metadata: authors: 0: author: Agenor, Pierre-Richard
1: author: Bayraktar, Nihal
count: Philippines,Korea, Republic of,Türkiye,Chile
docna: 0: docna: Contracting models of the Phillips curve -
            empirical estimates for Middle-income countries
docty: Policy Research Working Paper
subtopic: Consumption,Fiscal & Monetary Policy,International Trade and Trade Rules,Inflation,Macroeconomic Management,Inequality
teratopic: International Economics and Trade
abstracts: cdata!: This paper provides empirical estimates
            of contracting models of the Phillips curve for four
            middle-income developing economies-Chile, the Republic of
            Korea, the Philippines, and Turkey. Following an analytical
            review, models with both one lead and one lag, and two lags
            and three leads, are then estimated using Generalized Method
            of Moments (GMM) techniques. The results indicate that for
            both Chile and Turkey past and future inflation are of about
            the same magnitude in affecting current inflation. In Korea
            past inflation has a larger impact on inflation, whereas in
            the Philippines it is future inflation that plays a larger
            role. Homogeneity restrictions are satisfied for Korea and
            Turkey, but not for Chile and the Philippines.
geo_reg_key: 517208,119228,517198,119225,517190,119229,517191
repnme: repnme: Contracting models of the Phillips curve -
            empirical estimates for Middle-income countries
display_title: Contracting models of the Phillips
            curve - empirical estimates for Middle-income countries
listing_relative_url: /research/2003/09/2620960/contracting-models-phillips-curve-empirical-estimates-middle-income-countries
topicv3: Poverty m1326687 695,Inflation m1326709 0870F4727ACED1CF8525815C00471347,Trade m1326924 698,Macroeconomic and Structural Policies
            m1327380 439,Monetary Policy m1327609 444
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: International Economics and Trade
origu: WBI
no_of_pages: 32
author_keys: 0: author_key: NA
1: author_key: NA
model_extractions: | POLICY RESEARCH WORKING PAPER 3139

# Abstract

This paper provides empirical estimates of contracting models of the Phillips curve for four middle-income developing economies-Chile, the Republic of Korea, the Philippines, and Turkey. Following an analytical review, models with both one lead and one lag, and two lags and three leads, are then estimated using Generalized Method of Moments (GMM) techniques.

The results indicate that for both Chile and Turkey past and future inflation are of about the same magnitude in affecting current inflation. In Korea past inflation has a larger impact on inflation, whereas in the Philippines it is future inflation that plays a larger role. Homogeneity restrictions are satisfied for Korea and Turkey but not for Chile and the Philippines.

This paper-a product of the Poverty Reduction and Economic Management Division, World Bank Institute-is part of a larger effort in the institute to understand the dynamics of inflation in developing countries. Copies of the paper are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contactMaria Gosiengfiao, room J4-280, telephone 202-473-3363, fax 202-676-9810, email address mgosiengfiao@worldbank.org. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at pagenor @worldbank.org or nbayraktar@worldbank.org. September 2003. (24 pages) _The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about aeveiopment issues._ **_Ain_** _ojecwive_ **_of_** _te series is_ **_to_** _get_ **_tbe fnaings ouL_ qluciz;y,** _euen_ **_if_** _ebe_ presentations _are less_ **_tban suliy_** _pomlsnca. Tbe papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this_ **_paper a.rA ontire, tt-o of tbe auth-rs The¢o. not n4rcenrii- rflrcnrt tbe, iJ of th_** _W-orJd_ **_Rank, ;ts F-eCutibe flrenonrc -r th,_** _countries they represent._ Produced by the Research Support Team
# Contracting Models of the Phillips Curve: Empirical Estimates for Middle-Income Countries

Pierre-Richard Ag6nor and Nihal Bayraktar The World Bank Washington DC 20433 JEL **Classification Numbers:** E44, F32, F34
# I Introduction

The degree of wage and price stickiness plays an important role in the transmission of macroeconomic shocks. In traditional backward-looking Phillips curves, inertia in the wage- and price-contracting process is generally captured by introducing measures of past inflation.' By contrast, in models of overlapping contracts with forward-looking agents, inflation is represented as a function of its expected future realizations, based on all available information about the state of the economy. Indeed, several of these models, such as the Taylor-Calvo staggered contracts approach (see Taylor (1979, 1980) and Calvo (1983)) and the quadratic price adjustment cost approach of Rotemberg (1982), have a common formulation that is similar to an expectationsaugmented Philipps curve, with current prices depend on future prices.<sup>2</sup>

