The Quarterly Workforce Indicators are local labor market data produced and released every quarter by the United States Census Bureau. Unlike any other local labor market series produced in the U.S. or the rest of the world, the QWI measure employment flows for workers (accession and separations), jobs (creations and destructions) and earnings for demographic subgroups (age and sex), economic industry (NAICS industry groups), and detailed geography (county, Core-Based Statistical Area, and Workforce Investment Area, as well as experimental, unreleased block-level estimates). The current QWI data cover 47 states and about 98% of the private workforce in each of those states.

John Abowd and Lars Vilhuber have used the existing public-use data (and only those public-use data) to construct the first national estimates. The national estimates are an important enhancement to existing series because they include demographic and industry detail for both worker and job flows compiled from data that have been integrated at the micro-level by the Longitudinal Employer-Household Dynamics Program at the Census Bureau. The research paper (see below) compares the new estimates to national data published by the BLS from the Quarterly Census of Employment and Wages and the Business Employment Dynamics series.

Gender code:

QWI: Average employment:

`(E + B)/2`

Note: this variable is not present on the regular QWI, but it's derived from variables on the regular QWI.

QWI: average full-quarter (FQ) employment:

`(F_{t-1} + F_t)/2`

Note: this variable is not present on the regular QWI, but it's derived from variables on the regular QWI.

The concept of full-quarter employment estimates individuals who are likely to have been continuously employed throughout the quarter at a given employer. An individual is defined as full-quarter employed if that individual has valid UI wage records in the current quarter, the preceding quarter, and the subsequent quarter at the same employer (SEIN). That is, in terms of the point-in-time definitions, if the individual is employed at the same employer at both the beginning and end of the quarter, then the individual is considered full-quarter employed in the QWI system.

Full-quarter status is not defined for either the first or last quarter of available data.

Full-quarter employment is not a point-in-time concept. Full-quarter accession refers to the quarter in which an individual first attains full-quarter employment status at a given employer.

Full-quarter employment refers to an estimate of the number of employees who were employed at a given employer during the entire quarter. An accession to full-quarter employment, then, involves two additional conditions that are not relevant for ordinary accessions.

First, the individual (PIK) must still be employed at the end of the quarter at the same employer (SEIN) for which the ordinary accession is defined. At this point (the end of the quarter where the accession occurred and the beginning of the next quarter) the individual has acceded to continuing-quarter status. An accession to continuing-quarter status means that the individual acceded in the current quarter and is end-of-quarter employed.

Next, the QWI system must check for the possibility that the individual becomes a full-quarter employee in the subsequent quarter. An accession to full-quarter status occurs if the individual acceded in the previous quarter, and is employed at both the beginning and end of the current quarter.

Full-quarter new hires.

Accessions to full-quarter status can be decomposed into new hires and recalls. The QWI system accomplishes this decomposition by classifying all accessions to full-quarter status who were classified as new hires in the previous quarter as new hires to full-quarter status in the current quarter. Otherwise, the accession to full-quarter status is classified as a recall to full-quarter status.

Full-quarter employment is not a point-in-time concept. Full-quarter separation occurs in the last full-quarter that an individual worked for a given employer.

As previously noted, full-quarter employment refers to an estimate of the number of employees who were employed at a given employer during the entire quarter. An accession to full-quarter employment, then, involves two additional conditions that are not relevant for ordinary accessions.

First, the individual (PIK) must still be employed at the end of the quarter at the same employer (SEIN) for which the ordinary accession is defined. At this point (the end of the quarter where the accession occurred and the beginning of the next quarter) the individual has acceded to continuing-quarter status. An accession to continuing-quarter status means that the individual acceded in the current quarter and is end-of-quarter employed.

Next, the QWI system must check for the possibility that the individual becomes a full-quarter employee in the subsequent quarter. An accession to full-quarter status occurs if the individual acceded in the previous quarter, and is employed at both the beginning and end of the current quarter.

Full-quarter separation works much the same way. One must be careful about the timing, however. If an individual separates in the current quarter, then the QWI system looks at the preceding quarter to determine if the individual was employed at the beginning of the current quarter. An individual who separates in a quarter in which that person was employed at the beginning of the quarter is a separation from continuing-quarter status in the current quarter.

Finally, the QWI system checks to see if the individual was a full-quarter employee in the preceding quarter. An individual who was a full quarter employee in the previous quarter is treated as a full-quarter separation in the quarter in which that person actually separates. Note, therefore, that the definition of full-quarter separation preserves the timing of the actual separation (current quarter) but restricts the estimate to those individuals who were full-quarter status in the preceding quarter.

