هزینه‌های رفاهی تورم در یک اقتصاد پویا با بیکاری اصطکاکی

We present a monetary general equilibrium model with labor market frictions in the form of search unemployment which is calibrated for the US economy. Interestingly, both employment and output may even increase with the rate of inflation depending on the elasticity of labor supply. Considering the transition dynamics following a change in the monetary policy, the optimal quarterly inflation rate is found to amount to approximately −0.6% in the benchmark case. A reduction of the inflation rate from its current level to its optimal value only results in small welfare gains equal to 0.08% of total consumption.

Lucas (2000) argues that the money holding behavior at very low interest rate is central for estimating welfare costs of inflation. Furthermore, he provides estimates of the welfare costs of inflation. A reduction in the inflation rate from 10% to zero implies steady-state welfare gains of approximately 1% percent of real income. In order to derive his results, he calibrates both the Sidrauski model and the McCallum–Goodfriend model with the help of observations from the US economy. He concludes that the optimal monetary policy in these two models consists of a deflation consistent with a zero or near-zero nominal interest rate as advocated by Friedman (1969). In a variety of recent studies on the optimal quantity of money and the optimality of the Friedman rule, the use of cash has been motivated with a cash-in-advance constraint provided in Lucas and Stokey 1983 and Lucas and Stokey 1987.1 In the presence of a cash-in-advance constraint, higher inflation reduces the return from working as income earned in the previous period cannot be spent on the cash good until the next period. As a consequence, households substitute leisure for labor and employment and output decline. In the cash-in-advance economy of Cooley and Hansen (1989), the optimal growth rate of money entails a zero nominal interest rate so that the cash-in-advance constraint does not bind. They estimate the welfare costs of a reduction from an annual inflation rate of 10% to the optimal rate to amount to approximately 0.1–0.4% of GNP, depending on the measurement of money by either the monetary base or M1. Over the last decade, two different questions with regard to the welfare costs of inflation have been extensively analyzed in the general equilibrium model with a cash-in-advance constraint based on Lucas and Stokey 1983 and Lucas and Stokey 1987: (i) is the Friedman rule of a zero nominal interest rate still optimal in economies with distorting taxes, and (ii) what is the (quantitative) effect of inflation on welfare if monetary policy affects the growth rate of the economy. The first question is answered using standard results from public finance (as in Diamond and Mirrless 1971a and Diamond and Mirrless 1971b), e.g. in the studies of Cooley and Hansen (1991), Gillman (1993), or Chari et al. (1996). The second question is examined in models of endogenous growth where inflation reduces the growth rate. In Gomme (1993), endogenous growth arises through human capital accumulation as in Lucas 1988 and Lucas 1990. A 10% money growth rate (8.5% inflation rate) results in welfare costs of no more than 0.03% of income. Wu and Zhang (1998) analyze a monetary endogenous growth model based on Romer (1986). They find significant welfare costs of inflation in the range from half to 5% points for an annual monetary growth of 10%. Different from Gomme (1993), the growth rate effect is important in their model. In the present paper, we also analyze the welfare costs of inflation in a monetary general equilibrium model with a cash-in-advance constraint. However, our direction of research is different from the above studies which all assume Walrasian labor markets. Our model is based on Pissarides (1990). Unemployment results from time-consuming and costly matching of vacancies with searching agents. The presence of search unemployment and wage bargaining is shown to have an impact on optimal monetary policy. We find that inflation may help to increase employment. Furthermore, even though the Friedman rule may not be optimal, the resulting welfare losses from such a deflationary monetary policy are of small magnitude. At first glance, this result is surprising. Following a rise in the inflation rate, agents substitute search for leisure, similar to the leisure-labor substitution effect in Cooley and Hansen (1989) or in the endogenous growth models of Gomme (1993) and Wu and Zhang (1998). The reduction in search effort reduces the probability of firms to fill a job and tends to decrease employment. However, in our model, there is also an opposing employment-enhancing effect from a rise in the rate of inflation. High inflation also reduces the level of consumption (relative to the one of capital) as agents substitute real money balances and capital as in Tobin (1965). In our economy, wages result from decentralized Nash bargaining. Following a decline in consumption, the reservation wage of the households and, hence, the bargained wage decrease. Consequently, firms increase their vacancies, which boosts employment.2 The net effect of a rise of inflation on employment is positive for our benchmark calibration of the model for the US economy, but is shown to crucially depend on the labor supply elasticity. In addition to other studies on the welfare effects of inflation such as Cooley and Hansen (1989) or Lucas (2000), we will also account for the transition dynamics following a change in the money growth rate. Recent quantitative evaluations of policy measures find a significant effect of transition dynamics on welfare. For example, Lucas (1990) analyzes the abolition of capital income taxes in an endogenous growth model with human capital accumulation. In steady state, the change in welfare amounts to a 3% consumption equivalent increase. As demonstrated by Grüner and Heer (2000), also considering the transition from the old to the new steady state reduces the welfare gain of such a policy to 1% of total consumption. Furthermore, in our model of search unemployment, the transition dynamics and hence welfare results may be different from the one in standard models with Walrasian labor markets. Typically, welfare is measured by life-time utility of the households which is a function of leisure and consumption. Following a policy change, consumption and leisure immediately adjust in standard monetary general equilibrium models, i.e. they are jump variables. However, in the presence of labor market frictions, employment behaves fundamentally different and only adjusts gradually to the new steady state, i.e. employment is a sluggish variable. Consequently, the magnitude of instantaneous utility during transition differs significantly from the one in the new steady state and the analysis of the balanced-growth path without any further consideration of the transition might even lead to the wrong policy conclusion. Our model extends the search unemployment model of Shi and Wen (1999) by introducing a role for money with the help of a cash-in-advance constraint. The monetary general equilibrium model is presented in Section 2. In Section 3, the model is calibrated for the US economy using standard parameters from applied general equilibrium studies. We also briefly describe our computational methods. Section 4 presents a balanced-growth analysis. As one major result, inflation is shown to possibly increase employment, production, and steady-state utility in the presence of search unemployment and wage bargaining. In Section 5, the welfare costs of inflation are analyzed explicitly accounting for the transition dynamics. As our second major result, the optimal nominal interest rate is shown to be close but not equal to zero for realistic values of labor market parameters. Section 6 concludes.

This paper has examined the welfare costs of moderate inflation in a search equilibrium model. Our results challenge conventional wisdom that higher rates of inflation reduce employment, output, and welfare unanimously. As our first main result, low rates of inflation are demonstrated to reduce employment and output in the benchmark calibration of our model for the US economy, even though the quantitative effect is small. It is also straightforward to show that the reduction of employment also results in a lower growth rate in models of endogenous growth (see Heer, 2000). As our second main result, the optimal quarterly inflation rate is shown to be negative and amounts to −0.6% in our benchmark case. Employment effects of monetary policy and, to a smaller extent, the optimal inflation rate, however, depend on two parameters from the labor market. The lower the elasticity of labor supply and the elasticity of vacancies in job matches, the more likely is inflation to have adverse effects on both employment and welfare and the more pronounced is the quantitative welfare effect of a monetary policy that entails a zero nominal interest rate. For reasonable values for these two parameters, welfare gains from an optimal monetary policy are computed in the range of 0.08–0.65% of total consumption.