Why Most Published Results on Unit Root and ...

Why Most Published Results on Unit Root and Cointegration Are False* Hari S. Luitel Algoma University Sault Ste. Marie Ontario, P6A 2G4 [email protected] Gerry J. Mahar Algoma University Sault Ste. Marie Ontario, P6A 2G4 [email protected]

July 2, 2015 Abstract The method of cointegration analysis for modeling nonstationary economic time series variables has become a dominant paradigm in empirical economic research. Critics argue that a cointegration analysis produces results that are, at best, useless and, at worst, dangerous. In this research, we explain why and how the use of a cointegration analysis in economic research will likely lead to findings and subsequent recommendations for public policy that will be unsound, misleading and potentially harmful. We recommend that, except for pedagogical review of policy failure of a historical magnitude, this method not be used in any analysis that affects public policy. JEL Classification: C22, C50, E60 Key Words: cointegration analysis, unit root, time series, econometric modeling, economic policy, policy analysis

* We thank Brandon Mackinnon for his excellent research assistance.

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Why Most Published Results on Unit Root and Cointegration Are False 1.

Introduction Cointegration analysis for analyzing and modeling non-stationary economic time series

variables, proposed by Engle and Granger (1987), has become a dominant paradigm in empirical economic research 1 (Hendry 2004; Royal Swedish Academy of Science 2003). Critics, however, argue that a cointegration analysis produces results that are, at best, useless and, at worst, dangerous (Moosa 2011, pp. 114). In this research, we will explain why and how the use of a cointegration analysis in economic research will lead to spurious findings and why any recommendations for public policy will likely be unsound, misleading and potentially harmful. In economics, when a historical perspective is overlooked in a descriptive research design, misleading conclusions may often follow. 2 Here, by historical perspective, we refer to the understanding of a subject matter in light of its previous stages of intellectual development and successive advancement. We think, therefore, it is imperative to put our arguments against unit roots and cointegration analysis in a historical perspective. The recognition of a spurious regression problem in the late 1970s contributed decisively to the development of unit roots and cointegration (Granger and Newbold 1974; Hendry 1980, 1986; Granger 1981, 1986). A spurious regression problem arises when a regression analysis indicates a relationship between two or more unrelated time series variables because each variable has either a trend, or is nonstationary, or both. While working with economic time series data, researchers, attempting to account for spurious regression problem, began testing for nonstationarity before estimating 1

The knowledge that in response to the financial and economic crisis of 2007-2009, economists are open for reevaluating alternative approaches to neoclassical paradigm gave us an additional strength to carry out this research. [See Neck (2014)].

2

See Temin (2013) for an eloquent description of how or why economic history vanished both from the faculty and the graduate program at MIT, and subsequently its cost consequences to current economic education and overall societal scholarship.

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regressions. If, on the basis of an appropriate unit root test, data were found to be nonstationary, researchers would routinely purge the nonstationarity by differencing and then estimating regression equations using only differenced data as solution to the spurious regression problem. The practice of purging the nonstationarity by differencing would also result in the loss of valuable information from economic theory about the long-run equilibrium properties of the data (Kennedy 2003). It was in this context that Granger proposed that if two nonstationary variables were I(1) process, the bivariate dynamic relation between the two nonstationary variables would be misspecified when both of the nonstationary variables were differenced. This class of models has since become a dominant paradigm in empirical economic research and is known in the literature as cointegrated process (Hamilton 1994; page 562). In our review of the development of the concept of cointegration, we identified that the most important proposition of two integrated series was that if 𝑥𝑡 ~ 𝐼(𝑑𝑥 ), 𝑦𝑡 ~ 𝐼(𝑑𝑦 ) then

𝑧𝑡 = 𝑏𝑥𝑡 + 𝑐𝑦𝑡 ~ 𝐼(max�𝑑𝑥 , 𝑑𝑦 �) (Granger 1981, page 126). Put simply, this proposition states that the sum of two, time series, variables of different order of integration will always yield

another time series variable that will retain the “order of integration property” of the two series that has the higher order of integration. Granger’s proposition was subsequently clarified by Hendry (1986; page 202), Engle and Granger (1987; page 253), Cuthbertson, Hall, and Taylor (1992; page 131), and Royal Swedish Academy of Science (2003; page 5). The clarified proposition includes both the sum and the difference of the two time series. In this research, we offer evidence against this proposition and explain why its violation is substantial. The paper is organized as follows: Section 2 describes the econometric methodology to determine the order of integration and the data used in the analysis. Section 3 presents our empirical results, followed by a summary, a discussion and a conclusion in Section 4.

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2.

Test of Order of Integration and Data A time series is said to be strictly stationary if its marginal and all joint distribution are

independent of time. For practical purpose, however, it is the weak stationarity or covariancestationarity that is more useful. A time series is said to be weakly stationary or covariancestationary if the first two moments -- mean and autocovariances -- of a series do not depend on time. A stationary time series that does not need differencing is said to be integrated of order zero and is denoted I(0). A nonstationary time series that becomes stationary after first differencing is said to be integrated of order one and is denoted I(1). In general, a time series that needs differencing d times to become I(0) is said to be integrated of order d and is denoted I(d) (Granger 1986, page 214). Since the number d equals the number of unit roots in the characteristic equation for the time series (Said and Dickey 1984, page 599) unit root tests are often used to determine the order of integration of a series. Thus, we describe below the unit root tests that we will use in our analysis. Consider the following difference equation: 𝑌𝑡 = 𝜌𝑌𝑡−1 + 𝑢𝑡

(1)

where 𝑢𝑡 is a white noise error term. When 𝜌 = 1, equation (1) is known as a pure random walk model -- a nonstationary stochastic process. This model can be alternatively expressed as: ∆𝑌𝑡 = 𝛿𝑌𝑡−1 + 𝑢𝑡

(2)

where 𝛿 = (𝜌 − 1) and ∆ is the first-difference operator (e.g. 𝑌𝑡 − 𝑌𝑡−1 ).

