Front. Econ. China 2011, 6(1): 76–91 DOI 10.1007/s11459-011-0123-7

RESEARCH ARTICLE

Hongmei Zhao, Vincent Hogan

Measuring the NAIRU — A Structural VAR Approach © Higher Education Press and Springer-Verlag 2011

Abstract This paper calculates the NAIRU for the US in a framework that allows inflation and unemployment to be jointly endogenous. We define the NAIRU as being the component of actual unemployment that is uncorrelated with inflation in the long run. We use a structural VAR to estimate the NAIRU and core inflation simultaneously and with greater precision than most of the previous literature. Our results show that the NAIRU fell dramatically at the end of the 1990s from 6.7% before 1997 to 5.2% afterwards. Keywords

NAIRU, inflation, unemployment, VAR

JEL Classification

1

E24, E25, E31

Introduction

Since the end of the 1990s, the joint decline of the US unemployment and inflation has focused attention on the non-accelerating inflation rate of unemployment (NAIRU). There has been some debate as to whether the NAIRU has actually fallen substantially or whether there have been a series of favorable (but temporary) shocks. In this paper we adopt a new approach and estimate the NAIRU using a structural vector autoregression (VAR). By bringing more structure to the estimation, this method provides more precise estimates of the NAIRU than much of the previous literature. It also produces estimates of core inflation, which is of Received July 10, 2010 Hongmei Zhao ( ) Institute of Econometrics and Statistics, School of Economics, Nankai University, Tianjin 300071, China E-mail: [email protected] Vincent Hogan School of Economics, University College Dublin, Dublin 4, Ireland E-mail: [email protected]

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independent interest. In addition, the empirical Phillips Curves generated by our procedure coincide with the traditional textbook presentation both in the long run and the short run. Traditionally there have been three approaches to the estimation of the NAIRU. It can be modelled as a deterministic function of time (as in Staiger et al., 1997); or as a stochastic process (as in Gordon, 1997); or as a function of labor market variables (as in Weiner, 1993). Staiger et al. (1996) shows that all three methods produce similar results with fairly high standard errors. For example, they report that a typical 95% confidence interval for the NAIRU in 1990 would be from 5.1% to 7.7%. Laubach (2001) adopts a different approach, modelling the unemployment gap as an autoregressive process. He shows that changes in the unemployment rate itself yield information about the NAIRU. This leads to a bivariate model of inflation and unemployment that can provide a more accurate estimation of the NAIRU. Laubach’s results suggest that the uncertainty of the NAIRU may be because the single Phillips equation cannot describe correctly the joint movement of inflation and unemployment. We extend this idea by using a VAR model to estimate the NAIRU. We place no restriction on the joint process of inflation and unemployment in the short run. In particular, we do not have to assume that the unemployment rate is exogenous or predetermined. This allows for far richer dynamics than is usual in the literature. The only restriction is that, in the long run, inflation is uncorrelated with the unemployment rate. This reflects the definition of the NAIRU as being the unemployment rate at which inflation is stable, i.e., the Phillips Curve is vertical in the long run. Formally our identification of the structural VAR is similar to that of Blanchard and Quah (1989) and Quah and Vahey (1995). We assume that the joint process of inflation and unemployment can be decomposed into two orthogonal disturbances. We assume that these disturbances can be distinguished by their long run effects on inflation: The first disturbance has no long run effect on inflation, while the second one may have. The estimated NAIRU corresponds to the first disturbance (or more precisely, to its accumulated effect on unemployment). Quah and Vahey (1995) adopted a similar procedure to separate core inflation from the joint movement of output and inflation. Our procedure will also supply an estimate of core inflation—which is to be that portion of inflation that is uncorrelated with unemployment in the long run. Thus as the unemployment rate tends to its long run rate (the NAIRU), actual inflation tends to core inflation. With our definition and the identifying restrictions, we obtain three basic results. First, the US NAIRU fell from 6.7% before 1997 to 5.2% afterwards. Second, in the short run, the change in the NAIRU typically accounts for only

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33% and 16% of the variation of inflation and the unemployment rate respectively. This suggests that demand side factors are more important at business cycle frequencies. Third, in contrast with that general result, it is the NAIRU disturbance turns out to be the main source of change in the late 1990s “Goldilocks” economy. The rest of the paper is organized as follows. In Section 2, we show how to identify the model. In Section 3, we analyze the economic interpretation behind our identification and assumptions. We discuss the estimation procedure and present our results in Section 4 and Section 5 concludes.

