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________________________________________________________ Contents (A) The Phillips Curve and the
Natural Rate Hypothesis (A) The Phillips Curve and the Natural Rate Hypothesis As noted earlier, Milton Friedman (1956) did not have a "Quantity Theory" properly speaking as he could only relate money supply changes to changes in nominal income, PY. In other words, if there is a rise in the supply of money, this will raise aggregate demand, but that can, in turn, lead to a rise in the price level and/or a rise in output. The Keynesian multiplier theory argues that output is the primary adjustment mechanism, at least in situations of unemployment, and that changes in the price level only emerge at full employment. Friedman's transmission mechanism lacked a "missing equation" to differentiate the effect on prices from the effect on output. The "missing equation" was provided inadvertently by a late Keynesian artifact - the Phillips Curve (Phillips, 1958; see also Lipsey, 1960; Samuelson and Solow, 1960). While the Phillips Curve may have provided Neo-Keynesians with an empirical rationale for the setting of the (dynamic) nominal wage which had been absent in their system, it also provided the Monetarists with their own "missing equation". It was the "natural rate hypothesis" introduced by Milton Friedman (1968) in his famous presidential address to the American Economic Association that would do the trick. Recall that the original Phillips Curve asserted that there is a negative relationship between nominal wage inflation, gw = (dw/dt)/w and unemployment rate, U, captured succinctly by gw = h(U) where h¢ < 0. The subsequent theoretical argument provided by the Keynesians was that when aggregate demand growth was greater than aggregate supply growth, and thus unemployment low, wage inflation would increase because of either demand-pull or cost-push pressures. The reasoning behind much of the Phillips Curve story is that if unemployment is low, then workers will demand higher nominal wages, whereas if unemployment is high, nominal wage demands will be tempered. To translate this into price inflation, recall that nominal output is denoted PY, so gp + gY denotes nominal output growth decomposed into price growth (gp, henceforth denoted p ) and real output growth (gY). Let gD be nominal aggregate demand growth. Then if nominal aggregate demand equals nominal aggregate supply, as is assumed in Keynesian theory, then, in growth terms, gD = p + gY, or:
so price inflation is related to the gap between nominal aggregate demand growth gD and real output growth gY. Output growth translates into productivity growth, and profit-maximization on the part of firms implies that they will set real wages (w/p) equal to the marginal product of labor (again, as assumed in Keynesian theory). In dynamic terms, this translates into gY = gw - p or, reversing this:
thus if the growth of nominal wage demands exceed productivity growth, firms will pass on the wage increases they give their workers into higher output prices. Now, the simple Phillips Curve hypothesizes that gw = h(U). Thus, assuming for simplicity that there is no productivity growth, so gY = 0, then we obtain the result that p = gw (where, notice, the real wage is constant) and thus:
which is the familiar Phillips Curve relating unemployment to price inflation, where h¢ < 0 and h(U*) = 0. Milton Friedman (1968) and Edmund S. Phelps (1967, 1968) disputed this Phillips Curve as a good representation of the labor market process. Unemployment, recall, is defined as U = (Ls - Ld)/Ls, where Ls is the labor supply and Ld is labor demand. Now, in Neoclassical theory, labor is supplied by households according to their utility-maximizing labor-leisure choice combination at a particular real wage level. Thus, given w/p, there is a particular amount of labor supplied, which we shall denote Ls*. Labor demand, Ld is established by the profit-maximizing conditions denoted earlier. Let us refer, then, to the Friedman-Phelps natural rate of unemployment at a particular real wage w/p as U* = (Ls* - Ld)/Ls*. Thus, we can think of the level of this "natural rate of unemployment" as being "ground out by the Walrasian system of general equilibrium equations" (Friedman , 1968). This is shown in Figure 2 as U*. This "natural" unemployment rate U*, later to be christened the NAIRU or simply NRU, reflects structural and frictional unemployment. In other words, all the unemployed who are temporary but full-time job-seekers, busily gathering information before making a final employment decision (so, in "transition" between jobs - thus "frictional" unemployment), or those whose skills have been left made redundant by structural changes in industries are in the process of moving or acquiring new skills necessary to catch up with the current labor market situation (thus "structural" unemployment). What it does not include is "cyclical" unemployment, i.e. those who have been made unemployed by the regular business cycle (e.g. from insufficient aggregate demand). Thus, we can consider the natural rate of unemployment U* to be "full employment". Assume, for the moment, that U* is the actual prevailing unemployment rate and, for simplicity, let the Phillips Curve p = h(U) pass through U* at zero inflation in Figure 2. Assume now that the government attempts to decrease