Identification of Rational Expectations Models Under Information Frictions Julian F. Ludwig∗ Texas Tech University September 19, 2019 Link to the most recent version: www.com Abstract Identification of full information rational expectations (FIRE) models suffers from Manski’s (1993) reflection problem. I extend the standard rational expectations (RE) model to allow for a more general information structure and introduce a new frame- work to identify the generalized model with forecaster data. Identification is no longer subject to the reflection problem when two changes are made to the information struc- ture: the addition of news shocks and imperfect information.
News shocks provide additional variation in expectations about the future. Imperfect information provides changes in beliefs about past states, through which the feedback between expectations and decisions goes only in one direction. Expectations data are consistent with both. An application to Greenbook forecasts illustrates the importance of both news shocks and learning about the past.
When I apply this framework to a Blanchard and Quah (1989) decomposition, I reach qualitatively new results. For example, expansionary supply shocks decrease unemployment. Supply shocks are also particularly subject to both news and information rigidities, so relaxing the information structure is key to correctly identifying these shocks. Keywords: Expectations, Information Rigidity, News Shocks, Survey Forecasts JEL Codes: C2, C3, C5, E3, E5, E6, E7 ∗ Ludwig: Assistant Professor, Department of Economics, Texas Tech University, 253 Holden Hall, Lub- bock TX 79409, U.
I am grateful to Olivier Coibion, Saroj Bhattarai and Haiqing Xu for their invaluable guidance and support. I also benefited from conversations with Chi Zhang, Stefano Eusepi, Christoph Boehm, Tatevik Sekhposyan, Jessie Coe, Kevin Kuruc, Cooper Howes, Choongryul Yang, Andrés Méndez Ruiz, and Shaofei Jiang as well as with many seminar participants from the University of Texas at Austin, and Texas A&M University. 1 Introduction In modern micro-founded macro models, the decisions of economic agents are inherently forward-looking and therefore depend on their expectations about the future. But if their expectations are also formed based on the current state, as is generally assumed in full- information models, it becomes difficult to determine to what extent expectations affect actions and vice-versa.
I relate this simultaneity to Manski’s (1993) reflection problem and introduce a new way to deal with its implications for identification. The importance of expectations has long been emphasized in rational expectations (RE) models (see e. Lucas, 1972, 1976; Kydland and Prescott, 1982). This paper provides a new methodology to identify the parameters of RE models using data on the expectations of economic agents at multiple horizons.
Specifically, I relax the full-information assumption and allow for information to diffuse to agents both before and after shocks are realized, which allows me to match both forecasts and backcasts in the data. The resulting variation in expectations is no longer proportional to current actions so that identification is possible. This flexible information structure brings together the literature on news shocks (see Beaudry and Portier, 2004, 2006), where information arrives before impact, and the literature on information frictions (see Mankiw and Reis, 2002; Woodford, 2003; Sims, 2003), where agents gather relevant information only after the period is realized. Combining both dimensions is the key to identifying the parameters of the model.
I relate the identification issue to Manski (1993), who describes the role of expectations about competitors and peers in social interaction models. His well-known reflection problem states that when expectations are modelled simply as the average among individuals, the researcher cannot distinguish whether expectations change individual behaviour or if they simply reflect behaviour without causing it. I extend his proposition to show that full information rational expectations (FIRE) models suffer from the same type of reflection problem as well: since information is only gathered in one period, expectations about the future are proportional to realizations today. The researcher can therefore not distinguish the 1 direct effect of a shock on the economy from the indirect effect of observing that shock.
The FIRE literature successfully bypasses this reflection problem by imposing a set of parameter restrictions on the FIRE model typically derived from a micro-founded model. I provide a new way to deal with this identification issue by incorporating data on expectations at multiple horizons and by relaxing the full information assumption. There are many ways to relax full information (FI). Mankiw and Reis (2002) introduce a sticky information approach where agents update their expectations infrequently, but when they update their expectations, they fully observe the state.
Woodford (2003) models in- formation rigidities with a noisy information approach where agents receive noisy signals about the state of the economy. Sims (2003) and Maćkowiak and Wiederholt (2009) make acquiring information costly so that agents need to choose whether they want to pay the cost to get information. The solution of this problem is characterized by rational inattention, where agents choose to deviate from full information. Models with such information rigidi- ties allow for information to arrive after the shocks are realized so that agents no longer fully observe the current state of the economy.
In contrast, news shock models allow for information to arrive before the shock hits the economy. Beaudry and Portier (2004) intro- duce news shocks as noisy signals about future developments of the economy, while Beaudry and Portier (2006), Davis (2007), and Christiano et al. (2010) model news shocks as future shocks that are fully observed today. My paper combines the two branches of the literature to formalize a much more general information structure than what is allowed in standard macroeconomic models.
The core identification property is that future outcomes only have an effect on today’s economy if agents observe these outcomes in advance. Hence, any fluctuations that are un- observed cannot be caused by future outcomes. These unobserved fluctuations are therefore fully backward-looking and can be used to identify the effect of current on future outcomes. Changes in expectations about the previous period, defined as backcast revisions, collect these unobserved fluctuations.
