrics: We must test for “cointegration.” More fundamentally, –Var(q t ) is greater in hyperinflation.

PPP holds better at longer horizons.

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University Estimation of, persistence parameter Frankel (1990): : δ =.7 (s.e.=.2) => t-stat.3/.2 = 1.5 < 5% significance level [conventional = 2.0] [Dickey-Fuller = 3.0] : δ =.8 (s.e.=.1) => t-stat.2/.1=1.8 < 5% significance. => Can’t reject H 0, random walk in q. But even if H A is true, we shouldn’t expect to be able to reject δ = 1.0, without more data <= low power. We need 100 years of data, to get enough power to reject.

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University The original Alan Taylor graph Again, each time a more flexible regime raises nominal variability, it raises real variability too.

Mussa (1986): Each time Ireland changed its exchange rate arrangements (₤, $, DM), bilateral real exchange rate variability has followed bilateral nominal exchange rate variability.

Copyright 2007 Jeffrey Frankel, unless otherwise noted API Macroeconomic Policy Analysis I Professor Jeffrey Frankel, Kennedy School of Government, Harvard University