> Several recent studies have provided estimates of forward-looking contracting models (also called New Keynesian models) of the Phillips curve,

> most notably Fuhrer (1997), Galf and Gertler (1999), Guerrieri (2002), Roberts

> (1995, 2001), and Rudd and Whelan (2001). However, all of these studies fo-

> cus on the United states; given the conflicting nature of some of the results, it is difficult to draw general inference from them for other industrial countries,

> or, for that matter, developing countries. In this paper, we provide empirical

'It is also argued that past inflation is a proxy for expectations of future inflation. 2See Roberts (1995). These two approaches are often referred to as "time-dependent" models (see Ball, Mankin and Romer (1988)), because firms set their prices for fixed periods of time. An alternative approach to sticky prices relies on "state-contingent" adjustment rules, in which firms change price when underlying determinants, such as demand and costs, reach some pre-specified upper or lower bounds. See, Romer (2000) and Sutherland (1995) for a discussion, and Mankiw and Reis (2001) for an effort to move away from the sticky-price models that underlie contracting models of the Phillips curve, in understanding inflation dynamics.

2
evidence on contracting models of inflation for four middle-income developing countries: Chile, Korea, the Philippines, and Turkey. These countries represent a fairly diverse experience in terms of inflation, with countries like Korea and the Philippines experiencing relatively low and stable inflation during the sample period, whereas Chile and Turkey experienced higher and more persistent episodes of inflation. Section II examines various types of backward- and forward-looking models of inflation, including specifically the model of Fuhrer and Moore (1995). Section III presents our econometric methodology, which is based on GMM estimation. We use in our empirical framework a weighted average of both past and expected future inflation, to reflect elements of both the backward- and forward-looking approaches to the Phillips curve, with the importance of each determined empirically. Section IV presents the empirical results, whereas Section V concludes.

# 2 Contracting Models of the Phillips Curve

Much of the recent research on the dynamics of price adjustment in Keynesian models dwells on the staggered contracts models of Taylor (1979, 1980), Calvo (1983), Rotemberg (1982) and Fuhrer and Moore (1995). These models are based on the assumption that wages are set in nominal terms at discrete periods of time in an asynchronous fashion (because they are set by different agents at different points in time) and, as a result, contracts overlap. Agents are assumed to contract a wage that reflects their anticipations of future price and output levels for the expected duration of the contract. These models typically assume that prices are a constant markup over wages and focus on the persistence induced in the aggregate price (average wage) level due to 3
the asynchronous and overlapping nature of wage contracts.<sup>3</sup> The main difference between Taylor-type contracts and Calvo and Rotemberg models is that the individual firm's price-setting decision is derived from an explicit optimization problem. In the latter group of models, the starting point is an environment with monopolistically competitive firms: when it has the opportunity, each firm chooses its nominal price to maximize profits subject to constraints on the frequency of future price adjustments. For instance, in the quadratic price adjustment model developed by Rotemberg (1982), firms are assumed to minimize the total costs of changing prices. Nevertheless, as shown by Roberts (1995), and as discussed by Clarida, Galf, and Gertler (1999), all of these models can be formulated in the form of a forward-looking Philipps curve, of the form where 0 < a 2 < 1, 7rt is the inflation rate, Et7rt+l denotes the one-period ahead expected inflation rate, conditional on period t information, Yt the output gap, and **et** a random shock with zero mean and constant variance. In this setting, it can also be shown that _cal_ is inversely related to the degree of price rigidity; the longer prices are held fixed (on average), the less responsive is inflation to cyclical fluctuations in output.

Various criticisms have been addressed to the Taylor-Calvo-Rotemberg (TCR) approach. Ireland (2001) has argued that the approach is flawed in the sense that it focused on the costs (or impossibility) of changing prices in relation to the previous period's level, instead of focusing on changes

> 3 Note that this approach does not postulate that formal contracts are actually written,

> but rather that nominal prices (wages) are preset for some period of time.

