Nonlinear Phillips curve,NAIRU and monetary policy rules

The US Phillips curve is modeled with a logistic smooth transition autoregression specification that allows various nonlinear shapes. Using this, the paper derives model-consistent estimates of the NAIRU. The NAIRU is defined as the level of unemployment rate that would correspond to a forecast of no inflation changes over the policy horizon. This paper also investigates the implications of nonlinearities in the Phillips curve for deriving optimal monetary policy rules. The optimal policy rule for interest rates and implied sacrifice ratios are found to be nonlinear as well.      

The empirical validity of the New Keynesian Phillips curve using survey forecasts of inflation

This paper investigates the performance of the New Keynesian Phillips curve when survey forecasts of inflation are used to proxy for inflation expectations. Previous authors such as Brissimis and Magginas (2008) have applied survey measures of inflation expectations to the NKPC, and have concluded that these estimates are superior to those estimated using actual data on future inflation. However this approach employs the use of the labor income share as the proxy for real marginal cost, something which is highly problematic once we consider the countercyclicality of this variable. This paper develops and tests a procyclical marginal cost variable alongside various survey measures of inflation forecasts in the NKPC, while recognizing the problem of weak instruments that occurs when estimating the model using conventional GMM. We find that the NKPC produces a counter-intuitive negative and significant coefficient on procyclical marginal cost when surveys of inflation forecasts are used, which casts serious doubt on the empirical viability of the NKPC model, even when estimated with survey inflation forecasts.     

Vacancies, unemployment, and the Phillips curve

The canonical new Keynesian Phillips curve has become a standard component of models designed for monetary policy analysis. However, in the basic new Keynesian model, there is no unemployment, all variation in labor input occurs along the intensive hours margin, and the driving variable for inflation depends on workers’ marginal rates of substitution between leisure and consumption. In this paper, we incorporate a theory of unemployment into the new Keynesian theory of inflation and empirically test its implications for inflation dynamics. We show how a traditional Phillips curve linking inflation and unemployment can be derived and how the elasticity of inflation with respect to unemployment depends on structural characteristics of the labor market such as the matching technology that pairs vacancies with unemployed workers. We estimate on US data the Phillips curve generated by the model. While we can reject the baseline new Keynesian Phillips curve in favor of the search-frictions specification, we show it is still too stylized to fully describe the dynamics of firms’ marginal costs.     

Cost-based Phillips Curve forecasts of inflation

It is a well-established idea that prices are a function of marginal cost, yet estimating a reliable measure of marginal cost is difficult to do. Stock and Watson (1999) use the Phillips Curve to forecast inflation for a variety of existing activity variables that researchers commonly use to proxy for marginal cost. This paper uses a similar type of approach to examine the performance of a new candidate for the activity variable, which is marginal cost measured following the theoretical methodology of Bils (1987), which we find to be simple yet powerful when implemented empirically. We then use the Phillips Curve to conduct pseudo out-of-sample inflation forecasts for the US using: output, unemployment, hours, the labor share, the capacity utilization rate, and the new measure of marginal cost. For almost all cases, forecast errors are lowest in the regressions with the new marginal cost variable, indicating that this new measure is an improvement over previous attempts to proxy for marginal cost.     

The elusive Phillips curve

The empirical evidence that has accumulated over the past twenty years for major countries, and especially the United States, Canada, and the U.K., suggests three distinct “phases” for the Phillips curve. In the “early” phase the coefficient on the unemployment variable was correctly signed and statistically significant; in the “middle” phase, as further studies were made and the data period extended, the unemployment coefficient tended to become numerically smaller and often to be statistically insignificant; in the “late” phase, as yet more studies accumulated and the data period was extended into the seventies, the unemployment coefficient was sometimes perversely signed and also statistically significant. This paper offers a possible theoretical interpretation of this phenomenon. The theoretical analysis is supplemented with some empirical simulations.     

