# Overview Of The Earliest Work On New Keynesian Phillips Curve

John M Roberts is a doctorate from Stanford University and currently an adviser at the Federal Reserve. He published the earliest article on New Keynesian Phillips Curve in the Journal of Money, Credit and Banking in the year 1995. He is one of the New Keynesians who believe in incorporating microeconomic fundamentals to Keynesian Economics.

Dr. Roberts in his paper titled ‘New Keynesian Economics and the Phillips Curve’, proposed to include the component of expected future prices in setting of price in the New Keynesian Framework, which inherently believes in price stickiness. In the backdrop of various models developed by Taylor (1979,1980), Calvo (1983) and Rotemberg (1982), he believed that there is a commonality between them which is analogous to Friedman and Phelps’ work on expectations-augmented Phillips Curve.

He used ‘limited information’ approach instead of full information techniques due to its shortcoming in providing inconsistent estimates when the model was misspecified. In this regard, the author took up two approaches and eventually compared them to discover the better method. In the first approach, presented by McCallum (1976), the actual future prices were taken as proxy for expected future prices. Whereas in the second approach, the proxy taken was the inflation expectations got through conducting surveys. The author also stuck to analysing time-dependent models of sticky prices due to its ability to have clear-cut closed- form solutions.

The author mainly considered three models, namely, The Quadratic Price Adjustment Framework, Calvo’s Staggered Contracts Model and Taylor’s Staggered-Contracts Model and captured the commonality of the three models to form the New Keynesian Phillips Curve model.

Firstly, under Rotemberg’s The Quadratic Price Adjustment Framework, the author undertook an optimisation procedure where he minimised the cost of prices which were changing, measured against the costs of deviating from the price the firm would opt in the absence of adjustment costs. Assuming an upward sloping aggregate supply curve and that firms are all identical, he obtained the following equation.

pt=Etpt+1+(c)yt-tc

where p= log of actual price at time t

β= positive parameter

c=parameter measuring ratio of costs of varying prices to costs of deviation from optimum price

t= random error term

Dr. Roberts considered equation (1) to be similar to the expectations-augmented Phillips Curve. Expected future rate of change in prices has been included as one of the exogenous variables in the context of sticky prices.

Secondly, Calvo’s Staggered Price Model was dealt with. The idea behind this model is that firms’ prices are staggered until it receives a random intimation to alter its price and this current price is considered to be a function of past prices set by other firms. The author introduced a probability value to whether a firm will receive a signal that it can change its price in any particular period and called it. This probability value was also considered to be representative of the fraction of firms which can alter its prices in any period by assuming that there were enough firms. In addition, firms were also presumed to have upward sloping supply curves.

After undertaking mathematical manipulations, the author derived the following equation

pt=Etpt+1 + 2(1-π)yt + 2(1-π)t

where >0 and 0< The author claimed the Equation (2) to an expectations-augmented Phillips Curve which shows a positive output-inflation relationship.

Finally, Dr. Roberts took up Taylor’s Staggered-Contracts Model and enunciated by simple addition how the model can be depicted as an expectations-augmented Phillips Curve as shown in equation (3). In this model, nominal rigidity was caused only due to wages unlike the earlier discussed models whose premise was sticky prices. Also, workers worry only about real wages, unemployment over the life of their contract period and price of firm equals wages plus a fixed mark up.

pt=EΔpt+1+c0-β(RUt-1+RUt+Et-1RUt+RUt+1)+2(t+t-1)+t

where c0 and are constants

>0 implying higher unemployment related to lower amount of wages

RU = unemployment rate

t= expectational error

Inflation was expected to fall when there is a rise in moving average of the unemployment.

The author eventually derived equation (4) which encompasses the vital elements of the first three models. (and equations).

pt-Etpt+1=c0+γ.yt + t ->New Keynesian Phillips Curve (NKPC)

where = positive constant

t= residual error term, which could be serially correlated

Current unemployment has been taken as a proxy for current, lagged and future unemployment due to unemployment possessing strong serial correlation.

The author considered equation (4) to be synonymous to Friedman and Phelps’ expectations-augmented Phillips curve. He also found it to be analogous to Lucas supply curve except for the fact that NKPC includes the expected future inflation instead of expectations of current inflation. This is mainly due to the New Keynesians’ belief of presence of sticky prices in the economy.

The author altered equation (4) to account for variation in t by considering changes in real oil prices as another exogeneous variable. The modified model is as follows:

pt-Etpt+1=c0+γ.yt +c1rpoilt+c2Δrpoilt-1+t

where rpoil = log of real price of crude oil

c1 and c2 are constants.

He further analysed a model substituting unemployment rate as an exogenous variable instead of output deviation from trend GNP.

pt-Etpt+1=c0+γ'RUt+c1rpoilt+c2Δrpoilt-1+t

Next, the author undertook an analysis by taking different proxies for expectations of future prices. Primarily, he took up a proxy based on two surveys each conducted by The Michigan Survey Research Center and Federal Reserve Bank of Philadelphia.

Secondly, the proxy used was actual future value of inflation, a method introduced by McCallum in 1976 and can be seen in the following equation.

pt-Δpt+1=c0+γ.yt+t+Etpt+1-Δpt+1

Non requirement of explicit measures of expectations made this approach famous among macro-econometric work. Comparatively, this method was expected to be less accurate given there was a new source of error. The author’s period of study was from 1949 to 1990. Twelve-month percent change in the CPI (from December to December) was used by the author as his measure of change in price in time period t. The exogeneous variable y was measured as percentage deviation of real Gross Domestic Product from a deterministic trend wherein the trend was estimated by undertaking regression of log of GNP on time and time squared.

The estimation resulted in a positive '' as expected by the author in both the cases. The coefficient turned out to be statistically significant when proxy was taken from surveys. On the other hand, results from McCallum’s approach produced statistically insignificant estimate due to large standard error. The author justified it by saying that proxy used from McCallum’s approach is relatively worse for inflation expectations. He found statistically significant coefficient on oil prices. When subsample stability tests on the estimates of parameters were conducted and observed, NKPC was found to be structurally stable. He summarised that changes in inflation didn’t cause a change in the coefficient of output and thus considered the estimates of to be structural.

The author concluded the paper by interpreting the strength of. The regression results gave a range of 0.2 to 0.4 for. Calvo’s model is believed to be best capable of explaining this coefficient. From Calvo’s model, we can see that is positively related to (supply elasticity of firm) and (how often firms change price). Dr. Roberts enunciated that, if a greater fraction of firms altered prices, say =0.9, it would imply =0.25 and =1/32 and thus a flatter supply curve. He concluded saying that unwillingness of firms to change their prices and flat supply schedules are equally crucial factors in producing nominal rigidity in the economy.

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