4
relative to the previous period's level _plus_ the average one-period<sup>inflation</sup> rate. Andersen (1998) has argued that focusing on price staggering,<sup>instead</sup> of wage staggering, does matter for output and price dynamics<sup>(namely,</sup> the degree of persistence of shocks), in contrast to the<sup>TCRapproachin</sup> which implicitly it is assumed that there is no qualitative<sup>differencebetween</sup> the two cases. Most importantly for our purpose here, it<sup>has beenpointed</sup> out that the TCR approach implies no persistence to the<sup>inflationrate(see</sup> Estrella and Fuhrer (2000) for a detailed discussion). It<sup>hastheimplausible</sup> implication that a credible disinflation program<sup>canbeimplementedatno</sup> output cost.

Fuhrer and Moore (1995) have developed a price<sup>formationequationthat</sup> can indeed generate inflation inertia. Their model can be summarized<sup>as</sup> follows. Suppose that agents negotiate nominal wage contracts<sup>that remain</sup> in effect for four quarters. Unlike Taylor (1980),<sup>however,thereisnofixed</sup> markup from wages to prices. This difference is essential,<sup>becauseitallows</sup> a meaningful distinction between prices and wages. The aggregate<sup>logprice</sup> index in quarter t, Pt, is a weighted average of<sup>thelogofcontractprices,</sup> **Xt-i,** that were negotiated in the current and the previous<sup>threequartersand</sup> are still in effect. The weights, 6i, are the proportions of the<sup>outstanding</sup> contracts that were negotiated in quarter t<sup>-i,</sup> where bi > 0 and i = 1. Fuhrer and Moore (1995) assume that the distribution of contract prices can be characterized by a downward-sloping 5
linear function of contract length, with 0 < _s <_ 1/6 and i = 0, ... 3. This distribution depends on a single slope parameter, s, and it is invertible. When s = 0, it is the rectangular distribution of Taylor (1980), and when s = 1/6, it is the triangular distribution.

Let vt be the index of real contract prices that were negotiated on the contracts currently in effect, where **bi** is the fraction of wage contracts negotiated in period t - i that are still in effect at period t.

> Agents set nominal contract prices so that the current real contract price equals the average real contract price index expected to prevail over the life of the contract, adjusted for expected excess demand, measured by the output gap, yt:

> where etis an error term. Substituting (2) in (3) yields the "relative" (or

> real) version of Taylor's (1980) contracting equation:

where 6
Letting 7rt = _Pt - Pt-1,_ the Phillips curve derived<sup>fromthemodelisa</sup> two-sided curve defined as where _6(L) =_ o0 _+ 6 1L_ + 62L<sup>2</sup> ... is the lag polynominal that<sup>describesthe</sup> distribution of price contracts in the model.

In the Fuhrer-Moore model, agents in their contracting<sup>decisionscare</sup> about the _relative_ real contract price in effect during<sup>the life of their contracts.</sup> They therefore compare the current real contract<sup>pricewithanaverageof</sup> the real contract prices that were negotiated in<sup>therecentpastand those</sup> that are expected to be negotiated in the near future;<sup>theweightsinthe</sup> average measure the extent to which the past and<sup>future contracts overlap the</sup> current one. When output is expected to be<sup>high,the currentrealcontract</sup> price is high relative to the real contract prices<sup>onoverlapping contracts.4</sup> In contrast, the Taylor (1980) specification assumes<sup>thatagents careabout</sup> relative _nominal_ contract wages (and prices) in<sup>effectduringthe lifeof their</sup> contracts.

The attractive feature of the Fuhrer-Moore contracting<sup>specificationis</sup> that it helps to explain the high degree of persistence<sup>ininflationthatis</sup> typically found in the data, whereas the conventional<sup>Taylorspecification</sup> does not. This high degree of persistence is<sup>wellillustrated inFigure1</sup> for the case of Chile and Turkey. While the Taylor specification can be shown to imply that prices depend symmetrically on<sup>pastand expectedfuture</sup> prices, thus imparting significant inertia to the price<sup>_level,_it implies that the</sup> 4Note that y measures the impact of the output gap on the<sup>log real contractprice,not</sup> on inflation or on the price index. The inflation rate<sup>isrelatedtothe realcontractprice</sup> via a complex lag/lead polynomial.