2

Identification

Our structural model assumes that the unemployment rate is composed of two parts. One part is the NAIRU. The other is the gap between the NAIRU and the actual unemployment rate. Accordingly, the shocks causing the fluctuations of the unemployment rate are separated into two kinds of disturbances—the kind of disturbances that affect the NAIRU (“NAIRU disturbance”) and the kind that affects only the unemployment gap (“gap disturbance”). As the NAIRU is determined by the characteristics of the labor market, such as market imperfections, market search etc., the NAIRU disturbance is similar to the aggregate supply shock in Blanchard & Quah (1989). Similarly, our gap disturbance is equivalent to their aggregate demand shock (e.g., monetary and fiscal policy shocks). Blanchard & Quah (1989) used this methodology to identify trend output in a VAR model of output and unemployment. In our paper, we use it to jointly measure the NAIRU and core inflation. After separating the two disturbances, we can estimate the NAIRU by setting the gap disturbance to be zero, i.e., the estimated NAIRU is accumulated by the effects of the NAIRU disturbance. The NAIRU disturbance and the gap disturbance are distinguished by their long run effects on inflation. This is the key identifying assumption of the paper. We assume that the NAIRU disturbance has no long run effect on inflation.1 The gap disturbance may or may not have significant long run effect on inflation. Both disturbances are assumed to be uncorrelated at all leads and lags. It is also important to note that the fact that the NAIRU disturbance does not affect inflation in the long run does not stop it from affecting inflation in the short run. We use the notation X = ( Δπ , u )′ and ε = (ε N , ε G )′ , where π and u denote

inflation and the unemployment rate; and ε N and ε G denote the NAIRU and gap disturbance respectively. We write X as the following: 1

The economic interpretation behind of these restrictions will be discussed in Section 3.

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X (t ) = C (0)ε (t ) + C (1)ε (t − 1) + " ∞

= ∑ C ( j )ε (t − j )

Var (ε ) = I

(1)

j =0

Eq. (1) is our structural model written in VMA form. This equation expresses Δπ and u as distributed lags of the two structural disturbances ε N and ε G . Coefficient C(j) is the matrix of impulse response functions to the disturbances. It gives the effect of shocks in period t on the variables in period t + j. There are three aspects of this equation that need clarification. First, due to the assumption that the NAIRU and gap disturbances are uncorrelated at all leads and lags, their variance-covariance matrix is diagonal; and for convenience, the disturbances are normalized so that var( ε1 ) = var( ε 2 ) = 1. Second, our structural model cannot be estimated directly, because there is no data for two disturbances. What we are going to do is recover model (1) from the VMA form of a VAR model. But a prerequisite for transforming VMA from VAR is that all the endogenous variables are stationary, hence we use the first difference of π and the level of u (see below). Third, as is standard in the literature, a constant, time trend and other exogenous variables are included in our model. Specifically, we include some supply shock variables (import price and unit labor cost). To remove them from the model would result in excessive small fluctuations of the estimated NAIRU which would not conform to most economists’ definition of the NAIRU. The key identifying assumption—in the long run, the NAIRU disturbance has no effect on inflation is shown in our model as following: ∞

∑ C11 ( j ) = 0

(2)

j =0

where C11 is the upper left element of the matrix C. To see why this is the case, note in the long run, if inflation is to be unaffected by the NAIRU disturbance, inflation must return to its original value after shocks. In another word, the increase of inflation must be positive first and negative afterwards (or negative first, then positive). So the cumulated effects of the NAIRU disturbance on the change of inflation must equal to zero. We impose no other restrictions on the model. So the long run impact of the gap disturbance and the short run effect of both disturbances are free to be determined by the data. The VAR model we estimate is: X (t ) = A( L) X (t − 1) + e(t ) where A(L) is a polynomial in lag operator. By the Wold Representation Theorem, we can invert the stationary VAR model (Vector Auto Regression) into VMA form (Vector Moving Average).