unemployment below U* (say, to U1) by increasing nominal aggregate demand. Firms will respond to this rise in demand by trying to increase output. To accomplish this, they need to increase employment and thus pull workers out of leisure by offering them higher nominal wages, so gw > 0. But, recall, as there is no productivity growth, then the profit-maximizing conditions imply that firms will pass off this nominal wage increase into output prices, i.e. in growth terms, gw = p1 > 0 as in Figure 2. However, as nominal wages and prices are rising by the same amount, then the real wage is actually unchanged. Friedman (1968) and Phelps (1967, 1968) suggested that workers' actual labor supply functions are functions of the expected real wage. They want real purchasing power, a real bundle of goods, independently of the rate of change of price tags. Suppose for the moment that they do not expect firms to pass on their nominal wage increases into price increases, i.e. expected inflation is zero, pe = 0. In this case, they perceive that their real wages have risen and will indeed supply more labor. The workers are suffering from "money illusion". In this case, unemployment might actually decline to U1 < U* as in Figure 2. Of course, we know that at U1, inflation is p1 by the Phillips Curve, but this was unexpected by the workers. Thus, we move from the no inflation, U* combination to the (p1, U1) combination at point a in Figure 2.
However, Friedman and Phelps argued, workers do not suffer from this "money illusion" forever. Eventually, the laborers will notice that the inflation rate is really p1 and thus realize they have been duped into increasing their labor supply as their real wage has actually not changed. As a result, those that entered the labor market enticed by higher nominal wages will leave again and unemployment will rise back up to U*. This movement is captured in Figure 2 by a jump from point a to b. [Notice, that this inflation-unemployment mechanism works in a "clockwise" direction in Figure 2 - while the original findings in Phillips (1958), suggest that the mechanism is anti-clockwise.] Crucial in this story is the theory of expectations. Friedman and Phelps proposed that agents have adaptive expectations of prices - as originally introduced Cagan (1956). Adaptive expectations states that current inflation expectations are extrapolated from past inflation experience - which can be expressed in distributed lag form as pte = å i ai pt-i where ai are declining weights. The specific form pte = pt-1 of adaptive expectations - known as static expectations - implies that workers expect inflation today to be what it was yesterday. Now, as labor supply is a function of the expected real wage, Ls = L(w/pe), then labor supply growth can be written in dynamic form as:
where l > 0. In the absence of productivity growth, recall that gw = p , so:
thus agents increase their supply of labor (gLS > 0) only if they misperceive what actual inflation is, i.e. if p ¹ pe. Alternatively stated, they will only increase their labor supply if firms increase nominal wages faster than expected inflation. This process can be captured by employing an "expectations-augmented" Phillips Curve. In this case, we have:
where inflation is related to unemployment in the old fashioned way, but also to expected inflation pe through the term b > 0. The expectation term enters because nominal wage demands are made on the basis of expected inflation and thus feed into inflation as well. For the moment, we will assume nothing about the value of b . Notice, then, if pe = 0, we have our old p = h(U) curve unchanged. But if there are positive inflationary expectations (pe > 0), then the Phillips Curve shifts upwards, as shown in Figure 2. So, for each level of expectations, there is a specific "short-run" Phillips Curve. For higher and higher expectations, the Phillips Curve moves northeast. Early Keynesians (esp. Samuelson and Solow, 1960) championed the Phillips Curve in the belief that it provided an output-inflation trade-off frontier that was policy-effective: i.e. governments could choose to lower unemployment by increasing aggregate demand growth, but the cost would be higher inflation; or they could choose to have low inflation by lowering aggregate demand, but then the cost would be higher unemployment. Clearly, such a potentially exploitable policy-effective relationship still exists for any given short-run Phillips Curve, i.e. assuming inflation expectations are given. But expecatations will catch up soon after. What happens in the long-run, i.e. when inflation expectations are incorporated concurrently? In the long-run, expected inflation will be equal to actual inflation so p = pe. In this case, gLS = 0 and the expectations-augmented Phillips Curve is p = h(U) + bp , so, rearranging, we obtain
which is known as the "long-run Phillips Curve". The slope of this curve is:
