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• (Generalized) Linear Models 广义线性模型
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• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|经济统计代写Economic Statistics代考|Comparing ADP- FRB to Official Data

In this section we evaluate the ability of ADP-FRB and CES to forecast the QCEW, which can plausibly be treated as “truth.” We restrict attention to annual changes (March-to-March) to avoid complications related to seasonality and seam effects in the QCEW.

We follow the CES in benchmarking the level of our ADP-FRB indexes to the QCEW each year. Our procedure closely follows that of the CES: we iteratively force each March value of ADP-FRB to match the corresponding QCEW value, and we linearly wedge back the pre/post benchmark revision. The wedge reaches zero at the previous (already benchmarked) March. At the time of writing of this paper, the data are benchmarked through March $2017 .$

Throughout the paper, we use our monthly ADP-FRB index starting in 2007. For the purpose of annual benchmarking, this means we begin annual benchmark comparisons with the 2008 benchmark year, which measures the change in private nonfarm employment from April 2007 through March 2008. In the 10 years starting from 2008, the pre-benchmark ADPFRB estimates were closer to the eventually published population counts in four years, while the pre-benchmark CES estimates were more accurate in six years (see table 5.1). Overall, the root-mean-squared benchmark revision is $0.49$ percent for the ADP-FRB data and $0.36$ percent for the CES data from 2008 onward. Interestingly, the ADP-FRB estimates markedly outperformed the CES estimates during the Great Recession (2008-2010). Specifically, from 2008 to 2010 the ADP-FRB absolute revisions averaged 200,000 per year, whereas the BLS-CES absolute revisions averaged 490,000 per year. In contrast, between 2013 and 2017 the pre-benchmark ADP-FRB estimates consistently overpredicted employment growth.

An evaluation of the CES benchmark misses should also take the net birth-death model into account, as the net birth-death adjustment adds roughly 40 percent to a particular year’s employment change. As a result, a comparison of the benchmark misses of ADP-FRB series to the CES data is not exactly direct, as the ADP-FRB data would likely only capture a portion of the contribution of employment births. The third row in table $5.1$ presents the benchmark miss of the CES data without the inclusion of the net birth-death adjustment. That is, the “CES no BD” row reflects the growth to the level of employment solely due to the sample of businesses for which the CES data are collected. ${ }^{19}$

## 统计代写|经济统计代写Economic Statistics代考|Predicting Monthly Employment

While annual forecasts of the benchmark revisions are important, the CES is a monthly measure of employment that revises over several releases as both more data and benchmarks become available. In this section we evaluate the ability of the ADP-FRB employment indexes to improve fore-casts of CES data in real time and in conjunction with other real-time indicators. Table $5.3$ reports forecasting models described in Cajner et al. (2018) using real-time ADP indexes and other variables to predict the final print of CES (i.e., after all the revisions). In particular, we estimated the following regression model:
(1) $\Delta E M P_t^{\mathrm{CES}, \text { final }}=\alpha+\beta_1 \Delta E M P_t^{\mathrm{ADP}-\mathrm{FRB}, R T 5}+\beta_2 \Delta E M P_{t-1}^{\mathrm{CES}, R T}+\beta X_t+\omega_t$.
The explanatory variables include current-month real-time (five weeks after the start of the month, which corresponds to the week before or the week of the Employment Situation release) ADP-FRB data, previous-month real-time (first print) CES private employment, as well as initial unemployment insurance claims, Michigan Survey unemployment expectations, the lagged (previous-month) unemployment rate change, and Bloomberg market CES payroll employment expectations. In addition, $\omega_t=\varepsilon_t+\rho \varepsilon_{t-1}$ is an MA(1) error term. ${ }^{24}$

Cajner et al. (2018) discuss similar results in more detail; here we simply note that the ADP-FRB indexes for active employment make statistically significant contributions to the model and generate modest improvements to forecasting accuracy. Column (1) of table $5.3$ reports the baseline forecasting model without the ADP-FRB data or market expectations. Adding market expectations in column (2) improves the forecast notably, as can be seen from the 15,000-job reduction in RMSE. In column (3) we add the ADP-FRB index and find that RMSE declines and the ADP-FRB coefficient is statistically significant; that is, the inclusion of the ADP-FRB index provides further marginal forecasting improvement beyond the inclusion of market expectations, in contrast to the Gregory and Zhu (2014) results using ADP-NER. In column (4) we report a model including ADP-FRB but omitting market expectations, which reduces RMSE by 7,000 jobs relative to the baseline. Finally, column (5) indicates that even when the first print of CES data is available, the real-time ADP-FRB data provide an additional signal about the final or “true” BLS measure of employment change.

# 经济统计代考

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## 统计代写|经济统计代写经济统计代考|预测月度就业

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(1) $\Delta E M P_t^{\mathrm{CES}, \text { final }}=\alpha+\beta_1 \Delta E M P_t^{\mathrm{ADP}-\mathrm{FRB}, R T 5}+\beta_2 \Delta E M P_{t-1}^{\mathrm{CES}, R T}+\beta X_t+\omega_t$解释变量包括当月实时(月初后五周，对应于就业形势发布的前一周或发布的那一周)ADP-FRB数据、上月实时(初版)CES私营就业、以及首次失业保险索赔、密歇根调查失业预期、滞后(前一个月)失业率变化以及彭博市场CES就业预期。此外， $\omega_t=\varepsilon_t+\rho \varepsilon_{t-1}$ 为MA(1)误差项。 ${ }^{24}$

Cajner等人(2018)更详细地讨论了类似的结果;这里我们只是指出，ADP-FRB的积极就业指数在统计上对模型做出了显著贡献，并对预测精度产生了适度的提高。表$5.3$的第(1)列报告了基线预测模型，没有ADP-FRB数据或市场预期。在列(2)中添加市场预期显著改善了预测，从RMSE中减少的15,000个工作岗位可以看出。在列(3)中，我们添加ADP-FRB指数，发现RMSE下降，ADP-FRB系数具有统计学意义;也就是说，与Gregory和Zhu(2014)使用ADP-NER的结果相比，纳入ADP-FRB指数在纳入市场预期之外提供了进一步的边际预测改善。在第(4)列中，我们报告了一个包含ADP-FRB但忽略了市场预期的模型，该模型相对于基线减少了7000个工作岗位的RMSE。最后，第(5)列表明，即使CES数据首次打印可用，实时ADP-FRB数据也提供了关于BLS就业变化的最终或“真实”度量的额外信号

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