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X (t ) = et + B (1)et −1 + B(2)et − 2 + " ∞

= et + ∑ B( j )e(t − j )

Var (e) = Ω

(3)

j =1

Eq. (1) is the model we need while Eq. (3) is the model we are able to estimate. So next we need to recover the structural disturbances ε from VAR residuals e. Now take one-step ahead forecast for the endogenous variables of Eq. (1) and Eq. (3): ( Δπ , u). The forecast errors should be equal, because Eq. (1) and Eq. (3) have the same endogenous variables. By doing so, we can get a relationship between ε and e: et = C (0)ε t (4) C ( j ) = B( j )C (0) (5) These expressions relating the structural disturbances to the VAR residuals allow the recovery of ε if C(0) is unique. From Eq. (4) we get C (0)C (0)′ = Ω , which gives three equations in the four unknowns of matrix C(0). In order to identify C(0) (and hence ε ), we need the fourth restriction. This comes from the long run restriction on the NAIRU disturbance given by Eq. (2). In order to impose this restriction on the VAR, we first rewrite Eq. (3) by using Eq. (4) to replacing e with ε . Then the coefficient of NAIRU disturbance ε N should be equal to zero according to the Eq. (2) which gives: ∞

∑ [( B( j )C (0)]11 = 0

(6)

j =0

With four conditions, we can solve for C(0). The rest of the coefficients can be easily solved by using Eq. (5). Finally, the NAIRU can be obtained by setting ε G equal to zero, as shown in Eq. (7) i.e., the time path of unemployment that would exist in the absence of the gap disturbance. Similarly, core inflation can be calculated by setting ε N equal to zero as in Eq. (8). This is the case because we assumed that the NAIRU disturbance has no long run effect on inflation. Therefore, in the long run, inflation is caused only by the gap disturbance. This long run inflation rate is our definition of core inflation. ∞

U NAIRU = ∑ C21ε Nt

(7)

0

∞

π core = ∑ C12ε Gt

(8)

0

3

Interpretation

The condition that the NAIRU disturbance has no effect on inflation in the long run is the key to identifying the whole model. It reflects the definition of the NAIRU—the component of the actual unemployment rate that is uncorrelated

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with inflation in the long run. This definition of the NAIRU is slightly different from the usual in the literature. The theoretical background for this definition is still the augmented Phillips Curve. Specifically, the reason why there is a short-term trade off between inflation and the unemployment rate is the existence of nominal rigidities. However, we assume that nominal rigidity cannot last forever. Eventually, the nominal wage must keep pace with the change of inflation. At that time, the unemployment rate will return to its long run rate (the NAIRU) regardless of the rate of inflation. Thus, at this point unemployment and inflation are uncorrelated. This is also the reason why we set up the model using the variable of inflation and the unemployment rate. Furthermore, we can define the rate of inflation that holds at that point to be the core rate of inflation, i.e., the rate of inflation with the effects of the business cycle stripped away. Note that we do not restrict the permanent effects of gap disturbance on inflation. Furthermore, we say nothing about the permanent effects of both shocks on the unemployment rate. However, inflation is usually considered as a non-stationary variable whereas the unemployment rate is treated as a stationary variable (see below). If the NAIRU disturbance has no long-run effect on inflation, the gap disturbance should have. Similarly, since the unemployment rate is stationary, none of the disturbances should have an effect on the unemployment rate in the long run. we do not restrict the short run effect of both disturbances on inflation and the unemployment rate. Following a shock, should inflation and the unemployment rate rise or fall? How long should it take them to return to their original level? We leave these questions to the data. Whether or not the results are reasonable will indicate the validity of our identification. Finally note a limitation of this analysis. Obviously, there are many real world shocks. We group them as the NAIRU and gap disturbance depending on whether or not they affect inflation permanently. However, the permanent effects of some shocks on inflation are not clear. For example, we might consider the productivity shock as part of the NAIRU disturbance. But the part it played in the double decline of inflation and unemployment at the end of 1990s is still an open question. Blanchard and Quah (1989) considere this problem and presented a sufficient and necessary condition to deal with it.2 However, this condition is unlikely to be reached in reality. Zhao (2005) examines this issue in more detail in by extending the model to allow for separate productivity and wage aspirations shocks. She shows that the qualitative results are not much different from those presented here. 2

Correct identification is possible if and only if the individual distributed lag responses in inflation growth and unemployment are sufficiently similar across the different NAIRU disturbances, and across the different supply disturbances.

