Dealing with small sample sizes, rotation group bias and discontinuities in a rotating panel design 4. Implementation

In this section we compare the results obtained with the time series model with the GREG estimator for the period before the change-over to the new design, since rolling quarterly data are not calculated during and after the implementation of the new design. Since June 2010 model (3.1) has been applied to produce official monthly figures about the unemployed labour force, the employed labour force and the total labour force at the national level, and for six domains (men and women in three age classes). The model is applied to each variable separately. Estimates are computed as the sum of the trend and the seasonal effects, which is further referred to as the signal. Furthermore, trend estimates are published, replacing previous seasonally corrected figures. The first years of the GREG series are used to obtain stable estimates for the state variables of model (3.1). At the moment of implementation, a series of monthly figures starting in January 2003 is published.

Table 4.1 provides an overview of the ML estimates of the hyperparameters and the autocorrelation in the survey errors. The assumptions underlying the state-space model are evaluated by testing whether the standardized innovations are standard normally and independently distributed, Durbin and Koopman (2001), Section 4.2.4. Bowman-Shenton normality tests, F MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpipeea0xe9LqFf0x e9q8qqvqFr0dXdbrVc=b0P0xb9pC0xbbf9=e0dfrpm0dXdirVu0=vr 0=vr0=fdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaaeOraiabgk HiTaaa@3A0B@ tests for heteroscedasticity, QQ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpipeea0xe9LqFf0x e9q8qqvqFr0dXdbrVc=b0P0xb9pC0xbbf9=e0dfrpm0dXdirVu0=vr 0=vr0=fdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaaeyuaiaabg facqGHsislaaa@3AEA@ plots, plots of standardized innovations and sample correlograms indicate that these assumptions are not violated under model (3.1).

Table 4.1
ML estimates of hyperparameters for monthly unemployed labour force figures before the survey redesign. Values are expressed as standard deviations
Table summary
This table displays the results of ML estimates of hyperparameters for monthly unemployed labour force figures before the survey redesign. Values are expressed as standard deviations. The information is grouped by Standard deviation (appearing as row headers), National
level, Men
15-24 , Women
15-24 , Men
25-44 , Women
25-44 , Men
45-64 and Women
45-64 (appearing as column headers).
Standard deviation National
level
Men
15-24
Women
15-24
Men
25-44
Women
25-44
Men
45-64
Women
45-64
Slope ( σ ^ η ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFepG0de9LqFf0xe9 vqaqFeFr0xbba9Fa0P0RWFb9fq0FXxbbf9=e0dfrpm0dXdirVu0=vr 0=vr0=fdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacu aHdpWCgaqcamaaBaaaleaacqaH3oaAaeqaaaGccaGLOaGaayzkaaaa aa@3CEE@ 2,079 248 179 724 463 412 228
Seasonal ( σ ^ ω ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFepG0de9LqFf0xe9 vqaqFeFr0xbba9Fa0P0RWFb9fq0FXxbbf9=e0dfrpm0dXdirVu0=vr 0=vr0=fdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacu aHdpWCgaqcamaaBaaaleaacqaHjpWDaeqaaaGccaGLOaGaayzkaaaa aa@3D0F@ 0.02 0.00 0.00 0.00 0.00 0.04 0.22
RGB ( σ ^ λ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFepG0de9LqFf0xe9 vqaqFeFr0xbba9Fa0P0RWFb9fq0FXxbbf9=e0dfrpm0dXdirVu0=vr 0=vr0=fdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacu aHdpWCgaqcamaaBaaaleaacqaH7oaBaeqaaaGccaGLOaGaayzkaaaa aa@3CF6@ 905 941 468 268 669 3 335
White noise ( σ ^ ε ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFepG0de9LqFf0xe9 vqaqFeFr0xbba9Fa0P0RWFb9fq0FXxbbf9=e0dfrpm0dXdirVu0=vr 0=vr0=fdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacu aHdpWCgaqcamaaBaaaleaacqaH1oqzaeqaaaGccaGLOaGaayzkaaaa aa@3CE9@ 6,884 1,528 3,521 4,359 4,294 3,329 2
Survey error panel 1 ( σ ^ e 1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFepG0de9LqFf0xe9 vqaqFeFr0xbba9Fa0P0RWFb9fq0FXxbbf9=e0dfrpm0dXdirVu0=vr 0=vr0=fdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacu aHdpWCgaqcamaaBaaaleaacaWGLbGaaGymaaqabaaakiaawIcacaGL Paaaaaa@3CE7@ 1.07 0.98 1.11 1.04 0.89 0.99 1.14
Survey error panel 2 ( σ ^ e 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFepG0de9LqFf0xe9 vqaqFeFr0xbba9Fa0P0RWFb9fq0FXxbbf9=e0dfrpm0dXdirVu0=vr 0=vr0=fdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacu aHdpWCgaqcamaaBaaaleaacaWGLbGaaGOmaaqabaaakiaawIcacaGL Paaaaaa@3CE8@ 0.99 0.95 1.03 1.03 0.94 1.17 1.02
Survey error panel 3 ( σ ^ e 3 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFepG0de9LqFf0xe9 vqaqFeFr0xbba9Fa0P0RWFb9fq0FXxbbf9=e0dfrpm0dXdirVu0=vr 0=vr0=fdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacu aHdpWCgaqcamaaBaaaleaacaWGLbGaaG4maaqabaaakiaawIcacaGL Paaaaaa@3CE9@ 1.01 1.06 1.12 1.03 0.96 1.04 0.92
Survey error panel 4 ( σ ^ e 4 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFepG0de9LqFf0xe9 vqaqFeFr0xbba9Fa0P0RWFb9fq0FXxbbf9=e0dfrpm0dXdirVu0=vr 0=vr0=fdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacu aHdpWCgaqcamaaBaaaleaacaWGLbGaaGinaaqabaaakiaawIcacaGL Paaaaaa@3CEA@ 1.13 1.07 1.21 0.99 0.96 0.99 0.95
Survey error panel 5 ( σ ^ e 5 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFepG0de9LqFf0xe9 vqaqFeFr0xbba9Fa0P0RWFb9fq0FXxbbf9=e0dfrpm0dXdirVu0=vr 0=vr0=fdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacu aHdpWCgaqcamaaBaaaleaacaWGLbGaaGynaaqabaaakiaawIcacaGL Paaaaaa@3CEB@ 1.06 1.00 1.03 0.99 0.99 1.08 0.87
Autocorrelation ( ρ ^ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFepG0de9LqFf0xe9 vqaqFeFr0xbba9Fa0P0RWFb9fq0FXxbbf9=e0dfrpm0dXdirVu0=vr 0=vr0=fdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacu aHbpGCgaqcaaGaayjkaiaawMcaaaaa@3B09@ 0.21 0.13 0.12 0.39 0.22 0.44 0.38

