I.O.Kitov

There is a principal assumption of the existence of a tight link between inflation and unemployment known as the Phillips curve. The concept of the Phillips curve serves as a basis for many macroeconomic models and business cycle theories. There is no "completely satisfactory explanation" [Mankiw, 2000] of this virtual tradeoff, however. Existing models meet severe problems to explain some outstanding features of the presumed tradeoff between inflation and unemployment, such as, for example, stagflation and disinflation accompanying decreasing unemployment, without using some exotic exogenous forces or shocks. This lack of proof or demonstration of even a weak empirical confirmation of the relationship does not prevent "central bankers and monetary economists" [Mankiw, 2000] from adhering to its usage in practice. Hence, any clear explanation of the existence of tradeoff between inflation and unemployment, or its absence, in which case the bankers, monetary policy-makers and economists are wrong in their unproven assumption, is of great value. We show below that there is no tradeoff between unemployment and inflation. Fortunately, the period between 1990 and 2010 is characterized by just minor changes of the studied variables. This is what makes current policy so "successful". There are some challenges arising in near future, however.

In the first section, we argue that the presumed relationship between inflation and unemployment is just a simple lagged linear function with a positive coefficient. This effectively means that, if accordingly modified, the Phillips curve is an upward-sloping function with a coefficient close to one, but where unemployment does not affect inflation.

If unemployment in the USA is a lagged linear function of inflation, it is important to find the potential forces driving the inflation itself. The macroeconomic model developed by Kitov [2005a,b] provides a consistent framework for such an analysis. The two principal findings of the model are as follows: 1) real economic growth in the USA depends only on the attained value of real GDP per capita and the relative change in the number of nine-year-olds in the population; 2) the personal income distribution (PID) is very rigid relative to real economic growth and inflation. The first finding allows effective decoupling of the study of inflation from the economic development � the real economic growth in terms of GDP per capita does not depend on inflation and vice versa. The second finding leads to a simple idea that inflation causes only nominal income changes but not relative changes in distribution of income, i.e. a given portion of population always has a predefined portion of the total GDP. Thus, any successful personal attempt to occupy a position with a larger income that is already occupied causes some forces directed to return the person to her/his original relative position, i.e. stretching the PID and inducing inflation. (One can imagine a climb by a downward running escalator � all efforts to climb up result in the same position relative to the ground but changing relative to the escalator itself. Similarly, persons enjoy a higher nominal income but the same relative place in the PID.)

Labor force change is a potential candidate for describing the process of personal attempts to advance in the PID. The second section describes the process and provides empirical facts supporting this concept. One of the findings is that the labor force change leads inflation by three years. Therefore, this causality principle excludes the current inflation value from being controlled by some contemporary means including monetary ones. One cannot exclude "insane" behavior of some monetary authorities, however, such as flooding an economy with money. This is not the case for the USA, but it happens sometimes in countries in transition. In our opinion, the driving force for such "strange" behavior is the redistribution of personal incomes in a new way after failure of the old economic and social organization. One can observe a fast evolution of PID in former socialist countries during the last 15 years from a truncated "socialist" version to a wide "capitalist" one.

Having in the first two sections demonstrated causal relationships between unemployment and inflation and between inflation and labor force change, one can easily apply the same methodology to the dependence of unemployment on labor force. The third section provides some details of this analysis and shows that the observed unemployment in the USA is a lagged linear function of labor force change and inflation. Thus one can consider unemployment to be a result of those who tried to enter the PID at higher incomes but who induced inflation. It consists of people who have failed to change their income positions and correspondingly increased inflation. All migrationary processes inside the PID have their characteristic times inducing observed delays between the acting forces and outcomes. These processes are out of the scope of the study and present a challenge to future investigation.

We also discuss briefly some potential outcomes and some directions for the future study and application. We insist that modern business cycle theories should be rejected as inappropriate and more efforts should be applied to study the processes responsible for the propagation of labor force changes through the real economy. Economics should advance to studying real processes, not artificial mathematic assumptions and "stylized" facts. Economics needs to cross from the realm of astrology to the realm of astronomy. The former may be more exciting, but the latter is more practical and can be tested and validated.

1. Unemployment and inflation

A standard way of presenting the relationship between inflation (INF) and unemployment (UE) is a scatter plot of simultaneous measurements. Unemployment is measured by the US Census Bureau (CB) during the Current Population Survey (CPS) [CB, 2002] and is published monthly by the Bureau of Labor Statistics (BLS) [BLS, 2005a]. Unemployment is not an accurately measured variable as described by the CB.