Gross worker flows are measured using the Worker Reallocation Rate:

`W\R\R_{agkst} =\ (A_{agkst} + S_{agkst})*(2/(B_{agkst} + E_{agkst}))`

where

`W\R\R` measures total accession and separation flows as a proportion of average employment over the quarter in the age, gender, industry and state. The `W\R\R` is a symmetric growth rate designed to approximate the logarithmic change over the time period (one quarter). In addition, the `W\R\R`, can be expressed as the sum of its inflow and outflow components, the distinct accession and separation rates are defined, respectively, as:

Accessions and separations satisfy the net job flow (`JF_{agkst}`) identity:

`JF_{agkst} \equiv \ E_{agkst} - B_{agkst} = A_{agkst} - S_{agkst}`

Gross job flows are measured in similar fashion using the symmetric Job Reallocation Rate:

`J\R\R_{agkst} =\ (JC_{agkst} + JD_{agkst})*(2/(B_{agkst} + E_{agkst}))`

where

`J\R\R` measures total job creations and destructions (called job creations/destructions in the QWI and gross job gains/losses in the BED) as a proportion of average employment over the quarter in the category. The gross job inflow and outflow rates, the Job Creation Rate (`JCR`) and Job Destruction Rate (`JDR`) , can be defined as additive components of the `J\R\R`:

Gross job flow measures are defined at an establishment, not job, level. Let `B_{agjt}` be beginning-of-quarter employment for demographic group `ag` at establishment `j` in quarter `t`, and similarly let `E_{agjt}` be end-of-quarter employment for the same category and time period. Then:

so that, as originally specified by Davis and Haltiwanger, job creations are the change in employment when employment is growing at the establishment and job destructions are the change in employment when employment is shrinking at the establishment. Net job flows also satisfy the identity `JF_{agkst} =\ JC_{agkst} - JD_{agkst}`

We define the excess reallocation measured using the symmetric Excess Reallocation Rate (see variables "qwi_wrr" and "qwi_jrr" for further information):

`E\R\R_{agkst} =\ W\R\R_{agkst} -\ J\R\R_{agkst}`

which measures the difference between gross worker flow and gross job flow rates, sometimes called the labor market ?churning? rate. The `E\R\R` measures the rate of gross worker flow activity in each category in excess of the minimum rate required to account for the observed gross job reallocation. Separate inflow and outflow excess reallocation rates can be defined using the components of the `E\R\R`?specifically, the Excess Inflow Rate (`EIR`) and the Excess Outflow Rate (`EOR`):

where the additive and symmetric growth rate properties of the measure within categories continue to hold. Because of the net job flow identities, `EIR_{agkst} \equiv \ EOR_{agkst}`.

Gross worker flows are measured using the Worker Reallocation Rate:

`W\R\R_{agkst} =\ (A_{agkst} + S_{agkst})*(2/(B_{agkst} + E_{agkst}))`

where

`W\R\R` measures total accession and separation flows as a proportion of average employment over the quarter in the age, gender, industry and state. The `W\R\R` is a symmetric growth rate designed to approximate the logarithmic change over the time period (one quarter). In addition, the `W\R\R`, can be expressed as the sum of its inflow and outflow components, the distinct accession and separation rates are defined, respectively, as:

Accessions and separations satisfy the net job flow (`JF_{agkst}`) identity:

`JF_{agkst} \equiv \ E_{agkst} - B_{agkst} = A_{agkst} - S_{agkst}`

Gross worker flows are measured using the Worker Reallocation Rate:

`W\R\R_{agkst} =\ (A_{agkst} + S_{agkst})*(2/(B_{agkst} + E_{agkst}))`

where

`W\R\R` measures total accession and separation flows as a proportion of average employment over the quarter in the age, gender, industry and state. The `W\R\R` is a symmetric growth rate designed to approximate the logarithmic change over the time period (one quarter). In addition, the `W\R\R`, can be expressed as the sum of its inflow and outflow components, the distinct accession and separation rates are defined, respectively, as:

Accessions and separations satisfy the net job flow (`JF_{agkst}`) identity:

`JF_{agkst} \equiv \ E_{agkst} - B_{agkst} = A_{agkst} - S_{agkst}`

Gross job flows are measured in similar fashion using the symmetric Job Reallocation Rate:

`J\R\R_{agkst} =\ (JC_{agkst} + JD_{agkst})*(2/(B_{agkst} + E_{agkst}))`

where

`J\R\R` measures total job creations and destructions (called job creations/destructions in the QWI and gross job gains/losses in the BED) as a proportion of average employment over the quarter in the category. The gross job inflow and outflow rates, the Job Creation Rate (`JCR`) and Job Destruction Rate (`JDR`) , can be defined as additive components of the `J\R\R`:

Gross job flow measures are defined at an establishment, not job, level. Let `B_{agjt}` be beginning-of-quarter employment for demographic group `ag` at establishment `j` in quarter `t`, and similarly let `E_{agjt}` be end-of-quarter employment for the same category and time period. Then:

so that, as originally specified by Davis and Haltiwanger, job creations are the change in employment when employment is growing at the establishment and job destructions are the change in employment when employment is shrinking at the establishment. Net job flows also satisfy the identity `JF_{agkst} =\ JC_{agkst} - JD_{agkst}`

Gross job flows are measured in similar fashion using the symmetric Job Reallocation Rate:

`J\R\R_{agkst} =\ (JC_{agkst} + JD_{agkst})*(2/(B_{agkst} + E_{agkst}))`

where

`J\R\R` measures total job creations and destructions (called job creations/destructions in the QWI and gross job gains/losses in the BED) as a proportion of average employment over the quarter in the category. The gross job inflow and outflow rates, the Job Creation Rate (`JCR`) and Job Destruction Rate (`JDR`) , can be defined as additive components of the `J\R\R`:

Gross job flow measures are defined at an establishment, not job, level. Let `B_{agjt}` be beginning-of-quarter employment for demographic group `ag` at establishment `j` in quarter `t`, and similarly let `E_{agjt}` be end-of-quarter employment for the same category and time period. Then:

so that, as originally specified by Davis and Haltiwanger, job creations are the change in employment when employment is growing at the establishment and job destructions are the change in employment when employment is shrinking at the establishment. Net job flows also satisfy the identity `JF_{agkst} =\ JC_{agkst} - JD_{agkst}`

We define the excess reallocation measured using the symmetric Excess Reallocation Rate (see variables "qwi_wrr" and "qwi_jrr" for further information):

`E\R\R_{agkst} =\ W\R\R_{agkst} -\ J\R\R_{agkst}`

which measures the difference between gross worker flow and gross job flow rates, sometimes called the labor market ?churning? rate. The `E\R\R` measures the rate of gross worker flow activity in each category in excess of the minimum rate required to account for the observed gross job reallocation. Separate inflow and outflow excess reallocation rates can be defined using the components of the `E\R\R`?specifically, the Excess Inflow Rate (`EIR`) and the Excess Outflow Rate (`EOR`):

where the additive and symmetric growth rate properties of the measure within categories continue to hold. Because of the net job flow identities, `EIR_{agkst} \equiv \ EOR_{agkst}`.

We define the excess reallocation measured using the symmetric Excess Reallocation Rate (see variables "qwi_wrr" and "qwi_jrr" for further information):

`E\R\R_{agkst} =\ W\R\R_{agkst} -\ J\R\R_{agkst}`

which measures the difference between gross worker flow and gross job flow rates, sometimes called the labor market ?churning? rate. The `E\R\R` measures the rate of gross worker flow activity in each category in excess of the minimum rate required to account for the observed gross job reallocation. Separate inflow and outflow excess reallocation rates can be defined using the components of the `E\R\R`?specifically, the Excess Inflow Rate (`EIR`) and the Excess Outflow Rate (`EOR`):

where the additive and symmetric growth rate properties of the measure within categories continue to hold. Because of the net job flow identities, `EIR_{agkst} \equiv \ EOR_{agkst}`.

Gross full-quarter worker flows are measured using the Full-Quarter Worker Reallocation Rate:

`FW\R\R_{agkst} =\ (FA_{agkst} + FS_{agkst})*(2/(F_{agkst} + F_{agkst-1}))`

where

`FW\R\R` measures total accession and separation flows as a proportion of average full-quarter employment in the age, gender, industry and state. The `FW\R\R` is a symmetric growth rate designed to approximate the logarithmic change over the time period (one quarter). In addition, the `FW\R\R`, can be expressed as the sum of its inflow and outflow components, the distinct accession and separation rates are defined, respectively, as:

Accessions and separations satisfy the net full-quarter job flow (`FJF_{agkst}`) identity:

`FJF_{agkst} \equiv \ FA_{agkst} - FS_{agkst}`

where the net change in full-quarter is defined as `FJF_{agkst} = F_{agkst} -\ F_{agkst-1}`

Gross full-quarter job flows are measured using the symmetric Full-Quarter Job Reallocation Rate:

`FJ\R\R_{agkst} =\ (FJC_{agkst} + FJD_{agkst})*(2/(F_{agkst} + F_{agkst-1}))`

where

`FJ\R\R` measures total job creations and destructions (called job creations/destructions in the QWI and gross job gains/losses in the BED) as a proportion of full-quarter average employment in the category. The gross job inflow and outflow rates, the Full-Quarter Job Creation Rate (`FJCR`) and Full- Quarter Job Destruction Rate (`FJDR`) , can be defined as additive components of the `FJ\R\R`:

We define the full-quarter excess reallocation measured using the symmetric Full-Quarter Excess Reallocation Rate (see variables "qwi_fwrr" and "qwi_fjrr" for further information):

`FE\R\R_{agkst} = FW\R\R_{agkst} - FJ\R\R_{agkst}`

which measures the difference between full-quarter gross worker flow and full-quarter gross job flow rates, sometimes called the labor market ?churning? rate. The `FE\R\R` measures the rate of gross worker flow activity in each category in excess of the minimum rate required to account for the observed gross job reallocation. Separate inflow and outflow excess reallocation rates can be defined using the components of the `FE\R\R`?specifically, the Full-Quarter Excess Inflow Rate (`FEIR`) and the Full-Quarter Excess Outflow Rate (`FEOR`):

where the additive and symmetric growth rate properties of the measure within categories continue to hold. Because of the net job flow identities, `FEIR_{agkst} \equiv \ FEOR_{agkst}`.