 

In Figure 4.1, the filtered estimates for the monthly unemployed labour force at the national level based on model (3.1) are compared with the monthly GREG estimates and with the rolling quarterly GREG figures. Both GREG estimates are corrected for RGB using the ratio correction described in Section 2. The three series are at the same level, since they are calibrated to the level of the first panel. The series of the monthly GREG estimates has more pronounced peaks and dips than the filtered estimates. Under the times series model these fluctuations are partially considered as survey errors and filtered from the GREG estimates. The rolling quarterly figures have a less pronounced seasonal pattern, since monthly patterns are averaged over three subsequent months.

Figure 4.2 compares the filtered trend estimates with the seasonally adjusted estimates of the rolling quarterly data for the unemployed labour force at the national level. The seasonally adjusted rolling quarterly data, computed by X-12-ARIMA (U.S. Census Bureau 2009), were published before the new estimation method was implemented, and are available until May 2010. They are computed as the original estimates minus the seasonal effects. Besides the trend, they also include the sampling errors and other irregularities. Seasonally adjusted rolling quarterly figures and the filtered trend therefore measure slightly differently defined concepts. After the implementation of the time series model, the seasonally adjusted figures are replaced by the filtered trend, so it is interesting to compare the differences between both figures mainly to judge how large the consequences are for the users of these data.

There are some minor differences in the levels of the series in Figures 4.1 and 4.2. They are the result of large sampling errors and differences between the methods used to account for RGB. Firstly, the monthly GREG estimates and the rolling quarterly GREG estimates are more sensitive to large sampling errors. This in contrast with the time series model that filters the survey errors from the GREG estimates.

Figure 4.1 of section 4 Implementation

Description for Figure 4.1

This figure is made of two line charts. For both, the horizontal axis is the time and the vertical axis is the unemployed labour force.