Inflation is an even more obscure variable. There are numerous definitions of inflation resulting in different values. The principal problem for any of these definitions is the estimation of the price of new products. In the world of goods and services renewed at accelerating rate, there is no reliable procedure to estimate the price change for new goods even if they are substitutes for some old goods. Thus, the concept of inflation and hence the concept of real economic growth is partly artificial and bears a flavor of subjective judgment. All these problems make the finding of any strict relationship between the variables not only difficult but also a slightly unreliable task. Because of these problems, the original Phillips curve implying the existence of a well defined relationship is currently under strong doubt and may be replaced by a general assumption concerning the possibility to influence inflation and unemployment by monetary means [Mankiw, 2000].

We develop a new approach based on dynamic representations of the studied variables (including smoothed and cumulative values) and their evolution in time. Instead of a straightforward plotting of inflation against unemployment and the construction of a standard scatter plot, one can plot both variables as a function of time and check if the curves have some resemblance. Figure 1 shows the measured unemployment in the USA for the period between 1948 and 2004 along with two inflation estimates � annual CPI values (not seasonally adjusted - NSA) published by the Bureau of Labor Statistics [2005b] and annual GDP deflator values published by the Bureau of Economic Analysis of the Department of Commerce [2005]. The original unemployment readings are corrected by -3% in order to equalize values of the variables during the last twenty years.

One can observe a clear overall similarity of the inflation curves in spite of some small variations in amplitude and years of peak values, especially between 1975 and 1990. As expected, the CPI curve is consistently above the GDP deflator one. Surprisingly, the unemployment curve repeats the shape of those for inflation. The best correlation is observed during the last twenty years.

The means synchronizing the curves is very simple � the unemployment curve is shifted by 2.5 years back in time. This time shift contains two years of actual shift and half a year of artificial shift. For the latter shift the annual readings of unemployment are obtained by averaging corresponding monthly values over the year. This effectively makes the unemployment values to be associated with the center of the given year rather than with the end. Conversely, the inflation values are cumulative ones and correspond to the last day of the year, which is why the artificial half-year shift arises.

Neglecting some small variation in peak and trough timings, one can conclude that the observed inflation is a leading variable relative to the measured unemployment, or that the unemployment is a lagged linear function of the inflation in the USA. One of the immediate implications of this observation is a possibility for predicting unemployment evolution during the two years following from a measured inflation value. For example, the decreased unemployment consistently observed during the last two years is just a short-term feature. The recent evolution of the inflation indicates that the year 2006 is a pivot point to an unemployment increase from the current 5% to 6% in the middle of 2008. Further development of unemployment can be easily predicted by the future inflation.

Figures 2 and 3 present two modified Phillips curves. The original unemployment values are replaced with those two years later, i.e. those synchronized with the inflation. The curve in Figure 2 corresponds to the period between 1960 and 2004 and that in Figure 3 to the last twenty years. The modified Phillips curves illustrate a simple linear relationship between inflation and unemployment. There is no conventional downward-sloping Phillips curve so important for describes as any monetary policy tradeoff between inflation and unemployment. On the other hand, there is also no vague and stylized relationship, which is often used in current theory and practice as a substitute for the original Phillips curve [Ball&Mankiw, 2002]. In reality, current unemployment rate depends on inflation observed two years ago.

