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NBE WO~G PAPER SERIES THE TIME-VARYING NAIRU AND ITS IMPLICATIONS FOR ECONOMIC POLICY Robert J. Gordon Working Paper 5735 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 August 1996 This research is supported by the National Science Foundation. I am grateful to Tomonori Ishikawa for research assistance and to Mark Watson for helpful discussions. This paper is part of NBER’s research program in Economic Fluctuations and Growth. Any opinions expressed are those of the author and not those of the National Bureau of Economic Research. O 1996 by Robert J. Gordon. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that fill credit, including 0 notice, is given to the source. NBER Working Paper 5735 August 1996 THE TIME-VARYING NAIRU AND ITS IMPLICATIONS FOR ECONOMIC POLICY ABSTRACT This paper estimates the NAIRU (standing for the ~on-~ccelerating unemployment) Inflation Rate of as a parameter that varies over time. The NAIRU is the unemployment is consistent with a constant rate of inflation. rate that Its value is determined in an econometric model in which the inflation rate depends on its own past values (“inertia”), demand shocks proxied by the difference between the actual unemployment rate and the estimated NAIRU, and a set of supply shock variables. The estimated NAIRU for the U.S. economy differs somewhat for alternative measures of the inflation rate. The NAIRU estimated for the GDP deflator varies over the past forty years within the narrow range of 5.7 to 6.4 percent; its estimated value for the most recent quarter(1996:Q1) 5.7 percent. In that quarter a lower NAIRU of 5.3 percent is obtained for the chain-weighted deflator. Recent research claiming that there is a three-percentage-point is PCE range of uncertainty about the NAIRU is rejected as inconsistent with the behavior of the American economy in the late 1980s and early 1990s. Robert J. Gordon Department of Economics Northwestern University Evanston, IL 60208-2600 and NBER [email protected]. nwu.edu The relationship monetary policy. between inflation and unemployment is central to the conduct of More than 35 years ago Paul Samuelson and Robert Solow (1960) coined the term “Phillips curve” at the 1959 AEA meetings, reacting promptly to the publication of Phillips’s seminal (1958) article. A few years later Milton Friedman “natural rate of unemployment,” which more recently has come to be known by the familiar acronym “NAIRU,” standing for the ~on-&ccelerating (1968) coined the term ~nflation Bate of ~nemployment. at any given time there exists a unique NAIRU, then the Phillips curve tradeoff at that unemployment rate. The Fed cannot make the actual unemployment the NAIRU in the long run, but it can maintain setting the actual unemployment rate of inflation, a stable rate of inflation rate equal to the NAIRU. the Fed desires to reduce the inflation is vertical rate differ from if it succeeds in If instead of maintaining rate toward If a stable zero or some other target, then it needs to keep the actual unemployment rate above the NAIRU. whether the Fed needs to know the value of the goal is steady inflation or lower inflation, Either way, the NAIRU. The NAIRU is not carved in stone. In Friedman’s is “ground out” by the set of ‘Walrasian” macroeconomic the structure change. and institutions of product There is a perception if so the NAIRU has doubtless exhibited pronounced (1968) interpretation, the NAIRU relations in the economy, including and labor markets, and any of these relations can that much about the economy has changed in the 1990s, and changed as well. cycles over the postwar Indeed, period, as we shall see, the NAIRU has albeit within a surprisingly narrow range. The Fed acts as if it already accepts the fact that the NMRU adapted policy procedures that implicitly incorporate new information can move and has to update previous The Time-Varying estimates of the NAIRU. around Whereas in early 1994 it implicitly believed that the NAIRU was 6.0 percent and sharply raised short-term that the actual unemployment not accelerate in response to an average unemployment dynamic simulations of regression rate. 2 Because these simulations without any appreciable drift, I had submitted were capable of sample the accuracy of such post-sample simulations as evidence that the NAIRU was still 6.0 percent. acceleration of inflation that occurred in 1988-89, 6.0 percent for a period of three years, is consistent and I equations rate accurately for many years after the end of the regression e.g., 1987-94, did rate well below 6.0 percent.1 to assume that the NAIRU was 6.0 percent, by running the value of the inflation tracking the inflation period, repeatedly for most of 1995 interest rates to drift down slightly when inflation For many years it was reasonable that predict interest rates when it correctly predicted rate was about to fall below 6.0 percent, and early 1996 it allowed short-term tested that assumption NAIRU, Page 2 when the unemployment The substantial rate fell below with the view that the NAIRU was at 6.0 percent or above as recently as 1988-89. 1. Even though the actual unemployment rate averaged 5.6 percent in the 21 months ending in May, 1996, below the Fed’s previous NAIRU estimate of 6.0 percent, the inflation rate did not accelerate. Indeed, one key measure of inflation, the personal consumption deflator (on the new chain-weighted basis) decelerated. The implicit price deflator for personal consumption expenditures on the new chain-weighted basis rose 2.7 percent in 1992, 2.6 percent in 1993, 2.4 percent in 1994, 2.4 percent in 1995, and only 1.9 percent in the four quarters ending in 1996:Q1. 2. The inflation equation was developed in a series of papers, including Gordon (1970, 1975, 1977a, and 1982b). King-Watson (1994) have called this approach the “Gordon-Solow model,” citing the first of my papers and Solow’s 1969 book. In order to determine whether the inflation relationship has changed, I have maintained unchanged the set of variables, lag lengths, and other features of the equation introduced in Gordon (1982b) and Gordon-King (1982). The most recent assessments of the performance of this equation are contiined in Gordon (1990a, 1994). The Time-Varying However, reduced numerous factors have changed the NAIRU, and indeed since 1988-89 in a way that may have the absence of an acceleration of inflation suggests that the NAIRU may well have fallen below 6.0 percent. and their penetration in the labor force continues under intense pressure from consumers The rest of the industrial to decline. and foreign competitors world has experienced as arguing that the economy at all” (Stevenson, Manufacturers have been to restrain price increases. and there is ample Business executives are quoted has changed drastically in the last ten years. John F. Welch Jr. recently stated that ‘There is no inflation in 1995-96 Labor unions are weak a sluggish recovery, foreign capacity to provide supplies to U. S. manufacturers. NAIRU, Page 3 General Electric’s . . . there is no pricing power 1996). The “Quiescence” of Phillips Curve Research Has the NAIRU declined? Surprisingly, macroeconomists If so, from what level a decade ago to what level today? have thus far provided be taken “off the shelf’ by policymakers little research has been conducted no answer to this question who need to know the answer. on the U. S. inflation contrast to feverish research activity in the 1960s and 1970s. on the “quiescence” of the field. One explanation process is so stable, and the models developed have been no behavioral economists” relation, mysteries to solve. have continued process For remarkably in the past decade, King-Watson in (1994) comment of this void is that the U. S. inflation in the early 1980s work so well, that there In the words of King and Watson, to view the Phillips curve as an essentially once the original econometric that can “Keynesian intact structural models of the 1960s were amended “to represent The Time-Varying supply shocks and build in a zero long-run been accomplished research, (as in Gordon, except periodically remarkable tradeoff” (1994, p. 160). NAIRU, Page 4 Once this task had 1977), there was no further agenda warranting checking that the relation remained continued stable, and indeed “the feature of the Phillips curve in the post war period was its stability” (Watson- King, 1994, p. 160). In this interpretation, macroeconomics has split into two camps. from the Keynesians are the “neoclassical and monetarist Sargent 1978) dismissed the long-run negative between models of the late 1960s contrasted 1970s. new breed tradeoff and did not notice, of post-1975 and included Phillips supply-shock negative or positive correlation the economy