Real wages,real interest rates,and the Phillips curve

This article argues that any analysis of a Phillips curve should include the real interest rate in addition to inflation and real wages as any changes in the interest rate changes the labour–capital input mix in the production process leading to a change in the level of employment in the economy. To justify this argument a Phillips curve model is developed, which includes the real interest rate in addition to inflation and real wages. After the diagnosis of the time series properties of the data, an error correction model is developed and estimated using a set of US annual data from 1948 to 1996. The estimated parameters of the model do suggest that one should really take into consideration of the real interest rate while analysing the Phillips curve. A non-nested test (F-test) also suggests that the Phillips curve model with real interest rate as an additional variable performs better than the conventional method that does not include the real interest rate.     

The Phillips curve,parameter instability and the Lucas critique

Empirical estimation of Phillips curve relationships typically indicates the presence of parameter instability. This is argued to be due to the fact that the parameters of these equations are reduced form rather than structural parameters. Estimation of a Phillips curve model by methods which allow for time-varying parameters permits investigation of the nature and timing of the structural breaks which generate instability. This paper estimates such a model by the Kalman filter using quarterly data over the period 1972.4 to 1993.3. We find evidence of a gradual decline in the private sector's assessment of the steady-state inflation rate during the 1980s, but little evidence of the sort of dramatic regime shift predicted by some of the more extreme rational expectations models.     

The long-run Phillips curve and non-stationary inflation

Modern theories of inflation incorporate a vertical long-run Phillips curve and are usually estimated using techniques that ignore the non-stationary behaviour of inflation. Consequently, the estimates obtained are imprecise and unable to test the veracity of a vertical long-run Phillips curve. We estimate a Phillips curve model taking into account the non-stationary properties in inflation and identify a small but significant positive relationship between inflation and unemployment. The results also provide some evidence that the trade-off between inflation and the rate of unemployment in the short-run worsens as the mean rate of inflation increases.     

Estimating a high-frequency New-Keynesian Phillips curve

This paper estimates a high-frequency New-Keynesian Phillips curve via the generalized method of moments. Allowing for higher-than-usual frequencies strongly mitigates the problems of small-sample bias and structural breaks. Applying a daily frequency allows us to obtain estimates for the Calvo parameter of nominal rigidity over a very short period—for instance for the recent financial and economic crisis—which can then be easily transformed into their low-frequency equivalences. With Argentine data from the end of 2007 to the beginning of 2011 we estimate the daily Calvo parameter and find that on average prices remain fixed for approximately two to three months which is in line with recent microeconomic evidence.     

Money illusion and the long-run Phillips curve in staggered wage-setting models

We consider the effect of money illusion – defined referring to Stevens' ratio estimation function – on the long-run Phillips curve in an otherwise standard New Keynesian model of sticky wages. We show that if households under-perceive real economic variables, negative money non-superneutralities will become more severe. On the contrary, if households over-perceive real variables, positive money non-superneutralities will arise. We also provide a welfare analysis of our results and we show that they are robust to the inclusion of varying capital into the model. Firms' (over-)under-perception of the real prices of production inputs (strengthens) weakens negative money non-superneutralities. In the Appendix, we investigate how money illusion affects the short-run effects of a monetary shock.     

Nonlinearity and structural stability in the Phillips curve: Evidence from Turkey

In this paper, we investigate possible nonlinearities in the inflation–output relationship in Turkey for the 1980–2008 period. We first estimate a linear bivariate model for the inflation rate and output gap, and test for linearity of the estimated model against nonlinear alternatives. Linearity test results suggest that the relationship between the inflation rate and output gap is highly nonlinear. We estimate a bivariate time-varying smooth transition regression model, and compute dynamic effects of one variable on the other by generalized impulse response functions. Computed impulse response functions indicate that inflation–output relationship in Turkey during the analyzed period was regime dependent and varied considerably across time.     