One of the prominent effects of the unemployment lag behind inflation is stagflation. Actual observations of unemployment and inflation in the USA have never given a better example of a contradiction to the conventional Phillips curve: one cannot expect unemployment growth when inflation rockets up. Let us study the period between 1970 and 1990 in more detail as displayed in Figure 4. We know now that the unemployment repeats the inflation path with a delay. In 1972, inflation starts its first growth session. The unemployment curve still follows the path the inflation that passed two years previously. In 1975, the inflation curve reaches its local peak of about 10%. A year before, in 1974 (there is some variation of the lag induced by the measurement accuracy and the variable used � GDP deflator or CPI), the unemployment "unexpectedly" jumped from its modest level below 6% to a value well above 8%. The first session of stagflation had happened. Nobody was worried too much by this first lesson. The stagflation period was very short. In 1976, the inflation dropped and unemployment showed some downward motion. The next session, however, was much more of concern. Starting in 1977, the inflation curve (GDP deflator) demonstrates a five-year long monotonic increase from 6% to 9.5%. This is two years longer than the previous period of growth. The unemployment curve stagnates at the start, but then shows a faster growth. A two-year long period of stagflation begins in 1979. By chance, the Federal reserve chairman P.Volker announced a new monetary policy exactly the same time. The growth in unemployment was attributed to the effectiveness of the new monetary technique according to the original Phillips curve assumption. The observed inflation started to drop in 1981 (CPI) or 1982 (GDP deflator). The drop was interpreted to be a result of the new monetary policy targeted to suppress inflation. The unemployment continued to grow for two more years in total agreement with the conventional Phillips curve but also in agreement with the two-year delay we have just shown. The new policy was wrongly considered to be the cause, which forced things to behave as prescribed by the Phillips curve during this short period. The next "strange" deviation from canonic behavior appeared about ten years later � in the early 1990s. One can see, however, that the unemployment curve just follows its prescribed path. In essence, inflation cannot depend on unemployment. Inflation leads unemployment by two years.

There are numerous potential implications of this linear lagged relationship between unemployment and inflation in economic theory and monetary practice. Here we would just like to stress that there is no monetary policy to "push inflation and unemployment in opposite directions" [Ball&Mankiw, 2002]. Below we also demonstrate that there is no feasible monetary policy to control the current value of inflation because the latter depends solely on labor force changes in past, at least in the USA. Hence, neither unemployment nor inflation is currently in hands of policy makers.

2. Inflation and labor force

In the previous section, we have learned that unemployment is a lagged linear function of inflation in the USA during the last twenty years. This observation, however, does not reveal the real cause of inflation itself. What is the perpetual source of inflation that forces economists around the world to study phenomena such as inflation persistence? Below we attempt to explain inflation as the effect of a single process � labor force (LF) change.

Labor force is a measurable variable equal to the sum of employed persons and those who currently want to have a paid job. In the USA, this definition implies that people announce their current status during the CPS. Because of a limited size of the survey, accuracy of the measurements is also limited and fluctuations in the obtained values are common.

Despite a relatively low reliability in the monthly readings, the long-term observations allow a better representation of the labor force behavior in the USA. Annual time series of the participation factor estimates for the period between 1948 and 2004 is presented in Figure 5. The observed behavior is characterized by a long period of intensive growth from about 58.5% in 1965 to 67% in 1990. There was a short period of very weak growth between 1979 and 1983, however. A decade of decelerating growth started around 1990. In 2000, a period of a relatively fast participation factor decrease began.

Figure 6 presents the US labor force growth rate (dLF/LF) for the same period. The current growth rate is about 0.01. This value is lower than the growth rate of the working age population itself (around 0.015), which effectively makes the growth rate of the participation rate negative. The mean value of the labor force change for the entire studied period is 0.016. So, one can distinguish the periods of elevated growth rate and low growth rate compared to this mean value. The period between 1965 and 1990 is characterized by a consistently elevated labor force growth rate.

Why do these fluctuations around the average value of the labor force growth rate not affect the personal income distribution? How does the rigid PID accommodate the new labor force? Our working assumption is that the accommodation process is similar to the process of a balloon inflation � the air influx creates overpressure inside the balloon and forces its wall to stretch elastically. The larger the overpressure, the large the stretch. Similarly, the newcomers obtain some new positions inside the PID and effectively increase "overpressure" in the income bins (the standard CB income bin is $2500). To accommodate this overpressure and to return to some normal pressure the income bins have to stretch elastically. The stretch depends on the elasticity of the PID. The stretch process is called inflation in economics. The elasticity can be measured in the standard physical analogue as a coefficient of a linear relationship between the force (labor force growth rate) and deformation (inflation).

At this point, we have to admit that we do not know any reason for the participation factor change. This reason may be of social, psychological or some other character. An important aspect, however, is that the observed labor force change in the USA leads inflation by two years. This finding invalidates many of the current economic assumptions and models. For example, no monetary policy can control inflation because the latter is a sole function of labor force change three years beforehand. Since unemployment is a lagged function of inflation, it has also to be driven by the labor force change, but with a larger lag.

Figure 7 illustrates the linear relationship between inflation (GDP deflator) and the labor force change rate in the USA for the period between 1960 and 2004. The readings of the labor force change rate are shifted by two and a half years ahead in time to synchronize the observed peak values with those of inflation in 1975 and 1984. The half year artificial shift has been explained already.

