f( )θ ≡βθ2− + +1 β ϕκ θ+ =1 0
The function f(θ) is a parabola that opens upward and has an intercept on the ordinate of 1. Since f(1) = –ϕκ < 0, it also has two positive roots, one on each side of 1. Denote the smaller root as θ . Since f′(1) = 21 β – (1+β+ϕκ) < 0, the minimum of f(θ) is to the right of θ = . This function is shown in Figure A. Note that when 1 θ lies on (0, )θ , there is no 1
lower bound for the probability limit and it might even be negative. On the other hand, when θ lies on ( ,1)θ1 , there is no upper bound for the probability limit. These results are summarized in Table A. When θ is close to θ1, however, the probability limit is τ-1. For this reason, we regard βF as informative about the parameter τ and hence about how monetary policy was conducted; hence, our analysis for the postwar period.
The OLS estimator of β converges in probability to G
( )
general result is summarized in Table A below.Table A. Dependence of Probability Limits on θ
θ plim β
Fplim β
G6.2 Probability Limits for the Contemporaneous Regressions
In case I, the OLS estimator of φ1 converges in probability to
( ) ( ) ( )
The OLS estimator of ϕ1 converges in probability to
[ ]
which is strictly positive and smaller than ½λ-1. Moreover, it is smaller, the larger var(µ ηt− vt) / varut is.
In case II, the OLS estimator of φ1 converges in probability to
( ) ( )( ) ( )
which is strictly less than τ ρ−1 −1 and can even be negative if varet varut.
Finally, the OLS estimator of ϕ1 converges in probability to
( )
6.3 Adjustment for Using the Call Money Rate
Let t be continuous and ct be the call money rate at time t. For simplicity, call money is assumed to have a maturity of zero. From the definition of the assorted premia below, we have
According to the expectation theory of the term structure, the last term of equation (24) should be zero. More generally, it may have a variance that is small relative to the variance of the other two terms, or it may be approximately uncorrelated with information available on or before time t–½. In either case, ε is approximately Ft uncorrelated with information available on or before time t–½. Then to a close approximation, equation (23) can be estimated consistently by using the quarterly average of the call money rate lagged two quarters as an instrumental variable.
References
Banking and Monetary Statistics, 1914-1941. Washington: Board of Governors of the Federal Reserve System, 1943.
Barsky, Robert B. “The Fisher Hypothesis and the Forecastability and Persistence of Inflation.” Journal of Monetary Economics 19 (January 1987): 3-24.
Barsky, Robert B., and J. Bradford de Long. “Forecasting Pre-World War I Inflation: The Fisher Effect and the Gold Standard.” Quarterly Journal of Economics 106, 3 (August 1991): 815-836.
Barsky, Robert B., and Lawrence H. Summers. “Gibson's Paradox and the Gold Standard.” Journal of Political Economy 96 (June 1988): 528-550.
Barsky, Robert B., and Lawrence H. Summers. “Forecasting Pre-World War I Inflation:
The Fisher Effect and the Gold Standard.” Quarterly Journal of Economics 106 (August 1991): 815-836.
Calomiris, Charles W., and R. Glenn Hubbard. “Price Flexibility, Credit Availability, and Economic Fluctuations: Evidence from the United States, 1894-1909.” Quarterly Journal of Economics 104 (August 1989): 429-452.
Clarida, Richard, Jordi Galí, and Mark Gertler. “Monetary Policy Rules in Practice: Some International Evidence.” European Economic Review 42 (1998): 1033-1067.
Clarida, Richard, Jordi Galí, and Mark Gertler. “The Science of Monetary Policy: A New Keynesian Perspective.” Journal of Economic Literature 37 (December 1999): 1661-1707.
Clarida, Richard, Jordi Galí, and Mark Gertler. “Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory.” Quarterly Journal of Economics 115 (February 2000): 147-180.
Dwyer, Gerald P., Jr. “The Gibson Paradox: A Cross-Country Analysis.” Economica 51 (May 1984): 109-127.
Fama, Eugene. “Short-Term Interest Rates as Predictors of Inflation.” American Economic Review 65 (June 1975): 269-282.
Fisher, Irving. The Theory of Interest. New York: Macmillan, 1930.
Friedman, Milton, and Anna Jacobson Schwartz. Monetary History of the United States, 1867-1960. Princeton NJ: Princeton University Press, 1963.
Friedman, Milton, and Anna Jacobson Schwartz. Monetary Trends in the United States and the United Kingdom. Chicago IL: University of Chicago Press, 1982.
Gayer, Arthur D., Walt W. Rostow, and Anna J. Schwartz. The Growth and Fluctuation of the British Economy 1790-1850. Oxford. 1953.
Gibson, A. H. “The Future Course of High-Class Investment Values.” The Bankers’, Insurance Managers’, and Agents’ Magazine 115 (1923): 15-34.
Hafer, R. W., and Dennis Jansen. “The Demand for Money in the United States:
Evidence from Cointegration Tests.” Journal of Money, Credit, and Banking 23 (May 1991): 155-168.
Hanes, Christopher, and James, John A. “Wage Adjustment under Low Inflation:
Evidence from US History.” American Economic Review 93 (September 2003): 1414-1424.
Homer, Sidney, and Richard Sylla, A History of Interest Rates. 3rd Edition. Rutgers University Press. New Brunswick and London. 1991.
Keynes, John Maynard. A Treatise on Money. 2 vols. London: Macmillan, 1930.
Kindleberger, Charles P. The World in Depression, 1929-1939. Berkeley CA: University of California Press, 1973.
Klovland, Jan Tore. “Zooming in on Sauerbeck: Monthly Wholesale Prices in Britain 1845-1890.” Explorations in Economic History 30 (1993): 195-228.
Macaulay, Frederick R., The Movements of Interest Rates, Bond Yields and Stock Prices in the United States Since 1856. New York: National Bureau of Economic Research, 1938.
Mitchell, Brian R., International Historical Statistics Europe 1750-1988. 3rd Edition.
Stockton Press, 1992.
Roll, Richard. “Interest Rates on Monetary Assets and Commodity Price Index Changes.”
Journal of Finance 27, 2(May, 1972): 251-277.
Romer, David, and Christina Romer. “A Rehabilitation of Monetary Policy in the 1950s.”
American Economic Review 92 (May 2002): 121-127.
Sargent, Thomas J. “Interest Rates and Prices in the Long Run: A Study of the Gibson Paradox.” Journal of Money, Credit and Banking 5, 1(February 1973): 385-449.
Sauerbeck, A. “Prices of Commodities and the Precious Metals.” Journal of the Royal Statistical Society 49 (1886): 581-649.
Shiller, Robert J., and Jeremy J. Siegel. “The Gibson Paradox and Historical Movements in Real Interest Rates.” Journal of Political Economy 85, 5(October 1977): 891-908.
Warren, George F., and Frank A. Pearson, Gold and Prices. London: John Wiley & Sons and Chapman & Hall, 1935.
Wicksell, Knut. “The Influence of the Rate of Interest on Prices.” Economic Journal 17 (June 1907): 213-220.