سیاست پولی بهینه با ورود و محصول مختلف درون زا

Deviations from long-run price stability are optimal in the presence of endogenous entry and product variety in a sticky-price model in which price stability would be optimal otherwise Long-run inflation (deflation) is optimal when the benefit of variety to consumers falls short of (exceeds) the market incentive for creating that variety—the desired markup; Price indexation exacerbates this mechanism. Plausible preference specifications and parameter values justify positive long-run inflation rates. However, short-run price stability (around this non-zero trend) is close to optimal, even in the presence of endogenously time-varying desired markups that distort the intertemporal allocation of resources.

A recent, fast growing literature argues that changes in the range of available product varieties contribute significantly to economic dynamics and movements in prices over time spans usually associated with the length of business cycles (Bilbiie et al., 2012 and Broda and Weinstein, 2010, and references therein). This paper investigates whether endogenous entry and product variety generate optimal deviations from price stability in a dynamic, stochastic, general equilibrium model with imperfect price adjustment. We study Ramsey-optimal monetary policy in a second-best environment in which lump-sum taxes are not available and inflation is the only instrument of policy. Therefore, our paper contributes to a large literature that seeks to describe optimal monetary policy in fully articulated, general-equilibrium models with nominal and real rigidities, using the tools of modern public finance (e.g. Khan et al., 2003 and Adão et al., 2003).1 Producer entry in our model takes place that subjects to sunk costs in the expectation of future monopoly profits. On the consumer side, entry is motivated by (general homothetic) preferences that exhibit a taste for variety. Price adjustment is costly, as producers incur a quadratic adjustment cost to change their prices (Rotemberg, 1982). This generates a Phillips curve that relates the markup to producer price inflation. The central bank may try to use inflation to influence markups, with the goal of closing the inefficiency wedge between the marginal rate of consumption–leisure substitution and the marginal product of labor. Furthermore, when the benefit of variety to consumers and the market incentive for product creation (the markup) are not aligned, an additional distortion occurs: if the former exceeds the latter there is too little entry, and vice versa (Bilbiie et al., 2008a). The central bank will use inflation to align markups (which govern entry incentives) with the benefit of variety. When preferences are such that the elasticity of substitution between varieties depends on their number, time-variation in desired markup introduces a dynamic dimension to the distortions in labor supply and product creation by generating a misallocation of resources across time and states of nature (Bilbiie et al., 2008a). The central bank can thus in principle use inflation to smooth the intertemporal path of the markup.2 The objective of this paper is to study how these distortions and possible objectives for the central bank shape the optimal conduct of monetary policy. Our results are twofold, pertaining to long-run and short-run inflation. Significant deviations from long-run price stability can be optimal, and their sign and magnitude depend on the balance of market incentives for entry and welfare benefit of variety. When the flexible-price market outcome results in too much entry (the net markup is higher than the benefit of variety), the central bank uses its leverage over real activity: the optimal path of producer price inflation has a positive steady-state level, which erodes the markup and precludes suboptimal entry. Long-run deflation occurs when the market provides too little entry, for deflation boosts entry by increasing markups. Optimal long-run inflation is zero if and only if preferences are such that the incentive for product creation by firms and the benefit of variety to consumers are perfectly balanced: for instance, when the utility aggregator takes the specific constant elasticity of substitution (C.E.S.) form introduced by Dixit and Stiglitz (1977-henceforth, C.E.S.-D.S.). Importantly, optimal deviations from long-run price stability generated by departing from this knife-edge scenario can be quantitatively significant: depending on the value of the parameter that measures the benefit of variety, the optimal inflation rate ranges from an annualized 4 percent to an annualized −8 percent; the numbers are even larger under price indexation. When preferences are such that the desired markup depends upon the scale of the economy (number of firms) and is higher than the benefit of variety, the degree of goods market regulation (which is irrelevant under C.E.S. preferences, because the scale itself is irrelevant) becomes an important determinant of the optimal long-run inflation rate. A higher entry cost reduces the steady-state number of firms, makes consumers less willing to substitute among their goods and increases desired markups; this creates more scope for using inflation in order to lower markups and discourage welfare-inefficient entry. Plausible preferences and parameter values justify the positive inflation targets adopted by central banks throughout