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Estimation and Results

We estimate the model using the US annual data over the period of 1961 to 2009. We use the data from the Bureau of Labor Statistics and OECD Economic Outlook. The details are given in Table 1. Before the analysis, we first test for a unit root in inflation and the unemployment rate in order to guarantee the variables in the VAR model are all stationary. The Augmented Dickey Fuller (ADF) test for the hypothesis that inflation and the unemployment rate have unit root shows that we cannot reject the null for inflation at any significant level.3 In contrast, for the unemployment rate, we can reject the null at 5% significant level.4 Therefore, inflation is a I(1) process and the unemployment rate is a I(0) process. All the tests include constant, but the unemployment test include time trend, time trend square and a time dummy for 2009 additionally, from which we know that the unemployment rate is actually a time trend stationary process. This implies that the unemployment rate is a typical stationary variable after being extracted the time trend. However, inflation is a strict I(1) process. It would not become stationary even if being extract the time trend. The stationarity of inflation is obtained by being taken the first order difference. Based on these results, we put the first difference of inflation and the level of unemployment rate in the VAR, but also add the time trend, time trend square term and time dummy for 2009 to the model in order to control the effects of time trend on the unemployment rate. Table 1

Definitions of Variables Definition

Inflation = ln(CPI t − CPI t −1 ) The unemployment rate = (LF – ET)/LF Change of import price = ln( PMGt ) − ln( PMGt −1 ) Real unit labor cost = ULC/PGDP Change of real unit labor cost =

ln( RULCt ) − ln( RULCt −1 )

Code CPI: consumer price index (BLS*) LF: labor force; ET: total employed (BLS*) PMG: import price goods, local currency, custom basis l (EO**) ULC: unit labor cost (EO) PGDP: deflator for GDP market price (EO) RULC: real unit labor cost (EO)

Note: BLS*—Bureau of Labour Statistics, EO**—OECD Economic Outlook.

The results that inflation is a I(1) process and it is added to the model in the form of first difference can be found in most of Phillips Curve studies like 3

Augmented Dicky Fuller test with two lags. The test statistics of the ADF test with 2 lags on inflation, the change of inflation and the unemployment rate are 1.258, –3.891 and –3.587.

4

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Gordon (1997) and Laubach (2001), etc. This reflects the property that inflation keeps increasing and never returns to the original level after being attacked by some particular shocks. Most of Phillips Curve studies also support to treat the US unemployment rate as stationary variable, but the evidence for the I(0) unemployment rate is relatively weak. For example, Evans (1989) does the ADF test for the unemployment rate using the data from 1950 to 1985 in which paper he tries to do the structural VAR study within the framework of GNP and the unemployment rate. The results give an evidence for the I(0) unemployment rate after he adds the time trend and time dummy to the ADF test equation. Recent studies like Ghosh and Dutt (2004) confirm the stationarity evidence about the US unemployment rate. But they find that the US unemployment rate has a non-linear adjustment process after a peak. Therefore, we follow these results and use the level variable of unemployment rate to estimate the VAR model. Additionally, constant, time trend, time trend squared and a dummy for 2009 are included into the VAR model in order to control the linear and non-linear effects of the time trend described in the above literature. The basic VAR model also includes some supply shock variables (the change of import price and the change of real unit labor cost). Controlling the supply shock variables should help eliminate the noise from the model. The final estimation results show that the stability of the NAIRU is greatly enhanced by the inclusion of the supply shock variables in the model. The changes of import price will pick up the effect of the oil price shock and a change in the value of the US dollar as well as changes in foreign currency prices of the US imports. The real unit cost of labor will include changes in wages, benefits and also temporary changes to productivity. Finally, we set the lag length at 4, which is chosen by AIC (akaike inflation criterion) and FPE (final predictor error) method.5 4.1

The NAIRU

As explained in the previous section, the NAIRU can be constructed as the time path of the unemployment rate that would exist in the absence of gap disturbance. Our estimated NAIRU is shown in Fig. 1. 6 The relative high-frequency movement of the NAIRU in the figure confirms that the NAIRU is time-varying 5

Different lag length criterions specify different optimal lag length. AIC and FPE set the 4th lag as the optimal one, but SC (Schwarz information criterion) chooses the 1st lag, HQ (Hannan-Quinn information criterion) chooses 2nd lag and LR (likelihood ration test) chooses 1st lag. To avoid losing useful information, we take 4 lags in the VAR model. Fortunately, the VAR results are quite stable by using different lag length. 6 The NAIRU in Fig. 1 starts from 1976 because we take 10 lags for the NAIRU disturbance to calculate the NAIRU. Together with 4 lags in the VAR model, 14 NAIRU observations are lost.