Testing for the presence of unit root involves simultaneously determining whether an

intercept and/or a time trend belong to the regression model -- not including enough of them biases the test in favor of the unit root null, whereas including too many of these parameters results in lost power (Elder and Kennedy 2001). With economic time series, the main competing

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alternative to the presence of a unit root is a deterministic linear time trend. We therefore modify equation (2) to include (i) a drift term, and (ii) a drift term and a linear trend term. ∆𝑌𝑡 = 𝛼 + 𝛿𝑌𝑡−1 + 𝑢𝑡

(3)

∆𝑌𝑡 = 𝛼 + 𝛽𝛽 + 𝛿𝑌𝑡−1 + 𝑢𝑡

(4)

Due to its simplicity, we will use the test procedure proposed by Fuller (1976) and

Dickey and Fuller (1979, 1981) -- known as the Dickey-Fuller (DF) test. In DF test, it is assumed that 𝑢𝑡 are uncorrelated and iid. If 𝑢𝑡 are correlated, Said and Dickey (1984) showed that the DF

test may still be used provided that the lag length in the autoregression increases with the sample size. The test modified by Said and Dickey (1984) is known as the augmented Dickey-Fuller (ADF) test, and is given by: ∆𝑌𝑡 = 𝛽1 + 𝛽2 𝑡 + 𝛿𝑌𝑡−1 + ∑𝑘𝑖=1 𝛼𝑖 ∆𝑌𝑡−𝑖 + 𝑢𝑡

(5)

The problem with ADF test is that the choice of the lag length is arbitrary. Although

Akaike or Schwarz information criteria are generally used to decide the lag length, they do not always yield identical results. According to Harris (1992), the size and power properties of the ADF test are improved if a fairly generous lag is used. He proposes a formula, 𝑙𝑖 =

𝑖𝑖𝑖{𝑖(𝑛/100)1/4 }, to determine the lag length that allows for the order of autogression to grow

with sample size (page 383). Previously, Schwert (1989, page 151) used lag lengths based on the formulas 𝑙4 = 𝑖𝑖𝑖{4(𝑛/100)1/4 } and 𝑙12 = 𝑖𝑖𝑖{12(𝑛/100)1/4 }. In contrast, Taylor (2000) recommends selecting a lag length using a data-based algorithm or using a much higher

significance level (e.g. 0.2 level rather than the traditional 0.05 level) in the general-to-specific rule framework. Note that the critical values for the ADF test differ very little from the DF critical values, so in practice researchers often used the DF critical values. Above all, if the 𝑢𝑡

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are not iid and are correlated, the DF tests do not have the correct asymptotic size (Phillips and Perron 1988, page 339). In our analysis, we do not use ADF test for reasons discussed elsewhere. Moreover, using nonparametric methods, Phillips (1987) and Phillips and Perron (1988) show that the PhilipsPerron (PP) unit root test takes into account of the serial correlation in the error terms without adding lagged difference terms and thus has an advantage over DF and ADF test procedures. We will use PP test procedure because it is believed to allow for a wide class of time series models in which a unit root may be present. Controversy still surrounds the most powerful test for unit roots. To contribute toward overcoming such controversy, Elliot, Rothenberg and Stock (1996) proposed a modified version of the Dickey-Fuller t test, known as DF-GLS test, in which the time series is transformed using a generalized least square (GLS) method, rather than OLS, before performing the unit root test. Elliot, Rothenberg and Stock (1996) argue that DF-GLS test has substantially improved power when an unknown mean or trend is present, and as such, this test dominates all other unit root tests currently in common use such as DF, ADF and PP unit root tests. We will use DF-GLS test in our data analysis. In order to show the violation of Granger’s proposition, we use two sets of data: (i) Gross Domestic Product (GDP) and some of its components and (ii) unemployment rate and its components. Many macroeconomic variables are either a sum or a difference or some algebraic manipulation of other macroeconomic variables. For example, consider the openness index, an economic variable, defined as the sum of exports and imports divided by GDP �𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝐼𝐼𝐼𝐼𝐼 =

𝐸𝐸𝐸𝐸𝐸𝐸𝐸+𝐼𝐼𝐼𝐼𝐼𝐼𝐼 𝐺𝐺𝐺

�. We test whether the openness index and all its

components are stationary or nonstationary. For a second example of an algebraic manipulation

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of other macroeconomic variables, we use the unemployment rate, defined as the number of people unemployed and looking for work divided by the labor force (the sum of unemployed plus employed) �𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈 𝑅𝑅𝑅𝑅 =

𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈 𝐿𝐿𝐿𝐿𝐿 𝐹𝐹𝐹𝐹𝐹

�. We test whether unemployment rate

and all its components are stationary or nonstationary. We obtained annual data on GDP, exports and imports for the United States from 1929 to 2012. Similarly, we obtained annual data on number of people unemployed and number of people employed for the United States from 1947 to 2012. We created other desired variables using the appropriate algebraic manipulation as described above. The literature suggests that data in logarithmic form of a variable achieves stationarity than unlogged data. Nonetheless, we report results both for original series and for their natural logarithmic transformation. Table 1A provides the summary statistics of data for original series and Table 1B provides the summary statistics of data for their natural logarithmic transformation. [Table 1A and 1B, about here] 3.