On graph one, there are 3 series: the GREG monthly estimates, the rolling quarterly GREG estimates and the monthly filtered model estimates. The data are in the following Table:

Data table for Figure 4.1
Table summary
This table displays the results of Data table for Figure 4.1a. The information is grouped by Time (appearing as row headers), GREG monthly estimate, Rolling quarterly figure and Filtered signal (appearing as column headers).
Time GREG monthly estimate Rolling quarterly figure Filtered signal
Jan-03 339,970.60 318,000 322,005.61
Feb-03 363,072.83 332,000 360,922.29
Mar-03 401,922.65 369,000 372,429.98
Apr-03 395,282.09 384,000 363,515.94
May-03 374,476.31 385,000 370,461.69
Jun-03 424,248.36 397,000 418,427.18
Jul-03 414,206.71 407,000 414,725.09
Aug-03 390,651.85 405,000 388,686.49
Sep-03 411,606.61 408,000 413,097.01
Oct-03 408,788.54 400,000 399,912.85
Nov-03 420,594.86 420,000 420,372.89
Dec-03 407,082.08 423,000 402,597.50
Jan-04 468,813.57 451,000 460,295.06
Feb-04 471,674.69 474,000 482,541.43
Mar-04 499,451.23 503,000 491,674.77
Apr-04 471,001.37 500,000 473,397.46
May-04 451,919.77 496,000 465,524.79
Jun-04 478,056.04 485,000 497,750.42
Jul-04 475,785.21 484,000 482,551.60
Aug-04 429,405.24 477,000 442,263.37
Sep-04 434,374.17 457,000 448,789.73
Oct-04 468,955.03 458,000 451,157.69
Nov-04 464,836.05 466,000 467,479.14
Dec-04 449,864.75 472,000 450,145.78
Jan-05 478,620.64 479,000 492,067.27
Feb-05 515,862.99 495,000 515,538.37
Mar-05 515,805.40 516,000 520,083.00
Apr-05 483,393.45 514,000 490,688.50
May-05 478,480.28 501,000 486,210.67
Jun-05 491,367.96 492,000 505,743.94
Jul-05 507,513.84 497,000 501,456.18
Aug-05 451,780.93 488,000 461,027.16
Sep-05 459,627.39 476,000 464,208.71
Oct-05 448,391.88 456,000 453,169.47
Nov-05 452,724.12 459,000 462,798.83
Dec-05 419,947.86 447,000 426,572.07
Jan-06 440,689.15 450,000 457,253.64
Feb-06 460,060.74 454,000 472,462.60
Mar-06 447,642.08 460,000 460,671.39
Apr-06 401,321.47 447,000 418,506.09
May-06 414,590.98 430,000 412,018.37
Jun-06 377,296.86 407,000 408,889.18
Jul-06 430,370.31 415,000 416,084.50
Aug-06 353,646.48 400,000 358,056.44
Sep-06 367,346.01 407,000 372,135.87
Oct-06 384,353.78 390,000 375,318.90
Nov-06 368,481.98 390,000 380,604.20
Dec-06 329,967.25 377,000 342,375.01
Jan-07 390,366.13 374,000 383,121.85
Feb-07 405,736.62 384,000 402,897.78
Mar-07 371,710.31 401,000 385,448.50
Apr-07 328,501.75 375,000 337,009.42
May-07 351,126.81 354,000 339,413.42
Jun-07 337,867.79 346,000 343,468.04
Jul-07 376,899.33 363,000 355,707.82
Aug-07 288,555.10 342,000 295,804.04
Sep-07 297,839.74 328,000 297,086.71
Oct-07 318,190.58 307,000 303,304.34
Nov-07 303,920.53 306,000 305,263.72
Dec-07 283,538.93 301,000 281,114.16
Jan-08 326,788.76 308,000 321,816.24
Feb-08 334,773.85 321,000 336,265.78
Mar-08 332,207.24 336,000 325,264.85
Apr-08 318,356.98 326,000 302,053.96
May-08 297,632.54 313,000 300,367.11
Jun-08 317,260.16 310,000 311,466.27
Jul-08 319,351.89 308,000 314,606.56
Aug-08 268,723.58 294,000 263,171.01
Sep-08 286,852.19 284,000 276,818.11
Oct-08 281,006.51 276,000 277,244.13
Nov-08 297,978.73 280,000 285,322.74
Dec-08 304,564.06 285,000 275,483.69
Jan-09 315,124.33 298,000 315,780.77
Feb-09 347,034.86 314,000 344,297.02
Mar-09 347,705.79 341,000 337,957.73
Apr-09 380,605.40 360,000 343,723.23
May-09 351,813.51 358,000 346,716.92
Jun-09 370,957.77 373,000 367,240.01
Jul-09 414,031.12 386,000 394,337.84
Aug-09 361,491.21 390,000 351,030.15
Sep-09 379,056.60 394,000 370,362.70
Oct-09 392,771.55 387,000 377,248.15
Nov-09 426,196.89 400,000 399,623.49
Dec-09 394,196.93 410,000 390,070.74
Jan-10 471,612.05 430,000 443,351.17
Feb-10 479,235.71 441,000 470,440.67
Mar-10 464,818.93 472,000 460,814.95
Apr-10 436,887.03 459,000 432,538.84
May-10 441,342.24 437,000 430,202.25
Jun-10 435,426.98 435,000.24 440,297.99

