Inflation-Unemployment TradeoffThe Equation for Wage InflationSlide 3Slide 4A Companion Equation for Price InflationSlide 6Slide 7The Final Form Model of Wage and Price InflationSlide 9The Link Between Unemployment and Real OutputSlide 11The Full Links Among: Inflation, Unemployment and Real OutputSlide 13The Determination of Trend Potential GDPRecall the Determinants of Labor ProductivityThe Determinants of Labor ProductivitySlide 17Slide 18BRINNER1902mit12.pptInflation-Unemployment TradeoffLecture 12BRINNER2902mit12.pptThe Equation for Wage InflationRW=RP\1+A0-A1*(U-U@VOL)The rate of change of wages (RW) equalsthe rate of change in prices (RP) in the past year (“\1”) as a proxy for expected inflationplus a constant (A0) for productivity growth and other factors not defined hereminus an adjustment for the existence of involuntarily unemployed workers:total unemployment (U) - voluntary (U@VOL)BRINNER3902mit12.pptThe Equation for Wage InflationDependent Variable: @PCH(ECIWSP)Method: Least SquaresDate: 03/24/00 Time: 14:16Sample(adjusted): 1976 1999Included observations: 24 after adjusting endpointsVariable Coefficient Std. Error t-StatisticC 0.002674 0.004323 0.618574(RUC-RUFE)/100 -0.446966 0.102777 4.348886(@PCH(CPI)+@PCH(CPI(-1))+@PCH(CPI(-2)))/30.809404 0.049476 16.35956(@PCH(JQPERMH(-1))+@PCH(JQPERMH(-2)))/20.466850 0.154689 3.017989R-squared 0.936629 S.E. of regression 0.005501BRINNER4902mit12.pptThe Equation for Wage Inflation-0.020.000.020.040.060.080.1076 78 80 82 84 86 88 90 92 94 96 98Residual Actual FittedBRINNER5902mit12.pptA Companion Equation for Price InflationIf prices are a simple “mark-up” on wages adjusted for productivity “ QperH” (wages divided by productivity = unit labor costs)..P = K * W/QperHhence 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)BRINNER6902mit12.pptA Companion Equation for Price InflationDependent Variable: @PCH(CPI)Method: Least SquaresDate: 03/24/00 Time: 14:37Sample(adjusted): 1977 1999Included observations: 23 after adjusting endpointsVariable Coefficient Std. Error t-StatisticC 0.023543 0.002996 7.857116NEWCPI -0.006199 0.003771 -1.643598@PCH(ECIWSP/JQPERMH).576988 0.077744 7.421618@PCH(ECIWSP(-1)/JQPERMH(-1))0.256860 0.067738 3.791945@PCH(IMPORTPRICES/(ECIWSP/JQPERMH))0.120974 0.034859 3.470341@PCH(WPI05/(ECIWSP/JQPERMH))0.065891 0.020495 3.215051R-squared 0.969657 S.E. of regression 0.006245BRINNER7902mit12.pptA Companion Equation for Price Inflation-0.040.000.040.080.120.1678 80 82 84 86 88 90 92 94 96 98Residual Actual FittedBRINNER8902mit12.pptThe Final Form Model of Wage and Price InflationRP = B0 - B1 * (U-U@VOL) + RWAND, EARLIER,RW=RP\1+A0-A1*(U-U@VOL)THUS RP= (A0+B0) - (A1+B1)*(U-U@VOL)+RP\1OR RP-RP\1 =THE CHANGE IN INFLATION= (A0+B0) + (A1+B1)*(U-U@VOL); SIMILARLY, THE CHANGE IN WAGE INFLATION CAN BE SHOWN TO BE DRIVEN BY THE LEVEL OF UNEMPLOYMENT:RW=RP\1+A0-A1*(U-U@VOL)= B0 - B1 * (U\1-U@VOL) + RW\1 + A0-A1*(U-U@VOL)BRING RW\1 TO THE LEFT (and ignore the difference between U and U\1):RW - RW\1= THE CHANGE IN WAGE INFLATION= =(A0+b0) - ( A1+B1) * (U - U@VOL) I.E. A FUNCTION OF THE ADJUSTED LEVEL OF UNEMPLOYMENTBRINNER9902mit12.pptThe Final Form Model of Wage and Price InflationRP-RP\1 = (A0+B0) -(A1+B1)*(U-U@VOL)THE CHANGE IN INFLATION = A FUNCTION OF THE ADJUSTED LEVEL OF UNEMPLOYMENTA 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+B0) - (A1 + B1) * (U-U@VOL)Hence, U(NAIRU) = U@VOL + (A0+B0)/(A1+B1)A0 is the excess of wage growth over price growth from the wage equation: this tends to be the long-run productivity growth rate.B0 is the excess of price growth less wage growth in the price equation; this tends to be equal to the negative of the long-run productivity growth rate (i.e. prices only need to rise as rapidly as wage growth minus productivity).Thus A0+B0 = 0, and U(NAIRU) is the [email protected] Link Between Unemployment and Real OutputThe unemployment rate reflects the difference between the demand for and the supply of labor.The demand for labor is the number of employees (E) needed, with a given productivity (GDP/E) to produce a given output (GDP)–or, E = GDP / (GDP/E)The supply of labor is the number of workers (L) seeking to work at a given real wage The Potential output they can produce in a “Fully Employed economy” = “an economy operating at the “NAIRU” is called “Potential GDP” (GDP@ FE)–GDP@FE=L* (1-NAIRU) * (Productivity)–substituting from above for productivity = L *( 1-NAIRU) * (GDP/E)–hence L = GDP@FE / [ (1-NAIRU)*(GDP/E) ]Unemployment Rate = U/L = (L-E) /L = 1 - E / L=1- { GDP/ (GDP/E) } / { GDP@FE / [ (1-NAIRU) * (GDP/E) ] }=1- { GDP / GDP@FE } x (1-NAIRU)=(APPROX.) NAIRU + THE % “GDP GAP” VS GDP@FE ((GDP-GDP@FE)/GDP@FE)BRINNER11902mit12.pptThe Link Between Unemployment and Real OutputA small adjustment to this is required to reflect the short-run increases in productivity that occur during booms, and the symmetric short-run loss during recessionsSpecifically, the prior formula indicates the unemployment rate would fall a full 1% for each 1% increase in GDP (for any given GDP@FE)In fact, due to temporary shifts in productivity, the actual change is roughly 1/2 of this–In other words, on a cyclical basis, a 1% boost in output is met by firms with a 1/2% boost in employees and a 1/2% boost in temporary productivityThis relationship is known as Okun’s Law: –the change in Unemployment Rate=about half the growth rate difference between potential and actual GDP growth–or, the level of the Unemployment Rate=about half the % gap between potential and actual GDPBRINNER12902mit12.pptThe Full Links Among:Inflation, Unemployment and Real OutputThe critical relationships are:1. The change in inflation responds (with a negative derivative) to the unemployment rate2. The unemployment rate responds (with a negative derivative) to the GDP level, given GDP@FETherefore,3. The change in inflation responds (with a positive derivative) to the GDP level,
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