Washington — The cost of building a new house -- now averaging about $78,000 nationwide -- could be slashed by cutting through local red tape, said inflation adviser Alfred Kahn and Assistant Housing Secretary Lawrence Simons. Test projects showed costs could be cut by between 20 and 33 percent. Reductions resulted from speeding up issuance of permits and using new building techniques. Calling the results of the projects in Hayward, Calif., Shreveport, La., and Allegheny county, Pa., "very exciting," Mr. Kahn said excessive local regulations add 20 percent to the cost of housing. Nationwide there are 20,000 different rules for home building.