Empirical Results In this section, we report results of the unit root tests used in the determination of the

order of integration of a series. We performed five variants of three different unit root tests on each time series: Dicky-Fuller (DF) test, Phillips-Perron (PP) test and Elliot, Rothenberg and Stock (DFGLS) test. In each case, the null hypothesis was that the variable under investigation had a unit root, against the alternative that it did not have a unit root. A significant test statistic rejects the null hypothesis that the series has a unit root; thus, significant values indicate the series to be stationary. The results are presented in Table 2A for original series and in Table 2B for their natural logarithmic transformation. Tests were performed sequentially. The top half of Table 2A and Table 2B report the unit root test results for stationarity of the variable in levels.

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The bottom half of Table 2A and Table 2B report the results for the various tests of unit root on first differences of the variables. [Table 2A and 2B, about here] Consider the test results for an openness index and its components. The results in Table 2A indicate that each component in the numerator, exports and imports, is individually I(d=1), the variable in the denominator, GDP, is I(d=1), and the resultant openness index is also I(d=1). Denote exports + imports as 𝑥1𝑡 , GDP as 𝑦1𝑡 and openness index as 𝑧1𝑡 . The expression of openness index can be written as 𝑧1𝑡 =

𝑥1𝑡 𝑦1𝑡

. Taking the natural log of both side, the expression

becomes 𝑙𝑙𝑧1𝑡 = 𝑙𝑙𝑥1𝑡 − 𝑙𝑙𝑦1𝑡 . This equation offers an ideal condition to test Granger’s

proposition. The results in Table 2B indicate that 𝑙𝑙𝑥1𝑡 ~ 𝐼(1), 𝑙𝑙𝑦1𝑡 ~ 𝐼(1) and 𝑙𝑙𝑧1𝑡 ~ 𝐼(1).

This translates into I(1) ± I(1) = I(1), which supports the Granger proposition.

Next, consider the unemployment rate and its components. The results in Table 2A

indicate that the number of people unemployed, the number of people employed and the labor force, each individual series is I(d=1) but the unemployment rate is I(d=0). Our finding regarding unemployment rate is confirmatory to the finding of Nelson and Plosser (1982), who concluded “that the series (unemployment rate) is well described as a stationary process.” (Page 152). Furthermore, denote unemployed as 𝑥2𝑡 , labor force as 𝑦2𝑡 and unemployment rate as 𝑧2𝑡 . The

expression of unemployment rate can be written as 𝑧2𝑡 =

𝑥2𝑡 𝑦2𝑡

. Taking the natural log of both side,

the expression becomes 𝑙𝑙𝑧2𝑡 = 𝑙𝑙𝑥2𝑡 − 𝑙𝑙𝑦2𝑡 . This equation offers another ideal condition to test the Granger proposition. The results in Table 2B indicate that 𝑙𝑙𝑥2𝑡 ~ 𝐼(1), 𝑙𝑙𝑦2𝑡 ~ 𝐼(1) but 𝑙𝑙𝑧2𝑡 ~ 𝐼(0). This translates into I(1) ± I(1) = I(0), which contradicts the Granger proposition.

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Granger’s proposition was subsequently clarified by Hendry (1986; page 202), Engle and Granger (1987; page 253), Cuthbertson, Hall, and Taylor (1992; page 131), and Royal Swedish Academy of Science (2003; page 5). Their clarification has been summarized in Table 3 below. For ease of exposition, we only consider the values d = 0 and d = 1. [Table 3, about here] Since the above outcomes are collectively exhaustive, not surprisingly, allowing researchers to selectively pick one unit root test over another means that any outcome becomes possible. Thus, the finding of cointegration between two variables cannot be a special case as implied and/or emphasized in the literature. To put it in a nutshell, there is no uniqueness in the original Granger proposition. 4.

Summary, Discussion and Conclusion The method of cointegration analysis for modeling nonstationary economic time series

variables has become a dominant paradigm in empirical economic research. In our review of the development of the concept of cointegration, we identified that the most important proposition of two integrated series was that if 𝑥𝑡 ~ 𝐼(𝑑𝑥 ), 𝑦𝑡 ~ 𝐼(𝑑𝑦 ) then 𝑧𝑡 = 𝑏𝑥𝑡 + 𝑐𝑦𝑡 ~ 𝐼(max�𝑑𝑥 , 𝑑𝑦 �) (Granger 1981, page 126). In this research, we show that this proposition, not highlighted

previously, to be false for two reasons: First, it is not necessarily true that the sum or difference between two time series variables of different order of integration will always yield another time series variable and it will retain the “order of integration property” of the two series that has the higher order of integration. Second, as shown in Table 3, there is no uniqueness in the proposition to begin with. Thus, the finding of cointegration between two variables does not reveal any special relation as implied and/or emphasized in the extant literature.

