PAPERS
RESEARCH WORKING DEPARTMENT
WORKING PAPER NO. 02-7 CONSISTENT ECONOMIC INDEXES FOR THE 50 STATES Theodore M. Crone Federal Reserve Bank of Philadelphia May 2002
FEDERAL RESERVE BANK OF PHILADELPHIA
Ten Independence Mall, Philadelphia, PA 19106-1574 [phone] www.phil.frb.org
Working Paper 02-7 Consistent Economic Indexes for the 50 States
Theodore M. Crone Research Department Federal Reserve Bank of Philadelphia May 2002
The views expressed here are those of the author and do not necessarily represent those of the Federal Reserve Bank of Philadelphia or the Federal Reserve System. I thank James Stock and Mark Watson for supplying their original GAUSS program to estimate earlier versions of state index models and for suggesting the application of their national model to regions and states. I thank Keith Sill for assistance in applying that program to earlier state models. Alan Clayton-Matthews provided invaluable advice and a C++ program to estimate the current state models. Finally, I thank Jason Novak for excellent research assistance on this project. Any errors are mine alone.
Consistent Economic Indexes for the 50 States Abstract In the late 1980s James Stock and Mark Watson developed an alternative coincident index for the U.S. economy. They used the Kalman filter to estimate a latent dynamic factor for the national economy and designated the common factor as the coincident index. This paper uses the Stock/Watson methodology to estimate a consistent set of coincident indexes for the 50 states. The indexes are consistent in the following sense. (1) The input variables for estimating the common factor are the same for each state. (2) The timing of the coincident indexes is set to coincide with the same observable variable in each state (nonfarm employment). (3) And the trend of the index for each state is set to the trend of real gross state product in the state. The final indexes are available on the web at www.phil.frb.org/econ/stateindexes.
Consistent Economic Indexes for the 50 States
In the late 1980s James Stock and Mark Watson developed a coincident index for the U.S. economy as an alternative to the one published at that time by the Department of Commerce.1 Stock and Watson's alternative index is the latent factor estimated in a dynamic single-factor model using the Kalman filter. State versions of the Stock/Watson type index have been developed for the New England states, New York, New Jersey, Delaware, and Texas. This paper develops a consistent set of Stock/Watson coincident indexes for all 50 states. Besides their use in monitoring state economies, these indexes are useful in comparing the length, depth, and timing of recessions at the state level. They can also be useful in time-series analysis as a composite measure of monthly economic activity at the state level. Comparisons of state economies could be based on a number of economic indicators, e. g., real gross state product, real personal income, or payroll employment. Of these indicators, real gross state product is the most comprehensive measure of economic activity in a state, but it is available only annually and with a considerable lag. While real gross state product is a good metric for trend growth in a state's economy, the annual frequency of the data makes it an unsatisfactory indicator of state business cycles. At the national level a recession is characterized as a contraction in many economic activities, and the duration and depth of the contraction are factors in determining official recessions.2 Turning points in national business cycles (peaks and troughs) are dated by months, and at least two official recessions have occurred within the span of a calendar
1 2
The traditional index is now published by the Conference Board. See Zarnowitz (1992).
1
year. Thus, the appropriate metric for defining state business cycles is a monthly indicator or set of monthly indicators. The advantage of a Stock/Watson type index is that it combines several monthly indicators in a single measure of the state's economy. The state indexes developed in this paper do not break any new ground in modeling the indexes. They provide a consistent set of indexes for all 50 states based on the Stock/Watson model and some recent extensions of the model. The Stock and Watson Model Stock and Watson's model is based on the assumption that the observed indicators of the economy reflect a single, unobserved dynamic factor--the underlying "state of the economy." A Kalman filter is used to estimate this common factor. The assumptions of the model are set out in the following sets of equations. The measurement equations: )xt = " + $(L))ct + :t And the transition equations: ((L))ct = * + 0t D(L):t = ,t where xt = the log of an observed and measured variable in period t, ct = the log of the state variable to be estimated, and L denotes the lag operator. Equation (2) represents the law of motion for the state variable ct, which is interpreted as the underlying state of the economy. The state of the economy follows an autoregressive process in the model. The idiosyncratic components of the measurement variables (:) (2) (3) (1)
2
are assumed to be uncorrelated with one another and also follow an autoregressive process. The measurement equations allow for the inclusion of both leads and lags of the state variable (ct), so indicators that lead or lag the business cycle can be used to construct the coincident index. Equations (1) and (2) are estimated using the standardized log difference of the observed indicators and the state variable.3 Thus, " and * do not have to be estimated, and the procedure provides an estimate of the standardized log difference of the latent dynamic factor. The final coincident index is formed by setting the estimated state variable to 100 at a given date. The monthly changes are given by the estimated )ct, and a trend is established by the weighted average of the trends of the observed variables. The weights are determined by the contribution of the changes in the observed variables to the change in the latent dynamic factor.4 Stock and Watson used four monthly national variables to estimate their coincident index: hours worked by employees in nonagricultural establishments, real personal income minus transfer payments, industrial production, and real manufacturing and trade sales. The construction of state coincident indexes has led to some further developments of the original Stock and Watson model. In applying the Stock/Watson model to the Massachusetts economy, Alan Clayton-Matthews and James Stock (1998/1999) revised the model to base the trend of the coincident index on the trend in gross state product, which is published only annually and is therefore unsuited for inclusion in the
3
The average log difference over the sample period is subtracted from the log difference for each month and the result is divided by the standard deviation of the log differences.
3
measurement equations of the model. They outlined the procedures for converting the weighted average trend and standard deviation in the original Stock/Watson index to the trend and standard deviation of any measure of the economy that may have a monthly, quarterly, or annual frequency. The conversion can be done piecewise for different historical periods, if there is reason to believe there was a change in trend growth in the state's economy. Clayton-Matthews and Stock introduced a break in the trend for the Massachusetts index at the end of 1987. In a more recent expansion of the Stock and Watson model, Alan ClaytonMatthews developed a C++ program that allows for measurement equations in which some indicator variables (xt) are observed on a quarterly rather than a monthly basis. The common factor is still modeled as a monthly variable, but it enters the measurement equation for the quarterly indicator as the sum of three consecutive monthly changes. That is, $q ()ct + )ct-1 + )ct-2) where $q is the coefficient in the measurement equation for the quarterly indicator. The inclusion of quarterly indicators in the model is especially important for state indexes because fewer monthly indicators are available at the state level than at the national level. Most state models are based on three or four indicators.5 All the state indexes developed to date include monthly payroll employment and the state unemployment rate. Other monthly variables include average hours worked in
The weights are determined by calculating the cumulative dynamic effect on the state variable (ct) for a standardized unit change in each observed variable (xt). Each observed variable's share in the sum of these cumulative effects represents its weight in determining the trend. 5 See Clayton-Matthews and Stock (1998/1999), Crone (2000), Orr, Rich, and Rosen (1999). The state indexes in Crone (1998/1999) were constructed using only three indicator variables, as were the indexes for
4
4
manufacturing (Clayton-Matthews, Kodrzycki, and Swaine, 1994; Crone, 2000; and Orr, Rich, and Rosen, 1999) and state withholding taxes and sales taxes (Clayton-Matthews and Stock, 1998/1999). Quarterly variables used in Stock/Watson type state indexes include real earnings (Orr, Rich, and Rosen, 1999) and real personal income minus transfer payments (Crone, 2000). A Consistent Set of Indexes for the 50 States If state coincident indexes are used to compare business cycles across states, a certain degree of consistency must be imposed on the construction of the indexes. At a minimum, a set of consistent state indexes should meet the following criteria:6 (1) The indexes should be constructed from the same set of indicators for each state. (2) The timing of the index should be benchmarked to the same indicator variable in each state. In practice, this requires that the measurement equation for one particular indicator variable include only the contemporaneous value for the common factor in the model for every state.7 (3) The trend for each state index should correspond to the trend of the same variable for each state or to a weighted trend of several variables where the weights for the corresponding variables in each state are the same. Crone (1998/1999) produced a set of indexes for the 48 contiguous states based on payroll employment, the unemployment rate, and average hours worked in
Connecticut, Maine, New Hampshire, Rhode Island, and Vermont in Clayton-Matthews, Kodrzycki, and Swaine (1994). 6 This is not to imply that one cannot construct a better coincident index for any particular state by violating any of these criteria, but to the extent these criteria are violated, the comparability of the indexes is placed in question. 7 Model specification tests suggest that using different lag structures in the other measurement equations for different states can improve the specification of the models.
5
manufacturing. These indexes satisfied the first two criteria, but not the third. The indexes in the earlier Crone study had two major limitations. The underlying data series were all related to employment rather than to income or value added. And the trend for each state index was calculated according to the original Stock/Watson model, i.e., the weighted average trend of the components. Since the weights differed by state, the calibration of the trend was not consistent across states. The indexes developed for this paper overcome these limitations of the earlier study. They satisfy all three criteria listed above and include a quarterly variable that over the long run reflects the value of labor's contribution to output (real wage and salary disbursements). And the trend in the index for each state is based on the trend in gross state product. Indicator Variables Used in the State Indexes We have identified three monthly indicators and one quarterly indicator available for inclusion in the coincident indexes for all 50 states. The three monthly series are available on a consistent basis for most states since 1978, so our state indexes are estimated from that year.8 Nonagricultural payroll employment. This series is produced by the Bureau of Labor Statistics (BLS) in cooperation with the individual states. It is the most reliable employment series published for all the states. Its most obvious drawback is that it does not include the self-employed or farm workers. Therefore, it may be a less reliable indicator of economic activity in states whose economies are dominated by agriculture. The BLS publishes seasonally adjusted nonfarm employment data from 1982 for most states, but the Bureau publishes only nonseasonally adjusted data prior to that time. Since
8
The indexes in Crone (2000) also included industrial electricity sales, but a consistent series for that variable is no longer available from the Department of Energy.
6
our state indexes are estimated from 1978, we seasonally adjust the employment data ourselves using the X-11 procedure. The measurement equations for nonagricultural employment in all our state models include only the contemporary value of the latent dynamic factor. Thus, the timing of the final index is set to coincide with the timing of the employment series. Unemployment rate. This series is also produced by the BLS in cooperation with the states. It is published on a seasonally adjusted basis from 1978 for all the states except California. The California unemployment rate series begins in 1980.9 The data used to produce state unemployment rates are from the current population survey, the payroll employment survey, state population estimates, and unemployment claims. Since the peak of the unemployment rate often lags the trough in economic activity at the national level, the measurement equation for the unemployment rate in some of our state models includes lags of the latent dynamic factor as well as the current value. Also, the unemployment rate is entered in the measurement equation as the standardized first difference rather than the standardized log difference. Average hours worked in manufacturing. Stock and Watson's national index and the traditional coincident index published by the Conference Board include industrial production. There is no comparable measure of industrial output at the state level, but average hours worked in manufacturing, from the same survey as payroll employment, is used in our model as an indicator of industrial activity at the state level. These data are
9
The California model is estimated from 1978 with missing data for the unemployment rate in the first two years.