neoclassical of taking economists business-cycle that incorporated a vertical long-run the model to generate depending of a either a on whether or supply shocks. as the variable to be determined of aggregate nor explained. in the model (whether variety), the determination in the data of the the resurrection to real theories equations by the much less take seriously, variables that allowed behavior of inflation was neither explored by the set of behavioral predicted to empirical work on between inflation and unemployment, inflation turned and unemployment stopped paying attention curve estimates was subjected to demand Instead inflation failure on a grand scale,” since with the distinctly positive correlation At that point neoclassical economists the Phillips correlation economists, ” They (notably Lucas- the Phillips curve as “econometric correlation Across the street by their fluctuations models, in which the While real output was determined of the Lucas “surprise” or real- of the price levei was left unspecified. Implicitly, The Time-Varying the price level was left as a residual, i.e., as the level of nominal NAIRU, Page 5 GDP (in turn often equal to the money supply plus a stochastic error term) divided by whatever level of real GDP was determined by the model. Phillips curve approach, This treatment was the diametric to that implied in the the inflation rate, while the growth rate of real GDP is implicitly a residual equal to the rate of nominal GDP growth in which an equation opposite is specified to determine minus the rate of inflation. Agenda for this Paper The NAIRU is defined as the unemployment under a specified set of conditions. It is meaningful the inflation process. the inflation process that incorporated rate consistent with steady inflation only within a well-specified This paper begins by describing and resurrected the mainstream “triangle model” of the Phillips curve from what Lucas and Sargent (1978) had called the “wreckage” of the early and mid 1970s. NAIRU in terms of this model and examine We define the both what the model includes shocks and rate of change effects) and what it excludes model of (e.g., supply (any explicit role for expectations or wages). Then, instead of simply assuming a value for the NAIRU and testing the validity of that assumed econometric intituitively value in dynamic technique post-sample that allows a time-varying NAIRU this paper adapts an explicit to be esti~ted. We show why some previous authors, notably Staiger et. al. (1996), have found estimates of the NAIRU to be highly imprecise, of ambiguity simulations, which surrounds and we propose a simple criterion the topic. to clear the cloud We emerge with a set of alternative NAIRU The Time-Varying estimates for the 1955-96 on which inflation period which differ only moderately measure, specification, NAIRU, Page 6 from each other depending and sample period is used. As we shall see, the most interesting for the current period relate to the contrasting differences among the proposed behavior of alternative NAIRU series price indexes, and we suggest that the Fed needs to decide which inflation index it is trying to stabilize, e.g., the GDP deflator, the deflator for Personal Consumption Expenditures Price Index. After we identify the alternative NAIRU series, we then use preferred of the inflation equation to compute dynamic simulations on the assumption concludes of alternative by examining (PCE), or the Consumer of the inflation rate in future years paths for the actual unemployment implications versions rate. The paper for the past, current, and future conduct of monetary policy. Several important entirely concerned quite different topics lie outside of the research agenda in this paper. with the inflation behavior of inflation estimates the time-varying process developed process in the United States and does not treat the and unemployment in Europe in my previous work; it does not develop Second, it of monetary lagged responses policy such a model from scratch. rate should be the Fed’s target but does not inquire into the methods by which the Fed should attempt to accomplish subsequent or Japan. NAIRU within the context of the “triangle” model of the inflation Third, it asks which unemployment the channels First, it is that of output, To preview the main conclusions, link changes that goal, i.e., it does not study in the short-term income, employment, interest rate to and unemployment. at any given time there is a NAIRU for the U. S, The Time-Varying economy. Our alternative NAIRU estimates differ moderately the exact fevel of the 1996 NAIRU, depending regarding to be used. The alternative substantially since 1988-89, unemployment opening up the opportunity rate than was feasible then. marginally better explanation Further, among among primarily estimates all support the conclusion NAIRU, Page 7 themselves on the inflation index that the NAIRU has declined for the Fed to maintain the time-varying a lower NAIRU provides a of inflation behavior in the 1990s than the previously assumed fixed NAIRU of 6.0 percent. The “Triangle” Model of Inflation between the rate The “Phillips curve” has become a generic term for any relationship of change of a nominal price or wage and the fevel of a real indicator demand in the economy, relation was amended emerged such as the unemployment by incorporating was an interpretation of inflation Long ago, the simple Phillips supply shocks and a zero long-run the dependence inertia, demand, In this framework tradeoff.3 of the inflation lower-case letters What rate on a tripartite a general specification designate first set and supply. for the rate of price change (p,) is: (1) Pt = a(L)p~.l + b(L)D~ + c(L)z~ + et. Here of of the Phillips curve that I have called the “triangle” model — a label summarizing of basic determinants: rate. of the intensity differences of logarithms, upper-case letters 3. Schultze (1975) and Gordon (1975) introduced explicit variables to isolate the effect of food and energy prices and price controls on the U. S. inflation rate. The Time-Varying designate logarithms of levels, L is a polynomial demand so that D,=O indicates the absence of excess demand), z, is a vector of (normalized supply shock variables (normalized et is a serially uncorrelated of basic determinants, demand in the lag operator, NAIRU, Page 8 D, is an index of excess so that Zt =0 indicates an absence of supply shocks), and error term. The “triangle” rubric is associated with the three sets respectively “inertia” (i.e., the influence of the lagged inflation terms), (the D, terms), and supply (the z, terms). If the sum of coefficients “natural rate” of the demand While the estimated on lagged inflation equals uni~ variable (Wt ) consistent sum of coefficients with a constant on lagged inflation (see Tables 1-3 below), that sum must be constrained (Z ~ = 1), then there is a rate of inflation. is usually roughly equal to unity to be erectly natural rate of the demand variable to be calculated from (1). unity for a meaningful Among the demand variables that have been entered as proxies for D~ are the “output gap” (log ratio of actual to natural or potential real GDP), the “unemployment rate of unemployment gap” (difference between the actual and natural — or NAIRU), and the rate of capacity utilization. As written in (1) the model is incomplete, exogenous, since there are two endogenous even if the supply shock variables (z,) are variables, the inflation rate (PI) and the demand variable (D~). The model can be closed with one or more equations process. “output The simplest approach gap,” treats as exogenous defines D, as the log output the growth rate of nominal specifying the demand ratio (R, = /n&l ~, )) or GDP in excess of natural output growth (“excess nominal GDP growth”), and closes the model with a second equation which is simply an identity relating the change in the output gap to inflation and excess The Time-Varying nominal GDP growth. textbooks, This identity, used in one form or another in many macroeconomics states that the change in the output gap equals the growth rate in nominal (x,) relative to natural output growth R, - R,.l The model consisting exogenous exogenous NAIRU, Page 9 demand = xt-y*t (y’,), minus the inflation rate: -pt. (2) of (1) and (2) has two equations shock variable is excess in two unknowns, nominal GDP growth & and p,. Interpretations (xi - y*, ), the in previous time periods. of the NAIRU In this paper we are interested that is consistent in estimating with steady inflation. to (1) with the unemployment the NAIRU, i.e., the unemployment The equations gap substituted estimated the unemployment and the time-varying for Dt: gap is the difference NAIRU @t-U~t ). rate in this paper are identical (3) Pt = a(L)pt.l + b(L) Wt-wt ) + c(L)zt + et, exogenous, The supply shock variable is the vector Z1, an d the lagged elements pf.l and &.l are predetermined where GDP between If excess nominal the actual unemployment GDP growth the model can be closed by adding two equations, and the other of which is an “Okun’s Law” equation relating rate is again taken as one of which is (2) above, the unemployment gap to The Time-Varying the output gap.4 The NAIRU, unemployment inflation. standard or alternatively rate which The structure the “natural rate of unemployment,” is consistent of (3) suggests version is the “no-supply-shock” consistent with steady inflation emerges from the estimation with wo steady (nonaccelerating alternative concepts steady inflation NAIRU, that is, the unemployment The rate which is of (3) with the z, “supply shock” variables included to control For example, if the inflation rate has been steady in the rate is the “no-supply-shock in the absence of supply shocks. increase sharply in response that or decelerating) of the NAIRU. recent past, but then suddenly exhibits a “spike” that is entirely explained unemployment is simply in the absence of supply shocks. This is the NAIRU that for the influence of supply shocks. the current NAIRU, Page 10 by the Zj variables, NAIRU” that is compatible An alternative unqualified to an adverse supply shock by the estimated with NAIRU would amount of the shock [c(L)zJ divided by the sum of the b coefficients. focus By taking excess nominal GDP growth as exogenous, the triangle model allows us to on of building determinants the inflation of aggregate macroeconomics the determination process without demand. the distraction Admittedly, this simplification of the sweeps two-thirds under the rug, And it ignores channels by which inflation of nominal GDP, which may cause econometric a model of feeds back into bias in inflation equations 4. Using the symbols in the text, an Okun’s law equation that closes the model would be: U, - ~, = O(L)& + c,. Empirically the sum of the 8 coefficients has been around -0.5 for most of the postwar period, although in the 1990-95 subinterval that sum has been close to -1.0. The Time-Varying in which nominal proposition, GDP appears directly in the presence of contemporaneous and of supply shocks that are imperfectly equation coefficient (1) that use nominal on nominal is biased toward measured, the smaller zero, The more the bias.5 unemployment by finding estimates of the triangle-type accurately In their equation Alternatively, using the the influence consideration of the Granger-causes on the unemployment of supply shocks endogeneity support inflation, is of the the inclusion of but they do not variable in the presence supply shocks.G In general, supply shocks create an omitted variable problem in the traditional curve specification inflation (D~) variable will yield a like (2), King-Watson that unemployment the issue of bias in the coefficient measured measured, GDP gap as a proxy for the demand variable will yield a coefficient rate in an inflation of imperfectly As a general feedback from inflation to nominal GDP as a proxy for the demand unemployment consider variable. GDP which is biased away from zero. output gap or unemployment which an an explanatory NAIRU, Page 11 that includes only lagged inflation and the unemployment Phillips gap.’ One 5. Formal measures of the bias are developed in Gordon (1990b, Table 1, p. 1121). 6. “More specifically, in a reduced form vector autoregression, past unemployment is important for predicting current inflation but past inflation contains little information about current unemployment” (King-Watson, 1994, p. 161). 7. While early work on the Phillips curve focussed on wage behavior, and required a “markup” equation to relate inflation to wage changes, it has proven more useful since the mid-1970s to estimate a reduced-form equation in which inflation is directly related to unemployment, thus eliminating the need to be concerned with the two-way links between wages and prices. A complete set of wage equations for both the U. S, and for Germany, estimated with the same specification as in this paper, can be found in Franz-Gordon (1993). That paper determined that the U. S. wage NAIRU for 1990 was 6.2 percent, almost exactly the same as estimated in this paper for the GDP deflator by the time-varying approach described below. The Tim~Varying expects inflation extraneous to be negatively related to unemployment, positive correlation between inflation but if supply shocks create an and unemployment variables are inclu&d to proxy for the influence of supply shock, unemployment unreliable will be biased toward zero, and the resulting predictions NAIRU, Page 12 and no e~licit then the coefficient equation on is likely to produce in periods when supply shocks are absent. Rate of Change Effects In previous research I have found that wage and price change depend on both the level and change in the demand variable, i.e., the output gap or unemployment gap.a The role of the change effect is automatically allowed to enter as long as the gap variable is entered with more than one lag. For instance, if the gap variable is entered as the current value and one lagged value and the coefficients are estimated as -0.5 and +0.3, respectively, then this is identically equal to an equation of the gap are entered separately, in which the current level and current change with respective coefficients of -0.2 and -0.3. In light of the high statistical significance of the change effect in the results discussed below, time-series equations that do not allow for the change effect (either by entering it directly allowing the level of the gap to enter with one or more lags) are misspecified. effect is particularly important in explaining a result that I have found previously macroeconomic price behavior or by The change in the 1930s, and that Romer (1996) has recently substantiated. 8. I first noted the importance of the rate-of-change effect in Gordon (1977a, pp. 270-1). The Time-Varying Missing Eiements: Expectations The original unemployment. Phillips bter, article and Wages was about the relation These are issues of substantive adaptive above has no expectations Much attention is deliberate. to the interpretation lags in the formation price and wage inertia is compatible with rational can be delayed by wage and price contracts, level. promptly the and rationally formation upward movement explained. be~een yet everyone contracts, form about the aggregate price the dynamics delivery lags, or anything of else. The relationship of prices to wages markup equation of the type Labor’s share in national income exhibits a strong the mid-1960s The Fed’s goal is to control Price is the omission of wages in the triangle on wages was a mistake. literature. issues. can terms in (1) and (3) is to capture has changed over time and is not well described by a constant used in the eariy Phillips-curve and based on full information formation, of price and by the time needed for cost ~bie, as the omission of expectations The earlier fixation in the late The speed are two total] y different input-output related to expectation As important model. through The role of the lagged inflation inertia, whether and no wages. was diverted expectations. adjustment expectations Phillips Since then we have learned that of expectations. and the speed of expectation to percolate and of the lagged effect of prices on wages as adjustment increases wage changes significance. The omission of expectations reflecting between expected inflation was added and we had the “expectational curve. ” But the triangle model as summarized 1960s and early 1970s NAIRU, Page 13 and early 1970s that has not been adequately inflation, not wage growth, and models with The TimeVarying NAIRU, Page 14 separate wage growth and price markup equations do not perform as well as equations (1) and (2) above in which wages are implicitly solved out and only a reduced estimated. By treating the relationship change to unemployment, Samuelson of inflation the triangle approach to unemployment, returns form of a relationship implications of the original quadrant. The earliest credit for ignoring between the unemployment wages is the Phiilips curve in the rate and price changes, not wage changes. of the Triangie Model Whether the unemployment like (1) or (3) determining gap or some other demand variable enters an equation the inflation rate, this equation, GDP is exogenous excess growth To control of nominal together with the assumption that as in (2), generates several clear implications. In the long run inflation phenomenon.” equivalent rather than of wage to the framework claimed by Irving Fisher (1926), whose neglected article discovered 1. form is and Solow article (1960) that coined the term “Phillips curve” and plotted U. S. data on the inflation-unemployment nominal like inflation, is “always and everywhere policy needs a nominal GDP itself. Targeting an excess nominal anchor, the no-supply-shock most plausibly NAIRU, level of “natural” or “potentiai” real GDP, will lead to accelerating decade like the 1970s when supply shocks are significant, GDP serially correlated, the or the inflation in a and positive (i.e., adverse). 