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We are not first to criticize the usefulness of the methods of unit root and cointegration analysis. For example, see DeLong and Lang (1992, page 1270); Harvey (1997); Maddala and Kim (1998); Phillips (2003); Moosa (2011). We contribute to this research stream by highlighting the key proposition of two integrated series that legitimizes undertaking unit root and cointegration analysis in general and in particular, we provide evidence against the key proposition that has thus far remained an unquestioned foundation. The violation of Granger’s key proposition is substantial because all subsequent refinements in the method of cointegration analysis are unable to overcome the structural flaws in the basic model of cointegration analysis. As such, the method of cointegration analysis can also be criticized on the following grounds: (i) Lack of uniqueness of cointegration results; (ii) Lack of uniqueness of unit root results: The finding of unit root in a time-series is affected by the choice of a model (i.e. random walk without drift vs. random walk with drift vs. random walk with drift and time trend). The finding of unit root is also affected by the choice of lag length and by the frequency of a time-series (i.e. daily vs. weekly vs. monthly vs. quarterly vs. annual observations); (iii) Spurious introduction of unit root in a series; (iv) Spurious introduction of cointegration in two unrelated series; (v) A fundamental problem with the concept of cointegration (Moosa 2011); (vi) The problem of structural break (forthcoming); and, (vii) Failure of some researchers to understand the limitations of use of secondary data. Many of these issues are elaborated elsewhere. In summary, three analogies between cointegration analysis and a sandcastle may be appropriate. First, a sandcastle may be built on sand, so it falls down because the foundation is not solid. Second, a sandcastle may be badly built. Third, a sandcastle built on seashore with a bad design may stay up but will not withstand the ebb and flow of the tides. The cointegration

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analysis, like a sandcastle, collapses on all three counts. In several planned research publications, we will report the criticism of research outcomes (results) and the methods employed to obtain such results. Below we provide one example why a research finding using the methodology of cointegration analysis to be false. A study by Chintrakarn and Herzer (2012) used a cointegration analysis to examine the effect of income inequality on crime rates in the United States. Employing state level panel data in their analysis, they concluded that an increase in income inequality led to a reduction in crime rates in the United States. We respectfully disagree with Chintrakarn and Herzer’s conclusion that resulted from the use of cointegration analysis and appeal to logic and judgment to make our arguments. Contrary to the above conclusion, we have learned that the intensity of violent crimes involving automatic weapons has gone up in the United States. For example, consider the heinous incident that took place at Sandy Hook Elementary School in Newtown, Connecticut, on December 14, 2012. In that incident, a gunman killed 26 people, including 20 children, before taking his own life. Although this incident was one of the worst school shootings in US history, it was not the last of school shootings. Since the Newtown mass shooting, there have been well over 100 school shootings in the United States. Table 4 reports lists of school shootings in the United States since January 2013. From a sociological view point, these school shootings may not be fully explained by crime statistics alone. These incidents may reflect, thus far officially not recognized, symptoms of social strife because headline news report of such incidents may only be a tip of the iceberg -- many such incidents go unreported. About 66 percent of all crimes, and even 55 percent to 60 percent of violent crimes, are not reported to the police (DiIulio 1996, page 5). Consider other recent examples of civilian deaths from the hands of law enforcement officers without trial. Popular news media, such as BBC, CNN among others, unfalteringly

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reminded viewers that the civil demonstrations, protests, riots and looting that broke out following Michael Brown’s fatal shooting in Ferguson, Missouri, Eric Garner’s death from a chokehold in Staten Island, New York or Freddie Carlos Gray’s death due to spinal injuries in Baltimore, Maryland, were a reminiscent of the urban black uprisings of the 1960s that were preceded and accompanied by social strife. Events such as these only make the matter worse for reported official crime statistics. [Table 4, about here] Another example of grave social concern in the US involves rates of suicide. A study published in the Lancet, a leading medical journal, analyzed suicide data collected by the Centers for Disease Control and Prevention between 1999 and 2010 and showed that coinciding with the onset of the 2007-2009 recession, the suicide rate accelerated in the United States. The study reported that during the recessionary period after 2007, there were an estimated 4,750 suicide deaths over and above the level that would have been expected if historical trends had continued (Reeves et al. 2012). Other studies have documented that the 2008 global economic crisis was associated with an increased rates of suicide (Chang et al. 2013; Reeves et al. 2014). Similar findings have been reported for other countries and regions (Chang et al. 2009; Stuckler et al. 2009, 2011; Chen et al. 2009, 2012). What these studies underscore is that the failure of the economics discipline may lead to higher social costs than failures of other disciplines. Thus, we were motivated to explore the reasons for the apparently contradictory findings reported in the literature in economics and in other disciplines due, in part, to Chintrakarn and Herzer’s conclusion that an increase in income inequality led to a reduction in crime rates in the United States. The conclusion was inconsistent with theory and with empirical evidence.

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In our assessment, Chintrakarn and Herzer’s conclusion suffers from two major problems. First, Chintrakarn and Herzer did not take into account measurement problems in reported crimes statistics -- a potential source of bias in inferential statistics. For a discussion of measurement problems in reported crimes statistics, see Skogan (1975); DiIulio (1996); Buonanno et al. (2014). Second, Chintrakarn and Herzer’s conclusion also followed from the use of cointegration methodology in their descriptive research design. Several studies have reported that following the rise in crime rates during the 1970s 1980s, the United States experienced an unexpected drop in crime rates in the 1990s - 2000s (Blumstein and Wallman 2000; Cook and Laub 2002; Zimring 2006; Buonanno et al. 2011). It is not the intent of our research to question the official crime statistics per se. We assert that Chintrakarn and Herzer’s conclusion followed from the use of a flawed cointegration methodology. After a major economic crisis, there is usually widespread discontent over what is taught in economics, especially in macroeconomics, and what goes on in the economy (Shiller 2010, Colander et. al. 2009, Ormerod 1997). The subject of time series, unit root and cointegration analysis is one area. In conclusion, we report that the cointegration analysis does not withstand the test of time and is being employed in areas with little probability of producing true findings. In a research field, if there are no true findings to be discovered, what we have learned from the history of science is that scientific endeavors are often wasted efforts with absolutely no yield to true scientific knowledge (Kuhn 1962). The best scientific tradition involves observation of the problem followed by an explanation that can be independently verified by other observers. In the name of science, cointegration analysis has become a tool to justify falsehood -- something that few people believe but is false. We recommend that except for a pedagogical review of a policy

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failure of historical magnitude, the method of cointegration analysis not be used in any public policy analysis.

