wu.hausman.test: A Wu-Hausman Test for a single endogenous variable
In skranz/sktools: Helpful functions used in my courses

See e.g. Green (2003) Econometric Analysis for a description of the Wu-Hausman-Test

1	wu.hausman.test(y, X.exo, X.endo, Z)

`y`	the vector of dependent variables
`X`	the matrix of explanatory variables (endogenos & exogenous)
`Z`	the matrix of instruments (excluded & included instruments)
`endo`	vector or matrix of variables that might be endogenous

## Not run: 
  library(sktools)  
  # Ice cream model
  T = 100
  beta0 = 100; beta1  = -1; beta2 = 40
  
  s   = rep(0:1, length.out=T) # Season: winter summer fluctuating
  eps = rnorm(T,0,2)
  c   = runif(T,10,20)
  
  # Optimal price if the firm knows season s and u
  p = (beta0+beta2*s+eps - beta1*c) / (2*-beta1)
  
  # Alternatively: prices are a random markup above cost c
  #p = c*runif(T,1,1.1)
  
  # Compute demand
  q = beta0 + beta1*p+ beta2*s + eps

  
  
  # Matrix of instruments
  Z = cbind(1,c,s)
  
  # Run the Wu-Hausman test for testing endogeniety of p
  wu.hausman.test(y=q,X.exo=cbind(1,s),X.endo=p,Z=Z)

  ###########################################################################################
  # Run a systematic simulation study of 
  # the Wu-Hausman Test
  ###########################################################################################

  # This function simulates and estimates a demand function and
  # returns the p-value of a Wu-Hausman test for endogeniety of the price
  sim.and.test = function() {
    # Ice cream model
    T = 100
    beta0 = 100; beta1  = -1; beta2 = 40
    
    s   = rep(0:1, length.out=T) # Season: winter summer fluctuating
    eps = rnorm(T,0,2)
    c   = runif(T,10,20)
    
    # Optimal price if the firm knows season s and u
    p = (beta0+beta2*s+eps - beta1*c) / (2*-beta1)
    
    # Alternatively: prices are a random markup above cost c
    p = c*runif(T,1,1.1)
    
    # Compute demand
    q = beta0 + beta1*p+ beta2*s + eps
    
    # Matrix of instruments
    Z = cbind(1,c,s)
    
    # Run the Wu-Hausman test for testing endogeniety of p
    wu.hausman.test(y=q,X.exo=cbind(1,s),X.endo=p,Z=Z)$p.value
  }

  # Perform a simulation study of our implementation of the Wu-Hausman test
  sim = simulation.study(sim.and.test,repl=1000)

  # I just need to adapt the results (won't be neccessary in a
  # newer version of sktools)
  sim = as.data.frame(sim)
  colnames(sim)[2] = "p.value"
  
  # Show the results and draw a histogram
  head(sim)
  hist(sim$p.value)
  # If the data is generated such that the Null hypothesis that
  # p is exogenous holds, then the p-values should be uniformly
  # distributed.
  
  # Use a Kolmogorov-Smirnov Test for whether p-values are uniformely distributed 
  #ks.test(sim$p.value,"punif",min=0,max=1)
  
  

## End(Not run)