Fluctuations and rigidities in local labor markets. Part 1: theory and evidence. G L Clark. John F Kennedy School of Government, Harvard University, Cambridge, ...
Environment and Planning A, 1983, volume 15, pages 165-185
Fluctuations and rigidities in local labor markets. theory and evidence
Part 1:
G L Clark John F Kennedy School of Government, Harvard University, Cambridge, MA 02138, USA Received 12 October 1981; in revised form 1 March 1982
Abstract. Cyclical sensitivity in employment, wages, and hours worked are explored with reference to three industries and eleven US cities over the period 1972-1980. Conventional neoclassical discrete-exchange models of the labor market are shown to be inadequate because of marked rigidities in the patterns of short-run adjustment. Money wages are very stable, being dominated by a long-run trend, and firms tend to adjust hours worked and only then employment in the short run. There are, however, significant interregional variations in these patterns within the same industry. Spectral analysis and tests for periodicities in the patterns of residuals derived from trend-line estimates of money wages confirm a supposition that urban Phillips curves do not exist. The evidence supports the implicit notion of contract theory that continuous employer-worker relationships exist over the business cycle. The question of how useful, in general, this theory might be is left open for the present. 1 Introduction Imagine a firm is faced with a sudden and unanticipated decline in demand for its output. How is it likely to respond? Neoclassical models, based upon perfect competitive assumptions, suggest two possibilities. First, if the market price falls quickly enough, a compensating increase in demand could be induced via the bargain prices faced by consumers. Second, if prices do not adjust to fully compensate declining demand, or if there is a lag in response, the firm would be forced to reduce output and to lay off excess labor. As a consequence, with declining demand for labor relative to supply, wages should also fall. Only a minor modification to this second answer is required if money wages are sticky downwards. Phillips (1958), argued that although wages do not decline absolutely, their rate of increase does. What of workers' responses in this situation? Neoclassical models emphasize real wages as a key behavioral criterion. With declining commodity prices, a commensurate decline in money wages would be of little relevance because real wages would be maintained. A step further in this line of reasoning is to suggest that money wages vary according to workers' expectations of likely changes in prices (Grossman, 1980). Even if money wages are sticky downwards, neoclassical theory still implies a great deal of wage-rate inflation volatility over the short run. Studies of the dynamics of local labor markets have depended to a large extent on these types of propositions (Clark, 1980). In these analyses, short-run patterns of employment are typically linked to industry-specific demand patterns and the location of those industries, and local wage inflation models typically depend upon the Phillips curve and its implied neoclassical quantity and price adjustment mechanisms (Clark, 1981c). Essentially, the local labor market has been treated just like any other commodity market, albeit with the appropriate cautions regarding the significance of flexible versus fixed-price arrangements. Workers are not simply commodities. They can, and often do, enter into implicit and explicit contractual agreements with employers. Rather than supply and demand being the dominant means of setting wages, union and collective wage bargaining are key institutional characteristics of the labor market (Ross, 1948). In recent years Baily (1976) and Azariades (1975) have also shown that implicit contracts can
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dominate decisions regarding wages and employment. Over the economic cycle, workers can expect to be laid off and their overall wages reduced according to the severity of demand shifts. An option is to spread the risks and benefits of association with a particular employer over a longer period than any one phase of the business cycle. For example, a worker could agree to moderate wage demands during a boom in return for a guaranteed wage during a recession. In doing so, the worker seeks to minimize disruptions to income with respect to the timing and duration of subsequent booms and recessions. Implicit contracts also have advantages for firms. Imagine our firm requires a particular skilled worker to run a machine (compare Oi, 1962). If the firm cannot be sure it will be able to rehire that worker when demand picks up, the firm might agree to a longer-term contract that effectively ties the worker to the firm over the business cycle (Hicks, 1932). Also, firms often benefit from having long-term wage contracts in that their labor costs are to be predictable and the total wage will be relatively stable. Here, then, it is apparent that neither wages nor employment need be sensitive to business-cycle fluctuations. In fact, the implicit contract literature implies that conventional predictions of local labor-market adaptiveness to changing macroconditions need not occur. Even if output was to