BRINNER112.pptInflation-Unemployment TradeoffLecture 12BRINNER212.pptThe Equation for Wage InflationRW=A0+RP\1+RQ-A1*(U-U@VOL)The rate of change of wages (RW) equals the rate of change in prices (RP) in the past year (“\1”) as a proxy for expected inflation plus productivity growth minus an adjustment for the existence of involuntarily unemployed workers:total unemployment (U) - voluntary (U@VOL) plus a constant (A0) other factors not specifically defined here Note: many coefficients expected to equal 1BRINNER312.pptThe Equation for Wage InflationDependent Variable: %ch of Wage per HourMethod: Least SquaresDate: 03/24/00 Time: 14:16Sample(adjusted): 1976 1999Variable Coefficient Std. Error t-StatisticC 0.002 0.004 0.62(U-UFE)/100 -0.45 0.10 4.34Average inflation of recent years:%ch(CPI)+%ch(CPI(-1))+%ch(CPI(-2)))/30.81 0.05 16.36Average productivity growth:%ch(QPERH(-1))+%ch(QPERH(-2)))/2where QPERH=Output per Hour 0.47 0.15 3.02R-squared 0.936629S.E. of regression 0.0055Note: The coefficient for average price inflation over the past 3 years is just under 1.The coefficient for recent productivity growth is only about .5BRINNER412.pptThe Equation for Wage Inflation-0.020.000.020.040.060.080.1076 78 80 82 84 86 88 90 92 94 96 98R esidual Actual FittedBRINNER512.pptA Companion Equation for Price Inflation If prices are a simple “mark-up” on wages adjusted for productivity (QperH) (wages divided by productivity = unit labor costs).. P = K * W/QperH hence RP = RK + R(W/QperH) ..and this markup could fall when the economy is sluggish» RK = B0 - B1 * (U-U@VOL) Then:RP = B0 - B1 * (U-U@VOL) + R(W/QperH) Additional Factors Need to be Added for Aggregate Supply Shocks Such as Oil or Other Imported Goods PricesBRINNER612.pptA Companion Equation for Price InflationDependent Variable: @PCH(CPI) consumer price inflationMethod: Least SquaresDate: 03/24/00 Time: 14:37Sample(adjusted): 1977 1999Included observations: 23 after adjusting endpointsVariable Coefficient Std. Error t-StatisticC 0.02 0.003 7.86NEWCPI Definition Shift -0.006 0.004 -1.64@PCH(ECIWSP/JQPERMH) current wages relative to productivity=unit labor costs.58 0.08 7.42@PCH(ECIWSP(-1)/JQPERMH(-1)) lagged wages relative to productivity0.26 0.07 3.79@PCH(IMPORTPRICES/(ECIWSP/JQPERMH)) import prices rel. to. unit labor costs0.12 0.03 3.47@PCH(WPI05/(ECIWSP/JQPERMH)) energy prices rel. to unit labor costs0.07 0.02 3.21R-squared 0.969657S.E. of regression 0.006245Consumer price inflation was not found to be related to the unemployment rate, so this factor is not includedTheThe sum of the coefficients on unit labor costs is also just under the expected value of 1.0.BRINNER712.pptA Companion Equation for Price Inflation-0.040.000.040.080.120.1678 80 82 84 86 88 90 92 94 96 98R esidual Actual FittedBRINNER812.pptThe Final Form Model of Price InflationIf we assume the three key coefficients actually equal 1( if we had perfect measures of the concepts): price inflation affecting wages wage inflation affecting prices) And productivity affecting both wages (positively) and price(negatively), then:(1) RP = RW-RQ+Supply ShocksAND, EARLIER,(2) RW=RP\1+ RQ+ A0-A1*(U-U@VOL)Substituting (2) into (1) yields:RP=RP\1+ RQ+ A0-A1*(U-U@VOL) -RQ+Supply Shocks=RP\1+ A0-A1*(U-U@VOL) +Supply Shocks(Note: Productivity is neutral in this formulation)OR, RP-RP\1 =THE CHANGE IN INFLATION (i.e the acceleration in prices)= A0-A1*(U-U@VOL) +Supply ShocksBRINNER912.pptThe Final Form Model of Wage and Price InflationOR, RP-RP\1 =THE CHANGE IN INFLATION (i.e the acceleration in prices)= A0-A1*(U-U@VOL) +Supply ShocksTHE CHANGE IN INFLATION = A FUNCTION OF THE ADJUSTED LEVEL OF UNEMPLOYMENT, plus or minus any external supply shocksA stable, low rate of inflation is a valuable attribute of an economy: it promotes good decision making because economic life is predictable and unbiased by continually changing pricesIf inflation is constant, RP = RP\1 and the price level is “non-accelerating”, we can compute the associated “non-accelerating rate of unemployment” or “NAIRU”.For this to hold, 0= (A0) - (A1) * (U-U@VOL)Hence, U(NAIRU) = U@VOL + A0 / A1Note that in the estimated equations, the constant terms were very close to zero, thusU(NAIRU) is the [email protected] Link Between Unemployment and Real OutputRP-RP\1 = (A0) -(A1)*(U-U@VOL) + Supply Shocks is a solid relationship. We need to create a parallel relationship between the change in inflation and output to tie into the IS-LM model. Thus, we need to understand the relationship between output and unemployment.By approximate definition, the Change in the Unemployment rate = %ch (labor force)- %ch(employment)and %ch(employment) = %ch(GDP) minus %ch(productivity)Hence Change in U = %ch (labor force) - %ch(GDP) + %ch(productivity)When demand (real GDP) rises, employers must increase output by either raising the number of employees (E) or the productivity of those already employed. In the short-run context of IS-LM analysis, the applied technology cannot change and the capital stock is also fixed. However, assembly lines can be run somewhat faster, more overtime hours can be used, employees can be asked to be more efficient, etc. Thus each 1% short-run increase in demand for GDP tends to require only a fractional % increase in employment. Also, when the economy cycles, participation in the labor force changes in response---more people look for work when times are thought to be good.Therefore the % change in the unemployment rate is less than the % change in output, but a close relationship is likely.Cyclical Relatiosnhips-5.0%-3.0%-1.0%1.0%3.0%5.0%7.0%9.0%11.0%Mar-70Mar-71Mar-72Mar-73Mar-74Mar-75Mar-76Mar-77Mar-78Mar-79Mar-80Mar-81Mar-82Mar-83Mar-84Mar-85Mar-86Mar-87Mar-88Mar-89Mar-90Mar-91Mar-92Mar-93Mar-94Mar-95Mar-96Mar-97Mar-98Mar-99Mar-00Real GDP Growth vs Year Ago-4.0%-3.0%-2.0%-1.0%0.0%1.0%2.0%3.0%4.0%Change in Unemployment RateNote: 3% GDP Growth => No U Rate Change,and Each Extra 1% Growth =>1/2% U Rate DropBRINNER1212.pptThe Link Between Unemployment and Real Output The cyclical relationship between unemployment and real growth is known as Okun’s Law: – the changein Unemployment Rate=about half the growth rate differencebetween potential and actual GDP growth– or, the level of the Unemployment Rate=about half the % gapbetween potential and actual GDPCyclical Relationships: Output, Employment, Labor
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