7
inflation _rate_ is highly flexible-that is, it can jump in<sup>responsetonews.</sup> In contrast, the Fuhrer-Moore relative contracting specification<sup>impliesthat</sup> inflation depends symmetrically on past and expected future<sup>inflation,thus</sup> imparting significant inertia to _both_ inflation and the price level.<sup>In addition,</sup> the relative contracting model, because it implies a link between<sup>the</sup><sup>_inflation_</sup> _rate_ and excess demand, can account for a correlation<sup>betweendemand and</sup> inflation; the Taylor model, by contrast, links the _price_<sup>_level_andexcess</sup> demand and is thus not able to do so.<sup>5</sup> With two periods, the Fuhrer-Moore contracting equation<sup>is</sup> where Yt is (the log of) the output gap. If prices are a simple<sup>averageof the</sup> nominal contract wage negotiated at t and t - 1, and defining inflation as **_7rt_** = _Pt_ - Pt-1, we have where _9t_ is a moving average of current and past output.<sup>Inflationthus</sup> depends on its past value (which imparts inertia to both<sup>inflation andthe</sup> price level) as well as its future value.<sup>6</sup>

> 5However, as shown in Figure 2, the correlation between inflation and the (lagged) output gap is neither high nor persistent in middle-income<sup>countries.</sup>

> 6By contrast, a two-period contracting equation of the Taylor type would imply that the contract wage is given by an average of the lagged and<sup>expected futurewage contracts,</sup>

8
# 3 Econometric -Methodology

Some early tests of New Keynesian models have attempted to take into account both backward- and forward-looking elements in price setting by estimating an equation of the -form

> where all variables are as defined above. The relative importance of backwardand forward-looking components in inflation are thus measured by **I** and 1 - , respectively. Chadha, Masson and Meredith (1992), for instance, strongly reject values of 0 and lfor **IL** in their estimation for major industrial countries (excluding the United Kingdom), whereas Fuhrer (1997) cannot reject the assumption /s = 1 for the United States.

In this study, we use a more general approach and estimate two alternative equations, in an attempt to distinguish between Taylor-type price equations and the Fuhrer-Moore specification. The Fuhrer-Moore equation is specified as follows: where the output gap Yt is calculated as the log difference of the actual output level and its trend component, calculated using the generalized Baxter-King adjusted- for excess demand: This specification implies that-inflation is given by Thus, inflation persistence does not -result from the contracting specification _per se_ but rather from the persistence of **the** excess demand term, yt.

9
method (see below). The optimal number of lags for y is determined by Akaike statistics. The regression equation that produces the lowest Akaike statistics is used in the analysis. Zt is the rate of change of the real effective exchange rate, defined as the difference between inflation and the sum of the rate of nominal exchange rate depreciation and the rate of imported inflation, so that a positive value of _zt_ indicates that the real exchange rate is appreciating. We include the real exchange rate to account for the fact that our sample of countries consists of small open economies. The negative sign captures an "error correction" adjustment, in the sense that high inflation in period t _-_ 1 (relative to foreign inflation) tends to be followed by a reduction in domestic inflation. In addition, this specification means that in the steady state, with _61_ + _62 =_ 1, and given that Yt = Yt-, = ... = _Yt-m-i_ = 0 in the long run, domestic inflation will be equal to the sum of the rate of nominal exchange rate depreciation and the rate of foreign inflation, that is, relative purchasing power parity will hold.<sup>7</sup> The second price equation is a four-period, Taylor-type equation, as discussed in Fuhrer (1997):

> where the optimal number of lags for yt is again determined by using the

> Akaike criterion. If _/31_ + ,B2 + /33 + /34 + /53 = 1, and the output gap is zero in the long run, the inflation rate in the steady state will again be equal to

> 7The price equation leading to (4) could be derived by assuming that inflation in

> consumer prices is a weighted average of inflation in domestic prices (which are determined

> on the basis of a contracting framework) and foreign inflation measured in domestic-

> currency terms. We use the lagged value of z to reduce simultaneity bias.

10
the nominal rate of depreciation plus foreign<sup>inflation.</sup> The trend component of output is estimated<sup>by using a modified version of</sup> the "ideal" band pass filter of Baxter and<sup>King(1999).The Baxter-Kingfilter</sup> is a linear transformation of the data,<sup>whichleavesintactthecomponents</sup> of the data within a specified band of<sup>frequenciesandeliminatesallother</sup> components. But this methodology has a limitation:<sup>its applicationrequires</sup> a large amount of data. Christiano and Fitzgerald<sup>(1999)approximatethe</sup> Baxter-King filter using an optimal linear approximation.<sup>Their method can</sup> be explained as follows. Let yt be the data<sup>createdbyapplyingtheideal</sup> band pass filter to the raw data, **_xt._** yt<sup>isapproximatedby</sup><sup>**&,**whichisa</sup> filter of xt. The filter weights are chosen to<sup>minimizethe mean squareerror:</sup> Yt can be computed as where and _BT-t_ and _Bt_1_ are linear functions<sup>of</sup><sup>_Bj's:_</sup>
and Bt-1 solves with **_Pu_** = 24 and _pL_ = 2 in our case.