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and that imposing a fixed NAIRU on the model could be a serious misspecification. Moreover, the NAIRU exhibits a fairly steady decline, falling from 7% or 8% in the early eighties to as low as 5% more recently up to 2009.

Fig. 1 The Unemployment Rate and the NAIRU (NBER recessions shaded)

In Fig. 1, the business cycle is measured by an expansion and a contraction of the unemployment gap.7 The first business cycle of the US starts from 1975 and ends in 1986. The NAIRU in this period has a high value, and remains relatively stable. As shown in the figure, the expansion and contraction of the unemployment gap are much bigger than the change of the NAIRU, which indicates that the economic boom at the end of 1970s and the following economic recession at the beginning of 1980s are attributed to the impacts of the gap disturbance. This result is consistent with most of studies on the NAIRU. The second business cycle takes place during the period of 1986 to 1993. The NAIRU falls by 0.7% in the boom period and meanwhile the unemployment gap shows a decrease of the same amount. Similarly, during the recession period, both the NAIRU and the unemployment gap rise about 0.9%. Thus the fluctuations were caused by both the NAIRU disturbance and the gap disturbance. Many people assume that aggregate demand shocks (here represented by gap disturbance) were primarily responsible for the boom, especially considering the expansionary fiscal policy of the period. However, Fig. 1 shows that we cannot ignore the obvious shift of the NAIRU—perhaps due to structural changes of the labor market in late 1980s. 7

We add NBER recessions for reference (shown by the shaded areas in Fig. 1). However, NBER recessions are defined by a fall of real GDP rather than unemployment. We can see from the figure that when NBER recession happens, the unemployment gap is turning to be positive. It appears that the unemployment rate is a lagging indicator for GDP.

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In the economic boom at the end of 1990s, low unemployment co-existed with low inflation. As shown in the figure, the NAIRU falls from 6.5% in 1993 to below 5% in 2000, whereas the unemployment gap changes only slightly. The change in the unemployment gap is only 1/3 as much as the change in the NAIRU. Apparently, the structural change of the labor market related to the NAIRU disturbance occupies the dominant position in this economic boom. The particular structural changes lead the NAIRU to fall at the end of 1990s is beyond the scope of this paper. Zhao (2005) shows that, productivity growth ahead of wage aspirations, could explain a portion of the decline in the NAIRU. From the figure, we can see that there is economic recession between 2000 and 2001. During this period, both the NAIRU and the unemployment gap rise slightly, and are more or less equally responsible for the increase in unemployment. In fact, the recession was probably the result of many different economic shocks, for example, the bursting of “Tech bubble” may have led to a slowdown in the productivity growth (a negative NAIRU disturbance). the US budget surpluses at that time may have reduced aggregate demand (a negative “gap” disturbance). Either way, both the NAIRU disturbance and the gap disturbance had a part to play in the 2001 recession. After 2001, demand side shocks appear obvious in the economic activity, because the unemployment gap expands substantially. The expansion is nearly equal to that during the oil price shock period at the end of 1970s. The gap disturbance certainly appears to be more volatile in the early 1980s than in later years especially during the “Goldilocks” economy of the 1990s. This may reflect the success of monetary policy in stabilizing demand shocks during this period. But it should be noted that it was probably politically easier to stabilize demand during a period where the economy was being hit by favorable supply shocks manifest here in the declining NAIRU which was dragging down unemployment anyway. In order to judge the precision of the estimated NAIRU, we show it in Fig. 2 with 95% confidence bands. These bands are obtained by using Monte Carlo study with 1,000 replications.8 Fig. 2 shows that the precision of the estimated NAIRU is greatly improved by our method. The distance between the error bands has an average value of 1.5%. Comparing with the Staiger et al. (1997), univariate Phillips Curve derived a pair of standard error bands for the NAIRU with the distance of 2.6%. From the simple bivariate model (Laubach, 2001), the gap between two bands is about 2.3%. 8

We take the variance-covariance matrix of the error terms from the VAR model. Then select randomly 1,000 series of artificial error terms with the same (normal) distribution. We replace the true error terms in the VAR model by the artificial terms one by one, and apply the decomposition technique as described in the identification section. We get 1,000 NAIRUs. The standard deviation are calculated from these 1,000 NAIRUs generates the standard error band.