 

On graph two, there are 3 series: the standard error of the GREG monthly estimates, of the rolling quarterly GREG estimates and of the monthly filtered model estimates. The data are in the following Table:

Data table for Figure 4.1(cont.)
Table summary
This table displays the results of Data table for Figure 4.1b. The information is grouped by Time (appearing as row headers), SE of GREG monthly estimate, SE of Rolling quarterly figure and SE of Filtered signal (appearing as column headers).
Time SE of GREG monthly estimate SE of Rolling quarterly figure SE of Filtered signal
Jan-03 14,600.63 8,300.32 11,860.34
Feb-03 14,700.06 8,692.64 11,906.41
Mar-03 16,594.27 8,813.96 12,527.91
Apr-03 17,367.87 9,464.11 12,943.67
May-03 16,854.44 9,879.75 12,696.18
Jun-03 17,915.95 10,125.51 13,336.28
Jul-03 15,308.13 9,587.65 12,750.39
Aug-03 16,764.77 9,563.37 12,722.43
Sep-03 17,506.33 9,500.92 13,181.91
Oct-03 14,879.02 9,400.51 12,211.36
Nov-03 15,820.86 9,224.53 12,261.26
Dec-03 15,816.76 8,956.57 12,534.20
Jan-04 15,193.61 9,033.95 12,098.07
Feb-04 15,753.68 9,024.92 11,919.24
Mar-04 15,715.14 8,933.67 11,985.66
Apr-04 14,884.20 8,891.84 11,759.31
May-04 14,714.54 8,716.75 11,739.30
Jun-04 15,598.50 8,714.60 12,154.03
Jul-04 13,951.80 8,502.26 11,664.61
Aug-04 14,973.45 8,544.05 11,969.92
Sep-04 14,966.05 8,441.34 12,004.43
Oct-04 13,677.24 8,391.16 11,394.03
Nov-04 14,210.90 8,250.28 11,487.82
Dec-04 14,231.67 8,105.32 11,534.87
Jan-05 15,848.09 8,500.20 12,063.07
Feb-05 15,198.59 8,691.33 11,784.90
Mar-05 14,220.37 8,679.31 11,551.33
Apr-05 16,131.28 8,733.71 12,033.17
May-05 15,083.00 8,722.80 11,813.20
Jun-05 13,773.97 8,606.17 11,359.36
Jul-05 16,084.09 8,599.85 12,053.99
Aug-05 15,686.38 8,709.10 12,085.95
Sep-05 14,051.57 8,795.36 11,478.44
Oct-05 15,210.13 8,635.85 11,613.19
Nov-05 14,182.94 8,346.15 11,377.22
Dec-05 13,197.03 8,213.81 10,962.34
Jan-06 14,705.08 8,107.46 11,180.53
Feb-06 14,574.44 8,157.34 11,218.41
Mar-06 13,354.54 8,217.42 10,795.99
Apr-06 13,514.83 7,996.00 10,774.65
May-06 14,120.66 7,891.86 10,938.90
Jun-06 12,252.65 7,691.25 10,402.60
Jul-06 14,502.38 7,840.08 11,216.72
Aug-06 13,563.78 7,716.14 10,818.64
Sep-06 12,483.97 7,821.61 10,247.37
Oct-06 14,075.32 7,721.13 10,648.01
Nov-06 13,745.96 7,729.28 10,540.19
Dec-06 12,742.54 7,837.80 10,193.04
Jan-07 14,444.34 7,878.72 10,696.30
Feb-07 13,315.95 7,781.24 10,294.66
Mar-07 14,223.10 8,100.49 10,552.05
Apr-07 12,919.53 7,813.88 10,015.25
May-07 13,195.27 7,759.80 9,983.35
Jun-07 14,531.93 7,836.07 10,434.90
Jul-07 15,330.81 8,288.41 10,746.93
Aug-07 12,561.37 8,147.25 9,908.93
Sep-07 12,972.83 7,942.25 9,744.24
Oct-07 13,394.40 7,525.26 9,978.78
Nov-07 12,732.57 7,531.56 9,743.67
Dec-07 13,352.74 7,630.05 9,929.84
Jan-08 11,953.92 7,318.67 9,409.06
Feb-08 14,896.74 7,659.00 10,186.80
Mar-08 14,509.95 7,874.73 10,301.82
Apr-08 12,166.22 7,926.22 9,560.32
May-08 12,860.48 7,558.89 9,712.29
Jun-08 14,062.57 7,519.74 9,951.27
Jul-08 12,113.30 7,489.82 9,444.85
Aug-08 12,746.53 7,464.39 9,486.52
Sep-08 13,435.42 7,386.97 9,681.65
Oct-08 11,394.73 7,191.28 8,866.65
Nov-08 12,957.36 7,224.20 9,226.65
Dec-08 14,099.43 7,326.31 9,697.77
Jan-09 12,488.10 7,580.98 9,426.77
Feb-09 14,153.24 7,809.12 9,921.26
Mar-09 15,124.60 7,984.76 10,329.43
Apr-09 13,163.39 8,136.88 9,836.18
May-09 14,788.79 8,246.43 10,236.69
Jun-09 14,096.22 8,023.28 10,142.15
Jul-09 14,134.29 8,260.49 10,225.78
Aug-09 14,852.13 8,289.72 10,231.29
Sep-09 14,479.51 8,319.21 10,124.05
Oct-09 14,145.35 8,346.29 9,960.43
Nov-09 15,732.79 8,512.60 10,429.77
Dec-09 14,557.35 8,524.14 10,385.86
Jan-10 15,179.29 8,737.27 10,605.20
Feb-10 16,430.98 8,860.73 11,046.12
Mar-10 13,934.44 8,699.98 10,382.67
Apr-10 16,004.40 8,852.82 10,720.49
May-10 15,917.95 8,774.03 10,951.16
Jun-10 14,188.83 8,780.94 10,616.23