the industrialized world (see Table 1 in Schmitt-Grohé and Uribe, 2011, for a summary). In the short run, however, approximate price stability (around a possibly non-zero optimal trend) is a robust policy prescription. In particular, the volatility of inflation under Ramsey policy is small for all the preferences considered: the central bank uses its leverage over real activity in the long run, but not in the short run.3 The welfare costs (in units of steady-state consumption) of perfectly stabilizing prices relative to following Ramsey-optimal policy can indeed be sizeable. Since the volatility of inflation under Ramsey policy is negligible, it can be concluded that most of the welfare cost of targeting a constant level of prices is due to the “long-run” component, i.e. to failing to adopt the Ramsey steady-state level of inflation as the central bank׳s target. Therefore, our conclusion is that the introduction of endogenous entry and preferences for variety more general than C.E.S.-D.S. can dramatically alter the long-run policy prescriptions obtained under fixed variety, but not the short-run implications. Lastly, we also quantify the temptation facing policymakers to renege on the optimal policies, and discuss how this is affected by the presence of endogenous entry and variety. Our results contribute to a large and growing literature on optimal monetary policy and inflation by studying a hitherto unexplored motive for non-zero optimal inflation. To isolate the contribution of the novel feature considered here (entry and variety), our analysis abstracts from other, well understood features—e.g. government spending and monetary distortions—that have been shown to result in optimal deviations from price stability.4 In such an environment, price stability is optimal or at least close to optimal in many models: the monetary authority does not use inflation (a distortionary tax) to try to close the constant wedge between the marginal rate of consumption–leisure substitution and the marginal product of labor implied by monopolistic competition and endogenous labor supply.5 It is important to notice that even when optimal deviations from short-run price stability occur in the existing literature, the finding that price stability is the optimal long-run policy prescription is surprisingly robust across a wide range of economic environments. 6 Indeed, this is a common theme of all the variations of the baseline model with Calvo (1983)– Yun (1996) price rigidity considered by Woodford (2003): “The optimal long-run inflation target is zero in this model, no matter how large the steady-state distortions may be” (p. 462, emphasis in original). Schmitt-Grohé and Uribe (2011) comprehensively review the existing literature on optimal inflation and conclude that “the observed inflation objectives of central banks pose a puzzle for monetary theory”; optimal long-run inflation is zero or very close to zero under a wide range of economic frictions, including incomplete taxation, the zero lower bound on nominal interest rates, downward rigidity in nominal wages, and the quality bias in measured inflation. 7 Thus, endogenous entry and product variety yield a policy implication that is largely new to the literature. 8 This paper is not the first to study optimal monetary policy under endogenous entry. Bilbiie et al. (2008b) showed that, in a model with entry and sticky prices à la Rotemberg (1982), stabilizing producer price inflation at zero in all periods is Pareto optimal in a first-best environment in which lump-sum taxes are available to finance the subsidies (or taxes) needed to correct real distortions. Bergin and Corsetti (2008) also study a model with entry and predetermined prices and show the (constrained) optimality of producer price stability in a second-best environment. Lewis (2013) studies optimal monetary policy in an economy with entry, a cash-in-advance constraint, and sticky wages. In her model, optimal inflation is used over the cycle to improve upon the flexible-wage response to shocks. In independent work, Faia (2010) uses a framework similar to ours (essentially, the Bilbiie et al., 2008b model), but with C.E.S.-D.S. preferences and oligopolistic competition as in Portier (1995) and Cook (2001), as well as government spending shocks. She finds that the Ramsey long-run prescription is “zero inflation”; however, in the short run, significant deviations from price stability are required for optimality. While apparently in stark contrast with our short-run findings, the difference can be explained by the absence of government spending from our framework since, as noted above, government spending by itself implies optimal deviations from short-run price stability. In order to isolate the potential role of entry and variety in generating deviations from price stability, our framework therefore abstracts from government spending altogether. When considering these studies in relation to the conduct of monetary policy in reality, one may wonder whether it is appropriate for central banks to have distortions in product variety in mind when determining their inflation targets. There are two reasons for an affirmative answer. First, to the extent that variety is important for aggregate fluctuations and long-run welfare, generating the optimal amount of variety is consistent with the policy objective of a welfare-maximizing equilibrium. Second, even if one may argue that optimal variety is best implemented by regulation policy, reality shows that regulators intervene in the economy only under exceptional circumstances to affect the behavior of the largest firms (for instance, Microsoft). “Blanket” instruments that affect all producers at all points in time (such as inflation) are thus better suited to induce the optimal equilibrium for the aggregate economy. More generally, the exercise of this paper is one of finding the optimal monetary policy, given a certain economic environment—very much like all studies of optimal monetary policy on which this paper builds—rather than a more general public finance exercise that would try to assess which is the best policy instrument to use in order to address a certain distortion. 9

