FEATURE ARTICLE - Ministry of Trade and Industry

Economic Survey of Singapore 2011Feature ArticleANNEX A: DERIVATION OF WAGE GROWTH DECOMPOSITIONWe begin with the following identity:W = S × GDPWhere W = Total compensation to all employeesS = Labour share of Gross Domestic ProductGDP = Nominal Gross Domestic ProductWe then divide the identity throughout by the number of workers in the economy and the consumerPprice index (CPI), and multiply the right-hand-side byY:P YWGDPP Y= S ××N × P CN × P YP CWhere N = Number of workersP C= Consumer Price Index= GDP deflatorP YFinally, we take logs on both sides:logW= logGDP+ (logPY—logP C)+ logSN ×P CN × P YDifferentiating the whole equation with respect to time allows us to obtain the decomposition equationas follows:%∆ω =%∆p+%∆r+%∆SWhere %∆ω = %∆%∆p = %∆WN ×P C= Growth in real wages per workerGDP= Growth in labour productivityN × P Y%∆r = %∆P Y– %∆P C= Relative output price changes%∆S = Growth in labour share72 MINISTRY OF TRADE AND INDUSTRY