Stagflation, Persistent Unemployment and the Permanence of Economic Shocks

Brunner, Karl; Cukierman, Alex; Meltzer, Allan H. Article Stagflation, Persistent Unemployment and the Permanence of Economic Shocks Credit and Capital Markets – Kredit und Kapital Provided in Cooperation with: Duncker & Humblot, Berlin Suggested Citation: Brunner, Karl; Cukierman, Alex; Meltzer, Allan H. (2019) : Stagflation, Persistent Unemployment and the Permanence of Economic Shocks, Credit and Capital Markets – Kredit und Kapital, ISSN 2199-1235, Duncker & Humblot, Berlin, Vol. 52, Iss. 4, pp. 477-504, https://doi.org/10.3790/ccm.52.4.477 This Version is available at: https://hdl.handle.net/10419/293873 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Credit and Capital Markets 4 / 2019 Stagflation, Persistent Unemployment and the Permanence of Economic Shocks* Karl Brunner**, Alex Cukierman*** and Allan H. Meltzer**** Abstract When changes occur, people do not know how long they will persist. Using a simple stochastic structure that incorporates temporary and permanent changes in an augmented IS-LM model, we show that rising prices and rising unemployment – stagflation – is likely to follow a large permanent reduction to productivity. All markets clear and all expectations are rational. People learn gradually the permanent values which the economy will reach following a permanent shock and gradually adjust anticipations. In our model, optimally perceived permanent values take the form of a Koyck lag of past observations. I. Introduction The principal choices that people make in a market economy – choices between present and future consumption, between labor and leisure, between real and monetary assets – depend on beliefs about the future. In forming their beliefs, individuals attempt to separate transitory and ephemeral changes from permanent and persistent changes. Even individuals who are fully informed about past and current values cannot be certain about future values. A basic inference problem that individuals face is to distinguish permanent values of variables like income, wages and prices from current values.1 This paper analyzes an economy in which decisions depend not just on the changes that occur but on their persistence. The economy is subject to real shocks to the labor, commodity and money markets and to nominal shocks to the money shock. Each shock has a permanent and transitory component. Indi- * First printed in Journal of Monetary Economics., Vol. 6 (1980), pp. 467–492 (published by Elsevier) ** Prof. Dr. Karl Brunner † *** Prof. Dr. Alex Cukierman, Email: a[email protected] **** Prof. Dr. Allan H. Meltzer †. 1 Permanent income is related to Friedman’s (1957) permanent income hypothesis. Beliefs about permanent wages play an important role in the determination of current labor supply decisions. See Lucas/Rapping (1969) and Brunner/Meltzer (1978). Credit and Capital Markets, Volume 52, Issue 4, pp. 477–504 Scientific Papers OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.52.4.477 | Generated on 2023-01-16 13:28:12 478 Karl Brunner, Alex Cukierman and Allan H. Meltzer Credit and Capital Markets 4 / 2019 viduals know the deterministic structure of the economic model and, also, know the stochastic structure. They use all available information to form optimal forecasts of the permanent values of relevant variables, but their information does not permit them to distinguish permanent and transitory changes as they occur. All markets reach equilibrium and clear each period. The prices and quantities at which the markets clear depend, however, on the perceptions individuals in the aggregate hold about the persistence of the shocks that have occurred. Since people learn whether changes are permanent or transitory only by observing what has occurred, perceptions about permanent values change gradually, and differences between expected and actual permanent values can persist for a time.2 The distinction between permanent and transitory changes is particularly appealing for analysis of the labor market since it offers a potential means of reconciling sluggish adjustment of real wages and the persistence of ‘unemployment’ with market clearing and rational expectations. The usefulness of the distinction is not confined to the labor market. We show that a large permanent reduction in productivity causes, on impact, an increase in unemployment, which persists for a time, and an increase in prices. Real wages adjust toward their new equilibrium value as information about the permance of the shock accrues. During the transition real wages are ‘sticky’. The permanent reduction of productivity generates many of the patterns described as stagflation – changes in prices, wages, output and real rates of return.3 The model of the economy, presented in section 2, is an augmented IS-LM model. There is an aggregate demand function, a money demand function, and a demand and supplies function for labor. The demand for labor is derived from a neo-classical production function; the supply of labor depends on both the current and the perceived permanent wage rate. The various shocks and their (known) stochastic structure are also presented in this section. Section 3 explains the formation of beliefs or perceptions of permanent variables. First, we derive an optimal forecast of the current permanent value of any given shock. The forecasts are used to derive the structural beliefs4 regarding permanent income, permanent wages and the permanent values of the other endogenous variables. Section 4 investigates the effects of various shocks on the equilibrium levels of employment, prices, output and the real wage rate and discusses the working of the model. Section 5 shows that large permanent decreases in productivity are followed by periods of persistent underemployment of 2 Friedman (1979) obtains a similar result in different way. 3 This seems to have been the case in 1973–1974. For alternative hypotheses that explain stagflation see Friedman’s Nobel lecture (1977). 