The predicted and measured values of inflation are consistent throughout the whole period. The predicted values are obtained by a linear relationship displayed in the right-bottom part of the Figure. We intentionally distinguish two constants in the relationship. The first constant is 0.06 (6%) and corresponds to the mean inflation observed during the entire period between 1948 and 2004. The second constant is found by fitting the measured and predicted cumulative curves as discussed below. Its value is 0.0224. In the case of a constant labor force change rate of 0.0224 per annum, there would be no inflation change. The sensitivity factor or elasticity is 4. This implies that one per cent labor force change leads to four per cent inflation change.

The labor force has two components: an extensive component and an intensive one. The extensive component is associated with the growth of working age population. This growth was about 1.4% per year in average between 1948 and 2004. If the extensive component of the labor force does not change, inflation is defined only by the second component - the change of participation rate.

The most prominent feature is a complete coincidence of the peak values in time and in amplitude. Some short-term fluctuations in labor force and corresponding deviations of the predicted inflation are potentially induced by two factors: the accuracy of the labor force measurements and the corrections of the population estimates implemented by the US Census Bureau in census years. Due to a four times lower amplitude of the labor force change rate compared to that of the inflation one can expect that even small errors in the labor force estimates result in notable discrepancies between the predicted and observed inflation. These errors are visible in fluctuations between the census years. The fluctuations near the census years are characterized by much higher amplitude and are induced by the large-amplitude corrections (more than 1 %) in the working age population estimates. These corrections are especially large in 1963, 1993, and 2003 (because of the 2.5 year shift) and result in an almost four per cent change in the predicted curve due to the elasticity value.

There are some standard tools to reduce the measurement noise effects if they of a random character � apply a long-period filter or use cumulative values. The high-frequency uncorrelated noise is usually suppressed by averaging over a longer period. Figure 8 presents two smoothed inflation curves � the measured and predicted one. The smoothing was accomplished by averaging using a 7-year moving windows with a one-year step. The predicted curve is shifted by 2.5 years ahead in order to fit the actual inflation pick near 1978. The effects of the population corrections are also clear.

Figure 9 displays the observed and predicted cumulative curves of inflation starting in 1965. The predicted cumulative curve is obtained by a progressive summation of values from 1963 and is also advanced ahead by 2.5 years. There is an almost complete coincidence of the cumulative curves for the whole period. The only small deviation occurred around 1993 and corresponds to a sharp drop of the labor force growth rate induced by the baseline working age population correction. The cumulative predicted curve is very sensitive to the linear function coefficients. Even a change of 0.0001 in the free constant results in a visible deviation from the measured curve. Thus, the most accurate coefficients can be obtained by fitting the cumulative curves.

One can conclude that the observed inflation is completely controlled by the labor force change. Hence, there is no other parameter or process, which can potentially disturb this relationship from the inflation side. The two-year delay of the inflation relative to the labor force change is of critical importance. The delay means that all attempts to affect inflation during these years were almost worthless. Real processes in the economic structure of American society are self-consistent, objective and do not depend on personal will. Inherent bounds between people in the USA elaborated during a long history of economic interactions are objective and cannot be easily changed by any external force.

The curve displayed in Figure 5 indicates that the participation rate, which defines the evolution of the intensive component of the labor force change, has a strong downward tendency starting from 2001. The linear relationship we have just obtained from the cumulative curve fitting suggests inflation will decrease. As mentioned above, we currently have no idea about the factors controlling the participation rate. Thus, we cannot predict the overall behavior of inflation yet.

The extensive component of the labor force growth can be predicted with a larger accuracy from the population projections provided by the US Census Bureau [CB, 2005]. Figure 10 presents the change rate of the projected working age population for the period between 2005 and 2040 and compares the measured labor force and working age population change for the period between 1948 and 2004. As discussed above, the historical data sets demonstrate periods of just the extensive labor force growth (for example, the period from 1990 to 2000).

The extensive component of the labor force growth has a clear drop from 0.01 in 2005 to 0.002 in 2012. This drop is induced by the baby boomers retirement imminent in the near future. The young population cohorts cannot completely replace the boomers in the labor force. Hence, some intensive and quick measures to improve the current participation rate are critical to avoid negative effects. The currently observed tendency of the participation rate change is just the opposite to the desired direction, however.

