سیاست پولی بهینه در جهان فیلیپس منحنی

In this paper, we study optimal monetary policy in a model that integrates the modern theory of unemployment with a liquidity model of monetary transmission. Two policy environments are considered: period-by-period optimization (time consistency) and full commitment (Ramsey allocation). When the economy is subject to productivity shocks, the optimal policy is pro-cyclical. We also characterize the long-term properties of monetary policy and show that with commitment the optimal inflation rate is inversely related to the bargaining power of workers. Both results find empirical support in the data.

A robust empirical feature of post-war US data is the positive correlation between inflation and employment, which is commonly referred to as the Phillips-curve relation (see [28]). This empirical feature supports the view that inflationary monetary policies have expansionary effects on the real sector of the economy, at least in the short-run. The goal of this paper is to study the optimal monetary policy in a model in which there is a direct link between these policies and employment. We study a general equilibrium model where the real side of the economy is characterized by a search and matching framework with equilibrium unemployment. In this framework, we introduce a monetary sector in which changes in the supply of money affects the nominal interest rate by changing the supply of loanable funds (liquidity effect). The change in the interest rate, in turn, affects the financing cost of firms and impacts on the real sector of the economy. In this way the model captures the ‘‘cost channel’’ of monetary transmission that Barth and Ramey [5] find significant for the propagation of monetary shocks. This channel is also consistent with recent empirical studies that find significant liquidity effects of monetary policy shocks.1 We consider two policy environments. In the first environment we assume that monetary policy interventions are decided on a period-by-period basis, and the monetary authority cannot credibly commit to long-run plans (time-consistent policy). In studying the time-consistent policy, we restrict the analysis to policies that are Markov-stationary, i.e., policy rules that only depend on the current (physical) states of the economy. In the second policy environment, we assume that the monetary authority is able to commit to long-term plans (Ramsey allocation). There are two main findings. The first finding concerns the cyclical properties of the optimal policy while the second concerns the long-term properties. Regarding the cyclical properties, we show that in both policy environments the optimal policy is pro-cyclical when business cycle fluctuations are driven by technology shocks: it increases the stock of money when employment and output are high and reduces the stock of money when they are low. Further, the optimal growth rate of money is positively correlated with employment and output. Both features—the procyclicality of the monetary aggregates and the money growth—characterize the post-war history of the US economy as documented in [11]. The second finding is that there are important differences between the long-term properties of the time-consistent policy and the long-term properties of the optimal policy with commitment. We show that when the worker’s share of the matching surplus is small and the employer’s share high, the time-consistent policy is less inflationary than the optimal policy with commitment. This result contrasts with earlier studies of optimal monetary policy, such as [4,21]. The intuition for these results is simple. Consider first the pro-cyclicality of the optimal policy. After a positive productivity shock, the demand for loanable funds increases due to the firms’ desire to expand production. The increase in the demandfor loanable funds raises the nominal interest rate and this is inefficient. To prevent the interest rate increase, the policy maker has to expand the supply of loanable funds by increasing the stock of money. Because the search and matching frictions in the labor market generate a persistent response of employment to shocks (humpshaped response) and output grows for more than one period, the optimal growth rate of money is above its steady state level for more than one period. This implies that the growth rate of money is positively correlated with employment and output. In the absence of matching frictions, however, output will grow only in the first period and then return to the steady state. In this case, the optimal growth rate of money would be negatively correlated with employment and output: it would be below the steady state with the exception of the first period. Therefore, the search and matching frictions are key to generating the pro-cyclicality of money growth. Consider now the long-term properties of the optimal policy. In this economy there are two possible sources of inefficiency. The first inefficiency derives from the cost of financing the current production plan for firms. On this dimension a Friedman rule of a zero nominal interest rate is optimal because a positive interest rate distorts the production decisions of firms by increasing their financing cost. The second source of inefficiency derives from the matching frictions in the labor market. As shown in [19], if the worker’s share of the matching surplus is too small, there will be an excessive creation of vacancies due to the high profitability of a match for the firm. The policy maker can reduce the profitability of a match by increasing the nominal interest rates. However, the decision to create new vacancies is not affected by the current interest rate but only by future interest rates. The policy maker is able to credibly choose the future interest rates only if it can commit. Otherwise, after the new vacancies have been created, it no longer has the incentive to keep the high interest rate. The lack of commitment then implies that the time-consistent policy is given by a simple Friedman rule of a zero nominal interest rate while the optimal policy with commitment will set positive nominal interest rates. In the long run higher interest rates are associated with higher inflation rates (Fisher rule). As will be shown in Section 5, the importance of the worker’s share of the surplus for the longterm property of the monetary policy is supported by data for a cross-section of countries. There are several studies that are related to this paper. Shi [29] shows that with searching frictions the Friedman rule may not be efficient, although he does not conduct an explicit analysis of the optimal monetary policy. The optimal and timeconsistent policy is studied in Ireland [20], but in an environment in which there are no frictions in the labor market and monetary policy affects the real sector of the economy through the rigidity of nominal prices. In Ireland’s model the optimal monetary policy is also pro-cyclical when business fluctuations are driven by technology shocks. However, his results do not extend to our long-term results for which policy commitment can affect the properties of the optimal policy. Our novel results depend crucially on the consideration of search and matching frictions. A study of the differences between time-consistent policies and optimal policies with commitment in models with sticky prices and liquidity effects is conducted in [2]. In contrast to our paper, they do not find important long-term differences between theenvironment with and without commitment.We reach a different conclusion because of the more complex dynamics introduced by the matching frictions that characterize the labor market. The plan of the paper is as follows. In Section 1 we describe the model and in Section 2 we define the optimal policy in the two policy environments: absence of commitment and full commitment. Section 3 characterizes the analytical properties of the optimal policy and Section 4 examines their quantitative properties. Section 5 discusses the empirical relevance of our long-term results and provides cross-country evidence about the negative relation between the workers’ share of the surplus and the inflation rate. Finally, Section 6 concludes.

In this paper we have analyzed the properties of the optimal monetary policy in a world where inflationary monetary interventions have expansionary effects in the economy through the liquidity channel. We find that if technology shocks are the main driving force of business cycle fluctuations, then the optimal monetary policy is pro-cyclical and amplifies the response of the economy to these shocks. Theoptimality of a pro-cyclical policy derives from the assumption that technology shocks are the main source of business cycle fluctuations. Different conclusions may be reached if we consider alternative sources of fluctuations. We have also analyzed the long-run properties of the optimal and time-consistent policy and compared it to the long-term properties of the optimal policy under commitment. The main finding is that the ability to commit could lead to higher inflation if certain conditions pertaining to the structure of the labor market are satisfied. More specifically, higher inflation would be optimal if the employers’ share of the surplus is too large. In this case higher inflation and interest rates are optimal because they reduce the surplus generated by a match, and therefore, the excessive creation of jobs. This result requires only a weak version of commitment. For example, this would be the outcome if the policy maker chooses the policy instruments two periods in advance (two-period commitment). This weak form of commitment could derive from formal and informal institutional restrictions to the discretion of the policy maker, as well as from the lags through which the policy instruments impact on the real sector of the economy. In this sense, the assumption of commitment is not unreasonable and there is some cross-country evidence supporting our result. In particular, countries in which the fraction of value added paid in the form of wages (proxing for the bargaining power of workers) is lower, are also the countries that tend to experience higher inflation. We conclude by pointing out that there could be other mechanisms that make the Friedman rule suboptimal. One of this mechanism derives from the distributional effects of inflation which are ignored in this paper. This mechanism is studied in Albanesi [1].