7
not published on a seasonally adjusted basis, so we seasonally adjusted the series for each state.10 Real wage and salary disbursements. Personal income and its components are available at the state level on a quarterly basis from the Bureau of Economic Analysis (BEA). The state indexes estimated for this project include real wage and salary disbursements.11 The quarterly wage and salary disbursements reported by the BEA on a seasonally adjusted basis are deflated by the national CPI-U to obtain real wage and salary disbursements. We do not include in our state models proprietors' income or rent, interest, and dividends. In several farm states in our sample period, farm income represented more than 50 percent of proprietors' income in some years, and farm income can have a very irregular pattern across years and within years due in part to government price support programs. Therefore we excluded proprietors' income from the income measure in our models. Rent, interest, and dividends, unlike wages and salaries and proprietors' income, are reported by state of residence rather than by the state in which the income is generated. Since coincident indexes are meant to track economic activity or output in the state, rent, interest, and dividends were also excluded from our income measure. Since wages and salaries are reported only on a quarterly basis, the measurement equation for this variable in the state index models includes the latent factor as the sum of the log differences of the three months of the quarter as described in Clayton-Matthews (1999).
10
In Kansas the data on average hours worked in manufacturing are not available prior to 1979, and in Indiana the data are not available prior to 1989. 11 The national coincident indexes include monthly personal income minus transfer payments. Transfer payments are not considered payment for current production.
8
Seasonal Adjustment and Smoothing of the Data The data used in a Stock/Watson type model are assumed to be seasonally adjusted if the original data have a seasonal component. The unemployment rate and quarterly wages and salaries are seasonally adjusted by the BLS and the BEA, respectively. The BLS publishes a seasonally adjusted series of nonagricultural employment from 1982, but since our indexes start in 1978, we have independently adjusted the nonagricultural employment data for seasonal variation. The BLS does not publish a seasonally adjusted series for average hours worked in manufacturing at the state level. Therefore, we seasonally adjusted those data, using the X-11 procedure. No further smoothing of the data (beyond seasonal adjustment) is theoretically necessary before estimating a Stock/Watson type model because the Kalman filter procedure smoothes the series over time. However, data with high frequency noise might require a large number of lags or leads in the measurement and/or error equations in the model to adequately estimate a single dynamic factor. For this reason, Clayton-Matthews and Stock (1998/1999) used a band pass nine-period moving average filter on some series before estimating their Massachusetts model. Two series in our state models also required some pre-estimation smoothing beyond the normal seasonal adjustment to satisfactorily estimate the dynamic latent factor. Average hours worked in manufacturing are estimated from a survey taken during one week in each month. The estimates are particularly susceptible to unusual weather, work stoppages, and other exceptional factors; and the series exhibits a good deal of high frequency noise. We smoothed the manufacturing hours series in the process of seasonal adjustment. The X-11 seasonal adjustment uses a moving average procedure to
9
decompose the monthly data into three components--trend-cycle, seasonal, and irregular. The seasonally adjusted series includes both the trend-cycle and irregular components. One option in the X-11 procedure is to weight the extreme values of the irregular component based on their distance from the mean in standard deviation units.12 The default for this option in SAS is to give full weight to those irregular components that are less than 1.5 standard deviations from the mean and gradually reduce the weights to zero when the irregular component is more than 2.5 standard deviations from the mean. For 17 states the SAS default option did not smooth the manufacturing hours series sufficiently for the series to contribute to the estimation of the common factor. In those cases we gave full weight to irregular components that were less than one standard deviation from the mean and gradually reduced the weight to zero when the irregular component was greater than two standard deviations from the mean13 (Appendix A). In eight states we also used the SAS default option to weight the irregular component of the nonfarm employment data to produce a series smooth enough to estimate the common dynamic factor. And in seven states we applied the weights to irregular components of the employment series that were one standard deviation or greater from the mean (Appendix A). Several anomalies also appeared in the wage and salary data and in the unemployment series in several states. Nationally, wages and salaries declined more than 4 percent in real terms in the first quarter of 1993. That was more than four times greater than the average absolute percentage change since 1978 and more than 50 percent greater
12
The irregular component in the multiplicative version of the X-11seasonal adjustment procedure has a value that varies around one and is used to adjust the trend-cycle component, measured in units of the original data series. 13 A freezing rain and snow storm in the Northwest in January 1980 and a strike at Boeing in Seattle in October and November 1989 reduced hours worked in manufacturing in Washington state so dramatically that the manufacturing hours data for the state had to be eliminated (i.e., designated as missing data) in these months to satisfactorily estimate a common factor for the state's economy.
10
than the next highest absolute percentage change. This quarterly decline in wages and salaries is attributed in part to the movement of bonuses and other one-time compensation into 1992 in anticipation of an income tax increase proposed by the new administration.14 This did not represent a shift in economic activity but rather a shift in the timing of compensation and, therefore, should not be reflected in the coincident index. The impact of this shift was concentrated in 12 states in which the quarterly decline in real wages and salaries was greater than 4 percent. The wage and salary data for the first quarter of 1993 were eliminated, i.e., designated as missing data, in those states before estimating the coincident index model.15 Wage and salary data were also eliminated for two quarters in West Virginia (1978:I and 1981:II) because strikes by coal miners reduced real wage and salary disbursements by more than 10 percent in those two quarters (Appendix A). In several states there are one or more shifts in the level of the unemployment rate in a single month that may be the result of a change in the current population sample. In two instances this shift in the level of the unemployment rate was reversed in six to 10 months.16 In eight sates we eliminated one to three months of unemployment data on the basis that the data exhibited a shift of more than 1.5 percentage points in the level of the rate in a single month. In the eight states combined this resulted in the elimination of only 12 months of unemployment data since 1978 before estimating the coincident index models (Appendix A).
14 15
For a discussion of this issue see Feldstein and Feenberg (1996). In New York state real wages and salaries declined more than 10 percent in the first quarter of 1993 and increased more than 4 percent in the fourth quarter of 1992; so the fourth-quarter 1992 data were also eliminated from the wage and salary series in New York state. 16 Opposing shifts appear in the data for Oklahoma in June 1980 and December 1980 and in the data for Georgia in March 1991 and January 1992.
11
The pre-estimation smoothing of some data series and the elimination of some anomalous data points prevent outliers from distorting the estimation of a relatively smooth coincident index from the Stock/Watson model. Model Specification and Estimation Except for the restriction that the measurement equation for employment contain only the contemporaneous value of the latent dynamic factor, no a priori restrictions were placed on the lag structure of any of the measurement equations in our state models. But we did specify the autoregressive process for the common factor by an AR(2) equation in the model for each state. In the final models, 25 states had one or more lags of the state variable (common factor) in the measurement equation for unemployment, and 17 states had lags of the state variable in the measurement equation for wage and salary disbursements. In the measurement equation for average hours worked in manufacturing, 22 states had one or more leads of the state variable, and 10 states had one or more lags of the state variable. (See tables in Appendix B.) The models were evaluated on several criteria. First, the coefficients in the measurement equations had the expected signs and most were statistically significant. Second, in most states the relative contributions of the observed variables to the monthly change in the common factor were well distributed. Changes in employment were generally the largest contributor to monthly changes in the common factor (ct). In four states the change in employment contributed more than 70 percent to the change in the common factor, but in almost half the states it contributed less than 50 percent. The change in hours worked in manufacturing was often the least important determinant of
12
the change in the common factor. In 16 states manufacturing hours worked contributed less than 5 percent to the monthly change in the common factor. In two states the change in wages and salaries accounted for less than 5 percent of the change in the common factor, and the change in the unemployment rate accounted for less than 5 percent in one state. In their national model, Stock and Watson check the assumption of a single latent factor by testing whether the disturbances in the measurement equations are predictable by past values of the indicator variables or past values of the errors from the measurement equations (Stock and Watson 1989 and 1991). In a series of tests, they regress the errors from each measurement equation on a constant and six lags of the errors from each of the measurement equations and six lags of the indicator variables. If the single index model is the proper specification, the coefficients on the lags should jointly be insignificantly different from zero. We applied the same test to our state models and report the F-statistics for rejecting the hypothesis that the coefficients are not different from zero. (See tables in Appendix B.) The critical value of the F-statistic at the .05 level is approximately 2.14 for the monthly variables and approximately 2.2 for equations that contain quarterly wage and salary data.17 In most cases we cannot reject the hypothesis that jointly the coefficients on the six lags are not different from zero supporting the assumption of a single common factor. Of the 1600 F-statistics reported
17
There are always six degrees of freedom in the numerator. Except for Indiana, for which manufacturing hours data are not available from 1978 to 1988, the degrees of freedom in the denominator range from 245 to 269 for equations with only monthly variables. The degrees of freedom in the denominator range from 70 to 81 for equations that contain wages and salaries or the error from the wage and salary equation. For Indiana the monthly equations that contain manufacturing hours or the error from the hours equation have 139 degrees of freedom in the denominator, and for equations that contain both hours and wages and salaries the degrees of freedom in the denominator is 37.
13
for the 50 states, only 59 suggest a problem with the assumption of a single latent factor.18 Setting the Trend in the State Indexes Because the Stock-Watson index is estimated based on the standardized log differences in the components, a trend must be introduced into the index after it is constructed. Stock and Watson used a weighted average of the trends of the components to establish the trend of the index. The weights were based on the contribution of the components to the monthly change in the common factor. Therefore, the relative weights of the components in determining the trend will differ by state. Since the indexes developed in this paper are intended to be consistent across states, we re-trend the indexes based upon the trend in real gross state product for each state. Since the lag structure differs in each of the state models, the final indexes derived from the Stock/Watson model begin in different months in 1978 or 1979 for different states.19 Therefore, we re-trended the indexes beginning in 1979. Moreover, since gross state product is not yet available after 1999, we based our re-trending of the index on the data for the years 1979 to 1999. We reconstitute the state indexes from a standard Stock/Watson model so their average growth rate corresponds to the average growth of real gross state product from 1979 to 1999. If ct = the log of a Stock/Watson type index in which the trend is equal to the weighted average of the trends of the components, And
18
Except for Iowa, which has five of 32 F-statistics above the critical value, the most for any other state is three. 19 The indexes for seven states begin in various months in 1979--Louisiana, New Jersey, Ohio, Oklahoma, Texas, Virginia, and Wyoming.