2. inflation; There is no special connection between the growth in the money supply and any effect of money growth on inflation is shared by an identical effect of velocity The Time-Varying growth NAIRU, Page 15 on inflation. 3. In the short run, fluctuations loops on a diagram plotting in excess nominal inflation against the unemployment inertia, i.e., the role of the lagged dependent of the inflation 4. unemployment gap. and unemployment shocks can cause a positive The observation (3) in slowing the response gap. between inflation and that the Phillips curve correlation between inflation correlation was positive rather than negative in the 1970s is consistent triangle model, due to its explicit treatment 5. The triangle model is resolutely by the finite Phillips curve adjustment GDP growth. With excess nominal unemployment gaps are determined incorporate lead to clockwise gap. The loops come from variable in equation rate to a change in the unemployment Supply GDP growth the implication man that “unemployment Keynesian. Prices are prevented (b) from mimicking GDP growth as a residual. that King-Watson treated changes in nominal as exogenous, However, the output in oil prices) raises the inflation GDP growth, and the triangle model does not (1994) attribute by aggregate demand by inertia and to their “Keynesian” straw disturbances.” Instead, ktb demand and supply shocks influence both the inflation rate and the unemployment any given level of excess nominal with the of supply shocks like the rise in oil prices. coefficient is dominated the rate. For an adverse supply shock (e.g., an increase rate, reduces the output gap, and raises the unemployment gap. What theoretical story is consistent with the mainstream triangle implicitly are price setters and demand takers. Although the Patinkin-Clower model? Agents disequilibrium The TimeVarying framework, as developed by Barre-Grossman (1976) and others, setting, it is the right model of quantity determination macroeconomists curves by constraints while forgetting of price Agents are pushed off notional that spill over from rationed tend to brush off the disequilibrium of price determination, has no model given whatever sources of inertia and finite Phillips slopes prevent prices from clearing markets. supply and demand NAIRU, Page 16 framework markets. Today’s because it has no theory that it has the right theory of output determination. Validation of the Triangle Modei The triangle econometrics model may be unique in that its textbook and theory came after that. The textbooks version came first, and the were published equations were set out in 1976.9 The econometric version, developed validated experienced in 1981-87 percentage corresponded parameters through when loss in output associated almost exactly estimated through 1987 in post-sample of inflation the sacrifice to what with ratio the deceleration had been predicted the end of 1980.10 dynamic simulations observed in 1987-90 and the deceleration Versions in 1978; the basic in the late 1970s, was by the economy of inflation in advance (i.e., the that occurred) on the basis of of the equation estimated tracked quite precisely the acceleration of inflation that occurred in 1990-93. 9. See Gordon (1977b), a paper presented at the AEA meetings in October, 1976. A diagrammatic version originated in a classroom handout that Rudiger Dornbusch developed at the Chicago Business School in early 1975. Both my version and that of Dornbusch combined a Phillips curve, long-run neutrality, a nominal GDP identity like (2), and a role for exogenous supply shocks. 10. econometric deviation of was reduced Gordon-King (1982, Table 5, line 3) computed a sacrifice ratio of 6.2 from their version of the triangle model. Using the data avaiiable at the time, the cumulative actuai from potential output during the period 1980-87 was 26.2 percent and inflation by 4.1 percentage points from 1979-80 to 1985-86, for an actual sacrifice ratio of 6.4. The Time-Varying The positive performance of the triangle model NAIRU, Page 17 stands in sharp contrast shambles in which the Phillips curve literature found itself in the mid-1970s. of departure for Lucas’s new classical revolution A central point was the failure of the 1960s Phillips curve. In the language of Lucas and Sargent (1978, pp. 49-50), “that these predictions incorrect, and that the doctrine on which they were based is fundamentally simple matters of fact . . . the task which faces contemporary [is] that of sorting through the wreackage. . . of that remarkable Sargent wrote those lines; it has survived and thrived, Barro (1978) and others to valididate Estimating aground a macroeconomics textbook. force) event called the while empirical attempts by Robert proposition inertia. a time series for the NAIRU has been published My NAIRU series increases from the 1950s by using a demographic when in the late 1980s (Gordon, reversal of the 1980s (notably a reduced the NAIRU accordingly, I found other than its empirical performance, to 6.0 percent intellectual in my to the 1970s, adjustment to the rate to reflect the rising share of teenagers and females in the labor force had reduced justification of inflation Perry’s (1970) innovation during that era. However, the demographic of the business cycle the new classical policy ineffectiveness on the bedrock two decades George unemployment flawed, are now Time-varying NAIRU For almost following students were wildly The triangle model was in print in its present form before Lucas and Keynesian Revolution.” failed, running to the for the entire period after 1978. 1990) I tested to see whether share of teenagers that it had not. in the labor Without any I arbitrarily set the textbook NAIRU equal The NAIRU series that combines the The Time-Varying demographic adjustment 6.0 percent thereafter the relative through is henceforth performance 1978 with an assumption NAIRU, Page 18 that the NAIRU is conswnt at called the “textbook NAIRU series.” This paper assesses of the textbook NAIRU series and an alternative (’W’) NAIRU series that bases changes in the NAIRU on time-varying time-varying parameter estimates. Form of the Inflation Equation The estimation of the TV-NAIRU combines the above inflation equation here, with an explicit specification p, = (3), repeated of the TV-NAIRU: a(~)p,.1 + b(L)(u,-@, ) + c(L)z, + e,, (3) w,= UN,.,+ Et. (4) In (3) the error term ●, is iid with a mean of zero and a standard the standard deviation o, = O, then ~t is constant. E, each quarter. UNt to vary each time period, then the TV-NAIRU standard variation “stochastic time-varying Gaussian maximum previously applied likelihood The following would be free to jump up and down equation. regression by Hamilton (1994). using a very different (1995) and Staiger, Stock, and Watson are the key elements The model of the inflation The sample period is 1955:2-1996:1, (3)-(4) is a model” that can be estimated as described to the issue of the NAIRU, King, Stock, and Watson previous papers. methods When When a= # O, the model allows the in the inflation parameter of o.. If no limit were placed on the ability of NAIRU to vary by an amount and soak up all the residual deviation version using It was of (3), by (1996). equation or 164 quarters. (3), as developed All right-hand-side in The Tim~Varying variables are allowed to enter with unconstrained to be identical to those in Gordon to unity, inflation NAIRU ~, - ~, changes distributed lags. NAIRU, Page 19 Lag lengths are chosen (1990).11 Note that with a sum of a(L) coefficients remains constant in a steady state with the unemployment equal rate at the =0) and with supply shocks absent (z,= O). Supply shock variables include in the relative price of imports, the change in the relative price of food and energy, 12and the change in the real effective foreign exchange rate.13 Dummy variables are included for the “on” and “off’ effects of the Nixon price controls. These dummy variables, and indeed all the other variables, are defined exactly the same as in all my papers starting with (1982 b). Also included is the difference between productivity growth and its trend, reflecting the fact that, while most of any cyclical increase or decrease in productivity is reflected in a movement to in profits in the same direction, a small fraction remains 11. The only smoothing structure imposed on the lag distributions involves the lagged dependent variable, where 24 lagged terms enter. Rather than estimating 24 unconstrained coefficients, the lagged dependent variable is entered as a series of four-quarter moving averages of rates of change, e.g., the first variable is a four-quarter average of lags t-1 to t-4, the next t-5 through t-9, etc. The coefficients on the individual moving averages are unconstrained. Exclusion tests indicate that the moving averages representing lags 13 through 24 enter with a significance level of between 1 and 2 percent in the two equations displayed in Table 1 for the sample periods 1955-96 and are thus highly significant. 