economist forecast consistency check

economist-check.R

p_over_time = 
  read_csv("https://cdn.economistdatateam.com/us-2020-forecast/data/president/electoral_college_probability_over_time.csv") %>% 
  
  # convert win probabilites to logit scale
  mutate(win_prob_logit = boot::logit(win_prob)) %>% 
  
  # look only at one side
  filter(party == "democratic")

# take the variance of the differences
var_p_over_time = var(diff(p_over_time$win_prob_logit))

days_until_election = as.integer(ymd(20201103) - 
  ymd(last(p_over_time$date)))

# what does the forecast say today? 
current_logit_prob = last(p_over_time$win_prob_logit)

# the standard deviation the changes between now and the election
assumed_sd = sqrt(days_until_election * var_p_over_time)

# 95% confidence on the logit scale
confint_95_logit = current_logit_prob + assumed_sd * 1.96 * c(-1, 1)

# 95% confidence on the probability scale
confint_95_prob = boot::inv.logit(confint_95_logit)

confint_95_prob
# [1] 0.7331208 0.9832501

consistency_check = function() {
	
	v = 0:100 / 100
	
	l = boot::logit(v)
	d = pnorm(l, mean = current_logit_prob, sd = assumed_sd)
	dd = d[2:101] - d[1:100]
	sum(v[c(-1)] * dd)
	
}

consistency_check()
# [1] 0.9142117