capn (version 1.0.0)

psim: Simulation of P-approximation

Description

The function provides the P-approximation simulation.

Usage

psim(pcoeff, stock, wval = NULL, sdot = NULL)

Arguments

pcoeff

An approximation result from paprox function

stock

An array of stock variable

wval

(Optional for vfun) An array of \(W\)-value (need sdot simultaneously)

sdot

(Optional for vfun) An array of ds/dt, \(\dot{s}=\frac{ds}{dt}\) (need W simultaneously)

Value

A list of approximation resuts: shadow (accounting) prices, inclusive wealth, value function, stock, and W values. Use results$item (or results[["item"]]) to import each result item.

shadowp

Shadow price

vfun

Value function

stock

Stock

wval

W-value if wval is provided

Details

Let \(\hat{\beta}\) be the vector of approximation coefficents from the results of paprox function. The estimated shadow price (accounting) price of stock over the given approximation interval of \(s \in [a,b]\), \(\hat{p}\) can be calculated as:

\(\hat{p} = \mathbf{\mu}(s) \mathbf{\hat{\beta}}\).

The estimated value function is:

\( \hat{V} = \frac{1}{\delta} \left( W + \hat{p} \dot{s} \right) \).

For more detils see Fenichel and Abbott (2014) and Fenichel et al. (2016).

References

Fenichel, Eli P. and Joshua K. Abbott. (2014) "Natural Capital: From Metaphor to Measurement." Journal of the Association of Environmental Economists. 1(1/2):1-27. Fenichel, Eli P., Joshua K. Abbott, Jude Bayham, Whitney Boone, Erin M. K. Haacker, and Lisa Pfeiffer. (2016) "Measuring the Value of Groundwater and Other Forms of Natural Capital." Proceedings of the National Academy of Sciences .113:2382-2387.

See Also

aproxdef, paprox

Examples

## 1-D Reef-fish example: see Fenichel and Abbott (2014)
data("GOM")
nodes <- chebnodegen(param$nodes,param$lowerK,param$upperK)
simuDataP <- cbind(nodes,sdot(nodes,param),
                   dsdotds(nodes,param),dwds(nodes,param))
Aspace <- aproxdef(param$order,param$lowerK,param$upperK,param$delta)
pC <- paprox(Aspace,simuDataP[,1],simuDataP[,2],
             simuDataP[,3],simuDataP[,4])
GOMSimP <- psim(pC,simuDataP[,1],profit(nodes,param),simuDataP[,2])

# Shadow Price
plotgen(GOMSimP, xlabel="Stock size, s", ylabel="Shadow price")

# Value function and profit
plotgen(GOMSimP,ftype="vw",
        xlabel="Stock size, s",
        ylabel=c("Value Function","Profit"))