fall precipitously, employment and wages may not be affected. Given that most models of regional short-run adjustment use employment as the indicator of economic impact (compare King and Clark, 1978), the existence of contractual agreements amongst employers and workers may result in misleading conclusions regarding the actual nature of regional economic response. In this paper the cyclical sensitivity of local labor markets is explored over the period 1972-1980 for three industries (apparel, electronics, and printing) and some eleven US cities. The second section details the familiar neoclassical discreteexchange theory of labor markets. Notions such as individual choice, autonomy, and aggregate efficiency are considered as central elements of this paradigm. Newer contract theory which eschews discrete exchange in favor of long-term continuous relationship is also reviewed and considered in terms of commodity exchange. The subsequent sections then consider the empirical evidence, utilizing time-series techniques such as spectral analysis. Local sensitivity is measured in terms of three strategic variables: employment, hours worked, and wages. Rigidities consistent with implicit contract theory are in fact found (compare Hall, 1980). However, in a second part to this project (to be published in the next issue of the journal) a critical assessment of this theory is provided which utilizes neomarxist notions of power and interdependence. The goal of this paper is to prompt a revaluation of the efficacy of neoclassical labor-market models and the possible relevance of contract theory given empirical evidence of major shifts in local labor-market dynamics. 2 Labor as a commodity Neoclassical economics is based upon two axioms: individual free choice and utility maximization. The decision to participate in the labor market (to supply labor) is a decision taken by individuals with respect to their utility (income, leisure, and lifecycle characteristics). Labor can be described by dimensions such as skill, training, and education which may or may not be job specific (Williamson, 1975). These dimensions are essentially the 'human capital' of the worker. Whether or not individuals 'invest' in human capital depends upon actual and expected returns, including expected income from future job opportunities. On the other hand, the demand for labor depends on the technical requirements of production. As Oi (1962) pointed out, labor skills often have particular and fixed technical relationships with
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capital in the short run. Basically, one can imagine the worker as a complementary machine, with 'its' technical competence being determined by individual choice and utility maximization. Here, of course, the demand for labor is like that for any other commodity. When couched in terms of marginal productivity, labor is a divisable commodity arranged according to the most efficient mode of production. One way of describing the discrete-exchange (commodity) nature of the neoclassical labor market is to represent it as an auction. Labor is offered for sale by individuals at a minimum bid price (reservation wage) based upon their calculus of utility. Given that each individual can be valued in terms of his or her human capital, demand and supply for that particular individual (commodity) will set the market price. If there are no bids at or above the workers' reservation wages then labor will be withdrawn from sale (in essence the 'discouraged worker' effect). Labor is bought, competitively amongst employers, and is used to the point where its output is no longer required, or more significantly: to the point where it can be replaced by a cheaper worker with the same skills. Implied is a possibility that workers can be drawn from, and returned to, the auction at any point in time. An example that comes to mind are the day-laborer hiring halls that still exist in many American cities. Auction models of labor exchange may not be efficient under conditions of less than perfect information. To illustrate, assume that the total set of workers offering their labor at any point in time and their human capital dimensions, are known. But also assume that their reservation wages are unknown. The order in which each individual comes up for auctioning is then very important. Since it is unknown whether or not the first worker's reservation wage is indicative of the overall distribution of reservation wages, one employer strategy would be to wait for more information (that is, disclosure of other reservation wages). However, if demand is strong relative to supply, employers could only afford to wait through a portion of the auction before deciding what the wage distribution might look like. Of course, this does not guarantee that succeeding offers will be similar to previous offers. It is also plausible that workers themselves would revise their reservation wages according to previous offers and bids, leading to further uncertainty on both sides of the auction. Imagine a further example wherein there are many more workers than potential employment vacancies although, as before, the distribution of reservation wages is unknown. An employer could bid for a worker and employ him/her, but as other less expensive workers come up in the