C8D4 - True model Q = 1 + 2 Z + v C P = 2 Y P FRIEDMANS...

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Unformatted text preview: True model Q = 1 + 2 Z + v C P = 2 Y P FRIEDMANS CRITIQUE OF OLS ESTIMATION OF THE CONSUMPTION FUNCTION 1 Milton Friedmans Permanent Income Hypothesis provides a classic example of measurement error theory. The basic idea is that permanent consumption, C P , is proportional to permanent income, Y P . True model Q = 1 + 2 Z + v C P = 2 Y P FRIEDMANS CRITIQUE OF OLS ESTIMATION OF THE CONSUMPTION FUNCTION 2 Permanent consumption and income are subjective notions of sustainable, medium-term, consumption and income, respectively. They cannot be measured directly. True model Q = 1 + 2 Z + v C P = 2 Y P Measurement X = Z + w Y = Y P + Y T errors Y = Q + r C = C P + C T FRIEDMANS CRITIQUE OF OLS ESTIMATION OF THE CONSUMPTION FUNCTION 3 Actual (measured) income, Y , has two components: permanent income, Y P , and transitory income, Y T (a random, short-run component). Likewise actual (measured) consumption, C , has two components: permanent consumption, C P , and transitory consumption, C T . True model Q = 1 + 2 Z + v C P = 2 Y P Measurement X = Z + w Y = Y P + Y T errors Y = Q + r C = C P + C T FRIEDMANS CRITIQUE OF OLS ESTIMATION OF THE CONSUMPTION FUNCTION 4 According to the Permanent Income Hypothesis, an OLS regression of actual consumption on actual income will be subject to measurement error in both the dependent and the explanatory variables, the measurement errors being the transitory components C T and Y T . True model Q = 1 + 2 Z + v C P = 2 Y P Measurement X = Z + w Y = Y P + Y T errors Y = Q + r C = C P + C T True model, in Y = 1 + 2 X + v C = 2 Y + C T- 2 Y T measured + r- 2 w = 2 Y + u variables = 1 + 2 X + u FRIEDMANS CRITIQUE OF OLS ESTIMATION OF THE CONSUMPTION FUNCTION 5 From the first three equations we can derive an equation relating actual consumption to actual income. True model Q = 1 + 2 Z + v C P = 2 Y P Measurement X = Z + w Y = Y P + Y T errors Y = Q + r C = C P + C T True model, in Y = 1 + 2 X + v C = 2 Y + C T- 2 Y T measured + r- 2 w = 2 Y + u variables = 1 + 2 X + u Assumptions v , w , and r distributed Y T and C T distributed independently of independently of each other and Z each other and Y P and Q and C P FRIEDMANS CRITIQUE OF OLS ESTIMATION OF THE CONSUMPTION FUNCTION 6 To simplify the analysis, we will assume that the transitory components of consumption and income are independent of their permanent components and of each other. True model...
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C8D4 - True model Q = 1 + 2 Z + v C P = 2 Y P FRIEDMANS...

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