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6.4Apparent Violations of Rationality

We’ve seen that there are important dimensions of the data that the Lucas model with CRRA utility cannot explain.8 What other approaches have been taken to explain deviations from uncovered interest parity? This section covers the peso problem approach and the noise trader paradigm. Both approaches predict that market participants make systematic forecast errors. In the peso problem approach, agents have rational expectations but don’t know the true economic environment with certainty. In the noise trading approach, some agents are irrational.

Before tackling these issues, we want to have some evidence that market participants actually do make systematic forecast errors. So we Þrst look at a line of research that studies the properties of exchange rate forecasts compiled by surveys of actual foreign exchange market participants. The subjective expectations of market participants are key to any theory in international Þnance. The rational expectations assumption conveniently allows the economic analyst to model these subjective expectations without having to collect data on people’s expectations per se. If the rational expectations assumption is wrong, its violation may be the reason that underlies asset-pricing anomalies such as the deviation from uncovered interest parity.

7Backus, Gregory, and Telmer [4] investigate the lower volatility bound (6.28) implied by data on the U.S. dollar prices of the Canadian-dollar, the deutschemark, the French-franc, the pound, and the yen. They compute the bound for an investor who chases positive expected proÞts by deÞning forward exchange payo s on currency i as Iit(Fi,t − Si,t+1)/Si,t where Iit = 1 if Et(fi,t − si,t+1) > 0 and Iit = 0 otherwise. The bound computed in the text does not make this adjustment because it is not a prediction of the Lucas model where investors may be willing to take a position that earns expected negative proÞt if it provides consumption insurance. Using the indicator adjustment on returns lowers the volatility bound making it more di cult for the asset pricing model to match this quarterly data set.

8The failure of the model to generate su ciently variable risk premiums to explain the data cannot be blamed on the CRRA utility function. Bekaert [9] obtains similar results with utility speciÞcations where consumption exhibits durability and when utility displays ‘habit persistence’.

184CHAPTER 6. FOREIGN EXCHANGE MARKET EFFICIENCY

Properties of Survey Expectations

Instead of modeling the subjective expectations of market participants as mathematical conditional expectations, why not just ask people what they think? One line of research has used surveys of exchange rate forecasts by market participants to investigate the forward premium bias (deviation from UIP). Froot and Frankel [65], study surveys conducted by the Economist’s Financial Report from 6/81—12/85, Money Market Services from 1/83—10/84, and American Express Banking Corporation from 1/76—7/85, Frankel and Chinn [58] employ a survey compiled monthly by Currency Forecasters’ Digest from 2/88 through 2/91, and Cavaglia et. al. [23] analyze forecasts on 10 USD bilateral rates and 8 deutschemark bilateral rates surveyed by Business International Corporation from 1/86 to 12/90. The survey respondents were asked to provide forecasts at horizons of 3, 6, and 12 months into the future.

The salient properties of the survey expectations are captured in (117) two regressions. Let sˆet+1 be the median of the survey forecast of the log spot exchange rate st+1 reported at date t. The Þrst equation is the

regression of the survey forecast error on the forward premium

∆sˆte+1 − ∆st+1 = α1 + β1(ft − st) + ²1t+1.

(6.29)

If survey respondents have rational expectations, the survey forecast error realized at date t+1 will be uncorrelated with any publicly available at time t and the slope coe cient β1 in (6.29) will be zero.

The second regression is the counterpart to Fama’s decomposition and measures the weight that market participants attach to the forward premium in their forecasts of the future depreciation

∆sˆte+1 = α2 + β2(ft − st) + ²2,t+1.

(6.30)

Survey respondents perceive there to be a risk premium to the extent that β2 deviates from one. That is because if a risk premium exists, it will be impounded in the regression error and through the omitted variables bias will cause β2 to deviate from 1.

Table 6.4 reports selected estimation results drawn from the literature. Two main points can be drawn from the table.

1.The survey forecast regressions generally yield estimates of β1 that are signiÞcantly di erent from zero which provides evidence

6.4. APPARENT VIOLATIONS OF RATIONALITY

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Table 6.4: Empirical Estimates from Studies of Survey Forecasts

				Data Set
		Economist	MMS	AMEX	CFD	BIC—USD	BIC—DEM
			Horizon: 3-months
	β1	2.513	6.073	–	–	5.971	1.930
	t(β1 = 1)	1.945	2.596	–	–	1.921	-0.452
	t(β2 = 1)	1.304	-0.182	–	0.423	1.930	0.959
	t-test	1.188	-2.753	–	-2.842	5.226	-1.452
			Horizon: 6-months
	β1	2.986	–	3.635	–	5.347	1.841
	t(β1 = 1)	1.870	–	2.705	–	2.327	-0.422
	β2	1.033	–	1.216	–	1.222	0.812
	t(β2 = 1)	0.192	–	1.038	–	1.461	-4.325
			Horizon: 12-months
	β1	0.517	–	3.108	–	5.601	1.706
	t(β1 = 1)	0.421	–	2.400	–	3.416	0.832
	β2	0.929	–	0.877	1.055	1.046	0.502
	t(β2 = 1)	-0.476	–	-0.446	0.297	0.532	-6.594

Notes: Estimates from the Economist, Money Market Services, and American Express surveys are from Froot and Frankel [65]. Estimates from the Currency Forecasters’ Digest survey are from Frankel and Chinn [58], and estimates from the Business International Corporation (BIC) survey from Cavaglia et. al. [23]. BIC— USD is the average of individual estimates for 10 dollar exchange rates. BIC—DEM is the average over 8 deutschemark exchange rates.