Would I use the subjunctive in this sentence?
It will affect the economy in a manner that is bad.
la afectará la economía de una manera que [es/sea] mala.
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The relative clause should be in the indicative, as it refers to a fact as expressed by the future "afectará":
Notice that, in a context of possibility rather than certainty, or with the negative, the subjunctive will be used:
Note 1: As you can see in my sentences above, I have eliminated "la". Since "la economía" is the direct object, using the pronoun "la" would generate a double direct object, and that is ungrammatical in Spanish.
Note 2: The relative clause "de una manera que es/sea mala" is really poor in the language. We would usually do away with the copulative verb and use a phrase like: "de un modo negativo".