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This paper examines the implications of labor market search and matching frictions for determinacy and E-stability of rational expectations equilibrium (REE) in a sticky price model with interest rate policy. When labor adjustment takes place solely at the extensive margin, forecast-based policy that meets the Taylor principle is likely to induce indeterminacy and E-instability, regardless of whether it is strictly or flexibly inflation targeting. When labor adjustment takes place at both the extensive and intensive margins, the strictly inflation-forecast targeting policy remains likely to induce indeterminacy, but it generates a unique E-stable fundamental REE as long as the Taylor principle is satisfied. Therefore, the presence of search and matching frictions changes the determinacy properties of a strictly inflation-forecast targeting policy, and alters its E-stability properties when only an extensive margin is present but not when labor adjustment takes place at both margins.

Recent monetary policy literature has incorporated labor market search and matching frictions along the lines of Mortensen and Pissarides (1994) into a sticky price model and has studied their implications for optimal monetary policy (e.g., Thomas, 2008, Faia, 2009, Ravenna and Walsh, 2011 and Tang, 2010) and for determinacy of equilibrium under interest rate policy (Kurozumi and Van Zandweghe, 2010).2 In the latter paper, we find that strictly inflation-forecast targeting interest rate policy almost always induces indeterminacy of equilibrium in a sticky price model with only the extensive margin (i.e., variation in employment) when it meets the Taylor principle.3 In the present paper, we examine the implications for both determinacy and E-stability of rational expectations equilibrium (REE) under interest rate policy not only in a sticky price model with only the extensive margin but also in the one with both the extensive and intensive margins (i.e., changes in both employment and hours per worker). As McCallum (2007) points out, E-stability is very closely linked with least-squares learnability (i.e., stability under least-squares learning), and this learnability is arguably a necessary property for an REE to be plausible as an equilibrium for the model at hand. For a broad class of linear models with expectations (including the model of this paper), an REE is least-squares learnable when it is E-stable and non-explosive. If an REE is not E-stable, it is not stable under least-squares learning. Therefore, E-stability is an essential condition for an REE to be regarded as plausible. This paper has two main results. First, when labor adjustment takes place solely at the extensive margin, the strictly inflation-forecast targeting interest rate policy is likely to induce E-instability as well as indeterminacy. Specifically, this policy generates a unique E-stable fundamental REE only if the Taylor principle is satisfied and the policy coefficient on the inflation forecast is either not large or very large.4 Only a policy coefficient in these two intervals succeeds in guiding temporary equilibria under non-rational expectations toward the unique E-stable REE. Because the intermediate interval that yields indeterminate E-unstable REE contains all empirically plausible values of the policy coefficient, the equilibrium multiplicity induced by the strictly inflation-forecast targeting policy is a critical issue even from the perspective of E-stability or least-squares learnability of REE.5 Moreover, when the forecast-based interest rate policy is flexibly inflation targeting (i.e., it responds to an unemployment forecast in addition to the inflation forecast), it remains very unlikely to generate a determinate E-stable REE or a unique E-stable fundamental REE.6 This result is in contrast to that of Bullard and Mitra (2002), who show that, in the absence of labor market frictions, forecast-based policy yields a determinate E-stable REE or a unique E-stable fundamental REE as long as the Taylor principle is satisfied, regardless of whether it is strictly or flexibly inflation targeting. Second, when labor adjustment takes place at both the extensive and intensive margins, the strictly inflation-forecast targeting policy remains likely to induce indeterminacy. Despite the existence of multiple fundamental REE, however, this policy generates a unique E-stable fundamental REE as long as the Taylor principle is satisfied, in line with the result of Bullard and Mitra (2002). Therefore, in the presence of both margins, the equilibrium multiplicity induced by the strictly inflation-forecast targeting policy is not a critical issue from the perspective of E-stability or least-squares learnability of fundamental REE.7 Moreover, the flexibly inflation-forecast targeting policy is likely to generate a determinate E-stable REE. These two results suggest that the presence of the labor market search and matching frictions changes the determinacy properties of the strictly inflation-forecast targeting interest rate policy, and that it alters the E-stability properties of the policy when only an extensive margin is present but not when labor adjustment takes place at both margins. The remainder of the paper proceeds as follows. Section 2 describes a sticky price model with labor market search and matching frictions. Section 3 presents the analysis of E-stability as well as determinacy under interest rate policy. Section 4 conducts a sensitivity analysis with respect to values of structural parameters of the model. Section 5 concludes.

In this paper we have examined the implications of labor market search and matching frictions for determinacy and E-stability of REE in a sticky price model with interest rate policy. In the model with only the extensive margin, forecast-based policy that meets the Taylor principle is likely to induce indeterminacy and E-instability, regardless of whether it is strictly or flexibly inflation targeting. This is in contrast to the result of Bullard and Mitra (2002), who analyze the case of no labor market frictions and show that forecast-based policy is likely to ensure determinacy of REE and guarantees E-stability of fundamental REE. In the model with both the extensive and intensive margins, the strictly inflation-forecast targeting policy remains likely to induce indeterminacy, but it generates a unique E-stable fundamental REE as long as the Taylor principle is satisfied. These results suggest that the presence of the labor market search and matching frictions changes the determinacy properties of the strictly inflation-forecast targeting policy, and that it alters the E-stability properties of the policy when only an extensive margin is present but not when labor adjustment takes place at both margins. In the companion paper (Kurozumi and Van Zandweghe, 2010), we examined the model with only the extensive margin and found that strictly inflation-forecast targeting interest rate policy almost always induces indeterminacy if it satisfies the Taylor principle. Thus, the present paper has shown that this equilibrium multiplicity remains a concern even from the perspective of E-stability. Moreover, indeterminacy arises even when labor is adjusted at both the extensive and intensive margins. Only when labor adjustment takes place at both margins and E-stability is adopted as an REE selection criterion is the concern about equilibrium multiplicity under the strictly inflation-forecast targeting policy mitigated. This paper has not addressed questions regarding optimality of interest rate policy. Evans and McGough (2007) propose a method of selecting optimal coefficients of interest rate policy that yield a determinate E-stable REE, in the presence of uncertainty about model parameters. Because labor market search and matching frictions make indeterminacy and E-instability more likely and because such frictions increase the number of parameters about which there is uncertainty, the use of their method to examine robust optimal constrained interest rate policy is an interesting topic for future work.