14
D c = The average monthly log difference of the index in the years on which the re-trending is based (1979-1999), And D gsp = The average annual log difference in real gross state product in the years on which the re-trending is based (1979-1999), then an original Stock/Watson type index can be re-trended based on the average growth in real gross state product by calculating a new set of monthly changes, D t = D ct - D c + (D gsp / 12 ). Establishing a given month to equal 100 for the index (in our case July 1992), D t can be used to form a Stock/Watson type index with same trend as real gross state product.20 Conclusion The state indexes described in this paper have been constructed on a consistent basis for all 50 states. Despite the constraint of a certain level of consistency in the models, the coefficients in the measurement equations have the expected signs and are almost always statistically significant. Diagnostic tests of the single-index specification for the models generally support that assumption. The final indexes and accompanying graphs are available at www.phil.frb.org/econ/stateindexes. The goal of this project has been to provide researchers with a set of indexes of economic activity in each of the 50 states that can be used to examine other issues. Possible issues include the study of state business cycles, the effect of national economic
20
This procedure adjusts only the first moment of the change in the original index to the first moment of the change in real gross state product. Clayton-Matthews and Stock (1998/1999) adjust the first two moments of the original index. In some states the standard deviation of the annual change in real gross state product was so small that adjusting the second moment of the change in the original index obscured the business-cycle fluctuation in the state economy.
15
forces on individual states, and the effect of the state's overall economic activity on state fiscal conditions, poverty, or in-migration.
16
References Clayton-Matthews, Alan. DSFM Manual (version 2/23/99) mimeo, University of Massachusetts at Boston, 1999. Clayton-Matthews, Alan, Yolanda K. Kodrzycki, and Daniel Swaine. "Indexes of Economic Indicators: What Can They Tell Us about the New England Economy?" New England Economic Review, Federal Reserve Bank of Boston, November/December 1994, pp. 17-41. Clayton-Matthews, Alan, and James H. Stock. "An Application of the Stock/Watson Index Methodology to the Massachusetts Economy," Journal of Economic and Social Measurement, 25 (1998/1999), pp. 183-233. Crone, Theodore M. "A New Look at Economic Indexes for the States in the Third District," Business Review, Federal Reserve Bank of Philadelphia, November/December 2000, pp. 3-14. Crone, Theodore M. "Using State Indexes to Define Economic Regions in the US," Journal of Economic and Social Measurement, 25 (1998/1999), pp. 259-275. Feldstein, Martin, and Daniel Feenberg. "The Effect of Increased Tax Rates on Taxable Income and Economic Efficiency: A Preliminary Analysis of the 1993 Tax Rate Increases," in Tax Policy and the Economy. Vol. 10, James M. Poterba, ed. NBER, MIT Press, 1996, pp. 89-117. Orr, James, Robert Rich, and Rae Rosen. "Two New Indexes Offer a Broad View of Economic Activity in the New York--New Jersey Region," Current Issues in Economics and Finance, Federal Reserve Bank of New York, v. 5, No. 14 (October 1999). Stock, James H., and Mark W. Watson. "New Indexes of Coincident and Leading Economic Indicators," NBER Macroeconomics Annual (1989), pp. 351-394. Stock, James H., and Mark W. Watson. "A Probability Model of the Coincident Economic Indicators," in Leading Economic Indicators: New Approaches and Forecasting Records. K. Lahiri and G.H. Moore, eds. Cambridge University Press, Cambridge, 1991, pp. 63-89. Zarnowitz, Victor. Business Cycles: Theory, History, Indicators, and Forecasting. Chicago: University of Chicago Press, 1992.
17
Appendix A Seasonal Adjustment and Pre-estimation Smoothing of the Data We seasonally adjusted the nonfarm employment data and the average hours worked in manufacturing for all the states because these two series are not available on a seasonally adjusted basis for the time period over which we estimated our models. The pre-estimation smoothing of the data is described in this appendix.
Nonfarm Payroll Employment:
In addition to the normal seasonal adjustment, in the following states the irregular components that were between 1.5 standard deviations and 2.5 standard deviations from the mean were given a weight between one and zero. Those more than 2.5 standard deviations from the mean were given a weight of zero. Kentucky Michigan Nebraska Nevada Oregon Rhode Island Virginia West Virginia
In the following states the irregular components that were between one standard deviation and two standard deviations from the mean were given a weight between one and zero. Those more than two standard deviations from the mean were given a weight of zero. Delaware Iowa Ohio Minnesota Montana South Dakota Washington
Hours worked in manufacturing:
In addition to the normal seasonal adjustment, in all states except the following, the irregular components that were between 1.5 standard deviations and 2.5 standard deviations from the mean were given a weight between one and zero. Those more than 2.5 standard deviations from the mean were given a weight of zero. In the following
A-1
states the irregular components that were between one standard deviation and two standard deviations from the mean were given a weight between one and zero. Those more than two standard deviations from the mean were given a weight of zero. Alaska Delaware Florida Georgia Hawaii Louisiana Michigan North Carolina Oregon Pennsylvania Rhode Island South Dakota Tennessee Texas West Virginia Wisconsin Wyoming
In Washington state the hours worked in manufacturing were treated as missing data for January 1980 because a severe storm in the week of the survey reduced the hours worked by more than 5 percent. The entries for October and November 1989 were also treated as missing data because a strike at Boeing reduced manufacturing hours worked by more than 14 percent from the months immediately preceding.
Unemployment rate:
For the months indicated in the following states, the unemployment rate was treated as missing data because of an anomalous change of more than 1.5 percentage points in a single month: Delaware (September 1990) Georgia (March 1991, January 1992) Illinois (November 1993) Michigan (April 1980, December 1981, February 1991) New Jersey (May 1992) North Carolina (October 1981) Oklahoma (June 1980, December 1980) Rhode Island (December 1989)
Wage and salary disbursements:
Wage and salary disbursements were treated as missing data in the first quarter of 1993 for the following states because the shift of bonuses and other compensation into
A-2
1992 in anticipation of a tax increase resulted in a decline of more than 4 percent in real wages and salaries for the quarter: California Connecticut Delaware Illinois Massachusetts Michigan New Jersey New York Ohio Pennsylvania Rhode Island Washington
Because of the shift of compensation to 1992, wage and salary disbursements in New York increased more than 4 percent in the fourth quarter of 1993, so data in that quarter were also treated as missing for New York state. Strikes by coal miners reduced real wage and salary disbursements in West Virginia by more than 10 percent in the first quarter of 1978 and the second quarter of 1981, so wage and salary data for those quarters were treated as missing data.
A-3
Appendix B
The following tables present the coefficients on the equations in each of the state models with their standard errors and the F-statistics for the diagnostic tests of the single common factor assumption.
B-1
Alabama
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.426 0.057 Unemployment Rate Ct -0.776 0.075 C t-1 0.316 0.089 Average Weekly Mfg. Hours C t+2 0.129 0.034 Wage and Salary Dist. Ct 0.126 0.037 C t-1 -0.071 0.036 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.496 0.081 (2) -0.150 0.076 (1) Unemployment Rate 0.510 0.581 (2) 0.162 0.437 (1) Average Weekly Mfg. Hours -0.372 0.060 (2) -0.135 0.060 (1) Wage and Salary Dist. -0.142 0.113 (2) 0.028 0.106 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.382 0.087 Lag 2 0.362 0.067 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 0.366 Error(Employment) 0.834 0.897 0.733 Error(Unemployment Rate) 0.847 2.066 1.044 Error(Mfg. Hours) 1.753 3.003 1.482 Error(Wage and Salary Dist.) 1.760 0.979
t-statistic 7.53 -10.41 3.55 3.82 3.37 -1.94 -6.12 -1.98 0.88 0.37 -6.19 -2.27 -1.25 0.27 4.41 5.39 Error Wage and Salary Dist. 0.662 1.341 0.492 0.805
0.573 Employment 0.253 1.330 0.313 0.965 Unemployment Rate 0.892 1.844 1.911 0.829 Average Weekly Mfg. Hours 1.747 2.942 0.532 1.872 Wage and Salary Dist. 0.908 2.237 0.922 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 1.15 Cumulative dynamic multiplier -0.52 0.16 0.30 53.90 Relative Contribution (%) 24.33 7.72 14.05 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B2
Alaska
