Alternative Sampling Designs

Alternative Sampling Designs

Simple Random Sampling

Stratified Random Sampling

Cluster Sampling

1. Divide the population into non-overlapping areas or clusters

- Each cluster contains a wide variety of elements and the cluster is a miniature or microcosm of the population.

- Internally heterogeneous (the different with stratification)

- Commonly involves geographical locations (states, towns, companies, etc.)

2. Choose a number of clusters

3. Select element randomly from clusters

Two-stage sampling: if the clusters are too large, a second sets of clusters is taken from each original clusters

Advantages: convenient & lower cost

- The cost of sampling from the entire population is reduced

- Cluster sampling is less costly than simple/stratified random sampling if the cost of obtaining a frame is high or the cost of obtaining observations increases as the distance separating the elements increases.

Systematic Sampling (1-in-k systematic random sampling)

Randomized Response Sampling

- People often refute to give correct answers to sensitive questions that may embarrass them or be harmful to them is some way.

- Define

o Group A = people who have the characteristic of interest (giving false information)

o Group B = people who do not have the characteristic

o p =proportion of group A in the population (we want to estimate p without asking each person directly whether or not he/she belongs to group A (i.e. Have you given false information?)

-

Survey Sampling (ECON1320 – L10)

Survey Sampling (ECON1320 – L10)

Terms

1. Element: an object on which a measurement is take

2. Population: a collection of elements about which we wish to make an inference

3. Sampling units: non-overlapping collection of elements in the population

4. Sampling frame: a list of sampling units

5. Sample: a collection of sampling units drawn from a frame or frames

6. Efficient: an unbiased estimator is said to efficient if it has a lower variance than any other unbiased estimator. Such an estimator will, on average, yield smaller standard errors and narrower confidence intervals for a given sample size.

Errors in Survey Sampling

Non-sampling Errors

1. A faulty sampling frame (due to incomplete, out-of-date or otherwise unrepresentative)

2. Non-response (can maximize the response rate with a good questionnaire design, publicity well in advance, industry sponsorship, assurances of confidentiality, incentives)

3. Response and recording errors (due to errors in questionnaire design – ambiguous question, expectation errors – when answers to questions early in the interview condition the interviewer to expect particular responses to subsequent question, the manner of asking the question – when the interviewer is forced to deviate from the wording on the questionnaire)

4. Errors in the processing of data

Sampling Errors

- Is the difference between a sample statistic and the corresponding population parameter that occurs even with a random sample and a well-designed survey

- Is unavoidable consequence of being able to observe only a subset of the element in the population

- Is recognized in the statistical formula (e.g. a CI estimation = sample statistic +/- sampling error)

- Can be reduced by

o Increasing the sample size, and

o Using a different sampling method

Alternative Sampling Designs

Non –random samples

1. E.g. self selection surveys – invariably yield biased results.

Random samples:

1. Simple random sampling

a. SRS with replacement

b. SRS without replacement

2. Stratified random sampling

3. Cluster sampling

4. Systematic sampling

5. Randomized Response sampling

TBC…

Index Numbers (ECON1320 -L9)

Index Numbers (ECON1320 -L9)

Background on Index Numbers

1. Index numbers

a. Allow relative comparisons of a measure over time (i.e. intertemporal comparisons)

b. Especially useful in comparing changes in the levels of quantity, price or value (i.e. Price * Quantity) over time.

c. Are reported relative to a Base period Index whole value is equal to 100.

d. Measure changes in an individual item for changes in several variables.

Simple Index numbers

1. Price relative

a. Ist =Pt/Ps * 100

Unweighted Aggregate PI

1. Arithmetic Mean of PT (Simple Relative PI)

a. Ist = 1/n * [n ‘sum of’ i=1 (Pit/Pis)] *100

b. Dis. – consider every variables are equally important

2. Ratio of Unweighted Aggregate Prices (Simple Aggregate PI)

a. Ist = [ (n ‘sum of’ i=1 Pit) / (n ‘sum of’ i=1 Pis)] * 100

b. Dis. – each commodity has equal weight. Therefore, this index will be influenced greatly by those unit prices that are very much higher than the other.