4 This term is an adaptation of a concept due to Turnovsky (1977). OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.52.4.477 | Generated on 2023-01-16 13:28:12 Stagflation, Persistent Unemployment and Permanence of Economic Shocks 479 Credit and Capital Markets 4 / 2019 labor and by inflation. We show that inflation and unemployment can occur together – the pattern known as stagflation. A conclusion completes the paper. II. The Model The model developed in this section has many of the features of an IS-LM model that includes markets for commodities, money, bonds and labor.5 Equilibrium prevails on all markets, so we eliminate one market, the bond market, from explicit consideration. Current and permanent values differ, and the differences affect the equilibrium position of each market. Productivity, aggregate demand, labor supply, money demand and money supply are all subject to random shocks. Each shock has a permanent and a transitory component. The shocks to aggregate demand, labor supply and money demand are related through the budget constraint. For simplicity they are therefore entered in the various functions as the same shock, but each function has a different coefficient on the shock. Individuals in the economy have information on current and past values of all variables, but they are unable to observe the permanent and transitory components of each shock separately.6 They use information on the current and past values of the variables to form optimal predictions of the components of each shock and to calculate permanent values of all variables. Expectations about the permanent values of the variables are rational in Muth’s (1961) sense. 1. The Demand for Commodities Demand for commodities is given by (1) ( )[ ] *1 , 0 1, 0, + =+ + - - + < < < α β ε αβ p t t tt t t t ek y r p p where t e , p t y and t p are the logarithms of aggregate demand, real permanent income and the general price level respectively, t r is the nominal rate of interest, * 1 + tt p is the logarithm of the price level expected to prevail by the public in period t + 1 as of period t, and ε t is a random shock to aggregate demand. Eq. (1) states that aggregate demand depends on permanent income7 and is inversely 5 The model is a modified version of the model in Cukierman (1980). One important difference is that there is speculation in labor over time as in Lucas/Rapping (1969) and more recently in Brunner/Meltzer (1978). 6 As we shall see, this information limitation disappears gradually as new information becomes available. 7 This is in line with Friedman’s (1957) permanent income consumption function. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.52.4.477 | Generated on 2023-01-16 13:28:12 480 Karl Brunner, Alex Cukierman and Allan H. Meltzer Credit and Capital Markets 4 / 2019 related to the real rate of interest. The real rate is the nominal rate t r minus the rate of inflation expected by the public, * 1 tt t pp +-.8 2. The Supply of Commodities and the Labor Market Aggregate output, t Y , is produced with a Cobb-Douglas production function. The aggregate capital stock is assumed fixed,9 so aggregate output can be written as a function of labor input, t L , and a random productivity factor, t u ,10 (2) , 0 1= << δδ ut tt Y eL The demand for labor is obtained from the first-order condition by equating the marginal product of labor to the real wage, (3) ( ) log ,=- - + η ηδ d tt t l wu where ( ) 1/ 1 0, d t l ηδ º -> is the logarithm of labor demanded, and t w is the logarithm of the real wage rate in period t. Labor supply is (4) ( ) 2 log ,= -+ + ω η δ θε p s tt tt l ww where p t w is the logarithm of the real wage perceived as permanent in period t, and ω and 2 θ are positive constants. Workers compare the currently prevailing wage to the wage they currently perceive as permanent. Ceteris paribus, a decrease in t w , or an increase in p t w decrease the current supply of labor.11 A rise in t w relative to p t w induces workers to work now and substitute future for current leisure. When the current wage rate is below p t w , part of the labor force which looks for work abstains from accepting current employment. This group is counted as unemployed in the official statistics. When the actual and the permanent real wage rate are equal, unemployment is driven to zero.12 This suggests that, within the context of the model, unemployment may be defined as 8 The rate t r is the yield to maturity on a one-period bond. 9 We abstract from the long-run effects of investment on capital accumulation. 10 Wherever a non-random variable appears both by itself and in log form, a capital letter is used for the variable and a lower case letter for the logarithm of the variable. 11 For a derivation of a similar labor supply function from a microeconomic model see Lucas/Rapping (1969). For computational convenience we use log ηδ as the normalizing constant in labor supply. 12 Since the focus of this paper is on cyclical unemployment, we do not discuss types of unemployment that arise for other reasons. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.52.4.477 | Generated on 2023-01-16 13:28:12 Stagflation, Persistent Unemployment and Permanence of Economic Shocks 481 Credit and Capital Markets 4 / 2019 the difference between labor supply when =p tt ww and labor supply when the two wage rates differ. Hence the percentage rate of unemployment ( t n ) is given by (5) ( ) =- ω p tt t n ww . The formulation allows periods of over as well as unemployment and implies that the actual rate of unemployment can be on either side of zero.13 The term 2 θε t in labor supply expresses the idea that Walras’ Law applies to the random shocks affecting aggregate demand. A positive shock to aggregate demand must be balanced by one or more of the following changes: An increase in the supply of bonds, a decrease in the demand for money, or an increase in the supply of labor. A negative shock has the opposite responses in the bonds, money and labor markets. The term 2 θε t states how much of the shock to aggregate demand takes the form of a change in supply of labor.14 3. The Money Market The real demand for money is positively related to permanent income15 and inversely related to the nominal rate of interest. The specific form of the demand function in nominal terms is given by (6a) ( ) 11 , 1 0, 0, pp dt tt t tt t m B p y br g y y g b θε θ =+ + + + - - >> <  0, where d m is the natural logarithm of nominal money demand and B is a constant. The term ( ) -p tt gy y is the mirror image of the hypothesis that people relate their expenditure levels to permanent income even when permanent and actual income diverge. When permanent income is above actual income, the public reduces money balances to maintain spending. Conversely when actual income is above permanent income, the public increases money balances.16 The term 1 - θε t states that. Through Walras’ Law, any shock to aggregate demand is 13 Unlike Friedman (1968), Phelps (1967) and Lucas (1973), unemployment is not caused by faulty perceptions about the price level but results from unavoidable errors in the perception of permanent real shocks and the existence of transitory real shocks. 14 If 20= θ individuals finance increased demand for goods only by borrowing and by running down their money balances. 15 For a specification and estimation of a money demand function which depends on permanent income see Friedman (1959) and Laidler (1966). 16 The model does not rule out the possibility that some of the synchronization of expenditures to permanent income is achieved by changing the excess demand for bonds. As a matter of fact the constraint 1<g originates in the requirement that the excess deOPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.52.4.477 | Generated on 2023-01-16 13:28:12 482 Karl Brunner, Alex Cukierman and Allan H. Meltzer Credit and Capital Markets 4 / 2019 partly reflected as a shock to money demand in the opposite direction. The parameter 1 θ measures the portion of the shock to aggregate demand that individuals desire to finance by changing money balances. The stock of money is given by (6b) =+ ψ st t mm , where s t m is the logarithm of the nominal shock, in period t ; m is a constant, and ψ t is a random shock to money. 4. Equilibrium17 Given the current realizations of the three shocks – , , εψ tt t u – the permanent values of the wage rate ( p t w ), the level of permanent income ( p t y ) and the price level expected for next period ( * 1 + tt p), we use the market clearing equations for the next commodities, labor and money markets and the production function to determine the current values of output ( t y ), employment ( t l ) the price level ( t p ), the nominal rate of interest ( ) t r and the real wage ( t w ). Eqs. (7), (8) and (9) equate the quantity of commodities demanded ( ) t e to t y , and the quantities of money and labor demanded to the quantities supplied: Commodities market (7) ( )[ ] *1. p t t tt t t t yk y r p p αβ ε + =+ + - - + Money market (8) ( ) 1. pp t t tt t tt m B p y br g y y ψ θε + =+ + + + - - mand for bonds is an increasing function of actual income and a decreasing function of permanent income. For more discussion of the bond market, see footnote 17. 17 By using the budget constraint and the excess demands for labor, goods and money, we can derive the excess demand for bonds as a function of the variables and shocks in the model and use the resulting function to check the implications of the model. The model implies that, for sufficiently small values of 1 θ and 2 θ , the excess demand for bonds is a decreasing function of ε t; a positive shock to aggregate demand increases the demand for loans (excess supply of bonds) and the supply of labor and reduces the demand for money. For 1<g and income velocity of money greater than 1, increases in - p tt yy increase the excess demand for bonds. Increases in the money stock and in the real rate of interest also increase the excess demand for bonds. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.52.4.477 | Generated on 2023-01-16 13:28:12 Stagflation, Persistent Unemployment and Permanence of Economic Shocks 483 Credit and Capital Markets 4 / 2019 Labor market (9) ( ) 2 log 0 . p t tt t t t l wu w w η ηδ ω ω η δ ε =- - + = - + + Eq. (10) restates the production function in logarithmic form (10) .=+ δ tt t yu l 5. Permanent and Transitory Shocks – The Stochastic and Information Structures of the Ecoyomy Each of the three stochastic shocks ε t, ψ t, and t u , has a transitory component and a permanent component, (11) , , pq p q pq tt t tt t t tt uuu ε ε εψ ψ ψ =+ = + =+ An intuitive interpretation of the formal definition in (11) is that any shock which remains at its current value until something else happens is a permanent shock, whereas any shock which affects the system for only one period is a transitory shock.18 Let º+ pq ttt xxx , where , , = εψ i i ii t t tt xu and I = q, p. We assume that (12) ( ) ( ) 22 ~ 0, , ~ 0, ,∆ σσ pq xp xq tt xN xN where 1 ∆- º+ p pq ttt xxx . The permanent component, p t x, of each shock is expected to remain at its previous value unless the change in this component deviates from its expected value. The expected value of a change in p x is zero; p t x is a random walk. The transitory component q t x is expected to vanish to zero unless another transitory shock hits the system in the next period. , , , , ∆∆ ∆ ε ψ εψ p p pq q t t tt t u and q t u are mutually and serially uncorrelated. In each period, t, individuals in the economy have full information about the current and past values of the endogenous variables like , , tt t yrp , and t w and the current money stock t m . They also have beliefs about the current values of permanent income, the permanent real wage rate and the future expected price 18 In extreme interpretation of a ‘permanent shock’ cannot coexist with the notion that such a shock is subject to some non-degenerate probability distribution. If the shock is ‘permanent’ in the strictest sense it is expected to remain at its current level with probability 1 forever. Such a notion of permanence does not seem useful for the analysis of the type of random shocks that affect economic systems. Therefore a less extreme definition of permanence is used in the text. The meaning FI ‘permanent’ is not independent of the stochastic structure. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.52.4.477 | Generated on 2023-01-16 13:28:12 484 Karl Brunner, Alex Cukierman and Allan H. Meltzer Credit and Capital Markets 4 / 2019 level.19 For given beliefs about *1, , qq tt t t p yw + and the current values of , , tt t yrp and m, individuals in the economy can solve for the current values of the shocks , εψ tt and . t u Individuals observe only the sum of the permanent and transitory components of each shock and cannot separate the two reliably. Moreover this lack of information is not entirely dispelled by the passage of time. Even when they are in period t, individuals do not know with certainty how much of the shock , 1 tj xj -  , that they observed in the past is due to transitory changes and how much is due to permanent changes. And there is nothing in the aggregate statistics computed by the appropriate agencies which removes this lack of information with the passage of time. The fundamental inference problem confronting individuals arises from their inablility to separate the two components of each shock. The information structure of the model differs from the structure encountered in models which are based on a confusion between aggregate and relative price changes. See Lucas (1973), Barro (1976), Cukierman/Wachtel (1979) and Cukierman (1979). In these models, the publication of a general price index dispels confusion immediately. In our model, new information is useful but does not eliminate the confusion. There is no aggregate statistical data which informs people in the economy about the extent to which a shock to past productivity, to aggregate demand or to the money supply is permanent or transitory.20 III. The Formation of Beliefs about Permanent Variables 1. Optimal Forecasts of Permanent Values of the Exogenous Shocks This section explains how individuals form optimal forecasts of the various shocks and modify their beliefs or perceptions about permanent income. permanent wages and the permanent values of the other endogenous variables. We focus on the optimal prediction of p t x given the information on 12 , , -- tt t xx x … which is available in period t. The information set of period t includes the current value and all past values of x, and is denoted t I . The problem of forming an optimal forecast about p t x given t I can now be formulated as follows: Given 19 Differential information and beliefs are ignored. 20 This is the fundamental thesis of Brunner/Meltzer (1978). If the shock is permanent it becomes relevant for the prediction of the future course of the economy. If it is transitory, it is irrelevant as far as the prediction of the future is concerned. The oil shocks of the seventies, changes in rainfall, and the famous disappearance of the Peruvian anchovies are examples of real shocks that cannot be accurately labelled as permanent and transitory when they occur. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.52.4.477 | Generated on 2023-01-16 13:28:12 Stagflation, Persistent Unemployment and Permanence of Economic Shocks 491 Credit and Capital Markets 4 / 2019 Table 2 Solutions for Permanent Valuesa 2 æ öæ ö ÷÷ çç = +- + ÷÷ çç ÷÷ çç è øè ø ++ θ η ωω εε ηω η ηω η pp tt t tt w u Eu E ( ) ( ) 2log= -+ + + ++ θ ηω ηε ω ε η δ ηω ηω pp tt t tt l u Eu E ( ) [ ] ( ) 211 log pp t tt tt y u Eu E δθ η ω δη δηω ηε ω ε δη δ ηω ηω éù = ++ - + + + êú ëû ++ ( ) ( ) ( ) ( ) [ ] ( ) ( ) [ ] ( ) ( ) ( ) [ ] ( ) ( ) ( ) ( ) β δθ η η ω δη βψ θ β ε β ηω ηω βδηω β αβ β ηω η ω δη β βψ ψ ηω θ δη β θβ ε ηω ββδηω β β ηω ìé ù ü + ++ ïï ïï êú ++ - -+ ïï êú ïï ++ ëû ïï ïï =+ íý ïï - ïï ïï ++ + - - - ïï ïï + ïï îþ ++ + -- + éù + êú + +- êú + ëû =-+ + - -+ + + 2 1 2 1 1 1 11 1 1 11 t tt tp p pp t tt p tt t t bg b bg u pK bb g w b gy bp bg bE u bg b bbg gb ( ) [ ] ( ) ( ) αα βω α β δθ ϕ ε ηω ìü ïï ïï ïï ïï ïï ïï ïï ïï ïï ïï ïï ïï ïï ïï + íý ïï éù ïï ïï êú +- ïï ïï êú ïï ëû ïï ïï ïï ìé ù ü ïï + ïï ïï ïï êú - -+ - + ïï íý ïï êú ïï + ïï ïï î îë û þ þ 21 1 1 p p t p t K b Eu bg b g bE ( ) ( )( ) ( ) ( ) ( ) [ ] ββ βψ η ω δη δθ η θ β ε ηω ηω ββδηω α β β ηω ì é ùü ++ ïï ïï êú - + + + + -- ïï êú ïï ++ ëû ïï ïï =+ íý ïï -+ ïï ïï - -- - + ïï ïï + ïï îþ 21 11 11 1 111 tt t tr p pp t tt gg u rK bgw gy p ( ) [ ] 11 2 1º +- + - ϕ θ β δθ β α bb a p p K and p r K are combinations of parameters and have no importance for the discussion. Suppose there is a permanent change in t u . Initially p t Eu changes very little. If the shock is positive, real wages, employment, and output rise, and the price level falls. As the perception of permanence increases, p t Eu starts to adjust. Adjustment of p t Eu reinforces the effect of t u , on t w and, wholly or partly, offsets the effects of t u on employment and output. The distinction between permanent and actual changes helps to explain why real wages appear to be ‘sticky’. The initial response of the real wage to a permaOPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.52.4.477 | Generated on 2023-01-16 13:28:12 492 Karl Brunner, Alex Cukierman and Allan H. Meltzer Credit and Capital Markets 4 / 2019 nent productivity shock is a fraction, /( + ηηω ), of the response to a fully perceived permanent shock. Once the permanence of the shock is recognized, the effect of t u on