Generalized least squares and maximum likelihood estimation of the logistic function for technology diffusion

Given a simple stochastic model of technology adoption, we derive a function for technological diffusion that is logistic in the deterministic part and has an error term based on the binomial distribution. We derive two estimators—a generalized least squares (GLS) estimator and a maximum likelihood (ML) estimator—which should be more efficient than the ordinary least squares (OLS) estimators typically used to estimate technological diffusion functions. We compare the two new estimators with OLS using Monte-Carlo techniques and find that under perfect specification, GLS and ML are equally efficient and both are more efficient than OLS. There was no evidence of bias in any of the estimators. We used the estimators on some example data and found evidence suggesting that under conditions of misspecification, the estimated variance-covariance of the ML estimator is badly biased. We verified the existence of the bias with a second Monte-Carlo experiment performed with a known misspecification. In the second experiment, GLS was the most efficient estimator, followed by ML, and OLS was least efficient. We conclude that the GLS estimator of choice.     

Inflation convergence in Central and Eastern Europe vs. the Eurozone: Non‐linearities and long memory

In this paper, we consider inflation rate differentials between seven Central and Eastern European Countries (CEECs) and the Eurozone. We test for convergence in the inflation rate differentials, incorporating non‐linearities in the autoregressive parameters, fractional integration with endogenous structural changes, and also consider club convergence analysis for the CEECs over the period 1997 to 2015 based on monthly data. Our empirical findings suggest that the majority of countries experience non‐linearities in the inflation rate differential; however, there is only evidence of a persistent difference in some countries. Complementary to this analysis we apply the Phillips and Sul (2007) test for club convergence and find that there is evidence that most of the CEECs converge to a common steady state.     

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.     

Does a factor Phillips curve help? An evaluation of the predictive power for U.S. inflation

This article evaluates various models’ predictive power for U.S. inflation rate using a simulated out-of-sample forecasting framework. The starting point is the traditional unemployment Phillips curve. We show that a factor Phillips curve model is superior to the traditional Phillips curve, and its performance is comparable to other factor models. We find that a factor AR model is superior to the factor Phillips curve model, and is the best bivariate or factor model at longer horizons. Finally, we investigate a New Keynesian Phillips curve model, and find that its forecasting performance dominates all other models at the longer horizons.     

Nonparametric estimation of stochastic volatility models

This letter introduces nonparametric estimators of the drift and diffusion coefficient of stochastic volatility models which exploit techniques for estimating integrated volatility with high-frequency data. The performance of the proposed estimators is assessed on simulations of two popular stochastic volatility models.     

Is the NAIRU more useful in forecasting inflation than the natural rate of unemployment?

Recent studies have indicated that the terms ‘NAIRU’ (non-accelerating inflation rate of unemployment) and ‘natural rate of unemployment’ are not interchangeable. While NAIRU is an empirical macroeconomic relationship estimated via a Phillips curve, the natural rate is an equilibrium condition in the labour market, reflecting the market's microeconomic features. This study evaluates comparatively the inflation-forecasting power of alternative time-varying estimates of the natural rate of unemployment relative to the NAIRU. The natural rate of unemployment in the USA since the Second World War is estimated. Three alternative methods are utilized: the Kalman filter, a structural determinants approach, and the Hodrick-Prescott filter. The section that follows assesses how each estimator of the natural rate compares with the others – as well as with the NAIRU derived from a Phillips curve – in forecasting inflationary changes in the USA in the second half of the twentieth century. The analysis reveals that the overall inflation-forecasting utility of the natural rate of unemployment relative to the NAIRU is not very different. Moreover, the conclusion appears to be quite robust to various estimators of the natural rate.     

Asymptotic Properties Of The Estimator Of The Long-Run Coefficient In A Dynamic Model With Integrated Regressors And Serially Correlated Errors

In this paper we examine the asymptotic properties of the estimator of the long-run coefficient (LRC) in a dynamic regression model with integrated regressors and serially correlated errors. We show that the OLS estimators of the regression coefficients are inconsistent but the OLS-based estimator of the LRC is superconsistent. Furthermore, we propose an alternative consistent estimator of the LRC, compare the two estimators through a Monte Carlo experiment, and find that the proposed estimator is MSE-superior to the OLS-based estimator.     