where, since h' < 0 and if b < 1, this implies that dp/dU < 0. In other words, in the long run, inflation is still negatively related to the unemployment rate (the shape of the Phillips Curve) albeit steeper than the simple short-run Phillips curve (which had slope h¢ ). Already a few years before, Friedman (1966) had denied that there was an exploitable long-run trade-off between inflation and unemployment. With this natural rate hypothesis, Friedman (1968) and Phelps (1967) established that this was indeed the case. In other words, they argued that the coefficient b = 1. In this case, the long-run Phillips Curve is completely vertical at unemployment rate U*, as shown in Figure 2. In other words, there is no stable long-run trade-off between inflation and unemployment: policy-makers cannot, in the long-run, "pay" for lower unemployment with a little bit of inflation. Of course, Friedman allowed policy-makers to exploit such a trade-off in the short-run, but to even attempt it could have long-run costs in terms of higher inflations and no gains (i.e. no change in unemployment). To see this, suppose the government had it in mind that U1 was indeed their desired target unemployment. To obtain this, in the short-run, they would have to increase the rate of nominal aggregate demand growth. In the short-run, therefore, they would move to a point such as a in Figure 2 with unemployment at U1 and inflation at p1. However, by adaptive expectations, p1 would soon be expected and thus the short-run Phillips Curve would soon shift upwards to p = h(U) + bp1 and unemployment would return to U* and foil the government's attempt to keep it at U1. Thus, in order to push unemployment back to U1, the government would then have to increase the growth rate of aggregate demand even further, taking the economy from point b to point c in the short-run, which would again yield unemployment U1, but inflation would increase to p2. However, adaptive expectations would kick in again and the short-run Phillips Curve would rise again to p = h(U) + bp2, pushing unemployment back up to U*. Once again, to achieve their target U1, they would have to accelerate the rate of aggregate demand growth again, pushing the economy to e at inflation rate p3, etc. As we see, then, the only way of maintaining unemployment at U1 is for the government to continuously accelerate the rate of nominal aggregate demand growth. The inflation rate, of course, would spiral upwards to astronomical degrees of hyperinflation. At any rate, it would be futile in the end: if, at any point, the government relented in its acceleration, the unemployment rate would jump right back to U*, leaving in its wake only a very high inflation rate. Attempts to exploit the short-run trade-off, then, only yield long-run costs of higher inflation. This argument had already been expounded decades earlier by Keynes's nemesis, Arthur Cecil Pigou (1933: p.250-1; see quote above). Accelerating is quite costly and, for the most part, can only be temporary for the "evil" effects of ever-rising rates of inflation would soon outweigh the benefits of lower level of unemployment - although, as Edmund Phelps (1972) notes, if government has positive time preference, then it may be nonetheless worthwhile to pursue some amount of acceleration, an "optimum inflation", even if only to offset temporary shocks. However, if sustained, acceleration will ultimately lead to a point where either the government goes bankrupt or money loses its role as a medium of exchange and unit of account. In either case, the unemployment level would quickly return to the natural rate and the government's accelerating efforts would have been wasted. As a result, the natural rate of unemployment, U*, has gained the acronym NAIRU, for "non-accelerating inflationary rate of unemployment" - in fact, the only level of unemployment for which inflation does not accelerate forever. It is on the basis of this account that Friedman claimed that "inflation is always and everywhere a monetary phenomenon in the sense that it is and can be produced by a more rapid increase in the quantity of money than in output" (Friedman, 1970: p.24). Notice that he not only excludes "cost-push" theories of inflation from this, but he also does not recognize that fiscal policy (e.g. increased government spending) can generate inflation. This last arises at least in part from Friedman's earlier view that fiscal variables barely affect nominal aggregate demand. Furthermore, there is a limit to the amount of government spending that is possible - or, at least, at some point, it will have to be financed by printing money (if one presumes there is an upper limit to the amount of debt a government can issue and reasonably expect people to accept). Thus, in this manner, Friedman finally obtained a sort of "Quantity Theory" relationship between the money supply and prices - having output pinned down by NAIRU and having money supply growth do most of the accelerating of nominal aggregate demand. As he writes:
The reaction to Friedman 's natural rate hypothesis was manifold. Some commentators (e.g. F.H. Hahn, 1971; J. Tobin, 1972), deplored the conception of NAIRU, arguing that it was merely hypothesized that it existed and had no good "microeconomic" foundations. This criticism was soon met by the various "search" theories of unemployment developed in a volume edited by Edmund S. Phelps (1970) (esp. Phelps's introduction and the contributions of Dale T. Mortensen, 1970) and in later work of Robert E. Lucas and Edward C. Prescott (1974) and many others since. The effort of search theory was to explain not only U* but also the kind of expectations NAIRU theory needs. The basic idea is that at any one time, there is a group of workers who believe that they are able to get a better job elsewhere but before they can get it, they must engage in "job