 

Figure 4.2 of section 4 Implementation

Description for Figure 4.2

This is a line chart. The horizontal axis is the time. The vertical axis is the unemployed labour force. There are 2 series in this graph: the seasonally adjusted rolling quarterly figures and the monthly filtered trend estimates. The data are in the following Table:

Data table for Figure 4.2
Table summary
This table displays the results of Data table for Figure 4.2. The information is grouped by Time (appearing as row headers), Filtered trend and Rolling quarterly figures seasonally adjusted (appearing as column headers).
Time Filtered trend Rolling quarterly figures seasonally adjusted
Jan-03 316,554.41 325,000
Feb-03 323,712.51 332,000
Mar-03 344,627.57 350,000
Apr-03 371,374.87 367,000
May-03 382,709.84 380,000
Jun-03 391,044.99 399,000
Jul-03 398,096.59 398,000
Aug-03 404,225.37 404,000
Sep-03 408,479.92 411,000
Oct-03 421,771.20 416,000
Nov-03 427,576.60 429,000
Dec-03 443,562.69 438,000
Jan-04 460,023.14 458,000
Feb-04 456,504.76 473,000
Mar-04 465,906.18 479,000
Apr-04 477,931.43 480,000
May-04 479,625.36 490,000
Jun-04 473,987.33 488,000
Jul-04 468,194.81 476,000
Aug-04 461,478.06 478,000
Sep-04 451,174.23 461,000
Oct-04 468,759.69 475,000
Nov-04 475,006.84 476,000
Dec-04 488,162.24 488,000
Jan-05 488,720.88 485,000
Feb-05 488,899.07 494,000
Mar-05 491,157.98 491,000
Apr-05 492,071.71 493,000
May-05 495,852.98 496,000
Jun-05 483,881.37 494,000
Jul-05 486,191.35 489,000
Aug-05 482,576.67 490,000
Sep-05 473,410.21 482,000
Oct-05 471,791.46 473,000
Nov-05 470,413.88 470,000
Dec-05 464,785.70 462,000
Jan-06 454,988.59 456,000
Feb-06 446,124.43 453,000
Mar-06 433,156.23 437,000
Apr-06 420,313.36 427,000
May-06 418,622.59 426,000
Jun-06 391,944.46 408,000
Jul-06 395,430.86 406,000
Aug-06 379,776.01 400,000
Sep-06 379,546.10 412,000
Oct-06 387,902.58 407,000
Nov-06 386,265.09 402,000
Dec-06 378,591.08 391,000
Jan-07 376,989.63 381,000
Feb-07 374,089.88 385,000
Mar-07 359,831.33 379,000
Apr-07 341,160.54 357,000
May-07 342,601.64 350,000
Jun-07 331,253.61 347,000
Jul-07 334,318.54 353,000
Aug-07 321,663.43 339,000
Sep-07 308,724.72 333,000
Oct-07 312,671.68 323,000
Nov-07 309,782.20 318,000
Dec-07 315,115.49 315,000
Jan-08 313,875.16 315,000
Feb-08 306,615.62 322,000
Mar-08 299,384.14 316,000
Apr-08 305,344.80 309,000
May-08 303,473.70 309,000
Jun-08 300,074.60 310,000
Jul-08 293,261.95 296,000
Aug-08 289,699.53 290,000
Sep-08 290,102.91 287,000
Oct-08 287,578.65 293,000
Nov-08 289,883.56 292,000
Dec-08 305,564.38 300,000
Jan-09 307,733.61 306,000
Feb-09 314,203.40 315,000
Mar-09 313,109.05 320,000
Apr-09 342,328.97 342,000
May-09 349,662.94 353,000
Jun-09 356,099.27 373,000
Jul-09 371,526.93 375,000
Aug-09 378,611.92 388,000
Sep-09 385,272.40 399,000
Oct-09 389,879.92 404,000
Nov-09 405,065.47 413,000
Dec-09 419,926.70 424,000
Jan-10 435,906.25 436,000
Feb-10 442,334.19 441,000
Mar-10 439,465.97 447,000
Apr-10 432,196.18 438,000
May-10 433,636.95 431,000
Jun-10 430,478.39  