Weighted Aggregate PI

1. Laspeyres PI (Fixed weight Index)

a. I (L on the top) st = [n ‘sum of’ i=1 Pit Qis] / [n ‘sum of’ i=1 Pis Qis] * 100

b. Uses the base quantities as weight

c. Measure change in the cost of living

i. Changes between the aggregate cost of base period quantities at current period prices and the aggregate cost of base period quantities at base period prices

d. Dis. – compare to Paasche PI

i. Reasonable if there is not much change in consumption pattern

ii. Unrealistic over time as it makes no allowance for reallocation of budget or technological advance etc.

iii. Might overestimate changes in COL (give large weights on commodities that have become relatively more exp [on the items which are relatively changed more in quantity from base yr])

e. Adv. – Practicable (low cost)

2. Paasche PI

a. I (P on the top) st = (n ‘sum of’ i=1 Pit Qit) / (n ‘sum of’ i=1 Pis Qit) * 100

b. Use period t quantities as weights

c. Measure change in COL

d. Dis. (Compare to Laspeyres)

i. underestimate COL (give large weights to item that are now relative less expensive [on the items which are relatively changed less in quantity from base yr] )

ii. higher cost incurred for data collection

3. Fisher PI

a. Fisher st = square root of (Laspeyres st * Paasche st)

b. Geometric average method

Changes of Base period

a. Irt = Ist / Isr * 100

P/s – the used of 4 corner rule in the changes (or chaining of base period)

境

如果能懂，一想就懂，如果不能懂，就等会懂的那一刻来临。决定懂或不懂，不是因为聪明，而是你所站的高度，不是站在原地苦思就能明白。

Volcker recession in US 1981

(W)

The 1981 recession is thought to have been caused by the tight-money adopted by Paul Volcker, chairman of the Federal Reserve Board, before Ronald Reagan took office. Reagan supported that policy. Economist Walter Heller, chairman of the Council of Economic Advisers in the 1960s, said that “I call it a Reagan-Volcker-Cater recession.” The resulting taming of inflation did, however, set the stage for a robust growth period during Reagan’s administration.

Ricardian equivalence

(W)

The Ricardian equivalence proposition (also known as the Barro-Ricardo equivalence theorem) is an economic theory that suggests consumer internalize the government’s budget constraint and this the timing of any tax change does not affect their change in spending. Consequently, Ricardian equivalence suggests that it does not matter whether a government finances its spending with debt or tax increase, the effect on total level of demand in an economy being the same.

See David Ricardo, 1772-1823st book on economic theory Principles of Political Economy.

Introduction

In its simplest terms: governments can raise money either through taxes or by issuing bonds. Since bonds are loans, they must eventually be repaid – presumably by raising taxes in the future. The choice is therefore ‘tax now or tax later’.

“Essay on the Funding System” (1820) – people are subjected to a fiscal illusion.

Barro-Ricardo Equivalence

In 1974, Robert J. Barro provided some theoretical foundation for Ricardo’s hesitant speculation. Barro’s model assumed the following:

- Families act as infinitely lived dynasties because of intergenerational altruism

- Capital markets are perfect ( i.e., all can borrow and lend at a single rate) (c- liquidity constraints)

- The path of government expenditure is fixed

Under these conditions, if governments finance deficits by issuing bonds, the bequests that families grant to their children will be just large enough to offset the higher taxes that will be needed to pay off those bonds. Among his conclusion, Barro wrote:

… in the case where the marginal net-wealth effect of government bonds is close to zero … fiscal effect involving changes in the relative amounts of tax and debt finance for a given amount of public expenditure would have no effect on aggregate demand, interest rates, and capital formation

The model was an important contribution to the New Classical Macroecon. built around the assumption of rational expectations.

In the 1979, Barro defined the RE as follows:

… shifts between debt and tax finance for a given amount of public expenditure would have no first-order effect on the real interest rate, volume of private investment, etc. noting that “(t)he RE proposition is presented in Ricardo. However, Ricardo was skeptical of this equivalence.

TBC …

See Wikipedia