Final answer:
To declare a local variable for writing to a text file in Java, use the PrintWriter class. You can initialize it with 'new PrintWriter(new FileWriter("output.txt"));', and you must handle potential IOExceptions.
Step-by-step explanation:
To declare a local variable's output that is suitable for referring to an object that provides methods for writing to a text file, you would typically use a class that includes such capabilities. An example in Java would be the PrintWriter class. Here's how you might declare such a variable:
PrintWriter output = new PrintWriter(new FileWriter("output.txt"));
This creates a PrintWriter instance that will write to a file called 'output.txt'. Make sure to handle IOExceptions, which can occur when attempting to write to a file.