PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

204 MODELING FINANCIAL SCENARIOSUnemploymentThere are many plausible ways to link unemployment ratesto other economic variables. One approach to estimating unemploymentis based on the well-known Phillips curve. The Phillipscurve illustrates a common inverse relationship between unemploymentand inflation. The approach taken by Phillips seemsplausible: As the economy picks up, inflation increases to helptemper the demand-driven economy. At the same time, unemploymentfalls as firms hire to meet the increasing demand. Whenthe economy slows down, unemployment rises, and inflationarypressures subside.We also include a first-order autoregressive process in theunemployment process, in addition to the relationship suggestedby the Phillips curve:du t = ·u(¹ u ¡ u t )dt + ® u dq t + ¾ u dB ut : (3.19)It is expected that when inflation increases (dq t > 0), unemploymentdecreases (i.e., ® u < 0). One may argue that there isa lag between inflation and unemployment. To keep the modelsimple, we did not pursue any distributed lag approach.The discrete form of the unemployment model is shown asu t+1 = u t + ·u¹ u ¡ ·u¢t ¢ u t + ® u (q t+1 ¡ q t )+¾ u " utp¢t= ·u¹ u +(1¡ ·u¢t) p¢ u t + ® u (q t+1 ¡ q t )+¾ u " ut ¢t:(3.20)This suggests the following regression:u t+1 = ¯1 + ¯2u t + ¯3(q t+1 ¡ q t )+¾ u " 0 ut: (3.21)We use inflation data as described above and retrievemonthly unemployment data from the Bureau of Labor Statistics(http://www.bls.gov). Using data from 1948 to 2001 and