By Manmatha Nath Bhattacharyya

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1 Granger's Definition of Causality and Its Characterization In the previous sections of the book we developed adequate ARI~~ models for each of the selected endogenous variables and compared their forecasting efficiency with that of the corresponding econometric models. ~le now propose to examine the causal relationships between these variables. The causal relationship to be studied is in the sense defined by Granger (1969). Granger's definition of causality is in terms of predictability: a variable X causes another variable Y, with respect to a given universe of information set that includes X and Y, if the present Y can be better predicted by using the past values of X than by not doina so, all other information available (including past values of Y) being used in either case.

7) vt v(B)u t + f' t ut W(B)V t + g' t ... 12a) and ... 12b) where v(B) y (B)/o (B), f' t bt/o (B) weB) S (B) /a (B) and g' t at/a (B) ... 13) In the above discussion of causality we assume that the information set consists of two variables X and Y only; in other words we consider causal relationships pair-wise among a selected group of variables. 2 Detection of Causality: Pierce's Broad Tests Development of statistical tests for causality de~ecting is, however, beset with the difficulty that the white noise u and v are not observable in practice.

5 Causal Relationships Between Short-Term Interest Rate, 90-Day Honey Rate Frankfurt (RFFH) and Other Selected Variables A finer analysis of residual cross-correlations using progressive x2 tests, explained earlier, was done for one variable only, namely, short-term interest rate, 90-day money rate Frankfurt. The results of the analysis were incorporated schematically in Table 8. A part of the analysis is now shO"l'Tn in Table 9. Cross-correlations between short-term interest rate (RFFH) and saving deposits (PBDSP), liquidity ratio (BLQ), interest on current account loan (RKONT), money (BGM1) and yield on officially quoted bond (ROBLD) are given in Table 9.

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