searching". Since gathering information to find the ideal job is a time-consuming endeavor, they "quit" working to make their full-time search. In principle, they are not earning a wage during this time (but may receive unemployment benefits, or take out loans, etc. to keep on living). Thus, they are in a sense, "voluntarily" unemployed - albeit temporarily. At any single point in time, there will always be a given amount of such workers switching jobs - frictional unemployment - that is supposed to form the bulk of U*. Certain things, such as time preference, expectations, the amount of unemployment benefits, access to loans, etc. all affect the decision to search and thus will affect the precise value of U*. In his presidential address, Milton Friedman (1968) predicted the empirical break-up of the Phillips Curve and challenged economists to prove that his assertion that b = 1 was wrong. In his presidential address to the American Economic Association, James Tobin (1972) attacked both search theoretic explanations as incomplete and provided a theory of unemployment which retained some amount of "aggregate money illusion" due to sectoral differences. This enabled him to maintain a downward-sloping long run Phillips Curve (i.e. with b < 1) which was policy effective A series of studies were consequently conducted to prove which of the hypotheses - Friedman's b = 1 or Tobin's b < 1 - was correct. Early studies by George L. Perry (1966, 1970), Robert M. Solow (1968), Robert J. Gordon (1970, 1971) and S.J. Turnovsky and M.L. Wachter (1972) yielded estimates for b which were significantly less than 1. But these results soon began to falter. R.J. Gordon (1972), S.J. Turnovsky (1972), J.M. Parkin (1975) and M.L. Wachter (1976), confirmed that, indeed, they could not reject the hypothesis that b = 1. At any rate, the very notion of policy-exploitable macromodels were exploded soon after by the famous critiques of Robert E. Lucas (1972, 1976) and Thomas J. Sargent (1971), which relied on the notion of rational expectations. Specifically, they demonstrated that even if b < 1, there is still no exploitable long-run unemployment-inflation trade-off. In other words, if agents have rational expectations, then an anticipated government attempt to exploit that trade-off would lead to a response by agents and thus an adjustment in the parameters of the Phillips Curve that would foil the government's efforts. In short, even if the trade-off existed, it would immediately disappear the moment the government tried to exploit it. At any rate, the debate soon took a surprising twist with the stricter natural rate hypothesis of the New Classicals, as famously laid out by Robert E. Lucas (1972). When replacing adaptive expectations with rational expectations, then not only was there no long-run trade-off between inflation and unemployment, but that there was not even a short-run trade-off! The New Classicals objection was that Friedman's "adaptive expectations" assume that agents are making systematic error. There seems to be no good reason, they argued, for agents to expect next year's inflation to be this year's inflation. Intuitively, suppose we begin at NAIRU with zero inflation and zero inflationary expectations. Suppose there is a freakish and thus completely unexpected drought this year that leads to inflation. By Friedman's adaptive expectations, agents should consequently expect inflation next year to be the same. By why? Are agents expecting another freak drought? If so, then droughts can not really be that "freakish" to begin with but must be commonplace or at least systematically related to past droughts. But if droughts have these systematic features, then agents should have had some expectation of the first drought to begin with and thus inflationary expectations should not have been zero to begin with. Hence, the New Classical argument goes, in the initial period when agents had zero inflation expectations, either agents are not making full use of what they know (i.e. that droughts are common or systematic) or their extrapolation that this year's drought implies a drought next year is completely irrational. Either case would be inconsistent with rational expectations, introduced by John Muth (1961) and applied to this context by Robert E. Lucas (1972, 1973), Thomas J. Sargent (1973) and T.J. Sargent and Neil Wallace (1975, 1976). The rational expectations hypothesis argues that agents make full use of their information and do not make persistent, systematic error. In other words, either agents would realize the systemic component of the drought and would have had positive inflation expectations to begin with ("making full use of information") or they would realize that the drought was indeed freakish, in which case they would not expect a drought next year and thus not expect next year's inflation to be equal to this year's inflation ("no systematic error"). For the Phillips Curve context, replace the word "drought" with "accelerationist monetary policy". The argument then as an accelerationist monetary policy is systematic, then workers would have expected there to be accelerating inflation from the outset and would have refused to supply more labor in response to the higher money wages dangled before them. In other words, they would not have moved up the short-run Phillips Curve from the initial position (U = U*, p = 0) in Figure 1 