> Equations (4) and (5) contain future price expectations. We substitute these expected values by actual future inflation and use a Generalized Method of Moments (GMM) technique for estimation. In order to apply GMM, the

> moment condition that the parameter set, y, needs to satisfy is

> where ir is the dependent variable (inflation), and E(.) stands for the estimated value.

The GMM estimator is obtained by minimizing the following equation, which is defined as the distance between m(.) and 0:

> where X is the set of independent variables and Z the instrumental variables.

> Q is the weighting matrix. Here we use the lagged values of X as instrumental

> variables. The moment condition is written as an orthogonality condition

> between the residuals of the regression equation, -, and Z:

The weighting matrix is estimated as the heteroskedasticity and autocorrelation consistent covariance matrix: 12
## where

and k is the number of coefficients, q<sup>thebandwidth,andk(-)theKernel</sup> function, which is included to ensure<sup>thatQis a positivesemi-definite.The</sup> Bartlett Kernel is used in this study: The bandwidth is the Newey-West<sup>fixedbandwidth,whichis basedon</sup> the number of observations: which is equal to 3 here.

# 4 Empirical **Results**

We estimate equations (4) or<sup>(5)usingquarterlydataforfourcountries:</sup> Chile, Korea, the Philippines, and Turkey.<sup>8Theregressionresultsarepre-</sup> sented in Table 1. The rate of change of the real exchange<sup>rateisnot</sup> included in the regressions for Korea<sup>andPhilippinesbecauseitscoefficient</sup> had a wrong sign and was statistically<sup>insignificant.</sup> In order to decide on which price<sup>formation equationissuitableforeach</sup> country, we use an F test. Equation<sup>(4)isacceptedif onecannot rejectthe</sup> null hypothesis that _,31_ = **,**<sup>**3**</sup> **4** =<sup>_,35_=0 and that the coefficientsof the lagged</sup>

> 8See the Appendix for data sources and results of unit root tests.

> 9Because the data are quarterly, seasonal effects are captured by including seasonal dummies, in all regression equations.<sup>Thecoefficientsof thesevariablesarenotreported</sup> to save space.

13
output gap (which do not appear in equation (4)) are zero. The results indicate that specification (4) is accepted for Chile and Turkey, whereas specification (5) is the correct one for Korea and Philippines. Thus, the duration of contracts appears to be relatively short in Chile and Turkey, compared to Korea and the Philippines. Interestingly enough, the first two countries are precisely those where inflation was relatively high on average during the sample period.

For both Chile and Turkey, the estimated coefficients for the lead and lagged values of inflation are of about the same magnitude (as predicted by the Fuhrer-Moore specification). The sum of these coefficients is not significantly different from unity for Turkey, but not for Chile. In addition, for Chile, the estimated coefficient of the output gap measure has the right sign and is significant at the 10 percent level, whereas the rate of change of the real exchange rate has the correct sign and is highly significant. These results imply indeed that (relative) purchasing power parity holds in the long run. For Turkey, by contrast, the rate of depreciation of the real exchange is not statistically significant (despite having the expected sign), and the estimated coefficient of the output gap is wrongly sign and insignificant. For Korea, the total effect of lagged inflation on current inflation is much higher than the total effect of future inflation, whereas the reverse holds in the case of the Philippines. In both countries, the sum of coefficients on the output gap variable is positive and statistically significant, as expected.

In all of these regression equations, we do not restrict the sum of the estimated coefficients for past and future inflation to be equal to unity. Using the unrestricted estimates, however, we do test for the validity of the 14
constraint that weights sum to unity, in order<sup>toensurethatnolong-run</sup> trade-off exists between inflation and excess<sup>demandpressures.Specifically,</sup> we use a Wald test. The results, which are also<sup>reportedin Table1, indicate</sup> that the null hypothesis that the sum of the<sup>estimatedcoefficientsof past</sup> and future inflation is equal to unity is accepted<sup>for KoreaandTurkey,but</sup> is rejected for Chile and the Philippines.