the real wage is reinforced by the response of of t w to p t Eu . Eq. (15) implies, however, that p t Eu adjusts gradually, so the full adjustment of the real wage occurs gradually. The ‘stickiness’ of real wages means that the short-run elasticity of the real wage with respect to productivity is smaller than the long-run elasticity. The short-run elasticity of employment is larger than the long-run elasticity, however. Employment rises in response to a positive shock to productivity (and falls in response to a negative shock). The response to the actual shock increases the demand for labor. Growing recognition of the permanence of the shock, and the resulting gradual adjustment of real wages, reduces the demand for labor and lowers employment. The response of employment to a permanent productivity shock is reflected in output. Output initially overshoots, then gradually adjusts as the permanence of the shock is perceived and the increased or reduced productivity becomes fully reflected in the prevailing real wage. Permanent reductions in productivity permanently lower output. The unchanged labor force has lower productivity and produces less. During adjustment of perceived permanent changes to actual changes in productivity, the price level may rise or fall. The speed with which perception of the permanence of the shock grows and the relative effects of , pp wy and p determine the direction of adjustment. The ambiguity in the response of p to p t Eu arises because the positive effects of p t Eu on p t w and ( p t y for β sufficiently small) combine with a negative effect of p t Eu on . p t p The long-run adjustment. after the permanence of the productivity shock is fully perceived, is not in doubt. Permanent increases in productivity lower, and permanent reductions raise, the excess demand for output. The long-run elasticity of t p , with respect to tt u Eu , is ( )( ) [ ] 1 b/ 1 βα -+ - which is unambiguously negative. 3. Responses to Monetary Shocks Our model is neo-classical, so money does not affect output, employment or wages. The only effects of actual and perceived monetary shocks are on the price level and the hate of interest. A change in ψ t , changes the price level by changing the excess supply of money and market interest rates. The change in interest rates changes spending. A change in ψ p t E also affects spending by changing the perceived price level and the excess demand or supply on the commodity market. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.52.4.477 | Generated on 2023-01-16 13:28:12 Stagflation, Persistent Unemployment and Permanence of Economic Shocks 493 Credit and Capital Markets 4 / 2019 The equation for t p in table 2 shows that when all monetary shocks are permanent ( == ψ ψψ pp t tt E ), the price level changes equiproportionally. Transitory shocks change the price level less than proportionally because the transitory shock temporarily changes interest rates and the demand for money in an offsetting direction. If a permanent change in money is less than fully perceived, the price level undershoots the stationary equilibrium value. The price level remains below the stationary equilibrium value following monetary expansion and above it following monetary contraction until the permanence of the shock is correctly perceived. Substituting for p t pin the equation for t r in table 2 and expressing t r in terms of - ψψ p tt E shows that an unforeseen permanent increase in money lowers the nominal rate of interest.32 Market interest rates fall in response to increases in money and rise as the permanence of the change in money is perceived. The positive effect of perceived changes in money on interest rates is a result of their effect on perceived or anticipated prices. Once people expect the price level to rise, they reduce real balances. This causes a decrease in the current real rate of interest and therefore increases aggregate spending and the price level. The rise in the nominal rate re-establishes equilibrium in the money market. 4. Responses to Spending Shocks Changes in actual and perceived aggregate demand also affect the equilibrium positions of the output, labor, money and bond markets. Table 2 shows that the effects on output, employment and wages depend on the response of labor supply. If 20 θ =, the supply of labor is independent of the shock to aggregate demand, and the real wage and output are unaffected by – perceived and non-perceived – shocks to spending. The entire effect of the spending shocks is borne by the price level and the rate of interest. Prices and market rates of interest rise in response to positive shocks and fall in response to negative shocks. If we may treat government spending as one type of spending shock. we see that, in the absence of an effect on labor supply, government spending has no effect on output and employment. The initial effect of positive ε t, increases aggregate spending and reduces the demand for money. The excess demand for output raises the price level and the market rate of interest. Gradually the higher level of spending is perceived to be permanent. As this occurs the price level ris32 Such a phenomenon has been observed by Cagan (1972) for the U.S. and by Haberger (1963) for Chile. Frenkel (1975) and Mussa (1975) provide an explanation of this phenomenon that is based on an expectation formation process which combines adaptive and regressive elements. However the class for which their process is rather restricted. See Mussa (1975). OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.52.4.477 | Generated on 2023-01-16 13:28:12 494 Karl Brunner, Alex Cukierman and Allan H. Meltzer Credit and Capital Markets 4 / 2019 es further to reach a new permanently higher level. The market rate of interest remains at a higher level after the permanence of the shock is fully perceived.33 In the more general case of 20 θ > , positive shocks to