How to use gdal_rasterize with postgis vector?

I’m trying to convert a multipolygon vector layer to a raster using the GDAL tool gdal_rasterize. The command I am using is:

gdal_rasterize -b 1 -burn -9999 PG:"dbname=db password=password" 
    auckland auckland.png

However, it seems my specification of the source for the postgis layer is incorrect as I get an

ERROR 4: 'auckland.png' does not exist in the file system,
and is not recognised as a supported dataset name.` 

So how do I successfully connect to postgres and export a vector as a tif? Is it possible?

Numerous other attempts have included:

gdal_rasterize -b 1 -i -burn -9999 PG:"dbname=db password=" -l 
    auckland auckland.png

gdal_rasterize -b 1 -i -burn -9999 -l auckland PG:"dbname=db 
    password=password" auckland.png

And this one from Roger’s Rants:

gdal_rasterize -b 1 -i -burn -9999 PG:'host=localhost dbname='unep'' 
    -sql "SELECT ST_buffer(the_geom, .12) from coastlines where name='Poland'" 
    Poland_elev.tif

When I use ogr2ogr to export the layer out of postgres as a shapefile, and then gdal_rasterize to convert to a .tif file it all works smoothly.

Using GDAL 1.11.2 version on Ubuntu 15.10.

Still no love with either:

gdal_rasterize -b 1 -burn -9999 PG:"dbname=db password=pwd" 
    -l auckland auckland.tif

or:

gdal_rasterize -b 1 -burn -9999 -l auckland PG:"dbname=db 
    password=pwd" auckland.tif