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Fig. 2 The NAIRU with Standard Error Bands (within 95% confidence interval)

4.2

The Phillips Curves

After deriving the NAIRU, we can use the gap disturbance to identify core inflation in Eq. (7). The relationship between the NAIRU and core inflation forms the basis of the standard textbook model of the Phillips Curve. The long run Phillips Curve is formed by a plot of the NAIRU versus core inflation. The rest of unemployment (i.e. unemployment gap) and inflation (i.e. non-core inflation) describe the movement along a short run Phillips Curve. Both Phillips Curves are shown in Fig. 3.

Fig. 3

Short Run and Long Run Phillips Curve

The trade-off between inflation and the unemployment rate is very obvious in the short run Phillips Curve diagram. Although the fitted short-run line is obviously an average about which there is considerable fluctuation exactly as we would expect. Notably, after 1987 all the points gathered within a limited space, by which the trade-off is hardly recognizable. This might reflect the relative stable and cautious monetary policy period which appeared to make relatively little use of the short run trade-off. The long run Phillips Curve is close to the vertical line predicted by the

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standard model. But we can identify a shift in the long run curve. During the period of 1975 to 1987 the NAIRU averages around 7%. In more recent years, the long run Phillips Curve appears to have shifted left with the NAIRU now averaging 6%. Overall, these two diagrams show clearly that our identification produces a decomposition of unemployment ands inflation that is very close to the typical textbook model. 4.3

Impulse Response Function (IRF)

Plotting the impulse response function is a practical way to visually represent the behaviour of inflation and the unemployment rate in response to the various shocks and this tests the plausibility of our identification. The impulse response function is the coefficient of the disturbances of the structural model. All the impulse response functions in our paper are calculated from one percent increase of the disturbance and the increase of the disturbance can be understood to have a positive effect to the economy. Thus, no matter which disturbance rises by one percent, the unemployment rate should be reduced initially. Fig. 4 shows our impulse response functions and their confidence intervals.9

Fig. 4 9

Impulse Response Function

The standard error bands are obtained by using Monte Carlo study with 1,000 replications as described in Section 4.1.

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Inflation IRF to one percent increase of the NAIRU disturbance: In response to a shock that reduces unemployment, inflation falls by 0.29% points in the beginning. It keeps growing afterwards until reaches to the maximum three years later. Then, as imposed by identification, it eventually returns to its original level in the long run. The fall of inflation in the beginning is a bit of a puzzle as we would expect inflation to rise immediately following a shock that pushes down unemployment. Inflation IRF to one percent increase of the gap disturbance: After an increase of the gap shock, inflation goes up by 0.48 percentage points. This effect reaches the maximum in the first year. Then inflation eventually falls to a stable level three years later but the one that is higher than the initial level. The gap disturbance has permanent effect on inflation. This result is consistent with studies of the impact of monetary policy. Christiano et al. (1999) summarizes different structural VAR models and shows that monetary shocks (part of our “gap” disturbance) have effect on price over a period of 12 quarters. Unemployment rate IRF to one percent increase of the NAIRU disturbance: The unemployment rate falls by 0.26 percentage points at the beginning, and then returns to its original level quite quickly.10 Comparing with the gap disturbance, the NAIRU disturbance has less of an effect on the unemployment rate. Neither disturbance has a long run effect on unemployment reflecting the fact that unemployment is stationary. Unemployment rate IRF to one percent increase of the gap disturbance: The unemployment rate falls by 0.62 percentage points immediately. It takes the unemployment rate 3 years to recover itself. We can see clearly from the figure that the fluctuations of the unemployment rate caused by the gap disturbance are bigger than those caused by the NAIRU disturbance. This suggests that the movement of the unemployment rate is mainly attributed to the gap disturbance. In summary, we only imposed one restriction on the model: The NAIRU disturbance has no effect on inflation in the long run. Although we did not restrict the other effects of the NAIRU and gap disturbance, the estimated effects are plausible. This suggests that our identification is plausible and conforms to standard view of the Phillips Curve. 4.4