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.322 0.105 Unemployment Rate Ct -0.136 0.060 Average Weekly Mfg. Hours Ct 0.304 0.109 C t-1 -0.313 0.110 Wage and Salary Dist. Ct 0.058 0.019 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.282 0.073 (1) Unemployment Rate 0.003 0.058 (2) 0.193 0.057 (3) 0.221 0.059 (1) Average Weekly Mfg. Hours -0.467 0.072 (2) -0.162 0.072 (3) -0.094 0.066 (1) Wage and Salary Dist. -0.070 0.136 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.739 0.297 Lag 2 0.048 0.255 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 0.725 Error(Employment) 1.920 0.388 1.954 Error(Unemployment Rate) 0.831 1.260 1.649 Error(Mfg. Hours) 0.601 1.644 0.543 Error(Wage and Salary Dist.) 0.166 1.722
t-statistic 3.07 -2.26 2.78 -2.83 3.08 -3.85 0.06 3.37 3.73 -6.46 -2.25 -1.43 -0.51 2.49 0.19 Error Wage and Salary Dist. 0.345 0.671 1.519 1.159
1.017 Employment 2.045 0.308 0.371 1.807 Unemployment Rate 0.640 1.317 0.556 1.659 Average Weekly Mfg. Hours 0.704 1.877 0.887 1.352 Wage and Salary Dist. 0.653 1.555 0.547 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 1.22 Cumulative dynamic multiplier -0.15 0.89 0.65 41.83 Relative Contribution (%) 5.29 30.58 22.29 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B3
Arizona
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.361 0.049 Unemployment Rate Ct -0.311 0.062 Average Weekly Mfg. Hours Ct 0.073 0.035 Wage and Salary Dist. Ct 0.039 0.007 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.180 0.083 (2) -0.002 0.076 (1) Unemployment Rate 0.421 0.078 (2) 0.124 0.091 (3) 0.148 0.069 (1) Average Weekly Mfg. Hours -0.137 0.060 (2) 0.070 0.060 (1) Wage and Salary Dist. -0.306 0.118 (2) 0.133 0.117 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.309 0.113 Lag 2 0.591 0.117 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 1.745 Error(Employment) 1.096 1.046 1.052 Error(Unemployment Rate) 0.942 0.799 0.925 Error(Mfg. Hours) 1.536 1.641 0.280 Error(Wage and Salary Dist.) 1.381 0.466
t-statistic 7.42 -5.04 2.08 5.73 -2.17 -0.03 5.39 1.37 2.14 -2.29 1.16 -2.58 1.14 2.73 5.06 Error Wage and Salary Dist. 1.366 0.318 0.706 0.992
1.651 Employment 1.563 1.115 1.161 1.030 Unemployment Rate 0.353 0.950 0.167 0.984 Average Weekly Mfg. Hours 1.532 1.585 0.579 0.529 Wage and Salary Dist. 1.372 0.859 0.818 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 1.66 Cumulative dynamic multiplier -0.27 0.15 0.58 62.53 Relative Contribution (%) 10.00 5.55 21.93 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B4
Arkansas
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.390 0.055 Unemployment Rate C t-2 -0.373 0.057 Average Weekly Mfg. Hours C t+2 0.108 0.033 Wage and Salary Dist. Ct 0.192 0.059 C t-1 -0.149 0.058 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.103 0.082 (2) -0.063 0.083 (1) Unemployment Rate 0.175 0.077 (2) -0.039 0.077 (3) 0.079 0.069 (1) Average Weekly Mfg. Hours -0.320 0.061 (2) -0.169 0.063 (3) -0.068 0.060 (1) Wage and Salary Dist. -0.157 0.150 (2) 0.218 0.186 (3) -0.087 0.153 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.213 0.071 Lag 2 0.619 0.074 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 0.553 Error(Employment) 1.367 1.178 1.215 Error(Unemployment Rate) 0.305 0.648 1.736 Error(Mfg. Hours) 1.373 0.183 1.651 Error(Wage and Salary Dist.) 2.214 1.029
t-statistic 7.07 -6.56 3.24 3.24 -2.57 -1.25 -0.77 2.28 -0.51 1.15 -5.23 -2.68 -1.12 -1.05 1.17 -0.57 2.99 8.33 Error Wage and Salary Dist. 0.144 1.341 1.277 2.506
0.484 Employment 1.104 1.293 0.117 1.300 Unemployment Rate 0.629 2.439 1.503 1.810 Average Weekly Mfg. Hours 1.119 0.280 1.014 1.014 Wage and Salary Dist. 2.169 1.824 1.403 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 1.04 Cumulative dynamic multiplier -0.22 0.29 0.90 42.59 Relative Contribution (%) 8.91 11.69 36.81 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B5
California
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.295 0.043 Unemployment Rate Ct -0.732 0.054 C t-1 0.479 0.064 Average Weekly Mfg. Hours Ct 0.035 0.018 Wage and Salary Dist. Ct 0.028 0.006 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.343 0.082 (2) -0.218 0.070 (1) Unemployment Rate 0.692 0.109 (1) Average Weekly Mfg. Hours -0.310 0.059 (2) -0.190 0.059 (1) Wage and Salary Dist. 0.107 0.110 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.777 0.091 Lag 2 0.145 0.083 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 1.915 Error(Employment) 2.082 1.625 1.670 Error(Unemployment Rate) 1.912 1.423 1.572 Error(Mfg. Hours) 1.064 0.891 1.399 Error(Wage and Salary Dist.) 1.420 1.089
t-statistic 6.80 -13.59 7.50 1.99 4.51 -4.20 -3.11 6.35 -5.28 -3.25 0.98 8.50 1.75 Error Wage and Salary Dist. 0.890 0.460 0.348 0.997
1.624 Employment 3.009 2.818 0.485 1.696 Unemployment Rate 2.087 1.387 0.371 1.555 Average Weekly Mfg. Hours 0.988 0.715 0.414 1.209 Wage and Salary Dist. 1.539 2.182 0.605 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 2.33 Cumulative dynamic multiplier -0.81 0.11 0.20 67.71 Relative Contribution (%) 23.44 3.19 5.67 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B6
Colorado
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.247 0.061 Unemployment Rate Ct -0.561 0.172 C t-1 0.412 0.179 Average Weekly Mfg. Hours Ct 0.028 0.019 Wage and Salary Dist. Ct 0.026 0.008 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.324 0.097 (2) -0.131 0.093 (3) 0.112 0.078 (1) Unemployment Rate 0.261 0.132 (2) 0.234 0.100 (1) Average Weekly Mfg. Hours -0.354 0.059 (2) -0.152 0.059 (1) Wage and Salary Dist. -0.082 0.106 (2) 0.270 0.106 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.917 0.208 Lag 2 0.007 0.194 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 0.762 Error(Employment) 1.224 1.645 1.286 Error(Unemployment Rate) 1.012 1.019 1.169 Error(Mfg. Hours) 1.554 2.183 0.812 Error(Wage and Salary Dist.) 0.675 1.115
t-statistic 4.06 -3.25 2.30 1.46 3.27 -3.34 -1.40 1.44 1.98 2.33 -5.97 -2.57 -0.77 2.53 4.42 0.03 Error Wage and Salary Dist. 1.495 0.550 0.678 0.313
1.211 Employment 1.546 1.564 1.442 1.260 Unemployment Rate 0.656 0.960 0.657 1.190 Average Weekly Mfg. Hours 1.350 1.912 1.244 0.802 Wage and Salary Dist. 1.059 2.584 0.846 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 2.65 Cumulative dynamic multiplier -0.82 0.21 0.47 63.88 Relative Contribution (%) 19.70 5.05 11.36 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B7
Connecticut
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.283 0.077 Unemployment Rate Ct -0.275 0.079 Average Weekly Mfg. Hours C t+2 0.062 0.030 Wage and Salary Dist. Ct 0.039 0.011 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.129 0.092 (2) 0.026 0.087 (1) Unemployment Rate 0.000 0.073 (2) 0.147 0.068 (1) Average Weekly Mfg. Hours -0.301 0.060 (2) -0.098 0.063 (3) -0.073 0.060 (1) Wage and Salary Dist. -0.137 0.146 (2) -0.123 0.136 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.504 0.258 Lag 2 0.391 0.246 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 1.171 Error(Employment) 1.342 0.758 1.261 Error(Unemployment Rate) 1.047 0.936 1.670 Error(Mfg. Hours) 0.841 2.033 0.690 Error(Wage and Salary Dist.) 2.638 0.813
t-statistic 3.67 -3.46 2.10 3.68 -1.41 0.30 -0.01 2.17 -5.00 -1.56 -1.23 -0.93 -0.90 1.96 1.59 Error Wage and Salary Dist. 0.681 1.464 1.086 0.717
1.803 Employment 1.437 0.705 0.716 1.217 Unemployment Rate 0.331 0.529 1.769 1.556 Average Weekly Mfg. Hours 1.005 2.022 1.314 1.237 Wage and Salary Dist. 1.964 0.329 1.261 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 1.37 Cumulative dynamic multiplier -0.79 0.28 0.68 43.84 Relative Contribution (%) 25.40 8.95 21.82 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B8
Delaware
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.212 0.059 Unemployment Rate Ct -0.793 0.083 C t-1 0.738 0.088 Average Weekly Mfg. Hours C t+1 0.036 0.028 Wage and Salary Dist. Ct 0.024 0.007 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.248 0.078 (2) -0.028 0.082 (3) -0.075 0.081 (4) -0.050 0.071 (1) Unemployment Rate 0.520 0.204 (1) Average Weekly Mfg. Hours -0.182 0.059 (2) 0.040 0.060 (3) -0.006 0.060 (4) -0.142 0.059 (1) Wage and Salary Dist. -0.318 0.110 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.513 0.094 Lag 2 0.407 0.079 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 0.799 Error(Employment) 2.041 1.236 1.407 Error(Unemployment Rate) 1.163 1.541 2.454 Error(Mfg. Hours) 0.920 0.181 0.879 Error(Wage and Salary Dist.) 0.478 1.074
t-statistic 3.60 -9.50 8.41 1.28 3.43 -3.17 -0.34 -0.92 -0.71 2.55 -3.08 0.67 -0.10 -2.42 -2.90 5.48 5.16 Error Wage and Salary Dist. 0.533 0.431 0.807 1.535
0.802 Employment 2.052 1.526 0.506 1.391 Unemployment Rate 0.878 1.670 0.341 2.363 Average Weekly Mfg. Hours 0.936 0.199 0.889 0.924 Wage and Salary Dist. 0.434 1.221 1.142 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 2.33 Cumulative dynamic multiplier -1.67 0.26 1.24 42.42 Relative Contribution (%) 30.36 4.73 22.49 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B9
Florida
