# Fully Modified OLS

### Description

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

### Usage

1 2 |

### Arguments

`x` |
[ |

`y` |
[ |

`deter` |
[ |

`kernel` |
[ |

`bandwidth` |
[ |

`demeaning` |
[ |

`check` |
[ |

`...` |
Arguments passed to |

### Details

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

*y = δ * D + β * x + u*

with *D* as the deterministics matrix.
Then *θ = (δ', β')'* 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.

### See Also

Other cointReg: `cointRegD`

,
`cointRegIM`

, `cointReg`

,
`plot.cointReg`

, `print.cointReg`

### Examples

1 2 3 4 5 6 7 8 9 | ```
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)
``` |