12. The food-energy effect is defined as the difference of the rate of change of the chainweighted consumption deflator minus the rate of change of the chain-weighted consumption deflator net of food and energy. Chain-weighted deflators are available back to 1959 and are linked to the implicit deflator prior to 1959. 13. An additional supply shock variable, the change in sensitive raw materials prices, BCD series 99, was tested and found to be insignificant, with a t-ratio below 1. footnote 7). See Gordon (1994, The TimeVarying influence the inflation rate in the opposite Data on Unemployment Figure 1 displays direction.14 and infiation the actual unemployment difference between the actual unemployment unemployment 1969-70 business cycles, with short back-to-back that barely nudged the actual unemployment More excess demand followed in 1973-74, 1973-74, Another followed cycle occurred the U. S. National the context nominal NAIRU is the textbook recessions gap tells in 1957-58 by the mild rate above the NAIRU. in the late 1980s, with excess demand gap during 1991-93 comparable and another GDP growth, period of price indexes from which we will calculate three The chain-weighted GDP deflator (the basic deflator concept in Income and Product Accounts since early 1996) is convenient of the triangle to late 1994 and early 1996. Figure 2 compares three alternative NAIRU series. The followed by the severe recessions of 1974-75 and by a positive unemployment mild excess demand between alternative rate and the textbook NAIRU. and then a long period of excess demand in the 1960s followed recession 1981-82. rate and the textbook gap (separately dispiayed below in Figure 4). The unemployment a familiar story of poswar and 1960-61, NAiRU, Page 20 model, since it makes the definition and the inflation rate in equation linking output (2) above hold exactly. could be made that it makes more sense for the Fed to stabilize consumer to use in growth, A case prices than GDP 14. The productivity deviation variable was first introduced in exactly the same form in my (1970) paper. The productivity deviation is defined as the log ratio of actual nonfarm private output per hour to a Ioglinear piecewise trend running through 1950:Q2, 1954:Q4, 1963:Q3, 1972:Q2, 1978:Q3, 1987:Q3, and 1994:Q3. The 1987-94 growth rate of this trend is 1.07 percent per annum. The Tim~Varying NAIRU, Page 21 prices, and for this reason we compute alternative NAIRU series for the chain-weighted deflator, also shown in Figure 2. For reference is shown a third series, the inflation CPI-U-X 1.15 All three series show the mme basic cycles of acceleration the inflation (1974-75 rate, although and 1979-81) than the GDP deflator, there are notable the consumption differences. and in 1980-81 they rise further. rate of and deceleration In both supply-shock deflator and CPI inflation PCE in episodes rates accelerate earlier On average consumer price inflation was more rapid than GDP inflation from 1987 to 1994, and this is the counterpart of the fact that the real wage grew less rapidly in terms of consumer product prices. consumer The opposite price inflation smoothness completely occurred was slower than inflation Alternative Time-Varying As indicated phenomenon during prices than in terms of 1955-60 and 1965-73, when in the GDP deflator. NAIRU Series above, the model (3)-(4) requires that an assumption of the computed TV-NAIRU series. An assumption be imposed on the of a, = O implies constant NAIRU wries of 6.0 percent, as shown by the horizontal 3. At the other extreme an assumption a line in Figure of aC = 0.4 implies a highly variable NAIRU series, as shown by the line with the long dashes in Figure 3. In between are series with assumed standard deviations the standard of 0.1 and 0.2. deviation This problem Which of these and other possible assumptions about should we make? is analogous to the choice of a smoothness parameter for the Hodrick- 15. This hybrid series is equal to the CPI before 1967 and aher 1982, while between 1967 and 1982 substitutes the current rental-equivalence approach for owner-occuped housing in place of the official CPI pre-1983 treatment that is universally regarded as erroneous. The Time-Varying Prescott filter so often used to detrend deviation variables. may not be the same for every variable or topic. paraphraw Milton Friedman, of the economy, The most sensible standard If the NAIRU is viewed, as “ground out” by the macroeconomic then it should shift slowly. NAIRU incorporated inflation time-series into equation NAIRU, Page 22 structure to and behavior This is especially true, since the concept of the (3) is the unemployment rate consistent with steady in the absence of supply shocks. Allowing a shift in the NAIRU of 0.1 percentage point per quarter might be considered as excessively rapid. implausible; reasonable and of 0.4 percentage The zig-zags in the series assuming a standard why should the no-supply-shock we propose points per quarter deviation of O.4 appear NAIRU jump up and down from quarter to quarter? In essence, using a “smoothness presented by the various NAIRU series in Figure 3. We allow the NAIRU to move around as much as it wants to, subject to the qualification (negative serial correlation) As shown movements the ambiguity that sharp quarter-to-quarter in the rest of the paper, we wlect a standard deviation in Figure 3, this results in a NAIRU series that exhibits but just avoids sharp quarter-to-quarter zig-zags. in the mid-1950s to a minimum percent between 1967 and 1972, declines briefly between of 5.3 percent around hump of about 6.5 percent between percent in the final quarter, Figure 4 compares zig-zags are ruled out. In the series developed of 0.2, prior” to reduce (uc) substantial It declines from 6.0 percent 1962, rises to a plateau of about 6.2 1973 and 1978, then exhibits a 1978 and 1982, and then drifts down gradually to 5.7 1996:1. the unemployment gaps implied by the textbook NAIRU and The Tim~Varying NAIRU, Page 23 various TV-NAIRU series. We see that all the TV-NAIRU series indicate substantially excess demand than the textbook the TV-NAIRU somewhat wries corresponding less excess demand Previously (Gordon, expansion and assumption of 6.0 percent. textbook 1965-70, to a standard than the textbook and 1979-80. deviation 1990-91 recession period series. was consistent with Indeed, we shall see that the textbook rate in a dynamic simulation that this evidence presented NA.IRU prior to 1987 or so. For 1995-96 of 0.2 and 0.4 indicate 1994) we argued that the behavior of inflation job of tracking the inflation 4 demonstrates series in 1955-57, previously The textbook the in the 1988-89 textbook NAIRU NAIRU does a very good applied to 1987-96. is not sufficient NAIRU performs But Figure to support most of the period prior to 1987, the econometrically Understanding derived TV-NAIRU the well after 1987 simply because during that interval it happens to be quite close to the 7V-NAIRU. higher than the textbook more During is substantially NAIRU. the Ambiguity in Bounding the NAIRU Staiger, Stock, and Watson (1996) have cast doubt on the enterprise NAIRU, concluding that “a typical 95V0 confidence percent to 7.7 percent . . . . This imprecision of estimating the interval for the NAIRU in 1990 is 5.1 suggests caution in using the NAIRU to guide monetary policy.” Interestingly, our NAIRU estimate for the GDP deflator, using a standard deviation of 0.2, is 6.2 percent for 1990, close to the midway point of the Staiger et. al. band. Figure 4 displays five different unemployment gap series, that is, the actual The Time-Varying unemployment rate minus five alternative NAIRU series. almost the same, are very highly correlated, as well as each distinguished smoothness other. from Accordingly, the other, criterion leading proposed ambiguity regarding differences alternative measures acceleration, constancy, equations criteria, this ambiguity to choose between alternative see, the remaining among statistical gap series look that fit about one to the