Gross full-quarter worker flows are measured using the Full-Quarter Worker Reallocation Rate:

`FW\R\R_{agkst} =\ (FA_{agkst} + FS_{agkst})*(2/(F_{agkst} + F_{agkst-1}))`

where

`FW\R\R` measures total accession and separation flows as a proportion of average full-quarter employment in the age, gender, industry and state. The `FW\R\R` is a symmetric growth rate designed to approximate the logarithmic change over the time period (one quarter). In addition, the `FW\R\R`, can be expressed as the sum of its inflow and outflow components, the distinct accession and separation rates are defined, respectively, as:

Accessions and separations satisfy the net full-quarter job flow (`FJF_{agkst}`) identity:

`FJF_{agkst} \equiv \ FA_{agkst} - FS_{agkst}`

where the net change in full-quarter is defined as `FJF_{agkst} = F_{agkst} -\ F_{agkst-1}`

Gross full-quarter worker flows are measured using the Full-Quarter Worker Reallocation Rate:

`FW\R\R_{agkst} =\ (FA_{agkst} + FS_{agkst})*(2/(F_{agkst} + F_{agkst-1}))`

where

`FW\R\R` measures total accession and separation flows as a proportion of average full-quarter employment in the age, gender, industry and state. The `FW\R\R` is a symmetric growth rate designed to approximate the logarithmic change over the time period (one quarter). In addition, the `FW\R\R`, can be expressed as the sum of its inflow and outflow components, the distinct accession and separation rates are defined, respectively, as:

Accessions and separations satisfy the net full-quarter job flow (`FJF_{agkst}`) identity:

`FJF_{agkst} \equiv \ FA_{agkst} - FS_{agkst}`

where the net change in full-quarter is defined as `FJF_{agkst} = F_{agkst} -\ F_{agkst-1}`

Gross full-quarter job flows are measured using the symmetric Full-Quarter Job Reallocation Rate:

`FJ\R\R_{agkst} =\ (FJC_{agkst} + FJD_{agkst})*(2/(F_{agkst} + F_{agkst-1}))`

where

`FJ\R\R` measures total job creations and destructions (called job creations/destructions in the QWI and gross job gains/losses in the BED) as a proportion of full-quarter average employment in the category. The gross job inflow and outflow rates, the Full-Quarter Job Creation Rate (`FJCR`) and Full- Quarter Job Destruction Rate (`FJDR`) , can be defined as additive components of the `FJ\R\R`:

Gross full-quarter job flows are measured using the symmetric Full-Quarter Job Reallocation Rate:

`FJ\R\R_{agkst} =\ (FJC_{agkst} + FJD_{agkst})*(2/(F_{agkst} + F_{agkst-1}))`

where

`FJ\R\R` measures total job creations and destructions (called job creations/destructions in the QWI and gross job gains/losses in the BED) as a proportion of full-quarter average employment in the category. The gross job inflow and outflow rates, the Full-Quarter Job Creation Rate (`FJCR`) and Full- Quarter Job Destruction Rate (`FJDR`) , can be defined as additive components of the `FJ\R\R`:

We define the full-quarter excess reallocation measured using the symmetric Full-Quarter Excess Reallocation Rate (see variables "qwi_fwrr" and "qwi_fjrr" for further information):

`FE\R\R_{agkst} = FW\R\R_{agkst} - FJ\R\R_{agkst}`

which measures the difference between full-quarter gross worker flow and full-quarter gross job flow rates, sometimes called the labor market ?churning? rate. The `FE\R\R` measures the rate of gross worker flow activity in each category in excess of the minimum rate required to account for the observed gross job reallocation. Separate inflow and outflow excess reallocation rates can be defined using the components of the `FE\R\R`?specifically, the Full-Quarter Excess Inflow Rate (`FEIR`) and the Full-Quarter Excess Outflow Rate (`FEOR`):

where the additive and symmetric growth rate properties of the measure within categories continue to hold. Because of the net job flow identities, `FEIR_{agkst} \equiv \ FEOR_{agkst}`.

We define the full-quarter excess reallocation measured using the symmetric Full-Quarter Excess Reallocation Rate (see variables "qwi_fwrr" and "qwi_fjrr" for further information):

`FE\R\R_{agkst} = FW\R\R_{agkst} - FJ\R\R_{agkst}`

which measures the difference between full-quarter gross worker flow and full-quarter gross job flow rates, sometimes called the labor market ?churning? rate. The `FE\R\R` measures the rate of gross worker flow activity in each category in excess of the minimum rate required to account for the observed gross job reallocation. Separate inflow and outflow excess reallocation rates can be defined using the components of the `FE\R\R`?specifically, the Full-Quarter Excess Inflow Rate (`FEIR`) and the Full-Quarter Excess Outflow Rate (`FEOR`):

where the additive and symmetric growth rate properties of the measure within categories continue to hold. Because of the net job flow identities, `FEIR_{agkst} \equiv \ FEOR_{agkst}`.

Measuring earnings using UI wage records in the QWI system presents some interesting challenges. The earnings of end-of-quarter employees who are not present at the beginning of the quarter are the earnings of accessions during the quarter. The QWI system does not provide any information about how much of the quarter such individuals worked. The range of possibilities goes from one day to every day of the quarter. Hence, estimates of the average earnings of such individuals may not be comparable from quarter to quarter unless one assumes that the average accession works the same number of quarters regardless of other conditions in the economy. Similarly, the earnings of beginning-of-quarter workers who are not present at the end of the quarter represent the earnings of separations. These present the same comparison problems as the average earnings of accessions; namely, it is difficult to model the number of weeks worked during the quarter. If we consider only those individuals employed at the employer in a given quarter who were neither accessions nor separations during that quarter, we are left, exactly, with the full-quarter employees.