to point a (U = U1, p = p1) but rather would have jumped straight to point b (U = U*, p = p1) on the long-run Phillips Curve. In other words, the government would have been unable to lower unemployment to U1 even temporarily. This does not mean that unemployment cannot fall below U* from monetary acceleration. But this acceleration would have to happen unsystematically or randomly so that agents would not be able to form expectations. In this case, then inflation expectations could not be properly constructed and agents would indeed move up to point a (U = U1, p = p1). But this is temporary: as soon as they realized what happened, like the regular Monetarist story, they would consequently leave the labor market again and bring unemployment back up to U*. The main point of this story, then, is that only random, unexpected monetary accelerations can lower unemployment temporarily. A systematic accelerationist monetary policy will not lower it at all. In other words, there is no policy-effective short-run Phillips Curve trade-off. In order to make this conclusion work, several assumptions must be made. The most prominent is that information is generally known. If the government conducts an accelerationist monetary policy in complete secrecy, agents might not know it was systematic and supply more labor. However, as the New Classicals argued, secrecy is never really complete and the workers will soon enough wise up to the fact that the acceleration is systematic. In other words, by perceiving the inflation patterns, etc., they will gradually realize that the government is conducting a systematic acceleration policy, in which case they will incorporate this information and change their expectations accordingly -- and thus foil the government's policy again. The other necessary assumption is no systematic error. Why should not agents be stupid and irrational and just assume that this year's freakish drought implies a drought next year? The New Classicals admit, indeed, that people can be quite stupid: any particular agent can easily make strange extrapolations and systematic errors. However, they argue that it cannot be that all people make the same systematic error. As we are working with "aggregates", each worker may be make systematic errors and have idiosyncratic errors, but by an intuitive appeal to the law of large numbers, these idiosyncratic errors are washed out in the aggregate. In other words, one agent's peculiar stupidity cancels out another agent's stupidity so that, on average, the "representative agent", the "aggregate", is in fact quite smart - by which we mean, that, on average, workers does not make systematic errors. As Lucas (1972, 1973), Sargent (1973) and Sargent and Wallace (1975, 1976) made clear, the policy implication, then, is that systematic monetary policy has no effect on output. Only policy "surprises" or aberrant shocks can influence output. In moving from Friedman's "only money matters" to the New Classicals' "money does not matter" (or rather, "only surprise money matters"), the debate turned in a considerably more radical direction. Crucial to this process was the reintrepretation of the Phillips Curve as a sort of "aggregate supply" curve. In particular, recall that in its simple Monetarist form (where b = 1):
where we have made the slight notational modification of expressing the Phillips relationship as one between inflation and the difference between unemployment and the natural rate of unemployment (note that h¢ < 0 still). Okun's Law (Okun, 1962), argues that a 3% reduction in output implies a 1% increase in unemployment. Thus, we can argue that unemployment and output are related monotonically - so that higher output implies higher unemployment and vice versa. Thus, we can propose an Okun relationship along the lines of U - U* = g(Y - YF) with g¢ < 0, where YF is full employment output. So the degree to which actual output Y lies below full empoyment output YF, actual unemployment U lies above the natural rate of unemployment U*. We can refer to the deviation of output from full employment output as y = Y - YF. Consequently, the Phillips Curve can be rewritten as:
thus letting (h°g)(y) = h(g(y)), then:
or letting ¦ = (h°g)-1:
where ¦ ¢ > 0. Defining p = p - p-1 and pe = pe - p-1, then this becomes:
so that output is positively related to the difference between prices and price expectations (or, more precisely, the deviation of actual output Y from its full employment level YF is positively related to the difference between the price level and price expectations). This "aggregate supply" function (sometimed called the "Lucas supply function") is a Monetarist-New Classical construction for which the natural rate hypothesis is essential; it did not exist in the Neo-Keynesian system. Notice the natural rate result that when p = pe (in the long run), then y = 0, i.e. Y = YF. The New Classical rational expectations hypothesis would imply that, bar surprises, pe = p at all times, so Y = YF in short-run and the long-run. As we are moving beyond Monetarism at present, we shall end the story here. We shall only note that, by 1977, Franco Modigliani in his presidential address to the A.E.A. finally accepted the natural rate hypothesis at least for the long-run. Other Keynesians, such as James Tobin (e.g. 1980), have remained more irredentist.
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