Staiger et. al. conclusion. above cuts through rather than a statistical criterion The alternative and resuit in inflation by standard NAiRU, Page 24 cannot However, which NAIRU series. exhibit the by using an economic As we shall the NAIRU for the very recent period of inflation, be differing concerns degrees of or deceleration. Estimated Equations for the GDP Defiator The estimated equations each are estimated series (textbook dependent for 1955-87 in the four columns of Table 1. Two versions and 1955-96, corresponding and TV with a, = 0.2). (inertia) variable of the correct are presented sign. Estimated and on the unemployment No constant is included, sums of coefficients alternative version gap zig-zags, indicating of the equation change in the unemployment level, the coefficient in column gap are entered NAIRU on the lagged gap are always highly significant and an essential element demand variabie is defined as a deviation from the NAIRU. on the unemployment to the two alternative of the approach if the The pattern of lag coefficients the presence of a rate of change effect. (4), in which the current In an level and current instead of the current and four lags on the on the change is -0.99 with a t ratio of 4.0. The significance of the various supply variables differs, depending on the sample The Tlm&Varying period and on the length of the LDV distribution, percentage-point excess of productivity NAIRU, Page 25 but they all have the correct sign. A one- growth above trend reduces inflation percent. A one-percentage-point inflation by 0.06 to 0.09 percent, not far from the average share of imports in GDP during the sample period. through Between 30 and 40 percent of the food-energy to inflation real exchange increase in the relative price of imports by about 0.1 in the GDP deflator. first year. The Nixon explaining the dynamics of inflation during the 1971-75 that the TV-NAIRU point appreciation in the by about 0.1 percent within the “on” and “off’ dummy variables continue the middle of Table 1 indicate relative price effect feeds And a ten percentage rate of the dollar reduces domestic inflation raises domestic to be essential elements period. equation about 17 percent lower than the textbook NMRU equation, in The summary statistics in has residual variance that is in both the 1955-87 and 1955- 96 sample periods. The next-to-bottom versions of the equations to sum to unity. 1987:3-1994:3, alternative section of Table 1 lists the root-mean-squared in which the sum of coefficients on the LDV have been constrained These RMSE’S are shown and 1994:4-1996: for the TV-NAIRU versions. in 1955-57 for four sub-periods 1) in order NAIRU series. As would be expected, period, indicating by the textbook series. (1955-70, the measures of fit are uniformly of the superior in fit is during the pre-1970 NAIRU version mis=s an important namely that excess demand was substantially An important 1971-87:2, to assess the relative performance The largest relative improvement that the textbook and 1965-70, errors (RMSE) of result is that the equation source of inflation greater than implied errors are substantially The Time-Varying smaller during 1987-94 and in 1994-95 than the average standard sample period. This indicates that the basic structure NAIRU, Page 26 error for the entire of the inflation equation, more than fifteen years ago, has proven to be very successful in tracking quite different sets of economic as specified inflation during conditions. The final section at the bottom of Table 1 lists mean errors and RMSE’S for dynamic simulations in which the LDV is fed back endogenously Separate errors are listed from the same simulations the actual unemployment over the period 1987:4-1996:1. for the final six quarters during which rate fell below 6.0 percent, 1994:4-1996:1. The results in the left- hand column, based on the textbook NAIRU, uses absolutely no information 1987:1 interval to estimate NAIRU, uses post-1987 other post-1987 the coefficients. information The results in column from the post- (2), based on the TV- to estimate the NAIRU using model (3)-(4) but uses no information. When actual inflation turns out to be above the simulated a positive mean error, and this occurs for 1987-96 rate of inflation, in all four columns. there is This implies that during this interval the assumed NAIRU series is too low. A negative mean error means that the assumed simulations NAIRU series is too high. are quite encouraging. The results for the 34-quarter While the mean error is positive, both the textbook TV-NAIRU versions are almost exactly on track in the final six quarters. squared error of the simulations estimated equation. inflation and And the root mean in all four columns is lower than the standard The textbook series and overpredicts post-sample error of the NAIRU series predicts almost as well as the TV-NAIRU by only a modest amount during 1995-96. The Time-Varying The simulation full wmple period simulation. Here it is important sample period through is extended have been during (3) and (4) use the coefficients results in columns 1987-96 1996 and of course yield smaller to emphasize estimated from the perspective over the RMSE’S for the 1987-96 how little the coefficients and how stable the structure NAIRU, Page 27 change when the of the inflation of coefficients process seems to estimated for the pre-1987 period. How much do the supply-shock 5 displays two TV-NAIRU variables change the estimated series for the GDP Deflator differing only that the solid line displays the TV-NAIRU equation and a standard Figure deviation of 0.2, for the full version of the 1955-96 displayed in column (4) of Table 1, while the dashed line shows an alternative NAIRU series that omits all right-hand-side and the set of unemployment 1973-81 W-NAIRU? period influenced the contribution after 1982, gap terms. by adver= variables other than the lagged inflation The results are intuitively supply shocks, the TV-NAIRU of the supply shock variables to inflation presumably plausible due to the declining TVterms — during the is much higher when is ignored. The reverse is due real prices of oil and imports. Nonlinearity Recently both Robert Eisner (1996) and George Akerlof, George Perry (1996) have suggested that the linear specification is incorrect. unemployment Eisner argues that the Phillips rate is below the conventional rate is above the conventional NAIRU. William Dickens, of the inflation equation curve is concave, that is, flatter and (3) when the NAIRU and steeper when the unemployment I have tested Eisner’s proposition by adding to The TimeVarying equation (3), in the version displayed in Table 1, column to zero when the unemployment the latter is positive. negative unemployment (entered significance conventional a steeper slope for the short-run The sum of coefficients value and four lags) indeed of the sum is very weak, is negative, with a significance becomes conventional gap when Phillips curve at on the POSGAP variable -0.12, but the statistical level of 0.61, far from the 0.05 criterion. Akerlof et. al. (1996) argue for the opposite which variable equal this “POSGAP” variable would have a significant negative rates above the NAIRU. as the current (4), an additional gap is negative and equal to the unemployment If Eisner is correct, sign, indicating NAIRU, Page 28 much NAIRU. flatter when inflation a convex Phillips curve is low and unemployment To test their proposition, is above was below 3,0 percent. the I defined another variable equal to zero in gap was positive and the four-quarter all quarters except when the unemployment in the GDP deflator nonlinearity, The sum of coefficients change on this additional variable, entered again as the current value and four lags, is precisely zero. Thus I conclude that the short-run unemployment Phillips curve is resolutely linear, at least within the range of inflation and values observed over the 1955-96 period. Estimated Equations for the PCE Deflator Table 2 displays an identical weighted PCE deflator set of results that differs only by using the chain- in place of the chain-weighted Table 2 are similar to the corresponding except (as would be expected) elements the coefficients GDP deflator. of Table 1. Most elements Coefficients of are similar, on changes in the relative price of imports The Time-Varying and of food and energy are higher and more significant Table 2 than in the GDP deflator equations are uniformly small and insignificant NAIRU, Page 29 in the PCE deflator equations in in Table 1. The Nixon “off” dummy variables in Table 2, in contrast to Table 1. Goodness of fit statistics are similar in both tables. Perhaps the most notable difference occurs in the bottom two lines of Table 2, where improvement columns in performance (2) and (4), relative to the textbook much greater for the PCE deflator. of the inflation rate during of the TV-NAIRU NAIRU versions in columns The textbook NAIRU causes a substantial 1994-96 equation (1) and (3), is overprediction that does not occur with the TV NAIRU. Further insight into the “big miss” of the textbook NAIRU series is presented 6, which plots the textbook NAIRU against the TV-NMRU The TV-NAIRU deflator between was fairly close to that for the GDP deflator from 6.2 to 5.2 percent there is a sharp disagreement over the 1990-96 between the textbook regarding demand pressure in the economy; in Figure series, using a standard deviation of 0.2, for both the GDP deflator and the PCE deflator. plummets in period. series for the PCE 1980 and 1990 but then In late 1995 and late 1996 NAIRU and the PCE TV-NAIRU the former implies excess demand and the latter implies excess supply. Two other consumption-based for the fixed-weight consumption TV-NAIRU series are displayed in Figure 7. These are deflator and CPI-U-X1. The two PCE deflators roughly the same story up to the last few years, when PCE TV-NAIRU weighted PCE deflator drops well below that for the fixed-weight that the chain-weighted PCE deflator places a substantially series for the chain- PCE deflator. higher tell weight It appears on consumer The Time-Varying electronics, especially personal prices in the 1990s. computers, that have exhibited During the mid 1980s the TV-NAIRU for the two PCE deflators, NAIRU, Page 30 a drastic decline in relative for CPI-U-X1 but after 1990 it has been somewhat was lower than higher. Splitting the Sample Period of the preceding One possible criticism period. the length of the sample Why should the Fed base its estimate of the current NAIRU on more than forty Why is not the more recent past, say the last 20 years, a more years of previous data? relevant interval for which contrasts the full-sample deviation (the same series as was plotted to estimate the inflation jump in the estimated estimate, 0.0 and 0.3 percentage the purpows for 1996:1 of conducting is identical 8 The two sub-samples that is between 0.1 and 0.5 percentage and an estimate of the NMRU for 1975-96 points higher than the full-wmple estimate. result in points lower that ranges However, for current monetary policy, it is reassuring that the NAIRU estimate in the full-sample and split-sample alternatives. statistics of the split-sample equations the GDP deflator are displayed in Table 3. The sum of coefficients The mean error and root-mean-squared for on the unemployment higher in the second sub-sample, while the coefficients variables are quite different. estimates Splitting the sample period results in a sharp The estimated coefficients and performance gap is somewhat Figure in Figures 3, 5, and 6) with alternative NAIRU at the break point (1975:1). an estimate of the NAIRU for 1955-74 than the full-sample Accordingly, equation? NAIRU estimate for the GDP deflator with a 20 percent standard based on the two halves of the sample period. beween results concerns on the supply-shock error in the 1987-96 The TimeVarying dynamic simulation full-sample are considerably NAIRU, Page 31 lower for the split sample results in Table 3 than the results in Table 1. However, a Chow test just misses accepting of a structural break between the two sub-samples at the conventional the hypothesis 5 percent significance level.lg Simulations of Alternative Post-1996 Unemployment How rapidly economy, would inflation accelerate if the Fed “let her rip” (referring not interest rates) and allowed unemployment the NAIRU? to fall one percentage an acceleration of inflation. allows the unemployment The particular 96 inflation equation The unemployment point below coefficients predictions gap scenario that generates scenario plotted by the dashed line in Figure 9 gap (actual unemployment to -1.0 in 1997:2 and thereafter. NAIRU. to the We can simulate our inflation model, assuming all future values of the supply shock variables are zero, and specify an artificial unemployment 1996:2 Scenarios minus NAIRU) to decline from 0.0 in The prediction estimated of inflation is based on the 1955- in column (4) of Table 1, that is, using the TV- are compared with a baseline prediction that leaves the gap at zero forever, starting in 1996:2. The simulations of the acceleration of inflation during 1997, reflecting the fact that the pattern on the unemployment negative unemployment gap variable embodies gap a “rate-of-change” effect. After the economy settles down at an unemployment scenario display a rapid of lag coefficients effect as well as a “level” gap of -1.0 percent, the rate-of- 16. The F(28,108) ratio is 1.51, compared to a 5 percent significance value of 1.57 and a 1 percent significance value of 1.89. The TimeVa~ing change effect temporarily the acceleration and financial although interrupts the acceleration of inflation in early 1998, after which proceeds steadily, reaching 5.4 percent by the year 2005. market experts would be surprised NAIRU, Page 32 Many journalists at the slow pace of this acceleration, it is clear that the bond market would be “spooked” by the rapid pace of inflation acceleration during 1997. A constant unemployment settled down to an inflation gap set at zero causes the economy to rate of 2.3 percent forever. Conclusion The Triangle Model and the Time-Varying NAIRU The inflation macroeconomic process phenomena in the United in the world, States is one of by inertia. actual unemployment run. The best example one percentage accelerated of inflation point Inflation important is the 1988-90 over the three years 1987-90 small consequences period, when unemployment the 6.2 percent estimated NAIRU, from 3.1 to 4.4 percent. of a bit less than half a point per one percentage In the U. S. inflation process changes little from year to year, and any deviation rate from the NAIRU has extremely below most but it is also one of the best understood. contrast to the wild gyrations of inflation in many other countries, is dominated the of the in the short was on average about and the GDP deflator This implies a response point that unemployment remains below the NAIRU for a single year. The estimated coefficient on the unemployment gap in Table 1, line 2, ranges from -0.60 to -0.69, somewhat Because the U. S. inflation above one-half. process has been so stable, and is so well characterized by The TlmeVarylng the triangle model of inflation performed extremely developed well in dynamic in the late 1970s and early 1980s, that model has post-sample decade after the end of the sample period. capable of tracking the disinflation of the late 1980s, simulations extending In such simulations of the early and mid 1980s, and the subsequent NAIRU, Page 33 deceleration out for up to a the model has proven the acceleration of inflation of inflation in the 1990s. Those empirical successes were achieved despite the fact in previous research, the NAIRU inserted into the model was assumed arbitrarily after 1978 rather than estimated The main contribution of this paper has been to allow the NAIRU to vary each 1955 and 1996. close to 6 percent for the GDP deflator The resulting time-varying over the entire four-decade extreme values of 5.3 and 6.5 percent. the NAIRU from around at 6.0 percent for the entire period econometrically. quarter over the period between stays remarkably to be constant interval, (TV) NAIRU ranging between In recent years there has been a downward 6.2 percent in the late 1980s to current estimates and 5.2 percent for the PCE deflator. drift in of 5.7 percent The fact that the TV-NAIRU was very close to 6 percent during the expansion of the late 1980s and recession of 1990-91 helps to explain that the NAIRU was fixed at 6.0 percent performed surrounding criterion, assumption so well in tracking the acceleration This policy. how my previous paper rejects the recent and deceleration argument the NAIRU is so broad as to render We propose an economic criterion to choose among alternative that of that period. the band the concept of statistical uncertainty useless for the conduct based on smoothness, of rather than a statistical NAIRU estimates for any given measure of inflation. The Time-Varying NAIRU, Page 34 The recent suggestion of Staiger et. al. (1996) that the NAIRU for the year 1990 could range from 5.1 to 7.7 percent makes no economic sense. If the NAIRU had been 5.1 percent in the period since 1987, inflation would not have accelerated unemployment rate never fell below 5.1 percent in any calendar quarter. been 7.7 percent 1990-93, quarter. in the period since 1987, inflation since the actual unemployment The fact that the inflation the six quarters constant during 1987-90, would since the actual If the NAIRU had not have