By David F. Heathfield (eds.)
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24 Topics in Applied Macroeconomics Lagged Variables In many theories, the dependent variable is not only affected by current values of other variables, but also by lagged values of the variables. Current consumption might be affected by one's current income and also lagged values of income so that we have 00 c, = a + i=Q L bi Y'-i + U,. 32) Direct estimation of the equation cannot be made since there are an infinite number of the coefficients (bis) to estimate. Even if we are willing to ignore the effects of income far in the past, there may still be too many coefficients to estimate.
Interpolation is done by various proxies for value added, for example labour input, raw material inputs and gross output. These proxies are crucial for production-function analysis since they are justified precisely by an assumed production function. Estimating functions as if the index were an independent measure of output may be misleading in simply revealing the kind of 36 Topics in Applied Macroeconomics production function assumed by the compiler of the statistics. Perhaps the most that can be said for generated output measures is that they may well reflect changes in output at any rate over fairly short time periods.
R. 39) 26 Topics in Applied Macroeconomics If the weights are created from a polynomial approximation of the coefficients bi, the technique seems to have some meaning, that is the coefficients bi are considered as arising from a polynomial function such that f(i) = bi. The weights are determined by approximating the general polynomial of degree s, f(i). 8 illustrates this). f(;) XX6 x;l , x~ , 5 6 7 8 9 10 11 x 12 13 x x 14 15 16 17 18 x x 19 20 Fig. 8 Of course, the method may yield biased estimates due to specification error (the estimated equation does not have the true independent variables in it) and the properties of such estimates will be dependent on the approximation formula used, and how 'good' the function 'fits' the values, bi.