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.336 0.048 Unemployment Rate Ct -0.339 0.058 Average Weekly Mfg. Hours C t+2 0.148 0.106 C t+1 -0.084 0.134 Ct -0.045 0.110 Wage and Salary Dist. Ct 0.122 0.041 C t-1 -0.098 0.041 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.408 0.074 (2) -0.344 0.070 (1) Unemployment Rate 0.157 0.067 (2) 0.196 0.066 (1) Average Weekly Mfg. Hours -0.213 0.062 (2) 0.090 0.061 (1) Wage and Salary Dist. -0.187 0.108 (2) 0.223 0.117 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.393 0.129 Lag 2 0.511 0.127 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 0.645 Error(Employment) 0.438 1.222 0.750 Error(Unemployment Rate) 1.749 0.714 1.074 Error(Mfg. Hours) 0.905 0.868 0.771 Error(Wage and Salary Dist.) 0.785 0.762
t-statistic 7.02 -5.85 1.40 -0.63 -0.41 2.98 -2.39 -5.55 -4.93 2.34 2.95 -3.45 1.49 -1.74 1.91 3.05 4.03 Error Wage and Salary Dist. 0.633 1.680 0.202 1.410
0.454 Employment 0.512 1.278 0.437 0.555 Unemployment Rate 1.524 0.456 1.393 1.153 Average Weekly Mfg. Hours 0.851 0.820 0.212 0.527 Wage and Salary Dist. 0.631 0.774 1.386 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 2.02 Cumulative dynamic multiplier -0.42 0.17 0.41 66.99 Relative Contribution (%) 14.01 5.49 13.51 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B10
Georgia
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.353 0.052 Unemployment Rate Ct -0.651 0.087 C t-1 0.603 0.127 C t-2 -0.229 0.109 Average Weekly Mfg. Hours Ct 0.097 0.037 Wage and Salary Dist. Ct 0.144 0.035 C t-1 -0.111 0.034 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.395 0.083 (2) -0.187 0.076 (1) Unemployment Rate 0.317 0.178 (2) 0.106 0.092 (1) Average Weekly Mfg. Hours -0.051 0.060 (2) 0.021 0.060 (1) Wage and Salary Dist. -0.064 0.108 (2) 0.357 0.133 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.657 0.129 Lag 2 0.212 0.120 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 0.637 Error(Employment) 0.717 1.202 1.327 Error(Unemployment Rate) 0.924 2.109 1.148 Error(Mfg. Hours) 0.338 1.172 0.458 Error(Wage and Salary Dist.) 0.456 0.193
t-statistic 6.74 -7.50 4.73 -2.09 2.61 4.14 -3.22 -4.73 -2.46 1.78 1.14 -0.85 0.34 -0.60 2.69 5.09 1.77 Error Wage and Salary Dist. 0.616 0.485 0.602 1.387
1.506 Employment 0.818 1.566 0.602 1.024 Unemployment Rate 0.955 2.415 1.138 1.063 Average Weekly Mfg. Hours 0.342 1.180 0.768 0.469 Wage and Salary Dist. 0.501 0.985 1.539 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 1.66 Cumulative dynamic multiplier -0.67 0.12 0.42 57.98 Relative Contribution (%) 23.30 4.24 14.48 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B11
Hawaii
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.253 0.068 Unemployment Rate Ct -0.752 0.118 C t-1 0.148 0.298 C t-2 0.423 0.210 Average Weekly Mfg. Hours Ct 0.052 0.031 Wage and Salary Dist. Ct 0.028 0.010 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.220 0.068 (2) -0.134 0.072 (1) Unemployment Rate 0.331 0.349 (2) 0.351 0.255 (1) Average Weekly Mfg. Hours -0.186 0.059 (2) 0.068 0.060 (3) 0.169 0.059 (4) -0.095 0.060 (5) -0.248 0.058 (1) Wage and Salary Dist. -0.112 0.114 (2) 0.160 0.115 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.293 0.246 Lag 2 0.616 0.245 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 1.975 Error(Employment) 1.372 0.742 1.825 Error(Unemployment Rate) 0.951 1.249 0.132 Error(Mfg. Hours) 0.601 0.712 1.190 Error(Wage and Salary Dist.) 1.753 0.760
t-statistic 3.70 -6.39 0.50 2.01 1.70 2.80 -3.25 -1.86 0.95 1.37 -3.17 1.14 2.87 -1.60 -4.27 -0.98 1.39 1.19 2.51 Error Wage and Salary Dist. 0.936 0.967 0.223 0.909
1.804 Employment 1.271 0.815 1.150 1.769 Unemployment Rate 0.779 1.236 0.872 0.297 Average Weekly Mfg. Hours 0.710 0.971 0.282 1.570 Wage and Salary Dist. 1.617 0.601 1.306 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 2.16 Cumulative dynamic multiplier -0.79 0.32 0.68 54.71 Relative Contribution (%) 20.08 8.08 17.13 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B12
Idaho
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.542 0.062 Unemployment Rate Ct -0.774 0.088 C t-1 0.398 0.087 Average Weekly Mfg. Hours C t+1 0.099 0.036 Wage and Salary Dist. Ct 0.076 0.011 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.334 0.069 (1) Unemployment Rate 0.487 0.180 (1) Average Weekly Mfg. Hours -0.375 0.059 (2) -0.160 0.059 (1) Wage and Salary Dist. -0.274 0.115 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.373 0.095 Lag 2 0.339 0.081 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 1.648 Error(Employment) 0.572 0.885 1.795 Error(Unemployment Rate) 0.812 0.891 1.837 Error(Mfg. Hours) 1.000 0.771 0.470 Error(Wage and Salary Dist.) 1.026 1.035
t-statistic 8.75 -8.76 4.56 2.77 6.95 -4.84 2.71 -6.34 -2.73 -2.38 3.95 4.21 Error Wage and Salary Dist. 1.124 1.375 0.325 0.360
2.345 Employment 0.591 0.829 1.382 1.631 Unemployment Rate 0.946 0.901 1.434 1.707 Average Weekly Mfg. Hours 0.987 0.826 0.551 1.401 Wage and Salary Dist. 1.342 0.980 0.658 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 1.01 Cumulative dynamic multiplier -0.49 0.10 0.20 56.19 Relative Contribution (%) 27.04 5.82 10.95 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B13
Illinois
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.167 0.035 Unemployment Rate Ct -0.775 0.080 C t-1 0.617 0.096 Average Weekly Mfg. Hours C t+1 0.041 0.023 Wage and Salary Dist. Ct 0.090 0.028 C t-1 -0.067 0.028 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.193 0.071 (2) -0.052 0.069 (1) Unemployment Rate 0.660 0.151 (1) Average Weekly Mfg. Hours -0.160 0.060 (2) 0.092 0.060 (1) Wage and Salary Dist. -0.098 0.134 (2) 0.262 0.144 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.936 0.133 Lag 2 0.010 0.124 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 0.538 Error(Employment) 0.774 1.119 1.490 Error(Unemployment Rate) 0.717 1.846 0.374 Error(Mfg. Hours) 1.353 0.700 0.836 Error(Wage and Salary Dist.) 1.243 0.280
t-statistic 4.77 -9.64 6.40 1.81 3.19 -2.45 -2.72 -0.75 4.37 -2.67 1.53 -0.73 1.82 7.06 0.08 Error Wage and Salary Dist. 1.060 1.432 0.672 0.685
0.399 Employment 1.543 1.994 0.511 1.511 Unemployment Rate 0.483 1.492 1.369 0.656 Average Weekly Mfg. Hours 1.146 0.595 0.764 1.309 Wage and Salary Dist. 1.405 1.901 0.777 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 1.82 Cumulative dynamic multiplier -1.47 0.26 1.97 33.00 Relative Contribution (%) 26.68 4.65 35.67 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B14
Indiana
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.515 0.057 Unemployment Rate Ct -0.473 0.057 Average Weekly Mfg. Hours C t+1 0.192 0.074 Wage and Salary Dist. Ct 0.070 0.009 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.155 0.098 (2) 0.040 0.091 (1) Unemployment Rate 0.106 0.074 (2) 0.105 0.071 (1) Average Weekly Mfg. Hours -0.375 0.084 (2) 0.058 0.083 (1) Wage and Salary Dist. -0.237 0.133 (2) 0.065 0.123 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.455 0.130 Lag 2 0.324 0.126 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 1.285 Error(Employment) 0.799 0.782 0.991 Error(Unemployment Rate) 0.656 1.291 0.625 Error(Mfg. Hours) 0.372 1.103 0.063 Error(Wage and Salary Dist.) 0.917 1.386
t-statistic 9.02 -8.31 2.59 7.79 -1.58 0.44 1.44 1.48 -4.44 0.70 -1.79 0.53 3.49 2.57 Error Wage and Salary Dist. 1.028 0.545 0.368 0.333
1.419 Employment 0.939 0.872 0.601 1.114 Unemployment Rate 0.670 1.520 0.834 0.423 Average Weekly Mfg. Hours 0.414 1.212 0.486 0.592 Wage and Salary Dist. 0.705 0.769 0.726 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 1.02 Cumulative dynamic multiplier -0.39 0.19 0.22 55.75 Relative Contribution (%) 21.50 10.60 12.15 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B15
Iowa
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.611 0.064 Unemployment Rate Ct -0.383 0.041 Average Weekly Mfg. Hours Ct 0.087 0.035 Wage and Salary Dist. Ct 0.062 0.008 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment 0.256 0.131 (1) Unemployment Rate -0.223 0.067 (2) -0.071 0.069 (3) 0.203 0.064 (1) Average Weekly Mfg. Hours -0.279 0.058 (1) Wage and Salary Dist. -0.193 0.113 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.404 0.070 Lag 2 0.387 0.070 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 2.876 Error(Employment) 0.961 2.441 1.181 Error(Unemployment Rate) 1.589 1.589 0.797 Error(Mfg. Hours) 0.769 1.481 0.329 Error(Wage and Salary Dist.) 0.967 1.661
t-statistic 9.54 -9.29 2.48 7.83 1.95 -3.33 -1.03 3.17 -4.84 -1.70 5.76 5.54 Error Wage and Salary Dist. 0.842 1.048 1.153 1.084
3.160 Employment 1.818 3.097 0.905 0.862 Unemployment Rate 1.024 1.089 0.887 1.071 Average Weekly Mfg. Hours 0.400 1.418 1.389 1.034 Wage and Salary Dist. 0.792 2.776 0.565 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 1.20 Cumulative dynamic multiplier -0.30 0.06 0.13 71.05 Relative Contribution (%) 17.85 3.27 7.83 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B16
Kansas
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.404 0.074 Unemployment Rate Ct -0.349 0.073 Average Weekly Mfg. Hours Ct 0.119 0.043 Wage and Salary Dist. Ct 0.052 0.011 Estimated for Coefficients lags in the autoregressive equations for the error terms (1) Employment -0.409 0.077 (2) -0.312 0.075 (1) Unemployment Rate 0.039 0.069 (1) Average Weekly Mfg. Hours -0.296 0.061 (2) -0.182 0.060 (1) Wage and Salary Dist. -0.394 0.101 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.265 0.128 Lag 2 0.456 0.125 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 0.735 Error(Employment) 1.095 1.357 0.462 Error(Unemployment Rate) 0.741 1.796 1.066 Error(Mfg. Hours) 1.442 0.966 1.218 Error(Wage and Salary Dist.) 1.138 0.404
