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!)

Using the formula , where p_tis the annual percentage rate of inflation between years t–1 and t, and p_t is the value of the CPI in year t, calculate p_t 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
country A for the period 1980-2010.
country B for the period 1980-2010.
Assuming that the annual inflation rates of Countries A and B are normally distributed, and interpreting each country’s data on p_tfor 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:
95% confidence interval for the population mean inflation rate of Country A.
99% confidence interval for the population mean inflation rate of Country A.
95% confidence interval for the population mean inflation rate of Country B.
90% confidence interval for the population mean inflation rate of Country B.
Assuming that the annual inflation rates of Countries A and B are normally distributed, and interpreting each country’s data on p_tas 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

Country B’s (population) mean inflation throughout the period 2000-2010 was less than 3.5%.

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 p_tfor the two periods as independent samples.]
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 p_tfor 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).

Calculate the probability that Country C’s inflation rate in any future year is less than 1.5%.

Calculate the probability that Country C’s inflation rate in any future year is greater than 2.5%.

Calculate the probability that Country C’s average inflation rate over the next 4 years is greater than 2%.

Using the data on p_tin 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.

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

Calculate the probability that Country D’s inflation target will be breached in exactly 2 of the next 6 years.

Answer:

Years	Austria	Belgium	Finland	France	Germany	Ireland	Italy	Luxembourg	Netherlands	Spain	Australia	Denmark	Japan	Korea	Malaysia	New Zealand	Norway	Singapore	Sweden	Switzerland	UK	US
1979	44.7	46.54	37.9	43.3731	54.5	26.3	19.9	311.76	51.87	21.318	44.7	42.9	75	23.7	40.1	236.8	37.1	56.854	92.2	52.87	35.6	229.9
1980	47.6	50.05	43.2	49.2937	57.6	31.1	23.8	333.57	55.31	24.561	48.8	47.5	80.6	31.3	43	275.1	42.1	60.3	105.2	55.21	41	258.4
1981	50.7	54.13	47.4	56.2002	61.5	38.3	28.2	360.39	59.35	28.099	54.3	53.3	84.1	35.6	46.6	318.2	47.2	66.568	114.9	58.85	45.9	281.5
1982	53.1	58.51	51.6	61.6335	64.3	43	32.8	397.96	61.88	32.035	60.3	58.1	85.6	37.3	49.2	366.9	52.7	67.141	125.9	62.09	48.4	292.4
1983	55.1	62.7	56	67.3363	66	47.5	36.8	429.89	63.74	35.95	65.5	61.7	87.1	38	50.7	380.1	56.4	67.935	137.5	63.41	51	303.5
1984	57.9	66.06	59.4	71.8411	67.3	50.7	40.3	439.7	65.52	39.195	67.2	65.1	89.4	38.9	51.6	415.9	59.8	68.568	148.8	65.25	53.3	315.5
1985	59.6	68.71	62.2	75.2196	68.4	53.2	43.8	457.89	66.58	42.4	72.7	67.4	90.6	40.1	52.1	479.4	63.2	69.062	157.1	67.37	56.3	327.4
1986	60.2	69.12	64.1	76.815	67.6	54.8	45.7	451.39	66.39	45.9	79.8	70.4	90.1	40.7	52.9	566.8	68.8	68.138	162.3	67.39	58.4	331.1