aggregate demand increase employment and output and lower real wages. Perception that the positive shocks are permanent reinforces the initial response, further increasing output and employment and lowering the real wage. Both the perceived wage (table1) and the actual wage (table 2) fall in response to the rise in ε p t E , but the former falls more than the latter. Analysis of the permanent shock to spending implies that such changes cannot affect employment unless people are willing to work more, at lower wages, to buy the additional output they produce. The analysis implies, however, that positive transitory shocks to spending also increase output by shifting the labor supply function and lowering the real wage. V. Stagflation The sluggish adjustment of wages. prices, output and employment that results from the confusion between permanent and transitory shocks can produce rising unemployment and rising prices in response to a permanent decrease in productivity. This pattern, known as stagflation, is at times, taken as evidence that prices are set without regard to market conditions. We show that this is incorrect. ‘Stagflation’ can occur even in a neo-classical framework when there is uncertainty about the permanence of shocks. This section analyzes unemployment and inflation separately. Then we combine the responses and discuss the ‘stagflation’ that followed the 1973–1974 oil shock. 1. Unemployment Eq. (5) makes unemployment dependent on the difference -p tt ww . By substituting from tables (1) and (2) and leading unemployment j periods, we obtain (16a) ( ) ( ) 2 pp tj tj tj tj tj n Eu u E ωθ ωη εε ηω ηω + ++ ++ = -+ - ++ , 33 The effects of ε t and ε p t E on the price level, given θ = 2 0 , are ( ) 10 1 t t pb b θβ εβ ¶+ => ¶- and ( ) ( ) 10 1 t p t bb p b E βθ β ε -+ ¶ => - ¶ for small values of β . The rise in the market rate reflects the rise in the real rate. Substituting - pt t pp from tables I and 2, we can obtain the real rate ( ) =- - υ p tt t t rpp . For 20 θ =, υε β =¶ -> ¶/ 1/ 0 tt and / 0. ¶= δυ ε p tt E OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.52.4.477 | Generated on 2023-01-16 13:28:12 Stagflation, Persistent Unemployment and Permanence of Economic Shocks 495 Credit and Capital Markets 4 / 2019 or (16b) ( ) ( ) 12 + ++ ++ = -+ - εε pp tj tj tj tj tj n A Eu u A E . Unemployment is an increasing function of the difference between the permanent level of productivity and its current value and a decreasing function of the difference between the perceived and actual levels of aggregate demand. When the actual values of productivity and aggregate demand are equal respectively to their perceived permanent components, the unemployment rate is zero. When people believe that the permanent level of productivity is higher than the actual level, they refuse offers of employment at wages below the wage they believe should prevail, so unemployment is positive. Conversely, people supply labor in excess of the amount demanded at the current wage when they believe that the current wage and current productivity are above permanent levels. Similarly, when people believe that current aggregate demand is temporarily high, they must also believe that labor supply is temporarily high. They estimate that the current permanent wage is above the actual wage. Measured unemployment increases. The unemployment rate is not stationary. Each observation on unemployment, output, prices, wages and interest rates leads to revision of beliefs about permanent and transitory components, and each revision of beliefs changes perceived and actual values. But each period also brings additional shocks. The fundamental inference problem remains. To illustrate the inference problem, and its influence on unemployment, we start from a position in which the only reason for a difference between actual and perceived permanent productivity and aggregate demand is that the actual shocks include a transitory component.34 Formally, (17) 11 11 11 , -- -- -- == == εε ε pp pp qt qt tt tt E u u Eu E E , The only reason that (positive or negative) unemployment occurs is that productivity and aggregate demand are subject to transitory shocks. Unemployment is a white noise process with mean zero. Suppose now that in period t a large permanent shock to productivity reduces productivity by a large constant, . p Du People observe the effects of the shock, but they do not know whether the observed changes are permanent or transitory adjustments. For convenience, we assume that, without the shock, permanent productivity and permanent aggregate demand would have been constant at p u 34 The index q on the expectation operator indicates that the expectation is over the distribution of the transitory component of the variable. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.52.4.477 | Generated on 2023-01-16 13:28:12 496 Karl Brunner, Alex Cukierman and Allan H. Meltzer Credit and Capital Markets 4 / 2019 and ε p respectively.35 The rate of unemployment before and after the shock is given by (18) and (19) respectively.36 (18) [ ] 11 -=- - tj nA , ( ) 111 + = éù êú =- - - êú êú ëû å λλ jip tj u u io n A Du ( ) ( ) 11 11 ji qq uu u tji tj i A uu λλ λ +- + = éù êú + - -- êú êú ëû å (19) ( ) ( ) 11 1 1 , 0, j qq tji tj i Aj εε ε λ λε λε +- + = éù êú - - -- êú êú ëû å where 1 22 22 2 22 2 11 , , . 42 éù æö êú ÷ ç÷ º+ - = ç êú ÷ ç÷ ÷ ç èø êú ëû σσ σ λε σσ σ xp xp xp xxq xq xq xu By taking expected values (over q t u and ε q t )of eqs. (18) and (19) before and after the permanent reduction in productivity, p Du , we can compare the expected values of the rate of unemployment over the distribution of transitory shocks, (18’) 10. -= qt En (19’) ( ) 11 1 , 0. jip qtj u u io E n A Du j λλ + = éù êú =- - - êú êú ëû å Eq. (18’) shows that the expected value of the rate of unemployment before the change in permanent productivity is zero: unemployment deviates from its 35 In fact additional permanent shocks will continue to affect the economy according to the stochastic processes in (11) and (12). However if the permanent shock to productivity that occurs in period t large in comparison to 2 σ up and to 22 2 σ up A it will dominate the economy for a while. See also the discussion at the end of the subsection on unemployment and business cycles which follows. 