Several Authors Have Tried to Measure the "Persistence" in U $$u r _ { i , t } = \beta _ { 0 } + \beta _ { 1 } \times u r _ { i , t - k } + z _ { i , t }$$

Essay

Several authors have tried to measure the "persistence" in U.S state unemployment rates
by running the following regression: $$u r _ { i , t } = \beta _ { 0 } + \beta _ { 1 } \times u r _ { i , t - k } + z _ { i , t }$$ where $u r$ is the state unemployment rate, $i$ is the index for the $i$ -th state, $t$ indicates a time period, and typically $k \geq 10$ . (a)Explain why finding a slope estimate of one and an intercept of zero is typically
interpreted as evidence of "persistence."