The QWI system measures the average earnings of full-quarter employees by summing the earnings on the UI wage records of all individuals at a given employer who have full-quarter status in a given quarter, then dividing by the number of full-quarter employees.

An accession occurs when a job starts; that is, on the first occurrence of a SEIN-PIK pair following the first quarter of available data. When the QWI system detects an accession, it measures the number of quarters (up to a maximum of four) that the individual spent nonemployed in the state prior to the accession. The QWI system estimates the number of quarters spent nonemployed by looking for all other jobs held by the individual at any employer in the state in the preceding quarters up to a maximum of four. If the QWI system does not find any other valid UI wage records in a quarter preceding the accession, it augments the count of nonemployed quarters for the individual who acceded, up to a maximum of four. Total quarters of nonemployment for all accessions is divided by accessions to estimate average periods of nonemployment for accessions.

Average periods of nonemployment for new hires and recalls are estimated using exactly analogous formulas except that the measures are estimated separately for accessions who are also new hires as compared with accession who are recalls.

The within-implicate variance for QWI `W\R\R` is:

`V^{(l)}[\hat{W\R\R}_{agkt}] =\ 1/49 sum_{AAs}\frac{(\frac{B_{agkst}^{(l)}+E_{agkst}^{(l)}}{2})(W\R\R_{agkst}^{(l)}-\hat{W\R\R}_{agkt}^{(l)})^2}{sum_{AAv}(\frac{B_{agkvt}^{(l)}+E_{agkvt}^{(l)}}{2})}`

where `1/49` is the number of states minus 1.

The within-implicate variance for a generic variable `X` is:

`V^{(l)}[\hat{X}_{agkt}] =\ 1/49 sum_{AAs}\frac{(\frac{B_{agkst}^{(l)}+E_{agkst}^{(l)}}{2})(X_{agkst}^{(l)}-\hat{X}_{agkt}^{(l)})^2}{sum_{AAv}(\frac{B_{agkvt}^{(l)}+E_{agkvt}^{(l)}}{2})}`

where `1/49` is the number of states minus 1.

The within-implicate variance for a generic variable `X` is:

`V^{(l)}[\hat{X}_{agkt}] =\ 1/49 sum_{AAs}\frac{(\frac{B_{agkst}^{(l)}+E_{agkst}^{(l)}}{2})(X_{agkst}^{(l)}-\hat{X}_{agkt}^{(l)})^2}{sum_{AAv}(\frac{B_{agkvt}^{(l)}+E_{agkvt}^{(l)}}{2})}`

where `1/49` is the number of states minus 1.

The within-implicate variance for a generic variable `X` is:

`V^{(l)}[\hat{X}_{agkt}] =\ 1/49 sum_{AAs}\frac{(\frac{B_{agkst}^{(l)}+E_{agkst}^{(l)}}{2})(X_{agkst}^{(l)}-\hat{X}_{agkt}^{(l)})^2}{sum_{AAv}(\frac{B_{agkvt}^{(l)}+E_{agkvt}^{(l)}}{2})}`

where `1/49` is the number of states minus 1.

The within-implicate variance for a generic variable `X` is:

where `1/49` is the number of states minus 1.

The within-implicate variance for a generic variable `X` is:

where `1/49` is the number of states minus 1.

The within-implicate variance for a generic variable `X` is:

where `1/49` is the number of states minus 1.

The within-implicate variance for a generic variable `X` is:

where `1/49` is the number of states minus 1.

The within-implicate variance for a generic variable `X` is:

where `1/49` is the number of states minus 1.

The within-implicate variance for a generic variable `X` is:

`V^{(l)}[\hat{X}_{agkt}] =\ 1/49 sum_{AAs}\frac{(\frac{F_{agkst}^{(l)}+F_{agkst-1}^{(l)}}{2})(X_{agkst}^{(l)}-\hat{X}_{agkt}^{(l)})^2}{sum_{AAv}(\frac{F_{agkvt}^{(l)}+F_{agkvt-1}^{(l)}}{2})}`

where `1/49` is the number of states minus 1.

The within-implicate variance for a generic variable `X` is:

`V^{(l)}[\hat{X}_{agkt}] =\ 1/49 sum_{AAs}\frac{(\frac{F_{agkst}^{(l)}+F_{agkst-1}^{(l)}}{2})(X_{agkst}^{(l)}-\hat{X}_{agkt}^{(l)})^2}{sum_{AAv}(\frac{F_{agkvt}^{(l)}+F_{agkvt-1}^{(l)}}{2})}`

where `1/49` is the number of states minus 1.

The within-implicate variance for a generic variable `X` is:

`V^{(l)}[\hat{X}_{agkt}] =\ 1/49 sum_{AAs}\frac{(\frac{F_{agkst}^{(l)}+F_{agkst-1}^{(l)}}{2})(X_{agkst}^{(l)}-\hat{X}_{agkt}^{(l)})^2}{sum_{AAv}(\frac{F_{agkvt}^{(l)}+F_{agkvt-1}^{(l)}}{2})}`

where `1/49` is the number of states minus 1.