Are survey expectations theory-consistent? The role of central bank communication and news

In this paper we analyze whether central bank communication can facilitate the understanding of key economic concepts. Using survey data for consumers and professionals, we calculate how many of them have expectations consistent with the Fisher Equation, the Taylor rule and the Phillips curve and test, by accounting for three different communication channels, whether central banks can influence those. A substantial share of participants has expectations consistent with the Fisher equation, followed by the Taylor rule and the Phillips curve. We show that having theory-consistent expectations is beneficial, as it improves the forecast accuracy. Furthermore, consistency is time varying. Exploring this time variation, we provide evidence that central bank communication as well as news on monetary policy can facilitate the understanding of those concepts and thereby improve the efficacy of monetary policy.     

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.     

Small Sample Properties Of Existing And New Estimators Of The Autocorrelation Coefficient And Regression Coefficients In The Context Of Ar(1) Errors

This study systematically and comprehensively investigates the small sample properties of the existing and some new estimators of the autocorrelation coefficient and of the regression coefficients in a linear regression model when errors follow an autoregressive process of order one. The new estimators of autocorrelation coefficient proposed here are based on the jackknife procedure. The jackknife procedure is applied in two alternative ways: first to the regression itself, and second to the residuals of the regression model. Next, the performance of the existing and new estimators of autocorrelation coefficient (thirty-three in total) is investigated in terms of bias and the root mean squared errors. Finally, we have systematically compared all of the estimators of the regression coefficients (again thirty-three) in terms of efficiency and their performance in hypothesis testing. We observe that the performance of the autocorrelation coefficient estimators is dependent upon the degree of autocorrelation and whether the autocorrelation is positive or negative. We do not observe a direct link between the bias and efficiency of an estimator. The performance of the estimators of the regression coefficients also depends upon the degree of autocorrelation. If the efficiency of regression estimator is of concern, then the iterative Prais-Winsten estimator should be used since it is most efficient for the widest range of independent variables and values of the autocorrelation coefficient. If testing of the hypothesis is of concern, then the estimators based on jackknife technique are certainly superior and are highly recommended. However, for negative values of the autocorrelation coefficient, the estimators based on Quenouille procedure and iterative Prais-Winsten estimator are comparable. But, for computational ease iterative Prais-Winsten estimator is recommended.

     

System estimates of potential output and the NAIRU

This paper proposes a new approach for estimating potential output and the NAIRU. The methodology models these key unobservable economic variables as latent stochastic trends within a trivariate system of observables comprising information on unemployment, GDP, and inflation. Identification is achieved through the use of a standard version of Okun's law and a Phillips curve. The performance of the procedure is investigated using Swedish quarterly data covering the time period 1970:1–1996:3. First version received: June 1997/final version received: September 1998     

Macroeconomic determinants of the credit risk in the banking system: The case of the GIPSI

In this paper, we analyze the link between the macroeconomic developments and the banking credit risk in a particular group of countries – Greece, Ireland, Portugal, Spain and Italy (GIPSI) – recently affected by unfavourable economic and financial conditions.Employing dynamic panel data approaches to these five countries over the period 1997q1–2011q3, we conclude that the banking credit risk is significantly affected by the macroeconomic environment: the credit risk increases when GDP growth and the share and housing price indices decrease and rises when the unemployment rate, interest rate, and credit growth increase; it is also positively affected by an appreciation of the real exchange rate; moreover, we observe a substantial increase in the credit risk during the recent financial crisis period. Several robustness tests with different estimators have also confirmed these results.The findings of this paper indicate that all policy measures that can be implemented to promote growth, employment, productivity and competitiveness and to reduce external and public debt in these countries are fundamental to stabilize their economies.     

Identification and dimension of the NAIRU

In this paper, we have re-examined the identification of the NAIRU and presented a well-defined reduced form for analysing the equilibrium unemployment rate, using a cointegrated VAR model. We have stated that the NAIRU estimates using the conventional reduced form (or Phillips curve) models are misleading since the natural rate of unemployment cannot be considered as a fixed point calling for the ceteris paribus assumption for all the data involved. This implies that the NAIRU estimates are unable to provide valuable information on the labour market status.     

On Calculation of the Extended Gini Coefficient

The conventional formula for estimating the extended Gini coefficient is a covariance formula provided by Lerman and Yitzhaki (1989). We suggest an alternative estimator, obtained by approximating the Lorenz curve by a series of linear segments. In a Monte Carlo experiment designed to assess the relative bias and efficiency of the two estimators, we find that, when using grouped data with 20 or fewer groups, our new estimator has less bias and lower mean squared error than the covariance estimator. When individual observations are used, or the number of groups is 30 or more, there is little or no difference in the performance of the two estimators.     

