Variable slope forecasting methods and COVID-19 risk

There are many real-world situations in which complex interacting forces are best described by a series of equations. Traditional regression approaches to these situations involve modeling and estimating each individual equation (producing estimates of "partial derivatives") and then solving the entire system for reduced form relationships ("total derivatives"). We examine three estimation methods that produce "total derivative estimates" without having to model and estimate each separate equation. These methods produce a unique total derivative estimate for every observation, where the differences in these estimates are produced by omitted variables. A plot of these estimates over time shows how the estimated relationship has evolved over time due to omitted variables. A moving 95% confidence interval (constructed like a moving average) means that there is only a five percent chance that the next total derivative would lie outside that confidence interval if the recent variability of omitted variables does not increase. Simulations show that two of these methods produce much less error than ignoring the omitted variables problem does when the importance of omitted variables noticeably exceeds random error. In an example, the spread rate of COVID-19 is estimated for Brazil, Europe, South Africa, the UK, and the USA.