Some Econometrics

(1) “Variable trends in economic time series,”

(Stock and Watson, 1988) http://www.princeton.edu/~mwatson/papers/Stock_Watson_JEP_1988.pdf Figure 1 motivates discussion of “Long run trends” and “Cyclical fluctuations” around those trends. Notice that long run trends can vary over time and may be associated with the turning points evident in the cyclical fluctuations.

What is a “Variable Trend”? [see discussion]

Footnote 2, pp. 151-152

Skip pp. 153 – 159 and pp. 160-163

VAR’s mentioned, will discuss in following paper

Recent Developments in the Theory of Regression with Integrated Regressors, pp. 163 – 167.

Spurious regression

Unit roots

Cointegration

(2) [Extra, interesting reading] F.X. Diebold, “The past, present, and future of macroeconomic forecasting,” Journal of Economic Perspectives, vol. 12, no. 2 (Spring 1998), pp. 175-192.

http://www.ssc.upenn.edu/~fdiebold/papers/paper19/jep2.pdf

(3) Stock, J.H. and M. Watson, “Vector autoregressions,” Journal of Economic Perspectives, vol. 15, no. 4 (Autumn 2001), pp. 101-115.

http://www.aeaweb.org/articles.php?doi=10.1257/jep.15.4.101 http://scholar.harvard.edu/stock/publications/vector-autoregressions In the tool-kit of ALL macroeconomists of ANY type

Article assesses how well VARs aid macroeconomists in their 4 main tasks: (a) Describe and summarize macro data; (b) make macro forecasts, (c) quantify what we do and do not know about the true structure of the macroeconomy, and (d) advise macro policymakers.

Reduced form VARs, Recursive VARs, and “Structural” VARs

Reduced-Form VAR; 3-equations and 4 lags πt = α1,0 + α1,1πt-1 + … + α1,2πt-4 + α1,5ut-1 + … + α1,8ut-4 + α1,9Rt-1 + … + α1,12Rt-4 + Ɛ1,t ut = α2,0 + α2,1πt-1 + … + α2,2πt-4 + α2,5ut-1 + … + α2,8ut-4 + α2,9Rt-1 + … + α2,12Rt-4 + Ɛ2,t

Rt = α3,0 + α3,1πt-1 + … + α3,2πt-4 + α3,5ut-1 + … + α3,8ut-4 + α3,9Rt-1 + … + α3,12Rt-4 + Ɛ3,t

Recursive representation of this VAR πt = α1,0 + α1,1πt-1 + … + α1,2πt-4 + α1,5ut-1 + … + α1,8ut-4 + α1,9Rt-1 + … + α1,12Rt-4 + v1,t ut = α2,0 + ϓ2,1πt + α2,1πt-1 + … + α2,2πt-4 + α2,5ut-1 + … + α2,8ut-4 + α2,9Rt-1 + … + α2,12Rt-4 + v2,t

Rt = α3,0 + ϓ3,1πt + ϓ3,2Rt + α3,1πt-1 + … + α3,2πt-4 + α3,5ut-1 + … + α3,8ut-4 + α3,9Rt-1 + … + α3,12Rt-4 + v3,t

Structural VARs

Not necessarily recursive in structure (ordering)

Identification comes from economic theory

Are challenging to motivate/justify…