New Keynesian Phillips Curve and inflation dynamics in Australia

The New Keynesian Phillips Curve (NKPC) was developed as a response to the New Classical critique that Keynesian macroeconomics lacked micro-foundations. The NKPC provides theoretical micro-foundations that attempt to explain, inter alia, nominal rigidities and, explicitly price stickiness. This paper investigates the validity of the NKPC for Australia. In contrast to the findings for the USA and Euro area, we find that neither the output gap nor marginal cost appears to be a key driving force variable across different set of instruments and estimators (GMM and 2SLS) over the sample period from 1959 to 2009. The flattening of the NKPC along with significant presence of price stickiness is also found in the data. In particular, the reduced form coefficients and implied estimates from the structural parameters of the model support the view that inflation dynamics are forward looking while the role of lagged inflation is also statistically important only after 1980s. However, we claim that the forward looking baseline NKPC contrary to the hybrid NKPC is stable and better explains inflation dynamics for the Australian economy.     

(When) Should cointegrating regressions be detrended? The case of a German money demand function

If an economic relationship is superimposed by a linear time trend, the regression without detrending is misspecified. The estimators of such a regression do not converge to the true parameter values. First, the asymptotic limit arising from such misspecified regressions is characterized. Second, we observe with data before 1975 a significant time trend but no cointegrating relation between real money (M1), income and a long-term interest rate. The price level as a significant omitted variable is considered as an economic explanation for this feature. We find a price elasiticity larger than one. Third, with data after the breakdown of Bretton Woods (and the beginning of monetary targeting by the Bundesbank), real money, income and the interest rate alone are cointegrated. The long-run estimates seem to be fairly stable with data after the German union provided a step dummy accounts for a break in the mean. First version received: November 1996/final version received: June 1998     

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 micro-based non-inflationary rate of capacity utilisation as a measure of inflationary pressure: evidence for Austria

We derive a non-inflationary rate of capacity utilisation (NIRCU)—as recently proposed by Köberl and Lein (Can J Econ 44:673–694, 2011)—based on a large Austrian firm-level panel dataset ranging from 1996 to 2011. By conditioning the current capacity utilisation of firms on their current and planned price adjustments, a micro-level NIRCU is defined as the level of capacity utilisation at which there is no need for the firm to adjust its prices. In contrast to other measures of inflationary pressure, this measure (1) is timely available without revisions and (2) does not imply any need for rather arbitrary methods or concepts such as statistical filtering or potential output. In accordance with the results in Köberl and Lein (Can J Econ 44:673–694, 2011), we find that the NIRCU performs well as a driving variable of Austrian inflation in various Phillips Curve estimations. Compared to other inflation driving variables, such as real unit labor cost, the output gap and the unemployment gap, it delivers reasonable parameter estimates which are in line with existing Phillips Curve estimations in the literature.     

The New Keynesian Phillips curve and the role of expectations: Evidence from the CESifo World Economic Survey

We provide evidence on the fit of the hybrid New Keynesian Phillips curve for selected Euro zone countries, the US and the UK. Instead of imposing rational expectations and estimating the Phillips curve by the Generalized Method of Moments, we use direct measures of inflation expectations from the CESifo World Economic Survey. Our main findings are as follows: (i) The use of survey data gives empirical results, which are more reliable than those obtained from the GMM approach. (ii) The purely forward-looking Phillips curve can be rejected in favor of the hybrid New Keynesian Phillips curve. (iii) The estimated coefficients on past inflation are higher when using survey expectations than when using the rational expectations GMM approach. (iv) It remains unclear whether real unit labor costs or a measure of the output gap should be used as a proxy for real marginal costs. (v) Theory-based restrictions lead to an improvement of the empirical results.     

Response of inflation to shocks: New evidence from Sub-Saharan African countries

In this paper, we investigate whether or not the inflation rate of 17 Sub-Saharan African countries can be modelled as a stationary process. We achieve this goal through using univariate and panel stationarity tests for data over the period 1966 to 2002. We use the Kwiatkowski, Phillips, Schmidt and Shin (KPSS, 1992) univariate test and allow for multiple structural breaks. We find that except for Burkina Faso, Burundi and Gambia, the inflation rate is stationary for the rest of the 14 countries. We then apply the panel version of the KPSS test, developed by Carrion-i-Silvestre et al. (2005), which accounts for multiple structural breaks. We find strong evidence of panel stationarity of the inflation rate. However, for a panel consisting of Burkina Faso, Burundi and Gambia, we could not find evidence that the inflation rate is stationary.