# 5 Concluding Remarks

The purpose of this paper has been to provide<sup>empiricalestimatesofcon-</sup> tracting models of the Phillips curve with<sup>backward-andforward-looking</sup> expectations for four middle-income developing<sup>economies-Chile,Korea,</sup> the Philippines, and Turkey. The first part<sup>reviewedvariousNew Keyne-</sup> sian models of the Phillips curve, including<sup>thoseofTaylor(1979,1980)</sup> and Fuhrer and Moore (1995). The second part<sup>presentedtheeconometric</sup> methodology and the third the estimation results.<sup>Wefoundthatcontract</sup> duration appears to be shorter in Chile and Turkey,<sup>compared to Koreaand</sup> the Philippines. The output gap has a positive<sup>effectin allcountriesexcept</sup> Turkey, and the rate of change of the real exchange<sup>rateissignificant only</sup> in Chile. For both Chile and Turkey, past and future<sup>inflationareof about</sup> the same magnitude, whereas in Korea (the Philippines)<sup>past inflationplays</sup> a larger (smaller) role. Homogeneity restrictions<sup>are satisfiedforKoreaand</sup> Turkey, but not for Chile and the Philippines.

The analysis in this paper can be extended in<sup>various directions.Inpar-</sup> ticular, there is growing evidence for industrial countries<sup>suggestingthat the</sup> inflation process may be asymmetric, in that<sup>excessdemandtendstohave</sup> 15
a larger effect on inflation than an equivalent<sup>degree of excesssupply.Early</sup> contributions for industrial countries include Chadha,<sup>MassonandMeredith</sup> (1992), and Laxton, Meredith, and Rose (1995), with<sup>morerecentstudiesin-</sup> cluding Dupasquier and Ricketts (1998) and Clark, Laxton,<sup>and Rose(2001).</sup> Although some preliminary work on nonlinearities in the<sup>Phillipscurvehas</sup> been done for developing countries (see Ag6nor<sup>(2002)),the scopefor further</sup> research for these countries is significant.

16
Data Surces andi uJnt Root Taests The data used are obtained by from the quarterly database compiled by Agenor, McDermott and Prasad (2000). The quarterly dataset covers the following years for the countries in the sample: 1978:01-2001:01 for Chile and Korea, 1981:01-2000:04 for Philippines, and 1981:01-2001-01 for Turkey. The variables and the sources of them axe as follows

- 7r is the percentage change in the consumner price index. Source: International Monetary Fund (IMF).

- y is the log difference of output to the trend component of output, where output is the ir.dustrial production index. The trend component is calculated using a generalized version of the Baxter-King filtering method, as explained in the text. Source: IMF.

- z is the rate of change of the real effective exchange rate, defined as the difference between the inflation rate and the sum of the growth rate of nominal effect exchange rate and the growth rate of import prices. A rise is a depreciation for the nominal effective exchange rate. Source: IMF.

Each series used in the regressions is tested for stationarity. Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) unit root tests are employed. The null hypothesis is that a unit root exists and the alternative hypothesis is that the series is trend stationary. Results of these tests are reported in Table Al. In general, both test statistics give similar results. The presence 17
> of a unit root is rejected for all series, with most series being stationary at a

1 percent significance level.

18
Table Al Order of Integration: Unit Root Test St.atistics

|Country|Variable||ADlFtest|PIPtest|
|---|---|---|---|---|
|||k|teststatistic||
|Chile|?r|1|-2.63|-334*|
||y|3|-3.22**|-8.21***|
||z|1|-.3.43**|-2.95**|
|Korea|7r|0|-3.81*"||
||y|3|-3.83***'|-1.64*<br>|
||z|G|-4.37'>*|-4.12***|
|Philippines|7r|1|4512***.99**||
||y|0|-4.35"6|-4.2***|
||_z_|0|_44*':*_<br>*|_.56*_|
|Turkey|_7r_|1|-3.14**|-2.S4*|
||y|0|-8.24";*:c*|-8.24***|
||z|C|-3.5***|-3.83***|

Notes: Variables and estimated period are as defined in the<sup>text.</sup><sup>_1c_denotesthe number</sup> of lags in the ADF test. Asterisks *, ** and<sup>''**denote rejection of thenull hypothesisof</sup> a unit root at the 10%, 5%, and 1% significance levels.<sup>Criticalvaluesare from McKinnon</sup> (1991).