Current best-known Drake Equation values?

Question

Frank Drake's equation is used to estimate $N$ the number of civilizations we might be able to communicate with in our galaxy:

$$N = R_\star f_p n_e f_l f_i f_c L$$

where:

$R_\star$ is the average rate of star formation in the galaxy

$f_p$ is the fraction of stars with planets

$n_e$ is the average number of goldilocks planets per planetary system

$f_l$ is the fraction of goldilocks planets that actually develop life

$f_i$ is the fraction of life bearing planets that develop intelligent life

$f_c$ is the fraction of civilizations that broadcast their existence into space

and $L$ is the length of time for which a civilization broadcasts their existence

Question

Have the many exoplanets we've discovered in the last several decades improved our estimates of $f_p$, and $n_e$? Are these values different than what was guessed about prior to the discovery of the first exoplanets? What is our current best estimate for $R_\star$ for the Milky Way?

Answer 1

Have the many exoplanets we've discovered in the last several decades improved our estimates of 𝑓𝑝, and 𝑛𝑐?

Absolutely! The quantity $f_p n_e$ is a quantity of much interest in investigations of extrasolar planets, which effectively equates to the fraction of stars that have a habitable planet in their star's habitable zone. Plenty of studies have examined this specifically for Earth-sized extrasolar planets and place the value of $f_p n_e$ between ~$\frac{1}{6}$ (i.e. one in six stars have an earth-sized planet in a relatively close orbit to the host star) and ~$\frac{2}{5}$ [1][2]. A 2013 comprehensive study by Petigura is a great paper to get familiar with the specifics and assumptions of how the Kepler surveys are conducted and the quantities of interest calculated [3].

What is our current best estimate for 𝑅⋆ for the Milky Way?

Unfortunately the answer is: it varies. Roughly, we think that the Milky Way puts out about 3 solar masses worth of new star every year [4]. However, these don't have to be in one star. Since we think most stars are probably ~1 M$_\odot$, this works out to ~3 stars/year. However, some estimates go less, and some estimates (based on chemical decay of elements like aluminum) go as high as 7 stars/year [5].