Variance Decomposition

A variance decomposition separates the effects of two disturbances on the variation of inflation and the unemployment rate and demonstrates which is more important source of volatility and whether the effect diminishes over time. Table 10

Blanchard & Quah (1989) found a similar result regarding the speed of adjustment of the unemployment rate to their supply and demand shocks.

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2 shows the variance decomposition. The total variation of inflation and the unemployment rate is assumed to be 100%. The proportion of the variation that the NAIRU disturbance accounts for is shown in the table with the rest being due to the gap disturbance. Again, two standard errors bands (in parentheses) are obtained from 1,000 Monte Carlo replications. Table 2 Variance Decomposition of Inflation and the Unemployment Rate (Percentage of Variance Due to the NAIRU Disturbance) Horizon (year)

Inflation

Unemployment rate

1

33.302 87

15.718 18

(20)

(20)

30.596 56

14.533 3

(11)

(11)

33.643 97

15.737 19

(12)

(12)

36.224 84

15.810 33

(11)

(11)

5

37.001 37

15.001 14

(12)

(12)

6

39.604 09

14.882 35

(12)

(12)

39.495 79

14.886 64

(12)

(12)

39.640 69

14.875 86

(12)

(12)

39.780 57

14.860 68

(12)

(12)

39.646 15

14.954 32

(12)

(12)

2

3

4

7

8

9

10

Note: The numbers in parentheses represent the standard errors derived from 1,000 Monte Carlo replications.

The NAIRU disturbance has little effect on the variation of inflation at the beginning. The variations explained by the NAIRU disturbance are about 33% of the total. As time goes on, the explained variations become stable. Finally, the NAIRU disturbance contributes less to the variation of inflation than the gap disturbance. The contribution of the NAIRU disturbance to the unemployment

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rate variation remains small over the whole sample period. So most fluctuations of inflation and the unemployment rate are attribute to the gap disturbance.

5

Conclusion

We propose a structural VAR approach to estimate the NAIRU. The NAIRU is defined as the component of the actual unemployment rate that is uncorrelated with inflation in the long run. This definition is different from the traditional one in that it allows for the feedback between inflation and the unemployment rate. Another advantage of this approach is that both the NAIRU and core inflation can be estimated simultaneously. Our estimate of the NAIRU is based on the following assumptions: There are two uncorrelated disturbances that can be distinguished by their effects on inflation in the long run. The first disturbance has no long run effect on inflation, while the second one may have. The estimated NAIRU corresponds to the first disturbance and core inflation corresponds to the second one. Our model also appears to give more precise estimated of the NAIRU than much of the rest of the literature. Impulse response functions of both the NAIRU and gap disturbances are plausible and so give support to our identification. We conclude that the business cycle of the US from 1975 to 1985 is largely attributable to the impact of the gap disturbance. The business cycle during the period of 1986 to 1993 is caused by both NAIRU and gap disturbance. Policy shocks and the structural change of the labor market probably both played a role. In contrast, the NAIRU disturbance occupies the dominant position in the economic boom at the end of 1990s. The NAIRU falls during this period. Our results show that the NAIRU shifts back from around 6.7% before 1997 to 5.6 % afterwards. This paper provides some insight into the movement of the NAIRU. But further work is needed. Firstly, the model can be extended by identifying other shocks that may affect unemployment and inflation. As discussed in Ball & Mankiw (2002), dealing with the identification problem for the supply shock in a more satisfactory way would be helpful to increase the precision of estimating the NAIRU. Secondly, our estimation result shows that the NAIRU apparently falls in the second half of the 1990s. It would be interesting to explore what caused the fall of the NAIRU during this period. Productivity has been attractive candidate due to its extraordinary performance since late 1990s. Gordon (2003) explores the context, causes and implications of the recent productivity growth. It would be particularly interesting to examine the effect of productivity on the NAIRU and core inflation. Zhao (2005) does this work.

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