t-statistic 5.48 -4.80 2.77 4.56 -5.28 -4.19 0.57 -4.90 -3.03 -3.90 2.07 3.66 Error Wage and Salary Dist. 0.992 1.811 1.622 0.874
0.693 Employment 0.960 1.661 0.527 0.609 Unemployment Rate 0.623 1.450 1.297 1.023 Average Weekly Mfg. Hours 1.423 1.061 1.785 1.370 Wage and Salary Dist. 0.537 0.650 0.420 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 1.30 Cumulative dynamic multiplier -0.39 0.20 0.20 62.22 Relative Contribution (%) 18.57 9.51 9.71 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B17
Kentucky
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.510 0.071 Unemployment Rate Ct -0.463 0.065 Average Weekly Mfg. Hours Ct 0.081 0.039 Wage and Salary Dist. Ct 0.051 0.010 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.205 0.085 (1) Unemployment Rate -0.109 0.075 (1) Average Weekly Mfg. Hours -0.327 0.056 (1) Wage and Salary Dist. -0.118 0.091 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.377 0.110 Lag 2 0.366 0.109 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 1.391 Error(Employment) 3.654 1.343 1.680 Error(Unemployment Rate) 1.450 1.470 0.415 Error(Mfg. Hours) 1.720 0.338 0.886 Error(Wage and Salary Dist.) 1.419 1.106
t-statistic 7.21 -7.16 2.06 5.13 -2.42 -1.45 -5.79 -1.29 3.42 3.35 Error Wage and Salary Dist. 0.189 1.440 1.217 0.409
1.657 Employment 3.153 1.911 0.464 1.797 Unemployment Rate 1.981 2.045 1.575 0.552 Average Weekly Mfg. Hours 1.921 0.320 1.333 1.754 Wage and Salary Dist. 2.554 1.715 0.445 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 1.02 Cumulative dynamic multiplier -0.56 0.09 0.14 56.46 Relative Contribution (%) 30.97 4.72 7.85 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B18
Louisiana
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.474 0.074 Unemployment Rate Ct -0.169 0.069 Average Weekly Mfg. Hours Ct 0.076 0.036 Wage and Salary Dist. Ct 0.058 0.010 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.106 0.112 (2) -0.133 0.112 (1) Unemployment Rate 0.435 0.062 (2) 0.170 0.062 (1) Average Weekly Mfg. Hours -0.182 0.060 (2) -0.068 0.060 (3) 0.139 0.060 (4) -0.122 0.060 (1) Wage and Salary Dist. -0.285 0.126 (2) 0.159 0.134 (3) 0.102 0.123 (4) -0.045 0.112 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.251 0.109 Lag 2 0.575 0.112 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 0.029 Error(Employment) 1.226 2.366 1.204 Error(Unemployment Rate) 2.034 1.233 1.900 Error(Mfg. Hours) 1.440 1.035 1.419 Error(Wage and Salary Dist.) 0.658 1.141
t-statistic 6.42 -2.44 2.09 5.95 -0.94 -1.19 7.00 2.72 -3.02 -1.13 2.30 -2.05 -2.26 1.18 0.83 -0.41 2.31 5.12 Error Wage and Salary Dist. 1.867 0.856 0.345 0.142
0.024 Employment 1.205 2.105 1.720 1.304 Unemployment Rate 1.818 1.094 0.533 1.860 Average Weekly Mfg. Hours 1.582 1.377 0.331 1.619 Wage and Salary Dist. 0.856 1.075 0.268 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 1.45 Cumulative dynamic multiplier -0.08 0.11 0.31 74.52 Relative Contribution (%) 4.11 5.48 15.90 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B19
Maine
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.304 0.093 Unemployment Rate Ct -0.283 0.101 Average Weekly Mfg. Hours C t+2 0.062 0.043 Wage and Salary Dist. Ct 0.046 0.014 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.197 0.065 (1) Unemployment Rate -0.018 0.067 (2) 0.112 0.064 (3) 0.152 0.064 (1) Average Weekly Mfg. Hours -0.275 0.058 (1) Wage and Salary Dist. -0.266 0.110 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.412 0.212 Lag 2 0.416 0.197 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 1.416 Error(Employment) 0.449 0.381 2.448 Error(Unemployment Rate) 0.356 0.680 0.792 Error(Mfg. Hours) 1.539 1.040 1.328 Error(Wage and Salary Dist.) 1.115 0.428
t-statistic 3.29 -2.80 1.45 3.21 -3.02 -0.27 1.74 2.40 -4.78 -2.42 1.94 2.11 Error Wage and Salary Dist. 1.568 1.423 0.877 1.690
1.455 Employment 0.245 0.333 1.081 2.388 Unemployment Rate 0.383 0.731 1.048 0.763 Average Weekly Mfg. Hours 1.533 1.166 0.653 1.496 Wage and Salary Dist. 1.003 0.473 1.570 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 1.10 Cumulative dynamic multiplier -0.51 0.20 0.68 44.24 Relative Contribution (%) 20.59 7.99 27.18 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B20
Maryland
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.272 0.049 Unemployment Rate Ct -0.615 0.125 C t-1 -0.025 0.121 C t-2 0.399 0.131 Average Weekly Mfg. Hours C t+1 0.059 0.028 Wage and Salary Dist. Ct 0.039 0.009 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.317 0.081 (2) -0.180 0.082 (3) 0.092 0.080 (1) Unemployment Rate -0.107 0.097 (2) 0.376 0.149 (3) 0.131 0.094 (1) Average Weekly Mfg. Hours -0.335 0.056 (1) Wage and Salary Dist. -0.136 0.122 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.216 0.114 Lag 2 0.677 0.114 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 1.950 Error(Employment) 1.648 1.841 1.715 Error(Unemployment Rate) 0.779 1.027 0.950 Error(Mfg. Hours) 1.439 1.799 0.598 Error(Wage and Salary Dist.) 1.053 0.395
t-statistic 5.52 -4.90 -0.20 3.04 2.09 4.49 -3.89 -2.20 1.15 -1.10 2.52 1.39 -5.94 -1.11 1.90 5.97 Error Wage and Salary Dist. 0.311 0.375 1.344 1.497
2.124 Employment 1.840 1.805 0.138 1.826 Unemployment Rate 0.710 0.874 0.341 1.096 Average Weekly Mfg. Hours 1.486 1.890 0.993 0.517 Wage and Salary Dist. 0.603 1.078 1.290 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 1.59 Cumulative dynamic multiplier -0.95 0.22 0.64 46.69 Relative Contribution (%) 27.98 6.42 18.92 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B21
Massachusetts
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.441 0.045 Unemployment Rate Ct -0.473 0.059 Average Weekly Mfg. Hours C t+2 0.061 0.033 Wage and Salary Dist. Ct 0.045 0.009 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.366 0.097 (2) 0.097 0.087 (3) 0.454 0.102 (4) 0.309 0.097 (1) Unemployment Rate 0.084 0.087 (2) -0.034 0.092 (1) Average Weekly Mfg. Hours -0.440 0.059 (2) -0.025 0.064 (3) 0.180 0.064 (4) 0.202 0.059 (1) Wage and Salary Dist. -0.109 0.105 (2) 0.316 0.104 (3) 0.238 0.109 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.303 0.083 Lag 2 0.541 0.090 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 1.044 Error(Employment) 0.224 1.809 1.247 Error(Unemployment Rate) 1.728 1.320 0.483 Error(Mfg. Hours) 2.146 1.401 1.892 Error(Wage and Salary Dist.) 0.737 0.727
t-statistic 9.72 -8.05 1.84 4.78 -3.77 1.12 4.44 3.18 0.96 -0.37 -7.49 -0.40 2.82 3.45 -1.04 3.04 2.19 3.67 6.00 Error Wage and Salary Dist. 1.163 1.498 0.999 0.563
1.261 Employment 0.309 1.749 1.327 2.236 Unemployment Rate 0.718 1.447 1.625 0.447 Average Weekly Mfg. Hours 2.088 2.097 0.894 2.043 Wage and Salary Dist. 0.510 0.825 0.167 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 0.78 Cumulative dynamic multiplier -1.00 0.10 0.22 37.02 Relative Contribution (%) 47.64 4.63 10.71 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B22
Michigan
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.416 0.068 -0.454 0.121 Unemployment Rate Ct C t-1 -0.089 0.127 0.201 0.082 C t-2 0.368 0.078 Average Weekly Mfg. Hours Ct -0.232 0.172 C t-1 C t-2 0.255 0.184 -0.311 0.086 C t-3 0.126 0.025 Wage and Salary Dist. Ct C t-1 -0.076 0.021 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.136 0.082 (2) 0.244 0.079 (3) 0.116 0.086 (1) Unemployment Rate -0.214 0.083 (2) 0.222 0.086 (3) 0.202 0.086 (4) 0.218 0.075 (1) Average Weekly Mfg. Hours -0.274 0.078 (2) -0.018 0.073 (3) 0.218 0.065 (1) Wage and Salary Dist. -0.534 0.212 (2) -0.180 0.196 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.822 0.199 Lag 2 0.029 0.185 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 1.110 Error(Employment) 1.625 0.359 0.973 Error(Unemployment Rate) 1.607 0.670 1.064 Error(Mfg. Hours) 0.625 1.096 0.526 Error(Wage and Salary Dist.) 0.367 0.920
t-statistic 6.11 -3.75 -0.70 2.43 4.70 -1.35 1.38 -3.62 5.15 -3.64 -1.65 3.09 1.36 -2.58 2.58 2.35 2.89 -3.53 -0.25 3.37 -2.52 -0.92 4.13 0.16 Error Wage and Salary Dist. 0.265 1.176 0.750 0.675
1.416 Employment 1.663 0.682 0.553 1.694 Unemployment Rate 1.907 0.735 1.993 1.196 Average Weekly Mfg. Hours 1.264 1.157 0.888 1.100 Wage and Salary Dist. 1.791 1.108 0.972 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Wage and Salary Average Weekly Unemployment Employment Rate Mfg. Hours Dist. 0.60 Cumulative dynamic multiplier -0.34 0.33 1.19 24.39 Relative Contribution (%) 13.85 13.45 48.31 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B23
Minnesota
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.491 0.095 Unemployment Rate Ct -0.431 0.086 C t-1 0.107 0.104 Average Weekly Mfg. Hours Ct 0.108 0.034 Wage and Salary Dist. Ct 0.044 0.009 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment 0.010 0.110 (2) 0.351 0.085 (3) 0.347 0.121 (1) Unemployment Rate -0.038 0.070 (2) 0.080 0.068 (3) 0.266 0.069 (1) Average Weekly Mfg. Hours -0.375 0.060 (2) -0.060 0.060 (1) Wage and Salary Dist. -0.318 0.110 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.516 0.139 Lag 2 0.321 0.120 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 0.772 Error(Employment) 1.156 1.409 1.169 Error(Unemployment Rate) 0.524 1.481 0.444 Error(Mfg. Hours) 2.095 0.337 1.573 Error(Wage and Salary Dist.) 0.624 0.750