1987	61.2	70.12	66.8	79.2082	68.4	56.5	48	454.34	66.06	48.011	85.5	73.2	90.6	43.1	53.1	621.1	73.9	69.195	170.7	68.67	60.6	345.7
1988	62.3	71.47	71.1	81.6482	69.7	58	50.6	463.05	66.85	50.816	92	76.6	91.4	46.2	54.9	650.4	78	70.179	180.9	70	64.7	360.9
1989	64.2	74.04	75.8	84.5575	71.7	60.7	53.8	481.16	67.72	54.316	99.2	80.3	93.8	48.6	56.1	697.2	81.3	72.504	192.8	73.52	68.2	377.6
1990	66.4	76.63	79.6	87.3	73.7	62.4	57.3	502.13	69.5	57.873	106	81.8	97.4	53.1	58	731.1	84.9	75.277	213.9	77.4	73.6	400.9
1991	68.4	78.76	82.9	89.9	78	64.6	60.7	515.22	72.08	61.072	107.6	83.7	100	58	60.4	738.2	87.3	77.454	230.8	81.44	78.8	413
1992	71.3	80.66	84.7	91.7	80.6	66.1	63.7	530.14	73.73	64.338	107.9	84.9	100.9	60.6	63.4	748	89.2	78.844	234.9	84.23	80.8	425.2
1993	73.8	82.83	86.1	93.6	84	67.1	66.5	549.29	75.66	67.507	110	86.2	101.8	64.1	65.5	758.4	90.9	80.861	244.3	86.32	82.6	436.8
1994	75.7	84.37	87.4	95.1	86.1	68.7	69.1	559.19	77.65	70.435	112.8	88.1	102.3	67.7	67.8	779.6	92.6	83.192	250.4	86.68	84.1	448.4
1995	77.1	85.6	87.4	97	87.4	70.3	73	566.23	78.95	73.477	118.5	89.8	101.8	70.9	70	802.4	94.6	83.899	256	88.37	86.5	459.9
1996	79.2	87.77	88.2	98.7	88.7	71.7	75.1	576.27	80.76	75.837	120.3	91.8	102.3	74.4	72.4	822.8	96.2	85.579	254.9	89.06	88.7	475
1997	80	88.77	89.9	99.8	90.5	73	76.5	584.75	82.63	77.365	120	93.8	104.1	79.3	74.4	829.7	98.5	87.331	259.1	89.41	90.4	483.2
1998	80.6	89.29	90.7	100	90.9	74.3	77.8	587.1	84.1	78.452	121.9	95.4	104.7	82.4	78.4	832.7	100.8	86.087	256.2	89.26	91.7	491
1999	81.7	91.02	92.5	101.3	91.9	76.8	79.5	600.49	85.91	80.741	124.1	98.4	103.4	83.6	80.3	836.9	103.6	86.673	259.6	90.74	92.7	504.1
2000	83.8	93.29	95.3	102.9	93.8	81.3	81.6	621.32	88.14	83.935	131.3	100.8	102.9	85.9	81.3	870.2	106.7	88.464	262.5	92.1	93.7	521.1
2001	85.4	95.33	97	104.3	95.3	84.7	83.5	632.02	91.8	86.208	135.4	103	101.2	88.6	82.2	886	108.9	87.948	269.5	92.4	94.5	529.2
2002	87	96.63	98.6	106.7	96.4	88.9	85.9	646.15	94.32	89.654	139.5	105.6	100.9	91.9	83.6	910.1	111.9	88.337	275.1	93.22	95.9	541.9
2003	88.1	98.31	99.2	109	97.4	90.7	88.1	659.49	95.92	91.989	142.8	107.1	100.5	95	84.6	924.3	112.6	88.994	278.6	93.78	97.2	552.1
2004	90.6	100.55	99.6	111.3	99.6	93.1	89.8	672.74	96.99	94.957	146.5	108.4	100.8	97.9	86.3	949.3	113.8	89.965	279.4	95.02	98.6	570.1
2005	92	103.45	100.2	113	101	95.3	91.6	689.43	98.97	98.504	150.6	110.8	100.1	100.5	89.1	979.2	115.9	91.148	281.8	95.98	100.7	589.4
2006	93.2	105.15	102.4	114.73	102.4	100	93.3	705.37	99.96	101.131	155.5	112.8	100.5	102.6	91.8	1005	118.5	91.924	286.43	96.58	103.4	604.5
2007	96.4	108.4	105.1	117.7	105.6	104.7	95.8	728.22	101.83	105.399	160.1	115.4	101.4	106.3	94	1037	121.8	95.767	296.32	98.51	105.6	629.174
2008	97.8	111.25	108.7	118.88	106.8	105.9	97.9	735.66	103.81	106.909	166	118.2	101.8	110.7	98.2	1072	124.4	100.89	298.99	99.2	109.9	629.751
2009	99	111.54	108.1	119.96	107.8	100.6	98.9	748.4	104.96	107.758	169.5	119.9	100	113.8	99.2	1093	126.9	100.374	301.69	99.48	112	646.887
2010	101.2	115	111.3	122.08	109.6	101.9	100.8	768.96	106.99	110.979	174	123.3	99.6	117.8	101.2	1137	130.4	104.971	308.73	100	115.6	656.563

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