The NIRCU and the Phillips curve: an approach based on micro data

Abstract In this paper we propose a straightforward method to derive a non‐inflationary rate of capacity utilization (NIRCU) based on micro data. We condition the current capacity utilization of firms on their current and planned price adjustments. The non‐inflationary capacity utilization rate is then defined as the rate where a firm feels no price adjustment pressure. One of the main advantages is that this methodology uses structural aspects and does not make it necessary to operate with – often rather arbitrary – statistical filters. We show that our aggregate NIRCU performs remarkably well as an indicator of inflationary pressure in a Phillips curve estimation.     

A Phillips curve interpretation of error-correction models of the wage and price dynamics

This paper presents a model of employment, distribution andinflation in which a modern error correction specification ofthe nominal wage and price dynamics (referring to claims onincome by workers and firms) occupies a prominent role. It isbrought out, explicitly, how this rather typical error-correctionsetting, which actually seems to capture the wage and pricedynamics of many large-scale econometric models quite well,is fully compatible with the notion of an old-fashioned Phillipscurve with finite slope. It is shown how the steady-state impactof various shocks to the model can be profitably conceived ofand interpreted in terms of (and to some extent even calculatedby means of) this long-run Phillips curve.     

Time-varying U.S. inflation dynamics and the New Keynesian Phillips curve

This paper introduces a form of boundedly-rational inflation expectations in the New Keynesian Phillips curve. The representative agent is assumed to behave as an econometrician, employing a time series model for inflation that allows for both permanent and temporary shocks. The near-unity coefficient on expected inflation in the Phillips curve causes the agent's perception of a unit root in inflation to become close to self-fulfilling. In a “consistent expectations equilibrium,” the value of the Kalman gain parameter in the agent's forecast rule is pinned down using the observed autocorrelation of inflation changes. The forecast errors observed by the agent are close to white noise, making it difficult for the agent to detect a misspecification of the forecast rule. I show that this simple model of inflation expectations can generate time-varying persistence and volatility that is broadly similar to that observed in long-run U.S. data. Model-based values for expected inflation track well with movements in survey-based measures of U.S. expected inflation. In numerical simulations, the model can generate pronounced low-frequency swings in the level of inflation that are driven solely by expectational feedback, not by changes in monetary policy.     

Policy implications of a non-linear Phillips curve in a stochastic environment

When the Phillips curve is non-linear, fluctuations of the unemployment rate below the mean will have a larger impact on the inflation rate than fluctuations above the mean. This paper shows that this causes conventional measures of the “natural unemployment rate” to underestimate the mean unemployment rate consistent with stable inflation in the long run. More importantly, it reveals a potential long-run trade-off between unemployment and economic stability.     

Comparing alternative Phillips curve specifications: European results with survey-based expectations

This article examines inflation dynamics in Europe. Econometric specification tests with pooled European data are used to compare the empirical performance of the New Classical, New Keynesian and Hybrid specifications of the Phillips curve. Instead of imposing any specific form of expectations formation, direct measures, i.e. Consensus Economics survey data are used to proxy economic agents’ inflation expectations. According to the results, the New Classical Phillips curve has satisfactory statistical properties. Moreover, the purely forward-looking New Keynesian Phillips curve is clearly outperformed by the New Classical and Hybrid Phillips curves. We interpret our results as indicating that the European inflation process is not purely forward looking and inflation cannot instantaneously adjust to changes in expectations. Consequently, even allowing for possible nonrationality in expectations results in a lagged inflation term entering the New Keynesian Phillips curve for inflation dynamics in Europe.     

Are monetary-policy reaction functions asymmetric?: The role of nonlinearity in the Phillips curve

This paper investigates the implications of a nonlinear Phillips curve for the derivation of optimal monetary policy rules. Combined with a quadratic loss function, the optimal policy is also nonlinear, with the policy-maker increasing interest rates by a larger amount when inflation or output are above target than the amount it will reduce them when they are below target. Specifically, the main prediction of our model is that such a source of nonlinearity leads to the inclusion of the interaction between expected inflation and the output gap in an otherwise linear Taylor rule. We find empirical support for this type of asymmetries in the interest rate-setting behaviour of four European central banks but none for the US Fed.