t-statistic 5.19 -5.04 1.03 3.23 4.98 0.09 4.13 2.86 -0.54 1.18 3.85 -6.22 -1.00 -2.88 3.71 2.66 Error Wage and Salary Dist. 0.748 1.232 0.563 1.229
0.773 Employment 1.071 2.343 0.323 1.525 Unemployment Rate 0.215 1.871 0.813 0.596 Average Weekly Mfg. Hours 1.628 0.456 0.631 1.693 Wage and Salary Dist. 0.297 2.109 0.931 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 0.66 Cumulative dynamic multiplier -0.55 0.36 0.84 27.40 Relative Contribution (%) 22.73 14.99 34.88 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B24
Mississippi
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.287 0.058 Unemployment Rate Ct -0.229 0.059 Average Weekly Mfg. Hours Ct 0.607 0.157 C t-1 -0.548 0.164 Wage and Salary Dist. Ct 0.039 0.009 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.251 0.081 (2) -0.121 0.070 (1) Unemployment Rate 0.268 0.061 (1) Average Weekly Mfg. Hours -0.274 0.117 (2) 0.139 0.132 (3) -0.149 0.124 (4) -0.109 0.092 (1) Wage and Salary Dist. -0.125 0.117 (2) -0.106 0.111 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.664 0.158 Lag 2 0.218 0.152 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 0.848 Error(Employment) 1.032 1.185 0.357 Error(Unemployment Rate) 0.166 1.712 1.079 Error(Mfg. Hours) 0.715 0.501 0.883 Error(Wage and Salary Dist.) 0.534 0.979
t-statistic 4.99 -3.92 3.88 -3.34 4.53 -3.10 -1.72 4.39 -2.34 1.05 -1.20 -1.18 -1.06 -0.95 4.21 1.44 Error Wage and Salary Dist. 0.539 0.619 0.319 0.687
0.433 Employment 0.985 1.236 0.558 0.653 Unemployment Rate 0.219 1.951 0.531 1.251 Average Weekly Mfg. Hours 0.907 0.512 0.313 0.801 Wage and Salary Dist. 0.653 1.589 0.947 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 1.71 Cumulative dynamic multiplier -0.35 1.61 0.61 39.85 Relative Contribution (%) 8.18 37.72 14.24 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B25
Missouri
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.228 0.048 Unemployment Rate Ct -0.247 0.055 Average Weekly Mfg. Hours Ct 0.491 0.127 C t-1 -0.446 0.128 Wage and Salary Dist. Ct 0.032 0.007 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.303 0.072 (2) -0.246 0.068 (1) Unemployment Rate 0.164 0.064 (2) 0.024 0.061 (3) 0.189 0.060 (1) Average Weekly Mfg. Hours -0.274 0.073 (1) Wage and Salary Dist. -0.333 0.108 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.775 0.178 Lag 2 0.122 0.166 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 1.050 Error(Employment) 1.243 2.149 1.168 Error(Unemployment Rate) 0.882 1.430 1.202 Error(Mfg. Hours) 0.687 1.136 0.725 Error(Wage and Salary Dist.) 0.951 1.059
t-statistic 4.79 -4.50 3.87 -3.48 4.43 -4.22 -3.60 2.56 0.39 3.15 -3.74 -3.08 4.36 0.74 Error Wage and Salary Dist. 1.333 1.150 0.509 0.930
0.593 Employment 0.453 1.941 0.603 1.352 Unemployment Rate 1.275 1.074 1.025 1.174 Average Weekly Mfg. Hours 0.840 1.227 0.520 1.502 Wage and Salary Dist. 0.497 0.999 0.714 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 1.89 Cumulative dynamic multiplier -0.59 1.29 0.80 41.34 Relative Contribution (%) 13.00 28.15 17.50 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B26
Montana
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.495 0.120 Unemployment Rate Ct -0.305 0.096 C t-1 0.085 0.108 Average Weekly Mfg. Hours Ct 0.031 0.034 Wage and Salary Dist. Ct 0.059 0.014 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.081 0.124 (2) 0.086 0.090 (3) 0.191 0.092 (1) Unemployment Rate -0.167 0.066 (2) 0.104 0.063 (3) 0.230 0.065 (4) 0.123 0.065 (1) Average Weekly Mfg. Hours -0.381 0.059 (2) -0.192 0.060 (1) Wage and Salary Dist. -0.273 0.153 (2) 0.027 0.162 (3) -0.037 0.133 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.432 0.217 Lag 2 0.314 0.185 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 0.588 Error(Employment) 1.163 0.940 0.607 Error(Unemployment Rate) 0.312 1.584 1.424 Error(Mfg. Hours) 0.803 0.761 2.833 Error(Wage and Salary Dist.) 1.749 0.378
t-statistic 4.12 -3.19 0.79 0.91 4.10 -0.65 0.96 2.08 -2.53 1.63 3.54 1.91 -6.46 -3.23 -1.79 0.17 -0.27 1.99 1.70 Error Wage and Salary Dist. 0.436 0.849 1.108 0.840
0.334 Employment 1.071 1.262 0.622 0.451 Unemployment Rate 0.507 1.467 0.950 1.478 Average Weekly Mfg. Hours 1.066 0.539 1.268 2.637 Wage and Salary Dist. 1.450 0.838 1.169 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 1.00 Cumulative dynamic multiplier -0.30 0.08 0.44 55.03 Relative Contribution (%) 16.53 4.25 24.19 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B27
Nebraska
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.452 0.125 Unemployment Rate Ct -0.230 0.073 Average Weekly Mfg. Hours Ct 0.064 0.034 Wage and Salary Dist. Ct 0.097 0.040 C t-1 -0.052 0.037 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.090 0.111 (2) 0.234 0.098 (1) Unemployment Rate -0.096 0.066 (1) Average Weekly Mfg. Hours -0.398 0.059 (2) -0.141 0.059 (1) Wage and Salary Dist. -0.166 0.116 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.634 0.291 Lag 2 0.135 0.248 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 0.283 Error(Employment) 1.695 1.445 0.766 Error(Unemployment Rate) 2.020 1.784 0.859 Error(Mfg. Hours) 0.774 0.272 0.947 Error(Wage and Salary Dist.) 1.006 0.167
t-statistic 3.61 -3.17 1.90 2.42 -1.41 -0.81 2.38 -1.46 -6.72 -2.38 -1.43 2.18 0.54 Error Wage and Salary Dist. 0.635 0.328 0.340 1.787
0.400 Employment 1.548 1.183 0.772 0.946 Unemployment Rate 1.320 2.130 0.319 0.683 Average Weekly Mfg. Hours 0.687 0.365 0.303 1.247 Wage and Salary Dist. 1.028 0.556 1.226 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 1.06 Cumulative dynamic multiplier -0.41 0.19 0.50 49.11 Relative Contribution (%) 19.00 8.80 23.09 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B28
Nevada
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.513 0.084 Unemployment Rate Ct -0.468 0.097 C t-1 0.113 0.111 Average Weekly Mfg. Hours C t+2 0.047 0.031 Wage and Salary Dist. Ct 0.118 0.033 C t-1 -0.069 0.032 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.251 0.149 (2) 0.174 0.091 (3) 0.387 0.099 (4) 0.375 0.142 (1) Unemployment Rate 0.203 0.075 (2) 0.164 0.069 (1) Average Weekly Mfg. Hours -0.305 0.060 (2) -0.062 0.063 (3) -0.027 0.060 (1) Wage and Salary Dist. -0.278 0.117 (2) 0.034 0.112 (3) 0.193 0.106 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.593 0.149 Lag 2 0.213 0.136 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 1.120 Error(Employment) 1.398 0.478 1.662 Error(Unemployment Rate) 0.722 1.806 1.262 Error(Mfg. Hours) 1.051 0.876 1.878 Error(Wage and Salary Dist.) 0.726 0.452
t-statistic 6.14 -4.81 1.03 1.52 3.54 -2.17 -1.69 1.91 3.91 2.65 2.70 2.39 -5.06 -0.99 -0.44 -2.38 0.30 1.82 3.98 1.57 Error Wage and Salary Dist. 0.581 1.712 0.660 1.128
1.456 Employment 0.794 0.489 1.489 1.639 Unemployment Rate 0.779 1.824 1.656 1.350 Average Weekly Mfg. Hours 0.991 0.968 0.636 1.400 Wage and Salary Dist. 0.688 1.060 1.830 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 0.73 Cumulative dynamic multiplier -0.36 0.11 0.91 34.63 Relative Contribution (%) 16.91 5.08 43.38 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B29
New Hampshire
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.300 0.062 Unemployment Rate Ct -0.648 0.060 C t-1 0.395 0.084 Average Weekly Mfg. Hours C t+2 0.025 0.020 Wage and Salary Dist. Ct 0.099 0.032 C t-1 -0.071 0.029 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.216 0.098 (2) -0.200 0.096 (3) -0.112 0.093 (4) -0.187 0.081 (5) -0.113 0.075 (1) Unemployment Rate 0.689 0.080 (1) Average Weekly Mfg. Hours -0.365 0.059 (2) -0.163 0.062 (3) 0.131 0.059 (1) Wage and Salary Dist. -0.138 0.114 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.743 0.123 Lag 2 0.170 0.108 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 0.779 Error(Employment) 0.402 0.595 0.547 Error(Unemployment Rate) 0.479 1.224 0.741 Error(Mfg. Hours) 1.434 1.534 0.123 Error(Wage and Salary Dist.) 0.702 1.932
t-statistic 4.83 -10.81 4.69 1.28 3.12 -2.40 -2.20 -2.09 -1.21 -2.32 -1.51 8.64 -6.19 -2.64 2.23 -1.21 6.03 1.57 Error Wage and Salary Dist. 0.703 0.751 1.414 1.221
1.248 Employment 0.442 1.055 1.262 0.477 Unemployment Rate 0.472 0.521 0.843 0.723 Average Weekly Mfg. Hours 1.233 1.445 1.662 0.538 Wage and Salary Dist. 0.587 1.644 1.422 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 2.10 Cumulative dynamic multiplier -0.59 0.08 0.58 62.76 Relative Contribution (%) 17.54 2.27 17.43 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B30
New Jersey
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.439 0.067 Unemployment Rate Ct -0.356 0.077 Average Weekly Mfg. Hours Ct 0.429 0.095 C t-1 -0.342 0.104 Wage and Salary Dist. Ct 0.039 0.012 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.225 0.202 (2) -0.068 0.208 (3) 0.177 0.176 (1) Unemployment Rate -0.054 0.079 (2) -0.020 0.078 (1) Average Weekly Mfg. Hours -0.310 0.075 (2) -0.027 0.071 (3) 0.200 0.075 (1) Wage and Salary Dist. -0.077 0.131 (2) 0.192 0.103 (3) 0.196 0.106 (4) 0.144 0.119 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.437 0.123 Lag 2 0.384 0.113 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 1.144 Error(Employment) 0.884 1.343 0.940 Error(Unemployment Rate) 0.127 1.505 1.541 Error(Mfg. Hours) 1.158 0.721 1.117 Error(Wage and Salary Dist.) 0.971 0.515
