Many Countries That Experience Hyperinflation Do Not Have Market-Determined Interest $$m = \beta _ { 0 } \times ( 1 + \Delta \ln P ) ^ { \beta _ { 1 } } \times e ^ { u }$$

Essay

Many countries that experience hyperinflation do not have market-determined interest
rates.As a result, some authors have substituted future inflation rates into money demand
equations of the following type as a proxy: $$m = \beta _ { 0 } \times ( 1 + \Delta \ln P ) ^ { \beta _ { 1 } } \times e ^ { u }$$
( $m$ is real money, and $P$ is the consumer price index).
Income is typically omitted since movements in it are dwarfed by money growth and the inflation rate. Authors have then interpreted $\beta _ { 1 }$ as the "semi-elasticity" of the inflation rate. Do you see any problems with this interpretation?