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ASB2411 Quantitative Methods for Business-Annual Consumer Price Index

In the spreadsheet file Country assignment_2017.xlsx (available on Blackboard), you have been assigned to study consumer price inflation in two countries, Country A and Country B. (The pair of countries assigned is different for each student).

Annual Consumer Price Index (CPI) data for the period 1979-2010 for your two assigned countries can be extracted from the spreadsheet file cpi.xlsx. (The data in this file for all other countries should be ignored!)

  1. Using the formula , where ptis the annual percentage rate of inflation between years t–1 and t, and pt is the value of the CPI in year t, calculate pt for each year from t=1980 to t=2010 for Country A and for Country B. Using these data, complete the following table of descriptive statistics
  2. country A for the period 1980-2010. 
  3. country B for the period 1980-2010. 
  4. Assuming that the annual inflation rates of Countries A and B are normally distributed, and interpreting each country’s data on ptfor the period 1980-1999 as a random sample of 20 observations drawn from a fixed population distribution of all possible inflation rates for each country, construct the following confidence intervals, commenting briefly on what the confidence interval is demonstrating:
  5. 95% confidence interval for the population mean inflation rate of Country A.
  6. 99% confidence interval for the population mean inflation rate of Country A.
  7. 95% confidence interval for the population mean inflation rate of Country B.
  8. 90% confidence interval for the population mean inflation rate of Country B.
  9. Assuming that the annual inflation rates of Countries A and B are normally distributed, and interpreting each country’s data on ptas a random sample, use appropriate hypothesis tests to evaluate the following assertions concerning the (population) mean inflation rates of Countries A and B. Use a significance level of α=0.05. Briefly comment on your answers.Country A’s (population) mean inflation throughout the period 1980-2010 was
  1. Country B’s (population) mean inflation throughout the period 2000-2010 was less than 3.5%. 
  1. Country A’s (population) mean inflation during the 11-year period of euro membership 2000-2010 was significantly less than Country A’s (population) mean inflation during the 20-year period prior to euro membership 1980-1999. [Treat the observations on ptfor the two periods as independent samples.]
  2. Country A’s (population) mean inflation during the period 2000-2010 was significantly different from Country B’s (population) mean inflation during the same period. [Treat the samples of observations on ptfor the two countries during the period 2000-2010 as matched pairs.], an applicant for EU membership, has an annual inflation rate that is known to behave as a normally distributed random variable, with a population mean and population variance identical to the numbers for the sample mean and sample variance reported for Country A during the period 2000-2010 (see Q1).
  1. Calculate the probability that Country C’s inflation rate in any future year is less than 1.5%. 
  1. Calculate the probability that Country C’s inflation rate in any future year is greater than 2.5%. 
  1. Calculate the probability that Country C’s average inflation rate over the next 4 years is greater than 2%.
  1. Using the data on ptin Country B for t=1980 to t=1999 (20 observations), calculate p = the proportion of years in which Country B’s rate of inflation was greater than 5%.

In a certain emerging country D, which has an economic structure similar to that of Country B during the 1980s and 1990s, episodes of annual inflation above 5% are known to occur randomly, with a probability of p (as calculated above). The Governor of Country D’s central bank had set a maximum annual inflation target of 5% in each of the next 6 years.

  1. Calculate the probability that Country D’s inflation target will not be breached in any of the next 6 years. 
  1. Calculate the probability that Country D’s inflation target will be breached in exactly 2 of the next 6 years. 

Answer:

YearsAustriaBelgiumFinlandFranceGermanyIrelandItalyLuxembourgNetherlandsSpainAustraliaDenmarkJapanKoreaMalaysiaNew ZealandNorwaySingaporeSwedenSwitzerlandUKUS
197944.746.5437.943.373154.526.319.9311.7651.8721.31844.742.97523.740.1236.837.156.85492.252.8735.6229.9
198047.650.0543.249.293757.631.123.8333.5755.3124.56148.847.580.631.343275.142.160.3105.255.2141258.4
198150.754.1347.456.200261.538.328.2360.3959.3528.09954.353.384.135.646.6318.247.266.568114.958.8545.9281.5
198253.158.5151.661.633564.34332.8397.9661.8832.03560.358.185.637.349.2366.952.767.141125.962.0948.4292.4
198355.162.75667.33636647.536.8429.8963.7435.9565.561.787.13850.7380.156.467.935137.563.4151303.5
198457.966.0659.471.841167.350.740.3439.765.5239.19567.265.189.438.951.6415.959.868.568148.865.2553.3315.5
198559.668.7162.275.219668.453.243.8457.8966.5842.472.767.490.640.152.1479.463.269.062157.167.3756.3327.4
198660.269.1264.176.81567.654.845.7451.3966.3945.979.870.490.140.752.9566.868.868.138162.367.3958.4331.1
198761.270.1266.879.208268.456.548454.3466.0648.01185.573.290.643.153.1621.173.969.195170.768.6760.6345.7
198862.371.4771.181.648269.75850.6463.0566.8550.8169276.691.446.254.9650.47870.179180.97064.7360.9
198964.274.0475.884.557571.760.753.8481.1667.7254.31699.280.393.848.656.1697.281.372.504192.873.5268.2377.6
199066.476.6379.687.373.762.457.3502.1369.557.87310681.897.453.158731.184.975.277213.977.473.6400.9
199168.478.7682.989.97864.660.7515.2272.0861.072107.683.71005860.4738.287.377.454230.881.4478.8413
199271.380.6684.791.780.666.163.7530.1473.7364.338107.984.9100.960.663.474889.278.844234.984.2380.8425.2
199373.882.8386.193.68467.166.5549.2975.6667.50711086.2101.864.165.5758.490.980.861244.386.3282.6436.8
199475.784.3787.495.186.168.769.1559.1977.6570.435112.888.1102.367.767.8779.692.683.192250.486.6884.1448.4
199577.185.687.49787.470.373566.2378.9573.477118.589.8101.870.970802.494.683.89925688.3786.5459.9
199679.287.7788.298.788.771.775.1576.2780.7675.837120.391.8102.374.472.4822.896.285.579254.989.0688.7475
19978088.7789.999.890.57376.5584.7582.6377.36512093.8104.179.374.4829.798.587.331259.189.4190.4483.2
199880.689.2990.710090.974.377.8587.184.178.452121.995.4104.782.478.4832.7100.886.087256.289.2691.7491
199981.791.0292.5101.391.976.879.5600.4985.9180.741124.198.4103.483.680.3836.9103.686.673259.690.7492.7504.1
200083.893.2995.3102.993.881.381.6621.3288.1483.935131.3100.8102.985.981.3870.2106.788.464262.592.193.7521.1
200185.495.3397104.395.384.783.5632.0291.886.208135.4103101.288.682.2886108.987.948269.592.494.5529.2
20028796.6398.6106.796.488.985.9646.1594.3289.654139.5105.6100.991.983.6910.1111.988.337275.193.2295.9541.9
200388.198.3199.210997.490.788.1659.4995.9291.989142.8107.1100.59584.6924.3112.688.994278.693.7897.2552.1
200490.6100.5599.6111.399.693.189.8672.7496.9994.957146.5108.4100.897.986.3949.3113.889.965279.495.0298.6570.1
200592103.45100.211310195.391.6689.4398.9798.504150.6110.8100.1100.589.1979.2115.991.148281.895.98100.7589.4
200693.2105.15102.4114.73102.410093.3705.3799.96101.131155.5112.8100.5102.691.81005118.591.924286.4396.58103.4604.5
200796.4108.4105.1117.7105.6104.795.8728.22101.83105.399160.1115.4101.4106.3941037121.895.767296.3298.51105.6629.174
200897.8111.25108.7118.88106.8105.997.9735.66103.81106.909166118.2101.8110.798.21072124.4100.89298.9999.2109.9629.751
200999111.54108.1119.96107.8100.698.9748.4104.96107.758169.5119.9100113.899.21093126.9100.374301.6999.48112646.887
2010101.2115111.3122.08109.6101.9100.8768.96106.99110.979174123.399.6117.8101.21137130.4104.971308.73100115.6656.563

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