36 Eq. (19) can be derived as follows. Rewrite (15a) as ( ) ( ) 1 1 0 11 + +- + = = - +- å λλ λ j ij pp tj i t tj i Ex x Ex for , , xu ε = substitute the result in (16b) and use the assumptions that 11 -- =p qt t E x Ex for , , xu ε = that + ε p tj is constant for a sufficient length of time and that += pp ts uu for 0<s and +=+ p pp ts u u Du for 0s . OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.52.4.477 | Generated on 2023-01-16 13:28:12 Stagflation, Persistent Unemployment and Permanence of Economic Shocks 497 Credit and Capital Markets 4 / 2019 expected value only because of the occurrence of transitory shocks as seen in (18). After the reduction in permanent productivity. the expected value of unemployment becomes positive since ( ) 1 10 i i j uu o λλ = - -> å for all i and 0< p Du . The expected value of unemployment is largest immediately after the decrease in permanent productivity then falls monotonically to zero as information about the permanence of the shock accrues. The length of time during which un employment persists depends on the relative variances of permanent and transitory shocks. The larger the variance of permanent productivity shocks, 2 σ up, relative to the variance of transitory productivity shocks, 2 σ uq, the shorter and the less severe is the period of unemployment following a shock of given magnitude. Inspection of (19’) also suggests that unemployment persists on the same side of zero for several periods. Persistent unemployment is a consequence of the more gradual adjustment of permanent productivity and permanent wages than of actual productivity and the actual wage rate. Initially, people interpret most of the decrease in the equilibrium real wage as transitory. If the shock persists, beliefs adjust gradually: the difference between perceived permanent wages and actual wages decreases, and the expected value of the rate of unemployment decreases. Formally, as j increases from 0 the coefficient of p Du decreases in absolute value towards 0. 2. Persistent Unemployment and Business Cycles Eq. (16) implies that the rate of unemployment in period t +j is a linear combination of the forecast errors of the productivity and aggregate demand shocks. Given the information set + tj I which includes the actual values of those two shocks up to and including period t+j, those forecast errors are serially uncorrelated. Therefore the rate of unemployment conditioned on + tj I is also serially uncorrelated.37 However, if a sample of unemployment rates is drawn for a period following a relatively large permanent shock, serial correlation will be found in the sample. This serial correlation is a property of the sample and provides no information about the underlying population or about a larger sample drawn from the same population, or about a sample of equal size drawn for a different time period. Evidence of ex post serial correlation in a particular sample is not evidence of inefficient use of information. Rational agents, looking back on the period, find support for the hypothesis that a large permanent shock occurred but was misperceived at the time. 37 We are indebted to Michael Parkin, Patrick Minford and Walter Wasserfallen for insisting on this point. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.52.4.477 | Generated on 2023-01-16 13:28:12 498 Karl Brunner, Alex Cukierman and Allan H. Meltzer Credit and Capital Markets 4 / 2019 At the time that the serial correlation is generated, there is no way in which people can use this evidence to improve their forecast. The reason is that the covariance between the forecast errors in the population is zero. In retrospect, however, the same people realize that a large negative shock to permanent productivity has occurred causing perceptions about productivity to be higher than actual productivity for a while and inducing a finite period of serial correlation in the rate of unemployment. By the time people realize that a large permanent shock has occurred, this information can no longer be used to improve the decisions they made in past periods. It is possible to show formally that the covariance between adjacent forecast errors conditioned on the knowledge (to the economist but not to the public) that a large permanent shock occurred in period t will be non-zero and large fog several periods after the shock.38 Footnote 38 shows that if ( ) 2 ∆p t x is large relative to 2 σ p the conditional expected value is positive and large for several periods following a large permanent shock. Standard tests for serial correlation may then detect serially correlated forecast errors and serially correlated unemployment. If ( ) 2 2 ∆< σ p tp x, there is negative serial correlation. In this case serial correlation is bound from above by 2 σ p, so it is less likely to be detected in sample data. Looking backward, economists and statisticians can identify some periods in which there is serially correlated unemployment or, more generally, there are serially correlated deviations of real variables from their trend. The amplitude and duration of unemployment. in such periods, depends on the relative variance of permanent and transitory components. The larger the relative variance 38 Let e be the forecast error. Then ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) λλ λλ λλ λλ λσ λσ λ λ λ ∆ ∆∆ ∆ ∆∆ ∆ ++ + ++ + +- + ++ + + + +- + +- éù êú ëû éù - + - +¼ êú = êú êú + + - +¼+ - +¼ ëû éù - + - +¼ êú êú êú + + - +¼+ - +¼ ëû - = +- +- + +- - 1 11 1 1 2 1 222 , | 1 11 1 11 (1 ) 1 (1 ) (1 ) 2 p tj tj t qq q tj tj tj j pp p t tj tj qq q tj tj tj j pp p t tj tj qq Ee e x xx x Exx x xx x xxx x [ ] ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) λ λ λσ λ σ λσ λ λλ λσ λ σ λ σ λλ λσ σ ∆ ∆ ∆ ∆∆ - + + + + +- + +- -- = + +- - -- éù = - - +- - ëû - =- - > > 2( 1) 2 221 22 2 21 2 2 21 2 22 2 22 21 2 2 (1 ) (1 ) 1(1 ) 2 (2 ) 11 (1 ) (2 ) (1 ) 0 .  