The within-implicate variance for a generic variable `X` is:

where `1/49` is the number of states minus 1.

The within-implicate variance for a generic variable `X` is:

where `1/49` is the number of states minus 1.

The within-implicate variance for a generic variable `X` is:

where `1/49` is the number of states minus 1.

The within-implicate variance for a generic variable `X` is:

where `1/49` is the number of states minus 1.

The within-implicate variance for a generic variable `X` is:

where `1/49` is the number of states minus 1.

The within-implicate variance for a generic variable `X` is:

where `1/49` is the number of states minus 1.

The within-implicate variance for a generic variable `X` is:

where `1/49` is the number of states minus 1.

The within-implicate variance for a generic variable `X` is:

where `1/49` is the number of states minus 1.

The within-implicate variance for a generic variable `X` is:

where `1/49` is the number of states minus 1.

The within-implicate variance for a generic variable `X` is:

where `1/49` is the number of states minus 1.

The within-implicate variance for a generic variable `X` is:

where `1/49` is the number of states minus 1.

The within-implicate variance for a generic variable `X` is:

where `1/49` is the number of states minus 1.

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The between implicate variance for a generic variable `X` is:

`B[\bar{X}_{agkt}] =\ 1/(M-1)sum_{l=1}^{100}(\hat{X}_{agkt}^{(l)} - \bar{X}_{agkt})^2`

The total variation for a generic variable `X` is:

`T[\bar{X}_{agkt}] =\ 1/M sum_{l=1}^{M}V^{(l)}[\hat{X}_{agkt}] + (M+1)/M B[\bar{X}_{agkt}]`

where `V^{(l)}[\hat{X}_{agkt}]` and `B[\bar{X}_{agkt}]` are respectively the within implicate variance and the between implicate variance of `X`.

The total variation for a generic variable `X` is:

`T[\bar{X}_{agkt}] =\ 1/M sum_{l=1}^{M}V^{(l)}[\hat{X}_{agkt}] + (M+1)/M B[\bar{X}_{agkt}]`

where `V^{(l)}[\hat{X}_{agkt}]` and `B[\bar{X}_{agkt}]` are respectively the within implicate variance and the between implicate variance of `X`.

The total variation for a generic variable `X` is:

`T[\bar{X}_{agkt}] =\ 1/M sum_{l=1}^{M}V^{(l)}[\hat{X}_{agkt}] + (M+1)/M B[\bar{X}_{agkt}]`

where `V^{(l)}[\hat{X}_{agkt}]` and `B[\bar{X}_{agkt}]` are respectively the within implicate variance and the between implicate variance of `X`.

The total variation for a generic variable `X` is:

`T[\bar{X}_{agkt}] =\ 1/M sum_{l=1}^{M}V^{(l)}[\hat{X}_{agkt}] + (M+1)/M B[\bar{X}_{agkt}]`

The total variation for a generic variable `X` is:

`T[\bar{X}_{agkt}] =\ 1/M sum_{l=1}^{M}V^{(l)}[\hat{X}_{agkt}] + (M+1)/M B[\bar{X}_{agkt}]`

The total variation for a generic variable `X` is:

`T[\bar{X}_{agkt}] =\ 1/M sum_{l=1}^{M}V^{(l)}[\hat{X}_{agkt}] + (M+1)/M B[\bar{X}_{agkt}]`

The total variation for a generic variable `X` is:

`T[\bar{X}_{agkt}] =\ 1/M sum_{l=1}^{M}V^{(l)}[\hat{X}_{agkt}] + (M+1)/M B[\bar{X}_{agkt}]`

The total variation for a generic variable `X` is:

`T[\bar{X}_{agkt}] =\ 1/M sum_{l=1}^{M}V^{(l)}[\hat{X}_{agkt}] + (M+1)/M B[\bar{X}_{agkt}]`

The total variation for a generic variable `X` is:

`T[\bar{X}_{agkt}] =\ 1/M sum_{l=1}^{M}V^{(l)}[\hat{X}_{agkt}] + (M+1)/M B[\bar{X}_{agkt}]`

The total variation for a generic variable `X` is:

`T[\bar{X}_{agkt}] =\ 1/M sum_{l=1}^{M}V^{(l)}[\hat{X}_{agkt}] + (M+1)/M B[\bar{X}_{agkt}]`

The total variation for a generic variable `X` is:

`T[\bar{X}_{agkt}] =\ 1/M sum_{l=1}^{M}V^{(l)}[\hat{X}_{agkt}] + (M+1)/M B[\bar{X}_{agkt}]`

The total variation for a generic variable `X` is:

`T[\bar{X}_{agkt}] =\ 1/M sum_{l=1}^{M}V^{(l)}[\hat{X}_{agkt}] + (M+1)/M B[\bar{X}_{agkt}]`

The total variation for a generic variable `X` is:

`T[\bar{X}_{agkt}] =\ 1/M sum_{l=1}^{M}V^{(l)}[\hat{X}_{agkt}] + (M+1)/M B[\bar{X}_{agkt}]`

The total variation for a generic variable `X` is:

`T[\bar{X}_{agkt}] =\ 1/M sum_{l=1}^{M}V^{(l)}[\hat{X}_{agkt}] + (M+1)/M B[\bar{X}_{agkt}]`

The total variation for a generic variable `X` is:

`T[\bar{X}_{agkt}] =\ 1/M sum_{l=1}^{M}V^{(l)}[\hat{X}_{agkt}] + (M+1)/M B[\bar{X}_{agkt}]`

The total variation for a generic variable `X` is:

`T[\bar{X}_{agkt}] =\ 1/M sum_{l=1}^{M}V^{(l)}[\hat{X}_{agkt}] + (M+1)/M B[\bar{X}_{agkt}]`

The total variation for a generic variable `X` is:

`T[\bar{X}_{agkt}] =\ 1/M sum_{l=1}^{M}V^{(l)}[\hat{X}_{agkt}] + (M+1)/M B[\bar{X}_{agkt}]`

The total variation for a generic variable `X` is:

`T[\bar{X}_{agkt}] =\ 1/M sum_{l=1}^{M}V^{(l)}[\hat{X}_{agkt}] + (M+1)/M B[\bar{X}_{agkt}]`

The total variation for a generic variable `X` is:

`T[\bar{X}_{agkt}] =\ 1/M sum_{l=1}^{M}V^{(l)}[\hat{X}_{agkt}] + (M+1)/M B[\bar{X}_{agkt}]`

The total variation for a generic variable `X` is:

`T[\bar{X}_{agkt}] =\ 1/M sum_{l=1}^{M}V^{(l)}[\hat{X}_{agkt}] + (M+1)/M B[\bar{X}_{agkt}]`

The total variation for a generic variable `X` is:

`T[\bar{X}_{agkt}] =\ 1/M sum_{l=1}^{M}V^{(l)}[\hat{X}_{agkt}] + (M+1)/M B[\bar{X}_{agkt}]`

The total variation for a generic variable `X` is:

`T[\bar{X}_{agkt}] =\ 1/M sum_{l=1}^{M}V^{(l)}[\hat{X}_{agkt}] + (M+1)/M B[\bar{X}_{agkt}]`

The total variation for a generic variable `X` is:

`T[\bar{X}_{agkt}] =\ 1/M sum_{l=1}^{M}V^{(l)}[\hat{X}_{agkt}] + (M+1)/M B[\bar{X}_{agkt}]`

The total variation for a generic variable `X` is:

`T[\bar{X}_{agkt}] =\ 1/M sum_{l=1}^{M}V^{(l)}[\hat{X}_{agkt}] + (M+1)/M B[\bar{X}_{agkt}]`

Degrees of freedom for a generic variable `X` are defined as:

`df[\bar{X}_{agkt}] =\ (M-1)(1 + 1/(M+1) \frac{1/M sum_{l=1}^M V^{(l)} [\hat{X}_{agkt}]}{B[\bar{X}_{agkt}]})^2`

Degrees of freedom for a generic variable `X` are defined as:

`df[\bar{X}_{agkt}] =\ (M-1)(1 + 1/(M+1) \frac{1/M sum_{l=1}^M V^{(l)} [\hat{X}_{agkt}]}{B[\bar{X}_{agkt}]})^2`

Degrees of freedom for a generic variable `X` are defined as:

`df[\bar{X}_{agkt}] =\ (M-1)(1 + 1/(M+1) \frac{1/M sum_{l=1}^M V^{(l)} [\hat{X}_{agkt}]}{B[\bar{X}_{agkt}]})^2`

Degrees of freedom for a generic variable `X` are defined as:

Degrees of freedom for a generic variable `X` are defined as:

Degrees of freedom for a generic variable `X` are defined as:

Degrees of freedom for a generic variable `X` are defined as:

Degrees of freedom for a generic variable `X` are defined as:

Degrees of freedom for a generic variable `X` are defined as:

Degrees of freedom for a generic variable `X` are defined as:

Degrees of freedom for a generic variable `X` are defined as:

Degrees of freedom for a generic variable `X` are defined as:

Degrees of freedom for a generic variable `X` are defined as:

Degrees of freedom for a generic variable `X` are defined as:

Degrees of freedom for a generic variable `X` are defined as:

Degrees of freedom for a generic variable `X` are defined as:

Degrees of freedom for a generic variable `X` are defined as:

Degrees of freedom for a generic variable `X` are defined as:

Degrees of freedom for a generic variable `X` are defined as:

Degrees of freedom for a generic variable `X` are defined as:

Degrees of freedom for a generic variable `X` are defined as:

Degrees of freedom for a generic variable `X` are defined as:

Degrees of freedom for a generic variable `X` are defined as:

Degrees of freedom for a generic variable `X` are defined as:

The effective missing data rate for a generic variable `X` is defined as:

`MR[\bar{X}_{agkt}] =\ \frac{B[\bar{X}_{agkt}]}{T[\bar{X}_{agkt}]}`

where `V^{(l)}[\hat{X}_{agkt}]` and `B[\bar{X}_{agkt}]` are respectively the within implicate variance and the between implicate variance of `X`, and `T[\bar{X}_{agkt}]` is the total variation of `X`.