The linear relationship between the labor force change and inflation allows estimation of the critical value when the inflation reaches zero value. Simple calculations give a rounded value of 0.003. If participation rate is constant, a deflation period starts from this threshold. Thus, if only the extensive component drop is observed during the next five years, then there is no danger of deflation. The labor force change rate (extensive component) will reach the critical value only in 2012.

Participation rate in the USA was consistently decreasing by 0.0025 between 2000 and 2004. This fact makes the danger of deflation very high right after 2010 if the tendency continues. A positive side of this observation, however, is that there is no special means are necessary in the next few years to keep inflation low.

The above consideration does not touch the principal problem of economic growth. Since inflation depends only on some past value of labor force change, one cannot expect real economic growth to affect inflation. And vice versa, no change of economic growth can be induced by inflation � whatever monetary policy is applied (except insane). The observed economic growth is defined by the just one factor � the number of young people of a specific age in the population as found by Kitov [2005a].

3. Labor force, unemployment and inflation

Unemployment might represent the people who tried to enter the PID at higher level of income and failed. These people are counted in the labor force. Unemployment is a linear lagged function of the inflation during the last twenty years. There was a period of nonlinear behavior, however. This period was characterized by a strong growth in the participation rate, which could potentially induce some nonlinear effects in the unemployment. One can assume that the extensive component growth is a steady process with just very small variations through time. Hence, very weak or no nonlinear effects are expected from the population growth.

The relationship between the rate of the labor force change and inflation is linear during the last forty-forty five years. Hence, all nonlinear processes in the labor force change, like the participation rate growth or decrease, are completely translated into inflation. The unemployment is thus potentially the residual of the inflation and the labor force change. If so, one can obtain a unemployment prediction for the whole period under consideration. This section tests the hypothesis according to the above-developed methodology.

We start with Figure 11 presenting the dynamic evolution of the observed and predicted unemployment in the USA. At this first step, the predicted unemployment is obtained as a linear lagged function of the labor force change only: UE(t)=0.024+2.1*dLF(t-5)/LF(t-5). The lag of the observed unemployment is five years � the value obtained by a simple visual fit of the curves. There is some discrepancy between the two curves, however. A natural explanation is a low accuracy of the labor force enumeration or presence of some weak nonlinear effects. Figure 12 displays the corresponding cumulative curves for the period between 1970 and 2004. The predicted curve is consistently above that predicted during the years of strong growth in the participation rate. The curves merge around 1993, when the nonlinear effects effectively disappear. We are not using any formal method to reach the best fit between the curves here. Our purpose is not to determine the corresponding coefficients of a linear regression but to provide a general understanding of the overall dynamic behavior of the variables under investigation. In principle, one can definitely reach a better agreement between the curves by varying the corresponding coefficients.

Figure 13 presents a prediction for the unemployment based on the labor force change with the potential nonlinearity compensated by the inflation. The following relationship is obtained:

UE(t)=INF(t-2)-2.5*(dLF(t-5)/LF(t-5)-0.0255)

Here the "neutral" value of the labor force change rate is 0.0255. The lags are two years for the inflation and five years for the labor force change. The inflation is represented by the GDP deflator. Figure 14 depicts the corresponding cumulative curves used to estimate the above coefficients. There are some weak deviations from the observed unemployment in the mid-1980s and mid-1990s. The overall agreement is better than for the labor force change only, as presented in Figures 11 and 12.

Figures 15 and 16 illustrate some results obtained where the CPI represents the inflation. Potentially, the CPI can provide a better unemployment prediction as a result of the dynamic and cumulative curves comparison. The corresponding relationship is very close to that obtained for the GDP deflator with the same lags:

UE(t)=INF(t-2)-2.2*(dLF(t-5)/LF(t-5)-0.0238).

These relationships provide a prediction of the unemployment for the next two to five years. There are two important aspects of this prediction: time horizon and accuracy. If one uses only the labor force change rate for the prediction of the inflation and unemployment, one can foresee five years ahead. The inflation measurements, however, appear to be important for a more accurate prediction. A shorter forecast compensates for outcome inaccuracy.

Fortunately, this is not the whole story. Methodology and technique for the inflation and labor force measurements can easily be improved. This is a standard situation in natural sciences when some general form of a relationship is revealed and only a relative improvement of description and prediction is sought. Actually, all fundamental physical laws are obtained by this procedure with a ultimate demand of improvement of the overall match of the measured and predicted values diminishing with increasing accuracy of measurement.

