This　paper　proposes　a　semiparametric　spatial　lag　model　and　develops　a　Bayesian　estimation　method　for　this　model.　In　the　estimation　of　the　model,　the　paper　combines　Reversible　Jump　Markov　Chain　Monte　Carlo　(RJMCMC)　algorithm,　random　walk　Metropolis　sampler,　and　Gibbs　sampling　techniques　to　sample　all　the　parameters.　The　paper　conducts　numerical　simulations　to　validate　the　proposed　Bayesian　estimation　theory　using　a　numerical　example.　The　simulation　results　demonstrate　satisfactory　estimation　performance　of　the　parameter　part　and　the　fitting　performance　of　the　nonparametric　function　under　different　spatial　weight　matrix　settings.　Furthermore,　the　paper　applies　the　constructed　model　and　its　estimation　method　to　an　empirical　study　on　the　relationship　between　economic　growth　and　carbon　emissions　in　China,　illustrating　the　practical　application　value　of　the　theoretical　results.　©　2024　by　the　authors.