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Maddala, G. S. and In-Moo Kim. 1998. Unit Roots, Cointegration, and Structural Change. Cambridge: Cambridge University Press. Moosa, Imad. 2011. “The Failure of Financial Econometrics: Assessing the Cointegration “Revolution”.” The Capco Institute Journal of Financial Transformation, Applied Finance # 32. (Available at: http://www.capco.com/sites/all/files/journal-32_article11.pdf) Neck, Reinhard. 2014. “Austrian Economics Today.” Atlantic Economic Journal 42 (2): 121122. Nelson, Charles R., and Charles R. Plosser. 1982. “Trends and Random Walks in Macroeconomic Time Series.” Journal of Monetary Economics 10 (2): 139-162. Ormerod, Paul. 1997. The Death of Economics, New York: John Wiley & Sons, Inc. Phillips, Peter C. B. 1987. “Time Series Regression with a Unit Root.” Econometrica 55 (2): 277-301. Phillips, Peter C. B. 2003. “Laws and Limits of Econometrics.” The Economic Journal 113 (486), C26-C52. Phillips, Peter C. B. and Pierre Perron. 1988. “Testing for a Unit Root in Time Series Regression.” Biometrika 75 (2): 335-346. Reeves, Aaron, Martin McKee, and David Stuckler. 2014. “Economic suicides in the Great Recession in Europe and North America.” The British Journal of Psychiatry 1–2. doi: 10.1192/bjp.bp.114.144766 Reeves, Aaron, David Stuckler, Martin McKee, David Gunnell, Shu-Sen Chang, and Sanjay Basu. 2012. “Increase in State Suicide Rates in the USA During Economic Recession.” Lancet 380 (9856): 1813-14.

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Royal Swedish Academy of Science, the. 2003. “Time-series Econometrics: Cointegration and Autoregressive Conditional Heteroskedasticity.” Advanced information on the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel 8 October 2003. (Available at: http://www.nobelprize.org/nobel_prizes/economicsciences/laureates/2003/advanced-economicsciences2003.pdf#search='Timeseries+econometrics%3A+cointegration+and+autoregressive+conditional+heteroskedasti city) Said, Said E., and David A. Dickey. 1984. “Testing for Unit Roots in Autoregressive-Moving Average of Unknown Order.” Biometrika 71 (3): 599-607. Schwert, G. William. 1989. “Test for Unit Roots: A Monte Carlo Investigation.” Journal of Business and Economic Statistics 7 (2): 147-159. Shiller, Robert J. 2010. “How Should the Financial Crisis Change How We Teach Economics?” Journal of Economic Education 41 (4): 403-409. Skogan, Wesley G. 1975. “Measurement Problems in Official and Survey Crime Rates.” Journal of Criminal Justice 3 (1), 17-31. Stuckler, David, Sanjay Basu, Marc Suhrcke, Adam Coutts, and Martin McKee. 2009. “The Public Health Effect of Economic Crises and Alternative Policy Responses in Europe: an Empirical Analysis.” Lancet 374 (9686): 315-23. Stucklera, David, Sanjay Basuc, Marc Suhrckee, Adam Coutts, and Martin McKeeb. 2011. “Effects of the 2008 recession on health: a first look at European data.” Lancet 378 (9786): 124-25.

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Taylor, A. M. Robert. 2000. “The Finite Sample Effects of Deterministic Variables on Conventional Methods of Lag-selection in Unit Root Tests.” Oxford Bulletin of Economics and Statistics 62 (2): 293-304. Temin, Peter. 2013. “The Rise and Fall of Economic History at MIT.” Massachusetts Institute of Technology, Department of Economics, Working Paper Series, Working Paper 13-11, June 5, 2013. Zimring, Franklin E. 2006. The great American crime decline, New York: Oxford University Press.

Page - 20

Table 1A: Summary Statistics (Original Series)

Variables

Time Period

Number of observations

Mean

Standard Deviation

Minimum

Maximum

Original Series Openness index Exports Imports Exports + Imports GDP

1929 – 2012 1929 – 2012 1929 – 2012 1929 – 2012 1929 – 2012

84 84 84 84 84

0.14564 386.419 493.394 879.8131 3839.294

0.07151 560.3179 752.014 1310.213 4816.381

0.05071 2 1.9 3.9 57.2

0. .30714 2195.9 2743.1 4939 16244.6

Unemployment rate Number of people unemployed Number of people employed Labor force

1947 – 2012 1947 – 2012 1947 – 2012 1947 – 2012

66 66 66 66

0.05774 6264.621 98625.92 104890.5

0.01641 3038.883 30165.08 32590.28

0.02910 1834 57038 59349

0.09689 14825 146047 154975

In First Differences First difference of openness index First difference of exports First difference of imports First difference of exports + imports First difference of GDP

