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I've noticed that economists have been very accurate when it comes to predicting unemployment rates.

Most of their predictions usually fall within a 0.2% difference between their forecasts and the actual unemployment rate or are dead on what the employment rate is. I've looked at this site for information on the forecast vs the actual unemployment rate recently, which prompted me to ask this question.

Im aware of Okun's law and the cross country differences in terms of the measure of its coefficient. (see: http://unassumingeconomist.com/wp-content/uploads/2016/08/cross-country-evidence-on-okun-sep-2016-paris-workshop-draft-with-tables-and-charts.pdf)

But I am generally unaware of forecasting methods used by economists to predict unemployment rates.

What are some basic formulas or models used to forecast unemployment rates? Is there a pdf book anyone can recommend?

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I think one might use either vector auto-regression or perhaps factor-augmented vector auto-regression to make such predictions. The later will allow an economist to condition on hundreds of time series to predict future unemployment values without encountering the degrees-of-freedom issues that plague VAR whenever VAR attempts to condition on larger information sets.

Here is a paper detailing Kalman filtering and VAR for predicting unemployment: https://www.degruyter.com/downloadpdf/j/ngoe.2015.61.issue-3/ngoe-2015-0009/ngoe-2015-0009.pdf

TLDR: VAR does better than does KF. This is for Romania's economy, FYI.

Here is another paper detailing the use of VAR to forecast unemployment: https://www.brookings.edu/wp-content/uploads/2012/09/2012b_barnichon.pdf

Here is the seminal paper that introduced FAVAR: http://faculty.wcas.northwestern.edu/~lchrist/finc520/QJE.pdf

Wiki for VAR: https://en.wikipedia.org/wiki/Vector_autoregression

within the wiki, you will find a link to the seminal paper by Sims that introduces the VAR methodology to economics. Fair warning: this paper is dense: http://www.ekonometria.wne.uw.edu.pl/uploads/Main/macroeconomics_and_reality.pdf

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