auction, the initial contract would be renegotiated in favor of the employer or the employee would be replaced. The only means of counteracting the power of employers would be to unionize and standardize the reservation wage. Consequently workers in the upper order of the auction would be employed first. Rationing employment would be on the basis of order in the auction queue. With no union and greater labor supply than demand, the auction model predicts tremendous instability in length of job tenure and overall employment (Hall, 1981). Depending upon changes in the demand for labor, the auction model also predicts rapid wage inflation at the onset of a boom. Thus wage and employment instability with respect to levels and rates of change are essential features of a neoclassical auction labor exchange. Neoclassical labor market could also be characterized as a bourse. All commodities (in the case of labor, differentiated by skill and experience), with their quantities and prices, are listed in a central market place for a given period of time [like Hicks's (1965) 'trading week']. As bids are made, prices are determined by supply and demand and the option of substitution between different commodities. For a bourse to operate efficiently there must be many buyers (employers) and sellers (workers), and there also must be a market coordinator. Under monopoly
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conditions, however, prices are unlikely to reflect the true dimensions of supply and demand, and without a coordinator the exchange process itself would collapse. Recontracting is a key feature of such an exchange system; as new bids are made, and quantities supplied are adjusted in accordance with bids, the 'best' market allocation changes. Hence, within the exchange period, recontracting is the means of facilitating the optimal price/quantity combination. In a system of local labor markets, we could imagine a set of bourses coordinated such that labor is allocated over time and space according to the pattern of final demand and supply. Given the recontracting process, prices and quantities are likely to be initially quite volatile, but to eventually attain a stable equilibrium. Whether or not equilibrium is actually attained in reality is quite problematic. Frictions of distance and implied problems of market coordination and information may result in a less than efficient spatial allocation of labor (Ballard and Clark, 1981). Migration is then a key mechanism in coordinating any spatial system of labor markets, and labor is assumed to respond to the spatial configuration of demand and supply, expressed in terms such as wages and unemployment (Lowry, 1966). Flows and exchanges between and within local labor markets have then an equilibrating function although the time-frame in which such flows adjust to changing prices is subject to some debate (Clark, 1982). Inevitably, the bourse model depends upon changes in prices and quantities as the signals for recontracting and allocating labor efficiently. When expressed as an exchange commodity, labor can be conceptualized just like any other good. Standard principles of supply and demand apply, as do notions of marginal pricing and adjustment. The actual form of the neoclassical labor market does have important implications for understanding the roles of prices and quantities. For example, in an auction system, the distribution of reservation wages provides important clues for employers in bidding for labor. Also, in a bourse prices (wages) are the signals for recontracting and exchange. Both types of market systems depend on assumptions of perfect competition and atomistic behavior. Under uncertainty both modes of exchange will not necessarily be efficient. For example, if the distribution of reservation wages is unknown, as in an auction, employers may be forced to bid on earlier offers in the queue thus generating wage inflation and the possibility of nonclearing markets. Similarly if prices do not truely reflect demand and supply conditions (perhaps because of time or space lags), false trading could occur leading to problems of coordination and disequilibrium. Prices and quantities are required to be adaptive to changing conditions if the market for labor is to be efficient (Okun, 1981). 3 Contracts and labor-market structure Dunlop (1944) argued that "... the labor market is not a bourse". He claimed that the "technical organization" of labor exchange does not conform to either an auction or a bourse. His argument concerned the structure of the labor market much more than its institutions. Dunlop observed that in labor markets there are many more sellers of labor (workers) than buyers (employers). Firms generally set the wage rate that they are willing to pay and then allow workers to sort themselves according to those who will offer services and those who will not at the given wage rate. By varying the quoted price for labor, firms are then able to attract different types of labor (for example, Clark and Whiteman, 1983). Unlike a bourse or even an auction, it is practically impossible for a worker to displace another by offering to work at a less than 'quoted price'. A likely effect will be market segmentation by workers and employers alike, around different clusters of wage offers and skill types.