Hence, data on expectations about both the contemporaneous and 2 the previous period are sufficient to identify one direction of the relationship between out- comes and expectations. The other direction is identified when data on expectations about the next period is available. Given the identified effect of current outcomes on expectations of future outcomes, the remaining variation in expectations of the next period must come from additional information that is obtained today about the future. The effect of the re- mainder on current outcomes thus identifies the effect of expectations so that the forward- and backward-looking components of the RE model are identified.
Key for identification is the timing assumption that expectations can only depend on information obtained up until today, but not on information obtained tomorrow. Timing restrictions on information sets are common in the production function literature (see Olley and Pakes, 1996; Blundell and Bond, 2000; Levinsohn and Petrin, 2003). To my knowledge, this is the first paper that uses the variation generated by relaxing full information to separately identify the parameters governing the backward- and forward-looking dynamics of RE models. The proposed strategy identifies the forward- and backward-looking components simul- taneously, without imposing additional restrictions on the model equations.
Instead of im- posing a particular structural model, this approach nests all models that have the form of RE models with a flexible information structure. Hence, estimation is less subject to model specifications other than the choice which variables to include, the number of lags and leads, and how the shocks are orthogonalized. Identification instead relies on the assumption that data on expectations across horizons, both future and past, is available and that this data correctly captures beliefs of agents. Moreover, identification requires a positive variance of backcast revisions, and noncollinearity between now- and forecasts, features which appear to be consistent with the data.
Hence, I impose a completely different set of assumptions to identify the RE model than what is common in the literature. I implement the identification strategy using data on expectations from the Greenbook, a collection of forecasts from the U. In the first application, I estimate an unrestricted multivariate RE model with output, consumption, and investment growth, as 3 well as inflation. I find that about half the information about shocks is gathered before and during realization, while the other half is obtained only after the shock materializes.
This provides evidence for information rigidities, where agents don’t fully observe the current state of the economy. Moreover, around one fourth of the information is collected before realization, which provides support for the news shock literature. I then produce counter- factuals by shifting arrival of information to simulate a full information environment, where everything is observed on impact. In this counterfactual, persistence of all variables signif- icantly declines.
Hence, the information structure seems to be a significant driver of the persistence in macro variables. In the second application, I estimate a RE model with output growth and changes in unemployment, and orthogonalize the shocks following Blanchard and Quah (1989): demand shocks are assumed to be transitory shocks, while supply shocks are the only shocks with a long run impact on output. The results indicate that demand shocks are much better observed than supply shocks, hence, agents seem to be better informed about the demand side of the economy, and less informed about the production side. Moreover, I find on average a significant response to supply shocks before impact, which is line with the news shock literature modelling anticipated supply side shocks.
Overall, both demand and supply shocks increase output and decrease unemployment which is consistent with standard real business cycles (RBC) models. The finding that supply shocks decrease unemployment is different from the conclusion of Blanchard and Quah (1989), who find increased unemployment in response to supply shocks. This illustrates the importance of properly controlling for timing of information arrival and processing when identifying economic shocks. This paper relates to the literature on structural vector autoregressions (SVARs), where economic shocks are identified with reduced form models (see Sims, 1980).
Similar to SVARs, my identification strategy does not require one to specify the structural equations of the RE model. However, while SVARs identify the reduced form version of the RE model, this paper identifies the structural version directly, where expectations about the future and dependence 4 on past are identified separately. My paper builds on and contributes to the literature on news shocks. Beaudry and Portier (2004, 2006) introduce the notion of TFP news shocks as changes in current expectations about future productivity, and they find that these news shocks have real effects today, even though they only materialize in the future.
Beaudry and Portier (2006, 2014), Barsky and Sims (2011, 2012), Beaudry, Dupaigne and Portier (2011), Barsky, Basu and Lee (2015) and others identify TFP news shocks in SVARs as changes in current expectations, measured for example in terms of stock prices or consumer confidence, that are orthogonal to current but contribute to future TFP. Today’s effects of the news shocks are then considered as effects of expectations, while the shock only realizes in the future when TFP increases. These papers therefore rely on structural assumptions about the dynamic effects of news shocks on economic variables. My approach relies on a different set of assumptions, yet yields results that confirm the importance of news shocks for macroeconomic dynamics.
This paper also contributes to the literature on VAR invertibility, which refers to the abil- ity to rewrite the RE model as a reduced form VAR of observables (see Fernández-Villaverde et al. Non-invertibility occurs if there are unobserved state variables causing a bias in VAR estimation (see Watson, 1986). Models with news shocks are particularly vulnerable to non-invertibility, because VAR variables might not be able to capture the information used to predict news shocks (see Leeper, Walker and Yang, 2013). Watson (1986), Sims and Zha (2006), and Sims (2012) address the invertibility issue by including forward-looking variables.
I introduce an alternative way to avoid non-invertibility by estimating the reduced form model (VAR) with backcast revisions, as described above.
