cointRegFM {cointReg} R Documentation

## Fully Modified OLS

### Description

Computes the Phillips and Hansen (1990) Fully Modified OLS estimator.

### Usage

cointRegFM(x, y, deter, kernel = c("ba", "pa", "qs", "tr"),
bandwidth = c("and", "nw"), demeaning = FALSE, check = TRUE, ...)


### Arguments

 x [numeric | matrix | data.frame] RHS variables on which to apply the FM-OLS estimation (see Details). y [numeric | matrix | data.frame] LHS variable(s) on which to apply the FM-OLS estimation (see Details). Usually one-dimensional, but a matrix or data.frame with more than one column is also possible. deter [numeric | matrix | data.frame | NULL] Deterministic variable to include in the equation (see Details). If it's NULL or missing, no deterministic variable is included in the model. kernel [character(1)] The kernel function to use for calculating the long-run variance. Default is Bartlett kernel ("ba"), see Details for alternatives. bandwidth [character(1) | integer(1)] The bandwidth to use for calculating the long-run variance. Default is Andrews (1991) ("and"), an alternative is Newey West (1994) ("nw"). demeaning [logical] Demeaning of residuals in getLongRunVar. Default is FALSE. check [logical] Wheather to check (and if necessary convert) the arguments. See checkVars for further information. ... Arguments passed to getBandwidthNW.

### Details

The equation for which the FM-OLS estimator is calculated:

y = \delta \cdot D + \beta \cdot x + u

with D as the deterministics matrix. Then \theta = (\delta', \beta')' is the full parameter vector.

The calculation of t-values and the variance-covariance matrix is only possible, if y is one-dimensional.

### Value

[cointReg]. List with components:

delta [numeric | matrix]

coefficients as vector / matrix

beta [numeric | matrix]

coefficients as vector / matrix

theta [numeric | matrix]

combined coefficients of beta and delta as vector / matrix

sd.theta [numeric]

standard errors for theta

t.theta [numeric]

t-values for theta

p.theta [numeric]

p-values for theta

residuals [numeric]

FM-OLS residuals (first value is always missing)

omega.u.v [numeric]

conditional long-run variance based on OLS residuals.

varmat [matrix]

variance-covariance matrix

Omega [list]

the whole long-run variance matrix and parts of it

beta.OLS [numeric | matrix]

OLS coefficients as vector / matrix

delta.OLS [numeric | matrix]

OLS coefficients as vector / matrix

u.OLS [numeric]

OLS residuals

bandwidth [list]

number and name of bandwidth

kernel [character]

abbr. name of kernel type

### References

• Phillips, P.C.B. and B. Hansen (1990): "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, 57, 99–125, DOI:10.2307/2297545.

Other cointReg: cointRegD, cointRegIM, cointReg, plot.cointReg, print.cointReg

### Examples

set.seed(1909)
x1 = cumsum(rnorm(100, mean = 0.05, sd = 0.1))
x2 = cumsum(rnorm(100, sd = 0.1)) + 1
x3 = cumsum(rnorm(100, sd = 0.2)) + 2
x = cbind(x1, x2, x3)
y = x1 + x2 + x3 + rnorm(100, sd = 0.2) + 1
deter = cbind(level = 1, trend = 1:100)
test = cointRegFM(x, y, deter, kernel = "ba", bandwidth = "and")
print(test)



[Package cointReg version 0.2.0 Index]