Sorry for my long absence. I had some health problems. I will get back to the economic problem soon.
Here is a plot of the costs of weather disasters in the USA since 1980 – data from the NOAA website, https://www.ncdc.noaa.gov/billions/time-series . These are the disasters costing more than $1,000,000,000. I fit the exponential trend by fitting a linear trend to the log of the cost data plus 1 (since there was a year with no billion dollar storms and the log of zero is minus infinity, while the log of 1 is zero), then taking the exponential of the fitted line and subtracting 1 from the result. I find the result scary, particularly with the costs of 2005 and 2017. These costs are inflation adjusted.
The Greenhouse Effect
Here is a plot that I did last year of a time series model, where I fit temperature anomaly to sunspot numbers, carbon dioxide levels, and the ENSO index.
Here is the R output.
arima(x = temp.anomaly.7.71.to.11.13, order = c(3, 0, 0), seasonal = c(2, 0, 0), xreg = xmat)
ar1 ar2 ar3 sar1 sar2 intercept enso co2 sunspot
0.4738 0.1751 0.0954 0.1187 0.1391 -2.9108 0.0563 0.0089 5e-04
s.e. 0.0241 0.0265 0.0242 0.0246 0.0243 0.1573 0.0074 0.0005 2e-04
sigma^2 estimated as 0.01281: log likelihood = 1297.64, aic = -2575.27
The temperature anomaly is from Berkeley Earth of monthly global average temperature data for land and ocean, http://berkeleyearth.org/data. The temperature series goes from July 1871 to November 2013.
The data for the sunspots come from the WDC-SILSO at the Royal Observatory of Belgium, Brussels, http://sidc.oma.be/silso/datafiles, where the data is the previous data from the site (the data changed in July of 2015). The sunspot series goes from April 1871 to August 2013.
The data for the CO2 level is from the NOAA website, The CO2 level has been smoothed by a twelve month moving average and some work went into combining the two series. See https://vanwardstat.wordpress.com/2015/08/14/fitting-sunspot-numbers-and-co2-concentrations-to-temperature-anomalies/ The data go from July 1871 to November 2013.
The index for the ENSO, at NOAA, has been averaged for the years for which the two data sets overlap and the resulting series has been shifted to the right by one half month using the average of two consecutive values. The data are at https://www.esrl.noaa.gov/psd/enso/mei.ext/table.ext.html and https://www.esrl.noaa.gov/psd/enso/mei/table.html. The seasonal component of the ENSO index was removed with a twelve month moving average. The data run from July 1871 to November 2013.
This is a quick and dirty regression. That the model fits so well is remarkable. Maybe someone who is getting paid for the work will do a more careful job.