Purchasing Power Parities, Price Levels and Measures of Regional and Global Inflation. D.S. Prasada Rao, Alicia Rambaldi and Bert Balk

Transcription

1 Purchasing Power Parities, Price Levels and easures of Regional and Global Inflation D.S. Prasada Rao, Alicia Rambaldi and Bert Balk

2 Outline Key Concepts and notation Purchasing power parities (PPPs) Price Levels Temporal-spatial comparisons GEKS Approach with Fixity Comparisons of World GDP over time Global Inflation Global Growth 2

3 Key Concepts and Notation Gross Domestic Product of country (in national currency units) GDP = p x n n Nominal GDP : GDP of country i in period t expressed in reference currency units using exchange rates GDP NGDP = XR Real GDP : GDP of country i expressed in reference currency units converted using PPPs GDP RGDP = PPP 3

4 Purchasing Power Parities (PPPs) PPPs are amounts of currencies, of different countries, that have the same purchasing power as one unit of a reference currency (e.g. US$) with respect to a selected basket of goods and services. 4

5 PPPs from ICP 2005 Country Exch. Rate PPP PLI% (US=00) P.R. China Hong Kong India Australia Japan Switzerland Ethiopia Source: World Bank, 2005 ICP Report 5

6 Price Level Indices Price Level Index (PLI): It is defined as the ratio of PPP to the exchange rate PLI = PPP XR Properties of PLIs: By definition PLI of reference country is Interpretation of PLI can be ambiguous PLIs for a country using two different reference countries are not directly comparable PLIs are transitive 6

7 Price Level Indices Price Level Index (PLI): It is defined as the ratio of PPP to the exchange rate PLI PPP GDP XR = = XR GDP PPP Properties of PLIs: By definition PLI of reference country is. For this country the nominal and real GDP are the same Interpretation of PLI can be ambiguous PLIs for a country using two different reference countries are not directly comparable PLIs are transitive 7

8 Price Level Indices Relative to World Average. A simple approach is to compute the geometric average of all PLI s and normalise PLI of each country using the geometric mean. Such a normalisation does not have any useful interpretation. 2. An alternative is to compute the weighted average of PLIs and use a normalisation based on the average. World average of PLIs I = µ = 3. Scale the PPPs to the world average as: = PLI W PPP = PPP µ I = RGDP RGDP 8

9 Price Level Indices Relative to World Average 4. PLI for country with world average is: PLI = PPP XR W W 5. World average of PLI s at new PPPs is equal to and, therefore: I I W GDP PPP = GDP XR = = World GDP at the new PPPs is equal to world nominal GDP at exchange rate 6. PLI s defined using world average are invariant to the choice of the reference country for PPPs. 9

10 Table : Price Level Indexes for Selected Countries, 2005 (Price level in USA =.0) Country PPP XR PLI with USA = Australia Denmark India Brazil South Africa USA.24 PLI with world average. = 0

11 Table 2: PPPs and Real Incomes for Selected Asia-Pacific Countries, 2005 and 2009 Reference Currency Hong Kong dollar Country PPP XR PLI* Real per capita GDP PPP XR PLI* Real per capita GDP Bangladesh , ,888 China, PR , ,706 Hong Kong , ,6 India , ,500 alaysia , ,524 Thailand , ,753 Vietnam , ,389 Note: (*) PLIs are defined relative to regional average with Asia = 00. Source: ADB (2007) and ADB (202)

12 GEKS Space-Time Comparisons The Problem: Consider the case of two periods and comparisons involving countries. Suppose we have ICP results for the two periods. We have PPPs for the two periods, denoted by for t =,2. Let the results for periods and 2 be represented 22 by matrices: and Since PPPs are transitive, elements of these matrices can be written as, for t=,2 t tt π k PPPk = t π tt PPP k 2

13 GEKS Space-Time Comparisons The Problem: We wish to construct a transitive matrix which allows comparisons between periods and 2. The problem is to fill the elements of the matrix, of order (2 x 2) of the form: = Note that and are given from the ICP. Typical element of 2 2 are of the form PPP k - PPP for country k in period 2 with country in period as the reference. 3

14 GEKS Space-Time Comparisons The approach: Fill the elements of the off-diagonal matrices, and using observed domestic deflators in the countries over the period to 2. We have the following choices: PPP = PPP d 2 2 k k k PPPk = PPPk / d Since both of these are equally desirable, we use the geometric mean. ( )( / ) PPP = PPP d PPP d k k k k We note that the matrix with the observed 2 2 and filled in and is not transitive. We apply GEKS to this matrix. 2 / 2 2 and 22 4

15 GEKS Space-Time Comparisons The approach (continued) We note that straightforward application of GEKS will disturb the PPP relativities in periods and 2 as obtained from the ICP. So, we apply GEKS imposing temporal fixity. Accordingly we minimise T T ts s t ln PPPk ln π* k + ln π* t= s= = k= subect to fixity restrictions: 2 s s s π* k = δ * πk for k = 2,,..., and s= 2,. The solution to GEKS with fixity is: δ * = and * 2 δ = 2 d = 23 5

16 GEKS Space-Time Comparisons In the context of Asia-Pacific Example our results suggest to link 2005 with 2009 using: δ * , 2009 = d i i= a geometric mean of price movements from 2005 to 2009 in each of the 23 countries. δ 2 can be interpreted as a measure of regional inflation. However, use of unweighted average of country specific inflations is not satisfactory. If we want to use weights, which weights do we use? 6

17 Regional/Global Deflator Using the plutocratic structure of the regional PLI, we may define regional deflator as: where w i δ 23 * , 2009 di i= = t wi + wi t RGDPi = with wi = 23 2 RGDP i= w i t i δ * 2 is like a Tornqvist index of price movements from 2005 to

18 easures of Global Inflation and Global Growth otivated by the result of GEKS with fixity, we proceed to obtain measures of global inflation and global growth. We use the following approach: We first define global GDP in periods s and t which are given by s s s s = = / = = RGDP RGDP GDP PPP t t t t = = / = = RGDP RGDP GDP PPP We note that these two aggregates are in the prices of periods s and t respectively. The ratio of these two aggregates is similar to the ratio of nominal GDP in two periods. 8

19 easures of Global Inflation and Global Growth The nominal growth in world GDP for period s to t is given by: = = GDP GDP t s / PPP / PPP The obective is to decompose this ratio as: Nominal growth in World GDP = WI(s,t)*WG(s,t) We provide expressions for WI(s,t) and WG(s,t) t s 9

20 easures of Global Inflation and Global Growth We first observe that t t GDP / PPP t t = GDP / PPP exp ln s s s s = GDP / PPP GDP / PPP = = Ψ t RGDP = exp Ψ ln s = RGDP where s t RGDP RGDP L, s t RGDPk RGDP k k= k= a b Ψ = where Lab (, ) = is the logmean. ln a ln b L(.,.) = 20

21 easures of Global Inflation and Global Growth Second, we decompose growth nominal GDP in country into price and quantity components. t GDP GDP GDP P (,) st Q (,) st s GDP = Then the World Inflation and World growth are measured by: PPP GDP WI(,) st = exp Ψ ln P (,) st = PPP It is quite easy to check that: s t GDP WGst (,) = exp Ψ ln Q (,) st = ( ) t t GDP / PPP = Nominal growth in World GDP = = WI( s, t) WG( s, t) s s GDP / PPP = 2

22 Empirical Application 22

23 Empirical Application Growth in nominal GDP in Asia = Asian Inflation =.2025 Asian Growth =

24 Thank you! 24