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, tests for heteroscedasticity, plots, plots of standardized innovations and sample correlograms indicate that these assumptions are not violated under model (3.1).
Standard deviation | National level |
Men 15-24 |
Women 15-24 |
Men 25-44 |
Women 25-44 |
Men 45-64 |
Women 45-64 |
---|---|---|---|---|---|---|---|
Slope | 2,079 | 248 | 179 | 724 | 463 | 412 | 228 |
Seasonal | 0.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.22 |
RGB | 905 | 941 | 468 | 268 | 669 | 3 | 335 |
White noise | 6,884 | 1,528 | 3,521 | 4,359 | 4,294 | 3,329 | 2 |
Survey error panel 1 | 1.07 | 0.98 | 1.11 | 1.04 | 0.89 | 0.99 | 1.14 |
Survey error panel 2 | 0.99 | 0.95 | 1.03 | 1.03 | 0.94 | 1.17 | 1.02 |
Survey error panel 3 | 1.01 | 1.06 | 1.12 | 1.03 | 0.96 | 1.04 | 0.92 |
Survey error panel 4 | 1.13 | 1.07 | 1.21 | 0.99 | 0.96 | 0.99 | 0.95 |
Survey error panel 5 | 1.06 | 1.00 | 1.03 | 0.99 | 0.99 | 1.08 | 0.87 |
Autocorrelation | 0.21 | 0.13 | 0.12 | 0.39 | 0.22 | 0.44 | 0.38 |
The hyperparameter estimates for the survey errors for panel 2, 3, 4 and 5 are divided by Therefore hyperparameters for the survey errors are, as expected, around 1. |
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.
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:
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:
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 |
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:
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.
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:
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 and women 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.
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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