jj pj i qp j qp t p j pq p t pp jpp tt x x x x as x OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.52.4.477 | Generated on 2023-01-16 13:28:12 Stagflation, Persistent Unemployment and Permanence of Economic Shocks 499 Credit and Capital Markets 4 / 2019 of the permanent component, the faster is the speed of adjustment to the shock. For the same realization of a given large permanent shock a relatively large variance of permanent shocks lowers the amplitude and decreases the duration of unemployment. Conversely a relatively small variance of permanent shocks implies that a given permanent shock lengthens the duration. Throughout the discussion of unemployment, we have made the convenient assumption that the only permanent change that occurs is the permanent productivity shock, p Du . This permitted us to trace the effects of a permanent change in isolation. We can now remove the assumption of a single permanent shock and discuss the qualitative effects of a large permanent productivity change in a world in which p t u and ε p t change continuously over time [in line with the assumptions in (12)] but usually by relatively small increments. If we now superimpose on this economy an unusually large negative permanent productivity shock39 in period t, it will dominate the scene for some time and all our results above will follow. In particular the lower the variance of permanent productivity shocks, the longer it takes people to learn about a permanent change of a given magnitude and the longer the period of unemployment following the shock. 3. Expected Inflation All of the shocks in the model affect the level of variables. Unless there are repeated shocks in the same direction, measured rates of change decline toward zero. There is no permanent inflation.40 Individuals form expectations about the price level they expect to prevail in period t+1 on the basis of information available in period t. The perceived or anticipated price level is p * tt t pp= . The anticipated rate of inflation, after substituting the equations in tables 1 and 2, and cancelling terms, is (20) ( ) ( ) ( )( ) ( ) *11 1, 11 pp tt t t t tt b p p E g u Eu bb η ω δη ψψ β ηω + ++ æö ÷ ç - =- - + + - ÷ ç÷ ç èø - -+ ( ) ( ) ( ) ( )( ) ( ) 12 // . 1 p tt b gb E b η ω θ β θ δη β εε ηω + +- + -- -+ 39 By the assumption (12) the probability that such a shock will occur is small but not zero. Hence large shocks will not occur very often but once they do, they will trigger the various effects described in the text. 40 The qualitative results are unaffected if we allow money stock to grow secularly. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.52.4.477 | Generated on 2023-01-16 13:28:12 500 Karl Brunner, Alex Cukierman and Allan H. Meltzer Credit and Capital Markets 4 / 2019 Eq. (20) shows that when the actual shocks are equal to their perceived permanent values, the expected rate of inflation is zero. Elsewhere, the expected rate of inflation is directly or inversely related (depending on the shock under consideration) to the difference between the current realization of the shock and the perceived permanent value. An increase in the money stock that is perceived as transitory induces a transitory increase in the price level. People believe that the price level will return to the permanent level, so 0 p tt E ψψ -> implies a negative expected rate of price change. A temporary, positive shock to productivity has the opposite effect. The shock lowers the price level but the lower price level is not expected to persist. The expected rate of price change is positive. In general, any shock that causes x to deviate from ( ) , , p t t ttt Ex x u ψε = affects the expected rate of inflation in a direction opposite to the effect of t x , on the current price level.41 This general rule leads to two propositions. First, a maintained increase in the permanent value of a shock that starts in period t causes an initial change in the anticipated rate of price change (inflation) opposite to the initial effect on the price level. Expected inflation reverses direction gradually. The reasoning is implicit in the gradual adjustment of permanent perceptions implied by eq. (15) and the fact that in (20) actual and permanent values have opposite effects on inflation. Second, the expected rate of inflation and the duration of expected inflation following a permanent shock depend on the relative variances of the permanent and transitory compones of the shock. This follows from the demonstration, in footnote 25 above, that the sum, n S , of the first n coefficients of the distributed lag increases as the relative variance increases. 4. Stagflation A permanent negative shock to productivity affects both unemployment and the rate of price change. This section brings some of our findings together to provide an explanation of the occurrence of stagnation – rising prices and unemployment. Suppose that a permanent, negative shock to productivity occurs in period t. Initially. the shock is not perceived as permanent. We know from the discussions of prices, unemployment and inflation that a shock of this kind initially causes the unemployment rate to increase and the price level to rise. The measured rate of price change is positive. Since the reduction in t u , is treated as tem41 Where the total response is ambiguous, as is the case for ε t with 2 0 θ ¹ , the proposition applies to the positive and negative components of the response. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.52.4.477 | Generated on 2023-01-16 13:28:12