Secondly, the RGB correction for the monthly GREG estimates and the rolling quarterly figures are based on a rigid and untested assumption of a constant ratio over a period of three years, see Section 2. In the time series model, the RGB is modelled as differences between the panels and is allowed to change gradually over time, see equation (3.7). Filtered estimates for the RGB in the monthly unemployed labour force at national level are plotted in Figure 4.3. This figure shows that the assumption of a constant ratio over a period of three years is not tenable, since the absolute value of the RGB increases in a period that the unemployed labour force decreases. It is therefore unlikely that the ratio used to correct the rolling quarterly figures is constant over three year periods. The model evaluation does not indicate that the assumptions underlying time series model (3.1) are not met. It can therefore be expected that a more reliable RGB correction is obtained with the time series modelling approach.

Thirdly, the methodology of X-12-ARIMA assumes that there is no autocorrelation in the sampling errors. This assumption is clearly not met in a rotating panel. Pfeffermann et al. (1998) showed that the use of X-12-ARIMA to series with autocorrelated survey errors results in spurious trend estimates. This partially explains the differences between the filtered trend and the seasonally adjusted rolling quarterly data in Figure 4.2.

Figure 4.3 of section 4 Implementation

Description for Figure 4.3

This is a line chart. The horizontal axis is the time. The vertical axis is the unemployed labour force. There are 4 series in this graph: the filtered estimates for RGB in the monthly unemployed labour force at national level for panels 2 to 5. The data are in the following Table:

Data table for Figure 4.3
Table summary
This table displays the results of Data table for Figure 4.3. The information is grouped by Time (appearing as row headers), RGB panel 2, RGB panel 3, RGB panel 4 and RGB panel 5 (appearing as column headers).
Time RGB panel 2 RGB panel 3 RGB panel 4 RGB panel 5
Jan-03 -32,468.70 -24,874.50 -36,601.30 -27,880.00
Feb-03 -31,866.20 -25,572.80 -36,977.40 -28,843.40
Mar-03 -31,434.70 -24,448.40 -35,921.80 -29,185.20
Apr-03 -34,023.90 -24,991.50 -36,749.40 -30,597.10
May-03 -33,661.20 -24,501.80 -35,999.10 -30,176.80
Jun-03 -34,115.10 -23,644.40 -34,731.10 -29,836.00
Jul-03 -34,409.60 -23,844.00 -35,783.50 -31,919.30
Aug-03 -33,230.60 -23,936.50 -34,002.90 -29,320.30
Sep-03 -33,677.40 -24,644.30 -33,106.10 -29,556.80
Oct-03 -34,643.70 -24,776.80 -33,007.40 -28,925.50
Nov-03 -35,477.20 -24,902.10 -33,678.50 -31,829.90
Dec-03 -34,473.40 -24,968.00 -32,221.60 -30,974.20
Jan-04 -34,102.50 -23,567.40 -31,988.00 -28,503.50
Feb-04 -32,807.70 -23,474.50 -34,393.10 -28,983.20
Mar-04 -33,122.10 -23,476.80 -34,170.90 -29,031.00
Apr-04 -33,442.10 -22,523.40 -35,031.70 -30,481.70
May-04 -33,346.60 -22,165.70 -32,666.30 -29,328.60
Jun-04 -32,763.20 -22,811.60 -32,010.40 -28,436.00
Jul-04 -30,982.60 -20,218.60 -30,313.70 -26,958.10
Aug-04 -31,794.10 -19,864.20 -31,064.20 -27,788.90
Sep-04 -32,163.80 -18,988.80 -33,357.10 -26,347.10
Oct-04 -31,096.80 -19,045.80 -34,509.80 -25,900.20
Nov-04 -30,866.90 -18,993.10 -34,436.60 -25,865.10
Dec-04 -31,825.80 -21,258.80 -35,868.10 -26,618.90
Jan-05 -33,412.00 -21,186.80 -35,876.60 -26,371.30
Feb-05 -32,952.90 -22,311.70 -36,848.60 -29,037.00
Mar-05 -32,400.00 -23,145.70 -36,435.00 -27,003.20
Apr-05 -32,444.90 -22,857.40 -34,592.70 -27,098.40
May-05 -32,697.60 -23,970.90 -33,503.50 -26,449.90
Jun-05 -31,343.20 -23,565.20 -32,130.00 -26,688.50
Jul-05 -32,573.50 -23,785.80 -31,638.10 -26,992.40
Aug-05 -31,604.10 -23,793.20 -30,493.60 -27,893.80
Sep-05 -33,496.80 -23,634.20 -28,915.00 -28,192.40
Oct-05 -35,612.90 -25,062.50 -29,832.50 -28,207.40
Nov-05 -35,500.40 -25,833.60 -31,234.50 -30,031.20
Dec-05 -35,243.60 -27,024.40 -30,319.40 -29,572.20
Jan-06 -34,767.70 -28,744.40 -30,936.20 -30,089.20
Feb-06 -35,613.00 -29,336.00 -31,288.50 -29,751.60
Mar-06 -35,633.20 -31,849.00 -31,571.00 -30,651.50
Apr-06 -36,848.80 -31,133.60 -32,436.00 -33,718.40
May-06 -38,051.60 -33,480.60 -32,662.90 -34,537.80
Jun-06 -36,987.20 -32,560.90 -32,710.60 -34,732.70
Jul-06 -37,231.50 -35,029.80 -33,310.70 -35,403.20
Aug-06 -37,950.50 -36,889.10 -33,108.30 -36,037.10
Sep-06 -38,684.40 -37,425.60 -33,192.80 -37,806.80
Oct-06 -38,121.70 -38,120.30 -34,696.60 -38,121.40
Nov-06 -40,061.20 -37,777.10 -35,614.90 -37,220.80
Dec-06 -40,661.20 -39,497.80 -35,186.90 -37,059.30
Jan-07 -40,337.10 -39,270.70 -34,738.40 -37,336.60
Feb-07 -41,006.90 -38,647.70 -35,098.40 -36,316.20
Mar-07 -40,244.00 -38,199.70 -36,715.60 -35,724.60
Apr-07 -40,937.80 -38,102.10 -36,568.10 -34,854.30
May-07 -41,288.70 -36,841.30 -36,519.70 -34,698.30
Jun-07 -41,785.60 -38,019.00 -35,160.00 -35,802.20
Jul-07 -41,661.10 -38,354.40 -35,255.10 -37,579.60
Aug-07 -42,313.30 -39,169.40 -35,979.10 -36,046.40
Sep-07 -42,964.50 -42,406.80 -36,733.70 -36,584.40
Oct-07 -43,113.50 -43,222.70 -37,517.90 -37,761.40
Nov-07 -42,050.40 -43,710.80 -37,662.80 -37,138.20
Dec-07 -41,415.60 -44,439.80 -38,413.40 -37,681.00
Jan-08 -41,710.70 -45,110.60 -39,547.90 -38,016.20
Feb-08 -41,414.00 -45,470.40 -38,641.70 -38,190.60
Mar-08 -42,331.40 -45,489.70 -37,768.50 -39,450.00
Apr-08 -43,482.70 -46,086.40 -35,907.50 -39,545.20
May-08 -43,105.30 -45,394.20 -37,010.40 -38,495.80
Jun-08 -42,802.20 -43,953.60 -36,043.40 -38,318.60
Jul-08 -42,787.20 -43,532.70 -36,765.70 -39,194.70
Aug-08 -41,116.10 -42,510.10 -35,300.80 -38,227.90
Sep-08 -40,588.60 -42,070.10 -35,329.90 -38,628.70
Oct-08 -39,228.40 -41,522.90 -37,536.20 -39,032.90
Nov-08 -39,409.90 -41,174.90 -38,259.00 -38,686.90
Dec-08 -39,676.50 -40,504.10 -38,467.70 -38,467.80
Jan-09 -39,856.30 -41,505.00 -37,822.50 -39,533.20
Feb-09 -39,886.80 -42,582.90 -37,659.90 -39,306.60
Mar-09 -40,064.40 -42,924.80 -37,775.80 -38,683.00
Apr-09 -40,513.40 -42,815.20 -36,975.30 -38,593.60
May-09 -40,168.00 -41,836.70 -35,913.40 -38,525.70
Jun-09 -40,993.10 -40,955.10 -37,697.80 -38,654.40
Jul-09 -40,920.90 -41,436.50 -38,224.10 -40,392.30
Aug-09 -40,617.00 -39,688.60 -38,734.40 -39,650.00
Sep-09 -40,533.40 -39,839.10 -38,676.00 -41,057.70
Oct-09 -41,938.70 -40,572.40 -38,465.30 -41,335.20
Nov-09 -42,943.30 -40,518.70 -38,818.60 -41,003.60
Dec-09 -43,433.60 -39,366.50 -39,982.40 -42,060.90
Jan-10 -42,012.60 -40,537.40 -40,014.80 -40,229.70
Feb-10 -41,702.20 -41,269.40 -40,308.00 -39,973.90
Mar-10 -42,171.20 -42,039.20 -39,960.10 -39,471.30
Apr-10 -40,855.00 -40,862.20 -41,334.30 -38,438.80
May-10 -40,263.30 -39,970.90 -41,194.70 -37,455.90
Jun-10 -40,283.40 -38,808.40 -40,799.00 -37,549.90