The effective missing data rate for a generic variable `X` is defined as:

`MR[\bar{X}_{agkt}] =\ \frac{B[\bar{X}_{agkt}]}{T[\bar{X}_{agkt}]}`

where `V^{(l)}[\hat{X}_{agkt}]` and `B[\bar{X}_{agkt}]` are respectively the within implicate variance and the between implicate variance of `X`, and `T[\bar{X}_{agkt}]` is the total variation of `X`.

The effective missing data rate for a generic variable `X` is defined as:

`MR[\bar{X}_{agkt}] =\ \frac{B[\bar{X}_{agkt}]}{T[\bar{X}_{agkt}]}`

where `V^{(l)}[\hat{X}_{agkt}]` and `B[\bar{X}_{agkt}]` are respectively the within implicate variance and the between implicate variance of `X`, and `T[\bar{X}_{agkt}]` is the total variation of `X`.

The effective missing data rate for a generic variable `X` is defined as:

`MR[\bar{X}_{agkt}] =\ \frac{B[\bar{X}_{agkt}]}{T[\bar{X}_{agkt}]}`

The effective missing data rate for a generic variable `X` is defined as:

`MR[\bar{X}_{agkt}] =\ \frac{B[\bar{X}_{agkt}]}{T[\bar{X}_{agkt}]}`

The effective missing data rate for a generic variable `X` is defined as:

`MR[\bar{X}_{agkt}] =\ \frac{B[\bar{X}_{agkt}]}{T[\bar{X}_{agkt}]}`

The effective missing data rate for a generic variable `X` is defined as:

`MR[\bar{X}_{agkt}] =\ \frac{B[\bar{X}_{agkt}]}{T[\bar{X}_{agkt}]}`

The effective missing data rate for a generic variable `X` is defined as:

`MR[\bar{X}_{agkt}] =\ \frac{B[\bar{X}_{agkt}]}{T[\bar{X}_{agkt}]}`

The effective missing data rate for a generic variable `X` is defined as:

`MR[\bar{X}_{agkt}] =\ \frac{B[\bar{X}_{agkt}]}{T[\bar{X}_{agkt}]}`

The effective missing data rate for a generic variable `X` is defined as:

`MR[\bar{X}_{agkt}] =\ \frac{B[\bar{X}_{agkt}]}{T[\bar{X}_{agkt}]}`

The effective missing data rate for a generic variable `X` is defined as:

`MR[\bar{X}_{agkt}] =\ \frac{B[\bar{X}_{agkt}]}{T[\bar{X}_{agkt}]}`

The effective missing data rate for a generic variable `X` is defined as:

`MR[\bar{X}_{agkt}] =\ \frac{B[\bar{X}_{agkt}]}{T[\bar{X}_{agkt}]}`

The effective missing data rate for a generic variable `X` is defined as:

`MR[\bar{X}_{agkt}] =\ \frac{B[\bar{X}_{agkt}]}{T[\bar{X}_{agkt}]}`

The effective missing data rate for a generic variable `X` is defined as:

`MR[\bar{X}_{agkt}] =\ \frac{B[\bar{X}_{agkt}]}{T[\bar{X}_{agkt}]}`

The effective missing data rate for a generic variable `X` is defined as:

`MR[\bar{X}_{agkt}] =\ \frac{B[\bar{X}_{agkt}]}{T[\bar{X}_{agkt}]}`

The effective missing data rate for a generic variable `X` is defined as:

`MR[\bar{X}_{agkt}] =\ \frac{B[\bar{X}_{agkt}]}{T[\bar{X}_{agkt}]}`

The effective missing data rate for a generic variable `X` is defined as:

`MR[\bar{X}_{agkt}] =\ \frac{B[\bar{X}_{agkt}]}{T[\bar{X}_{agkt}]}`

The effective missing data rate for a generic variable `X` is defined as:

`MR[\bar{X}_{agkt}] =\ \frac{B[\bar{X}_{agkt}]}{T[\bar{X}_{agkt}]}`

The effective missing data rate for a generic variable `X` is defined as:

`MR[\bar{X}_{agkt}] =\ \frac{B[\bar{X}_{agkt}]}{T[\bar{X}_{agkt}]}`

The effective missing data rate for a generic variable `X` is defined as:

`MR[\bar{X}_{agkt}] =\ \frac{B[\bar{X}_{agkt}]}{T[\bar{X}_{agkt}]}`

The effective missing data rate for a generic variable `X` is defined as:

`MR[\bar{X}_{agkt}] =\ \frac{B[\bar{X}_{agkt}]}{T[\bar{X}_{agkt}]}`

The effective missing data rate for a generic variable `X` is defined as:

`MR[\bar{X}_{agkt}] =\ \frac{B[\bar{X}_{agkt}]}{T[\bar{X}_{agkt}]}`

The effective missing data rate for a generic variable `X` is defined as:

`MR[\bar{X}_{agkt}] =\ \frac{B[\bar{X}_{agkt}]}{T[\bar{X}_{agkt}]}`

The effective missing data rate for a generic variable `X` is defined as:

`MR[\bar{X}_{agkt}] =\ \frac{B[\bar{X}_{agkt}]}{T[\bar{X}_{agkt}]}`