1929 – 2012 1929 – 2012 1929 – 2012 1929 – 2012 1929 – 2012

83 83 83 83 83

0.00233 26.38554 32.98193 59.36747 194.4578

0.01261 65.54907 102.3712 164.8533 229.5375

-0.05197 -259.2999 -580.3999 -839.7 -302.3994

0.03424 259.7 386 645.7 818.4004

First difference of unemployment rate First difference of number of people unemployed First difference of number of people employed First difference of labor force

1947 – 2012 1947 – 2012 1947 – 2012 1947 - 2012

65 65 65 65

0.000642 156.8462 1314.323 1471.169

0.01094 1143.038 1530.197 799.3574

-0.02086 -2178 -5485 -273

.03470 5341 4171 3242

Page - 21

Table 1B: Summary Statistics (Natural Logarithm)

Variables

Time Period

Number of observations

Mean

Standard Deviation

Minimum

Maximum

Natural Logarithm Log of openness index Log of exports Log of imports Log of exports + imports Log of GDP

1929 – 2012 1929 – 2012 1929 – 2012 1929 – 2012 1929 – 2012

84 84 84 84 84

-2.04698 4.34280 4.37441 5.05892 7.10591

0.49639 2.15375 2.30452 2.22732 1.75391

-2.98155 0.69314 0.64185 1.36097 4.04655

-1.18044 7.69434 7.91684 8.50491 9.69551

Log o unemployment rate Log of number of people unemployed Log of number of people employed Log of labor force

1947 – 2012 1947 – 2012 1947 – 2012 1947 – 2012

66 66 66 66

-2.89096 8.61941 11.45075 11.51038

0.28332 0.51716 0.31721 0.32423

-3.5368 7.51425 10.95147 10.99119

-2.33414 9.60407 11.89168 11.95102

In First Differences First difference of log of openness index First difference of log of exports First difference of log of imports First difference of log of exports + imports First difference of log of GDP

1929 – 2012 1929 – 2012 1929 – 2012 1929 – 2012 1929 – 2012

83 83 83 83 83

0.01225 0.07131 0.07462 0.07304 0.06078

0.09802 0.15646 0.13497 0.12840 0.06906

-0.34438 -0.41689 -0.42285 -0.39688 -0.26301

0.39549 0.73631 0.33506 0.39374 0.24907

First difference of log of unemployment rate First difference of log of number of people unemployed First difference of log of number of people employed First difference of log of labor force

1947 – 2012 1947 – 2012 1947 – 2012 1947 - 2012

65 65 65 65

0.01121 0.02597 0.01408 0.01476

0.19394 0.19330 0.01504 0.00799

-0.46694 -0.47000 -0.03846 -0.00305

0.64544 0.65536 0.04287 0.03221

Page - 22

Table 2A: Unit Root Test Results of Order of Integration (Original Series)

Variables In Level Openness index (𝑧1𝑡 ) Exports Imports Exports + Imports (𝑥1𝑡 ) GDP (𝑦1𝑡 )

Dickey-Fuller Test Model 1§ Model 2†

Phillips-Perron Test Model 3§ Model 4†

DF-GLS Test Model 5‡

0.690 5.157 3.205 4.029 11.411

-3.148 2.083 0.632 1.223 2.605

1.437 5.356 4.376 4.860 3.188

-12.772 4.453 2.437 3.441 1.361

-1.142 0.747 0.482 0.698 0.219

Unemployment rate (𝑧2𝑡 ) Number of people unemployed (𝑥2𝑡 ) Number of people employed Labor force (𝑦2𝑡 )

-2.760*** -1.109 0.062 0.970

-3.047 -2.599 -1.862 -2.287

-15.218** -4.043 -0.012 0.166

-18.338* -16.405 -7.641 -5.594

-3.293** -3.734*** -1.816 -1.344

In First Differences First difference of openness index First difference of exports First difference of imports First difference of exports + imports First difference of GDP

-9.025*** -7.282*** -9.119*** -8.547***

-9.261*** -9.046*** -10.623*** -10.325***

-72.051*** -67.329*** -83.560*** -79.284***

-73.718*** -76.641*** -84.439*** -82.058***

-6.200*** -6.848*** -7.623*** -7.676***

First difference of unemployment rate First difference of number of people unemployed First difference of number of people employed First difference of labor force

-7.153*** -5.999*** -5.237*** -3.857***

-7.091*** -5.949*** -5.203*** -3.868**

-48.735*** -40.639*** -37.007*** -24.507***

-48.716*** -40.559*** -37.154*** -25.470***

-6.229*** -5.893*** -5.141*** -2.754

Notes: ***indicates 1 percent significance level, **indicates 5 percent significance level and * indicates 10 percent significance level. §Model 1 and Model 3: 𝑦𝑡 = 𝛼 + 𝜌𝑦𝑡−1 + 𝑢𝑡 . †Model 2 and Model 4: 𝑦𝑡 = 𝛼 + 𝜌𝑦𝑡−1 + 𝛿𝛿 + 𝑢𝑡 . ‡Model 5: ∆𝑦𝑡 = 𝛼 + 𝛽𝑦𝑡−1 + 𝛿𝛿 + ∑𝑘𝑖=1 𝛾𝑖 ∆𝑦𝑡−𝑖 + 𝑢𝑡

Page - 23

Table 2B: Unit Root Test Results of Order of Integration (Natural Logarithm)