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Thus, the labor market is an exchange system that has inherent tendencies of segmentation, quantity rationing given quoted prices, and market power favoring employers (Piore, 1979). Unions, according to Dunlop, are actually a response by workers to the power of employers. However, it should be emphasized that for Dunlop the existence of unions is an outcome of the structure of labor markets, not their distinguishing feature. The quoted-price market will obviously favor the employer. Even if labor is scarce in the short run, labor has no direct means of forcing a change in its wage unless it switches to another employer (Clark, 1981a). In essence, recontracting is unlikely because price determination is set by one side of the market. If a firm cannot hire labor after repeated offers at a certain quoted price, then an increase may be forced although even the increase need not reflect overall supply and demand conditions. On the other hand, if labor is plentiful, repeated offers to work at a certain quoted price may encourage firms to change their quoted price. However, firms are rarely able to unilaterally restructure their wage contours, because new hires and quoted prices are typically made with reference to existing salary structures and it is only after a quoted price draws many more potential employees than expected that firms are able to reevaluate their quoted price for future hires. In Dunlop's model, wages only slowly adapt to labor supply even though employers have significant power in the exchange system. Dunlop (1944) severely criticized wage determination models based upon notions of power (for example, Ross, 1948), as being unecomonic. However, there are reasons to suppose that his critique was overdrawn. For example, it is clear that he considered that firms make price offers with reference to existing internal and external wage contours. Why should firms be so concerned with internal wage relativities given their power in the market? One answer is that the wage rate is more than a price—it classifies workers by prestige, status, and even responsibility in the firm. Consequently a change in the quoted price relative to existing standards will disrupt the internal social structure of the labor markets of firms. A second answer, one also noted by Dunlop (1944) is that changes (especially increases) in the quoted price for a given class of worker will initiate claims by other workers who use such prices as reference points for wage bargaining. Whether or not unions exist is irrelevant; workers and employers depend upon complex implicit contracts that relate as much to standards such as 'fairness' and 'equity' as to a simple price quoted by firms for labor services (Wood, 1978). Dunlop argued that this is the result of the technical organization of labor markets. However, the existence of wage relativities implies an important normative content. The newer implicit contract literature is based to a large extent on Dunlop's pioneering studies of the economics of labor-market exchange. Rather than viewing labor as a discrete-exchange commodity, these theories emphasise the pattern and determinants of long-term employment relationships. Moreover, there has been recognition that recontracting in the Walrasian sense is meaningless in labor markets. Agreements are made with significant time dimensions included that purposely preclude short-run market solutions. Like Dunlop, Azaraides (1975) and others have not been concerned with unions as the key institution of the labor market. They start from a commodity model of the labor market—both demand and supply —and then derive contractual solutions to problems such as uncertainty and risk, from the objective functions of those involved. To illustrate, assume that firms have specific labor requirements (skills) in their production processes and that labor efficiency is a function of years of experience on-the-job. A firm may hoard its labor over the short run, protecting itself from having to search for new labor, and perhaps pay extra for scarce supplies, in a tighter market.
G L Clark
On the other hand, workers typically face two kinds of uncertainty: uncertainty with respect to the duration of job tenure and with respect to the expected average flow of income (Grossman, 1980). Boom conditions mean higher wages, whereas busts mean greater unemployment and loss of income. If worker and employer uncertainties coincide one option is to draw up a contract. Essentially, the risks implicit in a discrete-exchange commodity market for labor are shared through implicit or explicit contracts that bind both workers and employers over the business cycle. The key issues here, hardly addressed by auction models, are the interdependence between workers and employers and the longer-term employment relationships which are a function of the production process. Notice, however, that contracts could be interpreted as discrete exchange, but with time lags to cover the transaction costs implicit in risks (MacNeil, 1981). However, some kind of prior agreement on conditions and compensation is required if the contract is to have any validity over time. Contracts may be explicit (that is, described by law) or implicit (that is, agreed to without any adjudicating third party) (MacNeil, 1980). Contracts describe the obligations and penalties that parties to any contract agree to, and are also promises that both parties will adhere to agreed conditions in the future (Fried, 1981). If, in a recession, demand for the output of a firm falls, the contract between a firm and its workers may call for reduced overtime and perhaps temporary lay-offs of certain segments of the work force. Contracts specify a range of possible market situations and the appropriate response. However, in reality all possibilities may not be known, so contracts may specify average responses based on the past and promise that particular rules will be adhered to in the future. It is the uncertainty inherent in the discrete-exchange market that makes the promise to adhere to contractual obligations most important. The effect of such promises is built-in rigidities of response to short-run