decelerated during rate never rose above 7.7 percent in any calendar rate for the GDP deflator was roughly constant (1994:4-1 996: 1), when the actual unemployment during rate was approximately at 5.6 percent, suggests that the TV-NAIRU for the GDP deflator during those six quarters was very close to 5.6 percent. The new TV-NAIRU measuring the real GDP that can be produced at the TV-NAIRU. that written series allows a new series for potential I have produced above in footnote such a series by estimating series on potential 1990:3 and 1996:1.17 is operating an Okun’s law equation output like increases at an Since the TV-NAIRU from 6.2 percent in 1990 to 5.7 percent in 1996, this potential 0.1 percentage to be created, each quarter when the economy 4; the resulting annual rate of 2.07 percent beween output declines output series grows at about point faster than would be implied by a NAIRU fixed at 6.0 percent. Thus 17. In estimating the Okun’s law equation written in equation (4), I invert it to regress the unknown output gap on current and leading values of the unemployment gap implied by the new TV-NA.IRU series based on the GDP deflator and a standard deviation of 0.2. I allow the sum of coefficients on the unemployment gap to differ during 1990-96 from their values in 1972-90. I calculate the fitted output gap, and then compute a trial value of potential output as actual real GDP minus the fitted output gap. The final potential output series is a 12-quarter centered moving average of the trial series. The Tim~Varying caution is advised regarding the advice of “growth hawks” that the U. S. economy grow at 3 percent or more per annum if only the Fed’s monetary Since the economy is currently NAIRU, Page 35 could policy is less restrictive. at the NAIRU, the ceiling on non-inflationary growth is about 2.1 percent a year, unless the NAIRU falls further below its values of early 1996. The Conduct of Monetary Policy What evaluation of past and current monetary on the NAIRU? According excess demand in 1955-57 to our new TV-NAIRU measures, there was considerably and 1965-70 series, suggesting that monetary than was previously thought. policy unemployment The new TV-NAIRU in 1995-96 rate during than implied by the previous NMRU in the= periods series also boosts modestly and 1988-90. has been the six quarters almost However, precisely on 1994:4-1996:1 more textbook policy was even more overly expansionary of estimated excess demand in 1979-80 monetary policy is implied by this new research the extent the new series implies that target, with of 5.6 percent, an average only slightly below the average estimated TV-NAIRU of 5.7 percent for the GDP deflator in that interval. If the Fed considers rather than its goal as the stabilization the GDP deflator, of the rate of change of the PCE deflator then the estimated interval was 5.3 percent, implying that monetary average TV-NAIRU during the same policy was slightly too restrictive in 1995- 96. The TV-NAIRU by any measure has declined deliberations about interest rate changes are intended rate roughly one year from now, should in the 1990s. If the Fed’s current to influence the actual unemployment the Fed extrapolate the recent decline in the The Time-Varying NMRU into the future, equal to the current or shouid value? the Fed set its estimate The TV-NAIRU walk and thus is just as likely to increase decrease. There is no information specified the lagged values of the explanatory of the NAIRU one year hence in equation over the subsequent about future inflation NAIRU, Page 36 (4) above is a random year as to continue to available beyond that contained in variables in the inflation equation that are already used to derive the NAIRU. While the TV-NAIRU technique does not provide a magic crystal ball that allows the Fed to see into the future, it makes two valuabie contributions policy. First, it quantifies to the conduct in a systematic way the Fed’s intuitive must have fallen in the 1990s, because as of early 1996 inflation did in 1988-90. alternative Second, inflation the differences concept movements had not accelerated in the NMRU series implied by and forces the Fed to take a over time naturally This question raise the question series of Figure 7. There only NO major changes occur, an increase in the NAIRU from about 5.8 percent 6.5 percent percent in 1990 to 5.3 percent in 1965 to in the two decades after 1970, and then a decline from about 6.4 in 1996. The late 1960s were a time of iabor militancy, relatively strong unions, a relatively high minimum share in national as to is most easiiy posed for the three price indexes used to generate the TV-NAIRU roughly as it it is trying to stabilize. which factors caused these movements. consumption feeling that the NAIRU in the TV-NAIRU measures, e.g., the GDP vs. PCE deflator, stand on what inflation Estimated it highlights of monetary income. wage, and a marked increase in labor’s The 1990s have been a time of labor peace, relatively weak The TlmeVarying unions, a relatively low minimum The role played structure, wage, and a very slight decline in labor’s income share. in the recent decline and other plausible topic for future research. 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TABLE 1 Estimated Equations for Quarterly Change in Chain-Weight GDP Deflator, Alternative Sample Periods and Unemployment Gaps > 1955:2-1987:3 Textbk Vartable (1) 1955:2-1996:1 u Tv (02) Textbook Tv (02) (2) (3) (4) 1.01*” 1.05”* 1.01”* 4.69”” -0.62” ● -0.64”” -0.60”” o-1 -0.10 -0.11” -0.08 -0.09” 4. ARelative Import Price 1-4 0.06 0.08” 5. ARelative Pria Food-Energy N 0.43 0.42” 7. AEff~e o-3 4.01 -0.01 -0.01 -0.01 8. Nixon “on” o -156” -1.62”* -159** -1.69** 9. Nixon “or o Ml.. 2.19*” 209”” 2.07”* F 0.85 0.88 0.85 0,87 S.E.E. 1.01 0.92 0.95 0,87 1. AChain-We@t GDP deflator 1-24 2. Unemployment Gap 0-4 3. AProductivity deviation Real Exchange Rate 104,8 S.S.R. Restricted Versio~ RMSE in sub internals of fitted sample 1955:2-70:4 1971:1-rn2 1987:3-94;3 1994:4-%1 Dynamic Simti 1987:Q4-lmQl Mean Emor Root Mean-Squared Error 1994:Q4-1996:Q1 Mean Error Root Mean-Squared Error Notes: 1.C%*” (*) bd.i~tes that -fflaent 1 pereent leveL %.7 - 0.07 0.09”” o.2a 0.30” 123.1 103.4 1.05 0.77 0.92 0.71 1.07 0.80 0.63 0.47 0.93 0.73 0.61 0.42 0.24 0.91 O.m 0.86 0.34 0.70 0.26 0.65 -0.10 o.4a 0.08 0,41 -0.01 0.39 0.12 0.40 or sum of coeMcients is si#lcant at 5 percent level; (**) at TABLE 2 Estimated Equations for Quarterly Change in Chain-Weight PCE Deflator, Alternative Sample Periods and Unemployment Gaps 19552-1987:3 Texttik (1) Variable 1955:2-19961 I Tv (02) (2) Textbook (3) 1-24 1.09”’ 1.01’” 2. Unemployment Gap o-4 -0.77”” -0.66”” 4.68*” -0.67”’ 3. AProduetivity detiation o-1 -0.02 4.03 -0.02 4.03 4. ARelative Import Price 1-4 O.11** 0.14”” O.11”* 0.14”” 5. ARelative Pn@ Food-Energy o-4 0.74”” 0.66”” 0.66”* 0.64”” 7. AEffetive Real Exeha.nge Rate o-3 -0.01 -0.00 -0.00 -0.00 -1.82”* -1.95”* -1.74*” -2.03”” 0.01 -0.47 0.05 439 R 0.87 0,88 0.86 0.88 S.E.E. 1.03 0.99 0.98 O.w 1. AFud-weight GDP deflator 8. Nixon “on” o 9. Nkon ‘oR o 108.8 S.S.R. Restricted Versio~ RMSE .b subintemals of fitted sample 1955:2-704 1971:1-m2 1987:3-94:3 1994:4%:1 sim1987:W19%:Q1 Mean Error Root Mean-Squared Error 1994:Q4-1S96:Q1 Mean Error Rwt Mean-Squared Error Notes: that -ffiaent (“) indicates 1 perunt level. 1.W** w (02) (4) - 99.6 129.8 1.01*” 111.4 1.11 0.80 0.99 0.75 1.11 0.82 0.68 0.75 0.99 0.77 0.57 0,52 0.19 0.83 0.35 0.72 0.24 0.75 0.35 0.65 -0.72 0.78 -0.07 0.26 -0.61 0.68 -0.03 0.25 or sum of coefficients is si~lcant - at 5 percent level; (**) at TABLE 3 Estimated Equations for Quarterly Change in Chain-Weight GDP Deflator, Alternative Sub-Sample Periods and Unemployment Gaps 1955:2-1974:4 Textbook (1) Variable Tv (02) (2) 1975:1-1996:1 I - Textbook (3) m (02) (4) 1.07** I.M** 1. AChain-we@t GDP deflator 1-24 1.02”* 0.94”” 2. Unemployment Gap o-4 -0.63”” -0.68”” 4.74”” -0.86”” 3. AProductivity denation o-1 -0.11 -0.u”” 4.04 -0.04 4. ARelative Im~rt 1-4 -0.02 0.02 0.11”” o.13** 5. ARelative Prie Food-Energy w 0.29 031 0.21‘• 0.03 7. AEffeuive Real Exchange Rate 0-3 4.05 -0.M 0.00 0.01 8. Nmon “on- 0 -1.80 -1.27 9. Nmn “or o Priu 4.74” 4.m” 3 0.78 0.83 0.92 0,93 S.E.E. 1.12 1.00 0.67 0.63 643 S.S.R. Restricted VersioG RMSE in sub internals of fitted sample 1955:2-704 1971:1-87:2 lm3-94:3 1994:4-%:1 0.93 Dynamic sire* 1987:Q4-19%al Mean ErTor Root Mean-Squared Error 1994:Q4-19%:Q1 Mean Error Root Mean-Squared Error Notes: that -ficient 1 percent level. (“) kdimtes 50.8 23.4 0.80 . or sum of mficients X.7 is si~lcant 0.55 0.42 0.4 0.24 033 0.63 0.08 0.39 -oOal 0.31 0.23 0.01 at 5 percent level; (**) at 1 1 I 1 1 1 I E ,- r--- . . . ... .. .. # “, .,.m.# ..>- -. “- .>. 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