4. Discussion and conclusions

There is almost nothing to discuss because the findings are orthogonal to the current theories and monetary policy. Many concepts related to business cycles and dependence between inflation and unemployment are currently considered to be valid. As a rule, they are denied by the empirical evidences presented in this paper. The author does not intend to recommend anything specific to "the central bankers and monetary economists" other than consider these results during their routine business. Some important changes to expected to surface in the next five-seven years including deflation will need attention. At the same time, the relationships obtained in this study are not accurate enough to be used in economic theory and practice as they are now. Massive efforts are needed to refine the unemployment, inflation and labor force readings in order to obtain precise coefficients of the linear or weakly nonlinear relationships predicting the evolution of the variables of interest. Potential outcomes, however, cannot be exaggerated � accurate knowledge of the future evolution of key social and financial parameters � unemployment and inflation. Moreover, a reasonable social policy associated with the labor force control is a straightforward requirement.

In order to confirm the general findings of this study we have conducted a similar study for France and Austria. These two countries present examples of intermediate- and small-size economies in terms of their labor forces. All the above relationships are confirmed. The lag times between the labor force change, inflation and unemployment are different: six years in France and one year in Austria. The labor force change-inflation elasticity in France is very high - 18. In Austria, the elasticity is low � 2.2. The high elasticity in France makes the accuracy of the labor force measurements of critical importance � strong fluctuations are observed. The predicted curves, smoothed and cumulative, are in better agreement with the observed ones. In Austria, the annual readings are also well predicted.

To conclude we repeat briefly the principal findings of the study:

• Inflation and real economic growth are independent and driven by different forces related to population.
• The driving force for inflation in the USA is the labor force change. The inflation lags two years behind the labor force change.
• Unemployment is a lagged linear function of the labor force change and inflation with lag times of five and two years respectively.
• Stagflation and decreasing inflation (disinflation) accompanied by decreasing unemployment are just natural results of the lag and the dependence of the inflation and unemployment on the labor force change.
• One can forecast inflation and unemployment two to five years ahead.
• The population projections constructed by the US Census Bureau provide a useful tool to evaluate the long-term behavior of the labor force changes. The current period of disinflation will probably transform into deflation starting 2010-2012.

Ball, L., N.G.Mankiw, (2002) "The NAIRU in Theory and Practice", Journal of Economic Perspectives, v. 16, n. 4, pp.115-136.

Kitov, Ivan, (2005a) GDP growth rate and population, Research Announcements, Economics Bulletin, Vol. 28 no. 9 p. 1.

Kitov, I. O., (2005b) "A model for microeconomic and macroeconomic development," Working Papers 05, ECINEQ, Society for the Study of Economic Inequality

Mankiw, N.G., (2000) "The Inexorable and Mysterious Tradeoff between Inflation and Unemployment", Harvard Institute of Economic Research, Discussion paper n. 1905, Harvard University, Cambridge , Massachusetts. http://post.economics.harvard.edu/hier/2000papers/2000list.html

U.S. Census Bureau, (2002) Technical paper 63RV, "Current Population Survey � Design and Methodology", http://www.census.gov/prod/2002pubs/tp63rv.pdf

http://www.census.gov/ipc/www/usinterimproj/usproj2000-2050.xls

U.S. Census Bureau, (2005) Table, " U.S. Interim Projections by Age, Sex, Race and Hispanic Origin" , Detail file, Last Revised August 26, 2004,

http://www.census.gov/ipc/www/usinterimproj/usproj2000-2050.xls

U.S. Department of Commerce, Bureau of Economic Analysis, (2005) Table, "Current-Dollar and "Real" Gross Domestic Product (Seasonally adjusted annual rates)", 12.21.2005, http://bea.gov/bea/dn/gdplev.xls

U.S. Department of Labor, Bureau of Labor Statistics, (2005a) Table, "Labor Force Statistics from the Current Population Survey", 12-15-2005, http://data.bls.gov/cgi-bin/surveymost?ln

U.S. Department of Labor, Bureau of Labor Statistics, (2005b) Table, "Consumer Price Index, All Urban Consumers", 12-15-2005, ftp://ftp.bls.gov/pub/special.requests/cpi/cpiai.txt