A large literature studies optimal monetary policy in the presence of imperfect price adjustment and other real or monetary distortions. A general conclusion of this literature is that the optimal long-run rate of inflation is zero or very close to zero. Moreover, in an environment in which productivity shocks are the only source of uncertainty, perfectly stabilizing prices over the business cycle (and hence replicating the flexible-price allocation) is optimal, or nearly so. This paper argues that the optimal long-run rate of inflation can be significantly different from zero in an environment with endogenous entry and product variety, but price stability (around this long-run trend) is close to optimal over the cycle. The sign and magnitude of the optimal long-run inflation rate depend on the balance between the market incentives for entry (measured by the desired markup) and the welfare benefit of product variety to consumers. When the market outcome results in too much entry relative to what the consumer values (when the markup is higher than the benefit of variety), positive long-run inflation is optimal because it erodes long-run markups and profit margins, and it reduces entry. In the opposite case, long-run deflation is optimal, because it increases steady-state markups and hence provides more incentives for entry. The long-run rate of inflation is zero only in the knife-edge case of C.E.S.-D.S. preferences, for which the net markup is equal to the benefit of variety. With translog preferences, an important determinant of the optimal long-run rate of inflation is the sunk entry cost: less regulation implies more firms, more closely substitutable goods, and lower desired markups. This instead means that there is less scope for using inflation in order to reduce markups. The welfare loss from having a flat price level can be sizeable, depending on the benefit of variety parameter and, under translog, on the degree of entry regulation. Since the volatility of inflation under Ramsey policy is negligible for all preference specification considered, it follows that the bulk of the welfare loss of pursuing a constant price level is due not recognizing the non-zero long-run target for inflation implied by Ramsey policy. Finally, we quantify the policymaker׳s temptations to renege on previously-chosen policies, for which our framework provides a new source: achieving higher utility through the product creation margin. Our analysis provides a hitherto unexplored argument for potentially significant deviations from long-run price stability, with deviations of potential magnitudes not encountered in other economic environments no matter the type of underlying distortions (Schmitt-Grohé and Uribe, 2011, review exhaustively the robustness of the “zero optimal inflation” prescription). While our conclusions for optimal monetary policy are derived using the Rotemberg (1982) model, they should in principle carry to other forms of nominal rigidity, such as the widely used Calvo (1983)–Yun (1996) model. Three ingredients are essential for our results to hold, and they are all likely to be robust to the specific type of price stickiness. The first consists of the distortions outlined in Section 2.4, which all depend on the markup; this is orthogonal to the type of price rigidity. The second is the inverse relationship between average markups and inflation outlined in Section 2.1; in the Calvo–Yun model too, a similar negative relationship between inflation and average markups holds, as explained originally in King and Wolman (1996) and Goodfriend and King (1997). The third is a direct welfare cost of inflation, such as the quadratic resource cost in the Rotemberg framework; but this is also true of the Calvo–Yun model through dispersion in relative prices, which can also be expressed as a quadratic function of inflation (see Rotemberg and Woodford, 1997). Since the single most important determinant of optimal long-run inflation is the balance of markups and benefit of variety, our findings point to the need for continued study of the determinants of markups and serious empirical investigation of the nature of preferences for variety.30 The one preference specification (translog) that is not subject to identification problems related to the benefit of variety (Lewis and Poilly, 2012) and has several merits in fitting business cycle facts pertaining to entry, markups and profits (Bilbiie et al., 2012), implies that the optimal long-run rate of inflation is at least 1 percent under reasonable parameter values but with no indexation, and is increasing with the degree of entry regulation and with price indexation.