Variables In Level Log of openness index (𝑙𝑙𝑙1𝑡 ) Log of exports Log of imports Log of exports + imports (𝑙𝑙𝑙1𝑡 ) Log of GDP (𝑙𝑙𝑙1𝑡 )

Dickey-Fuller Test Model 1§ Model 2†

Phillips-Perron Test Model 3§ Model 4†

DF-GLS Test Model 5‡

-0.082 0.442 0.730 0.726 -0.082

-4.359*** -4.357*** -4.933** -4.827*** -4.359***

-0.399 0.208 0.340 0.316 -0.399

-23.351** -26.697** -23.133** -24.368** -23.351**

-1.993 -2.439 -2.153 -1.946 -1.993

Log o unemployment rate (𝑙𝑙𝑙2𝑡 ) Log of number of people unemployed (𝑙𝑙𝑙2𝑡 ) Log of number of people employed Log of labor force (𝑙𝑙𝑙2𝑡 )

-2.892*** -1.597* -1.213 -2.004**

-3.198* -3.054 -0.102 1.417

-15.499** -4.156 -0.486 -0.424

-19.037* -17.259* -1.335 0.552

-3.152** -2.967* -1.425 -1.022

In First Differences First difference of log of openness index First difference of log of exports First difference of log of imports First difference of log of exports + imports First difference of log of GDP

-7.188*** -6.118*** -7.611*** -6.496*** -4.746***

-7.188*** -6.058*** -7.561*** -6.424*** -4.694***

-53.416*** -39.954*** -55.704*** -40.739*** -27.543***

-54.400*** -40.103*** -56.759*** -41.091*** -26.705**

-5.069*** -4.381*** -2.990* -3.322** -3.408**

First difference of log of unemployment rate First difference of log of number of people unemployed First difference of log of number of people employed First difference of log of labor force

-7.430*** -7.414*** -6.081*** -3.838***

-7.368*** -7.354*** -6.114*** -3.965**

-49.901*** -49.901*** -45.196*** -24.912***

-49.917*** -49.961*** -45.417*** -26.648***

-6.357*** -6.262*** -5.720*** -2.809

Notes: ***indicates 1 percent significance level, **indicates 5 percent significance level and * indicates 10 percent significance level. §Model 1 and Model 3: 𝑦𝑡 = 𝛼 + 𝜌𝑦𝑡−1 + 𝑢𝑡 . †Model 2 and Model 4: 𝑦𝑡 = 𝛼 + 𝜌𝑦𝑡−1 + 𝛿𝛿 + 𝑢𝑡 . ‡Model 5: ∆𝑦𝑡 = 𝛼 + 𝛽𝑦𝑡−1 + 𝛿𝛿 + ∑𝑘𝑖=1 𝛾𝑖 ∆𝑦𝑡−𝑖 + 𝑢𝑡

Page - 24

Table 3: Algebra of Two Integrated Series Based on proposition if 𝑥𝑡 ~𝐼(𝑑𝑥 ), 𝑦𝑡 ~𝐼(𝑑𝑦 ), then 𝑧𝑡 = 𝑏𝑥𝑡 + 𝑐𝑦𝑡 ~𝐼(max�𝑑𝑥 , 𝑑𝑦 �) (Granger 1981, page 126). Cases

Outcome

Interpretation

1. 𝑑𝑥 = 0, 𝑑𝑦 = 1

I(0) ± I(1) = I(1)

The sum or difference between a stationary series and nonstationary series yields a nonstationary series.

2. 𝑑𝑥 = 1, 𝑑𝑦 = 0

I(1) ± I(0) = I(1)

The sum or difference between a nonstationary series and stationary series yields a nonstationary series.

3. 𝑑𝑥 = 1, 𝑑𝑦 = 1

I(1) ± I(1) = I(1)

The sum or difference between a nonstationary series and a nonstationary series yields a nonstationary series.

4. 𝑑𝑥 = 1, 𝑑𝑦 = 1

I(1) ± I(1) = I(0)

The sum or difference between a nonstationary series and a nonstationary series yields a stationary series.

5. 𝑑𝑥 = 0, 𝑑𝑦 = 0

I(0) ± I(0) = I(0)

The sum or difference between two stationary series yields a stationary series. This outcome is analogous to case 3 above for nonstationary series, so it is essentially a trivial case.

6. 𝑑𝑥 = 0, 𝑑𝑦 = 0

I(0) ± I(0) = I(1)

The sum or difference between two stationary series yields a nonstationary series. Although this outcome is explicitly ruled out by the Granger proposition, in practice this outcome is also possible if one is to selectively pick one unit root test over another.

Page - 25

Table 4: List of School Shootings in the United States since Sandy Hook

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48.

Date 1/08/2013 1/10/2013 1/15/2013 1/15/2013 1/16/2013 1/22/2013 1/31/2013 2/1/2013 2/7/2013 2/13/2013 2/27/2013 3/18/2013 3/21/2013 4/12/2013 4/13/2013 4/15/2013 4/29/2013 6/7/2013 6/19/2013 8/15/2013 8/20/2013 8/22/2013 8/23/2013 8/30/2013 9/21/2013 9/28/2013 10/4/2013 10/15/2013 10/21/2013 11/1/2013 11/2/2013 11/3/2013 11/21/2013 12/4/2013 12/13/2013 12/19/2013 1/9/2014 1/14/2014 1/15/2014 1/17/2014 1/20/2014 1/21/2014 1/24/2014 1/28/2014 1/28/2014 1/31/2014 1/31/2014 2/7/2014

