# waldtest

##### Compute Wald test for joint restrictions on coefficients

Compute a Wald test for a linear hypothesis on the coefficients. Also supports Delta-approximation for non-linear hypotheses.

##### Usage

```
waldtest(object, R, r, type = c("default", "iid", "robust", "cluster"),
lhs = NULL, df1, df2)
```

##### Arguments

- object
object of class

`"felm"`

, a result of a call to`felm`

.- R
matrix, character, formula, function, integer or logical. Specification of which exclusions to test.

- r
numerical vector.

- type
character. Error structure type.

- lhs
character. Name of left hand side if multiple left hand sides.

- df1
integer. If you know better than the default df, specify it here.

- df2
integer. If you know better than the default df, specify it here.

##### Details

The function `waldtest`

computes a Wald test for the H0: R beta = r,
where beta is the estimated vector `coef(object)`

.

If `R`

is a character, integer, or logical vector it is assumed to
specify a matrix which merely picks out a subset of the coefficients for
joint testing. If `r`

is not specified, it is assumed to be a zero
vector of the appropriate length.

`R`

can also be a formula which is linear in the estimated
coefficients, e.g. of the type `~Q-2|x-2*z`

which will test the joint
hypothesis Q=2 and x=2*z.

If `R`

is a function (of the coefficients), an approximate Wald test
against H0: `R(beta) == 0`

, using the Delta-method, is computed.

In case of an IV-estimation, the names for the endogenous variables in
`coef(object)`

are of the type `"`Q(fit)`"`

which is a bit dull to
type; if all the endogenous variables are to be tested they can be specified
as `"endovars"`

. It is also possible to specify an endogenous variable
simply as `"Q"`

, and `waldtest`

will add the other syntactic sugar
to obtain `"`Q(fit)`"`

.

The `type`

argument works as follows. If `type=='default'`

it is
assumed that the residuals are i.i.d., unless a cluster structure was
specified to `felm`

. If `type=='robust'`

, a heteroscedastic
structure is assumed, even if a cluster structure was specified in
`felm`

.

##### Value

The function `waldtest`

computes and returns a named numeric
vector containing the following elements.

`p`

is the p-value for the Chi^2-test`chi2`

is the Chi^2-distributed statistic.`df1`

is the degrees of freedom for the Chi^2 statistic.`p.F`

is the p-value for the F statistics`F`

is the F-distributed statistic.`df2`

is the additional degrees of freedom for the F statistic.

The return value has an attribute `'formula'`

which encodes the
restrictions.

##### See Also

##### Examples

```
# NOT RUN {
x <- rnorm(10000)
x2 <- rnorm(length(x))
y <- x - 0.2*x2 + rnorm(length(x))
#Also works for lm
summary(est <- lm(y ~ x + x2 ))
# We do not reject the true values
waldtest(est, ~ x-1|x2+0.2|`(Intercept)`)
# The Delta-method coincides when the function is linear:
waldtest(est, function(x) x - c(0, 1, -0.2))
# }
```

*Documentation reproduced from package lfe, version 2.8-2, License: Artistic-2.0*