fluctuations. For example, when demand for labor is low, employment and wages may be maintained at previous levels, and when demand is high, wage increases may be moderate, rather than reflecting actual labor-market demand and supply conditions. Baily (1976) argued that it is the mutual advantages inherent in any employment relation that binds the two parties (workers and employers) together over the short run: a joint decision is made over the nature and conditions of each contract. Thus, in accordance with Williamson (1979), the firm can be treated as a single maximizing unit which integrates the interests of workers and employers. Obviously this abstracts from the commodity exchange relationships argued above to be central to the neoclassical versions of how labor markets function. However, it should be emphasized that contracts are negotiated for specific length of time. Once the technical conditions have passed that encourage what amounts to collusion, then exchange can reoccur in the market. Theoretically, implicit contracts delay in time the exchange process, they do not replace exchange. The assumptions of neoclassical economics still apply. To summarize, neoclassical auction and bourse models narrowly conceive of labor as a discrete-exchange commodity. Price (wage) and quantity (employment) shortrun variations are predicted by both models as recontracting and bidding allocates labor to firms. On the other hand, Dunlop's argument predicts that with or without unions, wages will tend to be more stable than employment. The key concepts here are based upon the notion of a 'quoted price' for labor and the inherent difficulty of changing internal wage contours when recontracting does not exist. More modern neoclassical contract theorists, following Dunlop's earlier analyses, suppose that the labor market is structured around more continuous employment relationships (compare Simon, 1957). Contract theorists maintain that because the objective
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function of workers and employers is centered around maximum income, the crucial variable for workers is the real wage. To the extent that wages compensate for being laid off, workers are hypothesized to be indifferent to their employment status. Thus, contract theory predicts greater volatility in employment than wages. However, it is less clear what the order of rigidity versus volatility should be with regard to employment and hours worked. Moreover, it is unclear whether or not contracts are contingent upon more general economic conditions. That is, would an excess supply of labor in a geographical or industry labor market affect the terms of a particular employer's contract? And, if real wages are very unstable (as they are) how relevant would money wages be? Are there rigidities observable in money wages? 4 Methodology and data issues In this section of the paper empirical evidence is presented as a partial demonstration of the relevance of neoclassical implicit contract theory. Empirical studies of local labor-market dynamics generally use economic aggregates such as total employment and the unemployment rate. Local responsiveness to short-run fluctuations have been analyzed via regression models, spectral-Fourier transformations and Box and Jenkins (1976) autocorrelation (ARIMA) equations, all of which are modified for the structure of space-time lags [see Marchand (1981) for a recent example using a modified entropy-spectral analysis]. Implicitly these analyses have assumed that labor markets are just like discrete-exchange commodity markets, and are in the main, concerned with 'bourse-like' quantity and price adjustment mechanisms (Clark, 1980). Explanations of different space-time adjustment patterns focus upon the frictions of labor-market exchange and the location of industries (Clark, 1981b). It is often assumed that changes in the demand for the output of a firm should proportionally affect the level of employment. Local wage determination models also presume a very conventional format of labor demand and supply, which is dependent upon the Phillips curve. Discrete-exchange models predict price and quantity volatility and invoke market imperfections to explain rigidities. As such, rigidities are a minor element of the analytical paradigm. In contrast, contract theorists predict rigidities over the short run, and these are thus central to the analytical framework. The relative importance of these alternative claims of local labor-market adjustment were evaluated for a set of industries and cities in the United States over the period 1972-1980. In terms of aggregates, firms can adjust their work force in three ways: the total number of employees, hours worked, and wages paid (Medoff, 1979). Unpublished data for these variables were collected from the Bureau of Labor Statistics (BLS) for three industries and some eleven SMSAs. The employment measure was quite straightforward; simply total monthly employees in the particular industry and city. Hours worked were measured through average weekly hours worked per employee for a given month in the industry and city. In accordance with Dunlop (1944), wages were measured via the total monthly wage bill standardized by the number of employees. Thus, the wage rate was not simply the standard wage per hour, but reflects other important elements such as overtime penalty rates, bonuses, and shifts of workers amongst different earning categories within firms. If, as Dunlop (1944) suggested, maximization of the total wage bill is the objective of unions (and minimization of the wage bill is the objective of firms), then the average hourly wage is a much better measure of compensation than the standard wage rate for a standard hour worked. At this point it should be acknowledged that the empirical analysis departs from implicit contract theory in that money wages, rather than real wages, are the focus of investigation. My reasons for this departure are pragmatic and, to a lesser extent, theoretical. In the first instance there are no reliable urban monthly price series
