vcovPL {sandwich} | R Documentation

## Clustered Covariance Matrix Estimation for Panel Data

### Description

Estimation of sandwich covariances a la Newey-West (1987) and Driscoll and Kraay (1998) for panel data.

### Usage

    vcovPL(x, cluster = NULL, order.by = NULL,
      kernel = "Bartlett", sandwich = TRUE, fix = FALSE, ...)

    meatPL(x, cluster = NULL, order.by = NULL,
      kernel = "Bartlett", lag = "NW1987", bw = NULL,
      adjust = TRUE, ...)

### Arguments

`x` | a fitted model object.
`cluster` | a variable indicating the clustering of observations, a `list` (or `data.frame`) thereof, or a formula specifying which variables from the fitted model should be used (see examples). By default (`cluster = NULL`), either `attr(x, "cluster")` is used (if any) or otherwise every observation is assumed to be its own cluster.
`order.by` | a variable, list/data.frame, or formula indicating the aggregation within time periods. By default `attr(x, "order.by")` is used (if any) or otherwise observations within clusters are assumed to be ordered.
`kernel` | a character specifying the kernel used. All kernels described in Andrews (1991) are supported, see `kweights`.
`lag` | character or numeric, indicating the lag length used. Three rules of thumb (`"max"` or equivalently `"P2009"`, `"NW1987"`, or `"NW1994"`) can be specified, or a numeric number of lags can be specified directly. By default, `"NW1987"` is used.
`bw` | numeric. The bandwidth of the kernel which by default corresponds to `lag + 1`. Only one of `lag` and `bw` should be used.
`sandwich` | logical. Should the sandwich estimator be computed? If set to `FALSE` only the meat matrix is returned.
`fix` | logical. Should the covariance matrix be fixed to be positive semi-definite in case it is not?
`adjust` | logical. Should a finite sample adjustment be made? This amounts to multiplication with n/(n - k) where n is the number of observations and k is the number of estimated parameters.
`...` | arguments passed to the `metaPL` or `estfun` function, respectively.

### Details

`vcovPL` is a function for estimating the Newey-West (1987) and Driscoll and Kraay (1998) covariance matrix. Driscoll and Kraay (1998) apply a Newey-West type correction to the sequence of cross-sectional averages of the moment conditions (see Hoechle (2007)). For large T (and regardless of the length of the cross-sectional dimension), the Driscoll and Kraay (1998) standard errors are robust to general forms of cross-sectional and serial correlation (Hoechle (2007)). The Newey-West (1978) covariance matrix restricts the Driscoll and Kraay (1998) covariance matrix to no cross-sectional correlation.

The function `meatPL` is the work horse for estimating the meat of Newey-West (1978) and Driscoll and Kraay (1998) covariance matrix estimators. `vcovPL` is a wrapper calling `sandwich` and `bread` (Zeileis 2006).

Default lag length is the `"NW1987"`. For `lag = "NW1987"`, the lag length is chosen from the heuristic floor[T^{(1/4)}]. More details on lag length selection in Hoechle (2007). For `lag = "NW1994"`, the lag length is taken from the first step of Newey and West's (1994) plug-in procedure.

The `cluster`/`order.by` specification can be made in a number of ways: Either both can be a single variable or `cluster` can be a `list`/`data.frame` of two variables. If `expand.model.frame` works for the model object `x`, the `cluster` (and potentially additionally `order.by`) can also be a `formula`. By default (`cluster = NULL, order.by = NULL`), `attr(x, "cluster")` and `attr(x, "order.by")` are checked and used if available. If not, every observation is assumed to be its own cluster, and observations within clusters are assumed to be ordered accordingly. If the number of observations in the model `x` is smaller than in the original `data` due to `NA` processing, then the same `NA` processing can be applied to `cluster` if necessary (and `x$na.action` being available).

### Value

A matrix containing the covariance matrix estimate.

### References

Andrews DWK (1991). “Heteroscedasticity and Autocorrelation Consistent Covariance Matrix Estimation”, Econometrica, 817–858.

Berger S, Graham N, Zeileis A (2017). “Various Versatile Variances: An Object-Oriented Implementation of Clustered Covariances in R.” Technical Report 2017-12, Working Papers in Economics and Statistics, Research Platform Empirical and Experimental Economics, Universitaet Innsbruck. http://EconPapers.RePEc.org/RePEc:inn:wpaper:2017-12.

Driscoll JC & Kraay AC (1998). “Consistent Covariance Matrix Estimation with Spatially Dependent Panel Data”, The Review of Economics and Statistics, 80(4), 549–560.

Hoechle D (2007). “Robust Standard Errors for Panel Regressions with Cross-Sectional Dependence”, Stata Journal, 7(3), 281–312.

Newey WK & West KD (1987). “Hypothesis Testing with Efficient Method of Moments Estimation”, International Economic Review, 777-787.

Newey WK & West KD (1994). “Automatic Lag Selection in Covariance Matrix Estimation”, The Review of Economic Studies, 61(4), 631–653.

White H (1980). “A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity”, Econometrica, 817–838. doi: 10.2307/1912934

Zeileis A (2004). “Econometric Computing with HC and HAC Covariance Matrix Estimator”, Journal of Statistical Software, 11(10), 1–17. doi: 10.18637/jss.v011.i10

Zeileis A (2006). “Object-Oriented Computation of Sandwich Estimators”, Journal of Statistical Software, 16(9), 1–16. doi: 10.18637/jss.v016.i09

### See Also

`vcovCL`, `vcovPC`

### Examples

    ## Petersen's data
    data("PetersenCL", package = "sandwich")
    m <- lm(y ~ x, data = PetersenCL)

    ## Driscoll and Kraay standard errors
    ## lag length set to: T - 1 (maximum lag length)
    ## as proposed by Petersen (2009)
    sqrt(diag(vcovPL(m, cluster = ~ firm + year, lag = "max", adjust = FALSE)))

    ## lag length set to: floor(4 * (T / 100)^(2/9))
    ## rule of thumb proposed by Hoechle (2007) based on Newey & West (1994)
    sqrt(diag(vcovPL(m, cluster = ~ firm + year, lag = "NW1994")))

    ## lag length set to: floor(T^(1/4))
    ## rule of thumb based on Newey & West (1987)
    sqrt(diag(vcovPL(m, cluster = ~ firm + year, lag = "NW1987")))

    ## the following specifications of cluster/order.by are equivalent
    vcovPL(m, cluster = ~ firm + year)
    vcovPL(m, cluster = PetersenCL[, c("firm", "year")])
    vcovPL(m, cluster = ~ firm, order.by = ~ year)
    vcovPL(m, cluster = PetersenCL$firm, order.by = PetersenCL$year)

    ## these are also the same when observations within each
    ## cluster are already ordered
    vcovPL(m, cluster = ~ firm)
    vcovPL(m, cluster = PetersenCL$firm)

[Package sandwich version 2.5-1 Index]