t-statistic 6.59 -4.62 4.53 -3.27 3.40 -1.11 -0.33 1.01 -0.68 -0.26 -4.15 -0.38 2.65 -0.59 1.86 1.85 1.21 3.57 3.41 Error Wage and Salary Dist. 0.162 0.536 0.958 1.142
1.877 Employment 1.013 0.871 0.178 0.792 Unemployment Rate 0.294 1.170 0.390 2.251 Average Weekly Mfg. Hours 1.209 0.773 1.223 1.312 Wage and Salary Dist. 0.843 1.349 0.362 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 1.31 Cumulative dynamic multiplier -0.58 0.52 0.13 51.56 Relative Contribution (%) 22.82 20.49 5.14 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B31
New Mexico
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.355 0.067 Unemployment Rate Ct -0.408 0.080 Average Weekly Mfg. Hours C t+2 0.131 0.088 C t+1 -0.055 0.107 Ct -0.077 0.089 Wage and Salary Dist. Ct 0.046 0.012 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.275 0.076 (2) -0.156 0.073 (1) Unemployment Rate 0.055 0.078 (2) 0.154 0.077 (3) 0.207 0.070 (4) 0.053 0.071 (5) 0.154 0.072 (1) Average Weekly Mfg. Hours -0.386 0.060 (2) -0.230 0.059 (1) Wage and Salary Dist. -0.262 0.109 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.279 0.132 Lag 2 0.472 0.126 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 0.246 Error(Employment) 0.304 0.239 1.118 Error(Unemployment Rate) 0.697 0.728 0.286 Error(Mfg. Hours) 0.221 0.283 1.110 Error(Wage and Salary Dist.) 1.027 2.007
t-statistic 5.30 -5.13 1.48 -0.51 -0.87 3.96 -3.64 -2.15 0.71 1.99 2.96 0.75 2.13 -6.45 -3.90 -2.40 2.11 3.73 Error Wage and Salary Dist. 1.600 1.106 0.633 0.376
0.249 Employment 0.685 0.286 1.489 1.004 Unemployment Rate 0.091 0.649 0.873 0.270 Average Weekly Mfg. Hours 0.236 0.273 0.746 0.991 Wage and Salary Dist. 2.881 1.788 0.390 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 1.30 Cumulative dynamic multiplier -0.30 0.25 0.41 57.33 Relative Contribution (%) 13.40 11.04 18.22 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B32
New York
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.252 0.055 Unemployment Rate Ct -0.201 0.046 Average Weekly Mfg. Hours Ct 0.544 0.129 C t-1 -0.526 0.130 Wage and Salary Dist. Ct 0.017 0.005 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.339 0.093 (2) -0.082 0.096 (3) 0.181 0.078 (1) Unemployment Rate 0.007 0.065 (2) 0.027 0.064 (3) 0.001 0.063 (1) Average Weekly Mfg. Hours -0.167 0.114 (2) -0.131 0.081 (3) 0.028 0.078 (1) Wage and Salary Dist. -0.373 0.100 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.815 0.207 Lag 2 0.112 0.196 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 1.094 Error(Employment) 0.697 1.289 0.373 Error(Unemployment Rate) 0.418 1.339 1.389 Error(Mfg. Hours) 0.587 1.186 1.011 Error(Wage and Salary Dist.) 0.700 1.989
t-statistic 4.56 -4.33 4.23 -4.05 3.48 -3.66 -0.86 2.32 0.11 0.42 0.01 -1.46 -1.63 0.36 -3.73 3.94 0.57 Error Wage and Salary Dist. 1.682 0.723 1.366 0.387
1.462 Employment 0.595 0.705 1.014 0.533 Unemployment Rate 0.496 1.521 0.598 1.396 Average Weekly Mfg. Hours 0.451 1.230 1.324 1.231 Wage and Salary Dist. 0.778 1.412 0.366 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 2.47 Cumulative dynamic multiplier -0.85 1.44 0.53 46.72 Relative Contribution (%) 16.04 27.23 10.01 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B33
North Carolina
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.392 0.049 Unemployment Rate Ct -0.846 0.050 C t-1 0.470 0.063 Average Weekly Mfg. Hours C t+2 0.079 0.060 C t+1 0.093 0.076 Ct 0.058 0.069 Wage and Salary Dist. Ct 0.094 0.031 C t-1 -0.053 0.030 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.182 0.077 (2) -0.043 0.073 (1) Unemployment Rate 0.300 0.190 (2) 0.638 0.104 (3) -0.207 0.178 (1) Average Weekly Mfg. Hours -0.117 0.061 (2) 0.234 0.060 (3) 0.263 0.065 (4) -0.031 0.067 (1) Wage and Salary Dist. -0.157 0.116 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.773 0.088 Lag 2 0.060 0.075 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 0.855 Error(Employment) 1.077 0.279 1.843 Error(Unemployment Rate) 1.318 0.534 0.903 Error(Mfg. Hours) 1.129 0.845 0.803 Error(Wage and Salary Dist.) 0.744 2.324
t-statistic 7.98 -16.78 7.47 1.33 1.22 0.84 3.02 -1.74 -2.38 -0.59 1.58 6.13 -1.16 -1.90 3.87 4.04 -0.46 -1.36 8.75 0.81 Error Wage and Salary Dist. 1.936 0.694 0.418 0.790
0.784 Employment 0.559 2.192 1.214 1.682 Unemployment Rate 1.203 1.435 0.603 1.139 Average Weekly Mfg. Hours 1.404 2.271 0.504 0.661 Wage and Salary Dist. 1.112 1.986 0.445 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 1.04 Cumulative dynamic multiplier -0.82 0.12 0.49 42.09 Relative Contribution (%) 33.22 4.89 19.79 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B34
North Dakota
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.683 0.093 Unemployment Rate Ct -0.524 0.074 Average Weekly Mfg. Hours Ct 0.193 0.066 Wage and Salary Dist. Ct 0.101 0.021 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.176 0.108 (1) Unemployment Rate -0.236 0.071 (1) Average Weekly Mfg. Hours -0.253 0.059 (1) Wage and Salary Dist. -0.147 0.116 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.102 0.112 Lag 2 0.137 0.102 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 0.929 Error(Employment) 0.361 1.899 1.100 Error(Unemployment Rate) 1.302 0.380 0.872 Error(Mfg. Hours) 1.041 1.829 0.417 Error(Wage and Salary Dist.) 0.192 1.921
t-statistic 7.35 -7.10 2.91 4.74 -1.62 -3.33 -4.33 -1.27 0.91 1.34 Error Wage and Salary Dist. 1.245 0.626 1.838 0.807
0.879 Employment 0.321 1.985 1.100 1.064 Unemployment Rate 1.235 0.313 0.702 0.942 Average Weekly Mfg. Hours 1.129 1.935 2.067 1.043 Wage and Salary Dist. 0.831 2.024 0.918 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 0.65 Cumulative dynamic multiplier -0.37 0.10 0.05 55.45 Relative Contribution (%) 31.42 8.51 4.62 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B35
Ohio
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.315 0.066 -0.222 0.050 Unemployment Rate Ct Average Weekly Mfg. Hours Ct 0.242 0.132 -0.077 0.234 C t-1 0.230 0.214 C t-2 -0.350 0.098 C t-3 Wage and Salary Dist. Ct 0.083 0.018 -0.054 0.015 C t-1 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.233 0.111 (2) 0.001 0.084 (3) -0.096 0.078 (4) -0.265 0.108 (5) -0.327 0.102 (1) Unemployment Rate 0.123 0.063 (2) -0.008 0.063 (3) -0.066 0.063 (1) Average Weekly Mfg. Hours -0.291 0.079 (1) Wage and Salary Dist. -0.028 0.120 (2) 0.243 0.114 (3) 0.263 0.111 (4) 0.079 0.109 (5) -0.040 0.103 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 1.143 0.191 Lag 2 -0.235 0.178 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 0.232 Error(Employment) 1.671 0.726 0.783 Error(Unemployment Rate) 0.147 0.729 0.273 Error(Mfg. Hours) 0.655 0.566 2.244 Error(Wage and Salary Dist.) 0.648 0.773
t-statistic 4.77 -4.44 1.82 -0.33 1.07 -3.57 4.49 -3.72 -2.11 0.01 -1.23 -2.45 -3.22 1.96 -0.12 -1.05 -3.67 -0.23 2.12 2.37 0.72 -0.39 5.97 -1.32 Error Wage and Salary Dist. 0.818 0.722 1.315 0.915
0.427 Employment 2.340 0.928 1.155 0.472 Unemployment Rate 0.510 0.394 0.435 0.369 Average Weekly Mfg. Hours 0.441 0.327 0.589 2.443 Wage and Salary Dist. 0.848 1.409 0.659 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Wage and Salary Average Weekly Unemployment Employment Rate Mfg. Hours Dist. 2.72 Cumulative dynamic multiplier -0.23 0.37 0.08 80.16 Relative Contribution (%) 6.78 10.85 2.21 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equation against six lags of the errors from the various measurement equations or six lags of the measurement variables.
B36
Oklahoma
Estimated Coefficients of the common factor (C) with leads (+) and lags (-) Asymptotic Variable Measurement Equation Coefficient Standard Error Employment Ct 0.495 0.125 Unemployment Rate Ct -0.284 0.091 C t-1 -0.078 0.094 Average Weekly Mfg. Hours C t+2 0.204 0.103 C t+1 -0.211 0.103 Wage and Salary Dist. Ct 0.076 0.020 Estimated Coefficients for lags in the autoregressive equations for the error terms (1) Employment -0.143 0.084 (1) Unemployment Rate -0.041 0.067 (2) 0.137 0.060 (3) 0.364 0.062 (4) 0.161 0.067 (1) Average Weekly Mfg. Hours -0.268 0.065 (2) -0.014 0.066 (3) -0.128 0.065 (1) Wage and Salary Dist. -0.220 0.132 (2) 0.087 0.131 (3) -0.072 0.131 (4) 0.261 0.127 (5) 0.197 0.134 Estimated Coefficients in the autoregressive equation for the common factor Lag 1 0.404 0.151 Lag 2 0.302 0.117 F-statistics for tests of single-index model* Error Avg. Weekly Error Employment Error Un. Rate Mfg. Hours 1.878 Error(Employment) 0.406 0.239 1.642 Error(Unemployment Rate) 1.145 0.681 1.167 Error(Mfg. Hours) 1.616 0.566 1.569 Error(Wage and Salary Dist.) 3.365 1.353
t-statistic 3.95 -3.13 -0.83 1.97 -2.05 3.71 -1.71 -0.60 2.28 5.90 2.41 -4.11 -0.20 -1.96 -1.66 0.67 -0.55 2.06 1.47 2.68 2.58 Error Wage and Salary Dist. 0.714 0.455 0.458 0.709
2.124 Employment 0.481 0.087 0.945 1.912 Unemployment Rate 0.682 0.670 0.398 0.992 Average Weekly Mfg. Hours 1.567 0.545 0.457 0.766 Wage and Salary Dist. 4.859 0.972 0.986 Relative Contribution of Observed Variables to Monthly Changes in the Common Factor Unemployment Wage and Salary Average Weekly Employment Rate Mfg. Hours Dist. 1.10 Cumulative dynamic multiplier -0.13 0.19 0.32 63.39 Relative Contribution (%) 7.30 11.05 18.26 * F-statistics for the hypothesis that the coefficients are zero in regressions of errors in the measurement equati...