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available for the period 1972-1980. But even if such price series were available it is doubtful if real wages would be of interest. Aggregate studies have suggested that real wages are unpredictable and independent of the path of the business cycle, being dominated by an important stochastic element (Geary and Kennan, 1982; Lucas, 1981). Obviously workers can hardly directly affect real wages (because they would have to be able to manipulate the aggregate price level); they can only approximate their expectations through money wage bargaining. In this respect the choice between money wages and real wages as the analytical category is a choice between assumptions concerning their behavioral relevance. Thus in the second instance, given the stochastic character of real wages and their dependence upon money wages, the focus of this study remains with the more conventional Keynesian category of money wages. Studies of the patterns of local economic adjustment to national fluctuations have suggested that differential local response can be linked to local industrial structure (King and Clark, 1978). To account for such a possibility, data on employment, hours worked, and wages were collected at the two-digit SIC level for three industries: apparel and textiles, electronics and electrical equipment, and printing and publishing. Three considerations dictated the choice of these industry groups. First, these industries are nationally quite responsive to economic fluctuations. Second, these industries can be found in a variety of regions of the USA, and thus comparisons can be made between the patterns of fluctuations and rigidities in northeastern and southern SMSAs, holding industry structure constant. Third, these industries are highly competitive, dominated by smaller firms, and are not significantly unionized. The data were collected on a monthly basis from January 1972 to December 1979. Again data availability helped dictate the period of analysis, although it should also be recognized that the 1970s were quite unusual, in terms of postwar economic history, for two reasons. First, the standard Phillips curve model apparently failed to predict persistent simultaneous high inflation and unemployment over the decade (Cagan, 1979); and, second, economic growth in the south and relative decline in the northeast dominated the US spatial economy (Chinitz, 1978). 5 The printing and publishing industry Four SMSAs, two from the south (Birmingham, Alabama, and Dallas, Texas) and two from the northeast (Boston, Massachusetts, and Rochester, New York) were selected to represent the diversity of local labor-market adjustment patterns in the printing and publishing industry. Figures 1 and 2 illustrate the patterns of local adjustment for the three key labor-market adjustment variables identified by Medoff (1979): total employment, average weekly hours worked per employee, and average hourly wages. In the first instance (figure 1), local adjustment is compared using a common vertical scale which measures total monthly man-hours, a series constructed for each city by multiplying total monthly employment by average weekly hours worked for the same month. Figure 2 then disaggregates total man-hours into its constituent series and this enables direct analysis of the particular patterns of adjustment for each city. Each series was smoothed using a running average with a span of five months. Extraneous month-to-month fluctuations were minimized and underlying business-cycle patterns highlighted. This was important for the employment and hours series of each SMSA, with the latter series being, by far, the most volatile of the three key adjustment variables. In figure 3, a periodogram of Rochester's printing and publishing employment and hours series is presented, which illustrates the character of the volatility of these two series.
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Periodograms are estimates of the spectra of a given set of time series. As such they indicate the intensity of amplitude (7) in each series over a range of frequencies (Wj) (Box and Jenkins, 1976). In the estimation procedure each series was detrended, corrected for its mean, and then tapered before being analysed. First differences were used to detrend each series assuming that this is simpler and more easy to interpret than fitting a polynomial of unknown order (Granger and Newbold, 1977). Correction for the series mean is a way of inducing stationarity although shifts in the series variance are not accounted for in such a procedure. Tapering was used to limit the amount of leakage of amplitude into adjacent frequencies (Bloomfield, 1976). Experiments were conducted with 10% and 20% tapering, the final choice being dictated by a goal of accentuating the peaks. In line with Bloomfield (1976), the periodograms presented in figure 3 are vertically scaled as logarithms. This is because the arithmetic intensity of amplitude estimates at each frequency tend to vary by very large orders of magnitude. Notice also that on the horizontal scale each periodogram starts at / = 1, since at / = 0— which is just the mean of each series—the estimate would be zero. Not surprisingly each series exhibits what Granger and Newbold (1977) have termed, the "typical shape of an economic variable". That is, high intensity at very low frequencies with a falling-off in intensity over higher-order frequencies, coupled with evidence of white noise. In this instance, because of the limited length of the series (ninety-six months), it is difficult to claim that any one frequency is the business-cycle component. For Rochester it is apparent that the hours series is more volatile than the employment series. The periodogram for hours worked decays more slowly and has uniformly higher intensity values than is the case with employment. Two fundamental frequencies can be identified in the hours worked periodogram; at 64 months and 25-26 months. Only one fundamental frequency can be identified in the employment periodogram; at 64 months. This frequency is clearly indicative of a longer-run trend cycle, although as suggested above, little more can be made of the significance of such an identified frequency. When the two series are combined i 1-0
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