5 Suppose we have monthly data on the CPI and quarterly data

5. Suppose we have monthly data on the CPI and quarterly data on the GDP. We have information only on the first two periods. We are given that the CPI increased by 0.5% from January to February, while GDP increased by 1.3% from Q1 to Q2. We would like to see if how growth and inflation rates compare. What would be the “annualized” growth rate of each?

CPI growth rate=6.17%; GDP growth rate=5.3%

CPI growth rate=6.17%; GDP growth rate=5.2%

CPI growth rate=2.02%; GDP growth rate=5.3%

CPI growth rate=2.02%; GDP growth rate=5.2%

Solution

CPI from monthly rate to annual rate -

1) Divide the rate by 100

   0.5% = 0.5/100 = 0.005

2) Add 1

   1+0.005 = 1.005

3) Raise the value to 12 (because there are 12 months in a year)

   1.005¹² =1.06167

4) Substract 1

   1.06167 - 1 = 0.617

5) Multiply by 100 to get the percentage

   0.617 * 100 = 6.17%

So the annual CPI is 6.17%

GDP from quarterly rate to annual rate -

1) Divide the rate by 100

   1.3/100 = 0.013

2) Add 1

   1+0.013 = 1.013

3) Raise the value to 4 (because there are four quarters in a year)

   1.013⁴ = 1.053

4) Substract 1

   1.053 - 1 = 0.053

5) Multiply by 100 to get the percentage

   0.053*100 = 5.3%

Sp CPI growth rate is 6.17% and GDP growth rate is 5.3%.