The standard errors of the monthly GREG estimates and the rolling quarterly figures are based on the variance of the Taylor approximation of the GREG estimator, Särndal et al. (1992), Chapter 6. The ratio used to correct for RGB is assumed to be known, although it is based on the samples of three years. The standard errors of the filtered estimates ignore the uncertainty of using ML estimates for the hyperparameters. Table 4.2 compares the means of the standard errors over the last 24 months for the three considered methods for the unemployed labour force, at the national level and for the six domains. Figure 4.1 compares the standard errors at the national level for the three methods for the entire series. In all cases, the precision of the monthly GREG estimates has been substantially improved by the time series model. The rolling quarterly figures have smaller standard errors than the model estimates in almost all cases. For the domains men 15 24 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpipeea0xe9LqFf0x e9q8qqvqFr0dXdbrVc=b0P0xb9pC0xbbf9=e0dfrpm0dXdirVu0=vr 0=vr0=fdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaaGymaiaaiw dacqGHsislcaaIYaGaaGinaaaa@3C36@ and women 45 64 , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrpipeea0xe9LqFf0x e9q8qqvqFr0dXdbrVc=b0P0xb9pC0xbbf9=e0dfrpm0dXdirVu0=vr 0=vr0=fdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaaGinaiaaiw dacqGHsislcaaI2aGaaGinaiaacYcaaaa@3CED@ the precision of the model estimates and of the rolling quarterly figures are similar. Nevertheless, the time series model produces sufficiently reliable monthly estimates to replace the rolling quarterly figures by monthly figures. This circumvents the aforementioned disadvantages of the rolling quarterly figures. Moreover it is not straightforward how rolling quarterly figures can be corrected for RGB in combination with discontinuities induced by the redesign in 2010.

Table 4.2
Mean standard errors unemployed labour force over 24 months (July 2008 – June 2010)
Table summary
This table displays the results of Mean standard errors unemployed labour force over 24 months (July 2008 – June 2010) National
level , Men
15-24, Women
15-24, Men
25-44, Women
25-44, Men
45-64 and Women
45-64 (appearing as column headers).
  National
level
Men
15-24
Women
15-24
Men
25-44
Women
25-44
Men
45-64
Women
45-64
Rolling quarterly estimate 8,118 3,126 2,831 4,041 3,809 3,452 3,260
Monthly GREG estimate 14,172 5,448 4,885 7,083 6,662 6,046 5,676
Model estimate 10,082 3,247 3,439 5,075 4,749 4,119 3,269
Ratio model and rolling quarterly figure 1.24 1.04 1.21 1.26 1.25 1.19 1.00
Ratio model and monthly GREG estimate 0.71 0.60 0.70 0.72 0.71 0.68 0.58

 

An artefact of applying model (3.1) to each variable and domain separately is that the sum over the domain estimates is not exactly equal to the estimate at the national level and that the sum of the employed and unemployed labour force is not exactly equal to the total labour force for each domain and at the national level. With the GREG estimator these estimates are consistent by definition, since one set of weights is used to compile all required estimates. The aforementioned restrictions for the model estimates are restored through an appropriate Lagrange function, which distributes the discrepancies over the model estimates proportional to their MSE estimates. Details are given in the Appendix. Finally, unemployment rates are obtained as the ratio of the model estimate for the unemployed labour force to the total labour force for the six domains and the national level.

The model-based domain estimates for the monthly employed and unemployed labour force are included as a weighting term in the GREG estimator for the quarterly and yearly releases. This enforces consistency between monthly, quarterly, and yearly labour force figures and corrects for the RGB in the GREG estimates of the quarterly and yearly labour force figures.

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