City, State Fort Myers, FL Taft, CA St. Louis, MO Hazard, KY Chicago, IL Houston, TX Atlanta, GA Atlanta, GA Fort Pierce, FL San Leandro, CA Atlanta, GA Orlando, FL Southgate, MI Christiansburg, VA Elizabeth City, NC Grambling, LA Cincinnati, OH Santa Monica,CA W. Palm Beach, FL Clarksville, TN Decatur, GA Memphis, TN Sardis, MS Winston-Salem, NC Savannah, GA Gray, ME Pine Hills, FL Austin, TX Sparks, NV Algona, IA Greensboro, NC Stone Mountain, GA Rapid City, SD Winter Garden, FL Arapahoe County, CO Fresno, CA Jackson, TN Roswell, NM Lancaster, PA Philadelphia, PA Chester, PA West Lafayette, IN Orangeburg, SC Nashville, TN Grambling, LA Phoenix, AZ Des Moines, IA Bend, OR

School Name Apostolic Revival Center Christian School Taft Union High School Stevens Institute of Business & Arts Hazard Community and Technical College Chicago State University Lone Star College North Harris Campus Price Middle School Morehouse College Indian River St. College Hillside Elementary School Henry W. Grady HS University of Central Florida Davidson Middle School New River Community College Elizabeth City State University Grambling State University La Salle High School Santa Monica College Alexander W. Dreyfoos School of the Arts Northwest High School Ronald E. McNair Discovery Learning Academy Westside Elementary School North Panola High School Carver High School Savannah State University New Gloucester High School Agape Christian Academy Lanier High School Sparks Middle School Algona High/Middle School North Carolina A&T State University Stephenson High School South Dakota School of Mines & Technology West Orange High School Arapahoe High School Edison High School Liberty Technology Magnet HS Berrendo Middle School Martin Luther King Jr. ES Delaware Valley Charter HS Widener University Purdue University South Carolina State University Tennessee State University Grambling State University Cesar Chavez High School North High School Bend High School Page - 26

Type K-12 K-12 College College College College K-12 College College K-12 K-12 College K-12 College College College K-12 College K-12 K-12 K-12 K-12 K-12 K-12 College K-12 K-12 K-12 K-12 K-12 College K-12 College K-12 K-12 K-12 K-12 K-12 K-12 K-12 College College College College College K-12 K-12 K-12

49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98.

2/10/2014 2/11/2014 2/12/2014 2/20/2014 3/2/2014 3/7/2014 3/8/2014 3/21/2014 3/30/2014 4/3/2014 4/11/2014 4/16/2014 4/21/2014 4/21/2014 4/16/2014 5/2/2014 5/3/2014 5/4/2014 5/5/2014 5/8/2014 5/8/2014 5/21/2014 6/5/2014 6/10/2014 6/23/2014 6/27/2014 8/13/2014 8/14/2014 9/2/2014 9/5/2014 9/10/2014 9/11/2014 9/24/2014 9/27/2014 9/29/2014 9/30/2014 9/30/2014 10/3/2014 10/8/2014 10/13/2014 10/18/2014 10/21/2014 10/24/2014 11/3/2014 11/20/2014 11/23/2014 12/5/2014 12/16/2014 12/17/2014 1/15/2015

Salisbury, NC Lyndhurst, OH Jackson, TN Raytown, MO Westminster, MD Tallulah, LA Oshkosh, WI Newark, DE Savannah, GA Kent, OH Detroit, MI Tuscaloosa, AL Griffith, IN Provo, UT Council Bluffs, IA Milwaukee, WI Everett, WA Augusta, GA Augusta, GA Georgetown, KY Lawrenceville, GA Milwaukee, WI Seattle, WA Troutdale, OR Benton, MO Miami, FL Fredrick, MD Newport News, VA Pocatello, ID Savannah, GA Lake Mary, FL Taylorsville, UT San Antonio, TX Nashville, TN Terre Haute, IN Albermarle, NC Louisville, KY Fairburn, GA Elizabeth City, NC Nashville, TN Langston, OK Memphis, TN Marysville, WA Dover, DE Tallahassee, FL Annapolis, MD Claremore, OK Pittsburgh, PA Waterville, ME Milwaukee, WI

Salisbury High School Brush High School Union University Raytown Success Academy McDaniel College Madison High School University of Wisconsin – Oshkosh University of Delaware Savannah State University Kent State University East English Village Preparatory Academy Stillman College St. Mary Catholic School Provo High School Iowa Western Community College Marquette University Horizon Elementary School Paine College Paine College Georgetown College Georgia Gwinnett College Clark Street School Seattle Pacific University Reynolds High School Kelly High School University of Miami Heather Ridge High School Saunders Elementary Idaho State University Savannah State University Greenwood Lakes Middle School Westbrook Elementary School Joel C. Harris Academy Tennessee State University Indiana State University Albermarle High School Fern High School Langston Hughes High School Elizabeth City State University Tennessee State University Langston University A. Maceo Walker Middle School Marysville-Pilchuck High School Delaware State University Florida State University St. John’s College Rogers State University Sunnyside Elementary School Benton Elementary School Wisconsin Lutheran High School

Page - 27

K-12 K-12 College K-12 College K-12 College College College College K-12 College K-12 K-12 College College K-12 College College College College K-12 College K-12 K-12 College K-12 K-12 College College K-12 K-12 K-12 College College K-12 K-12 K-12 College College College K-12 K-12 College College College College K-12 K-12 K-12

99. 100. 101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 126.

1/16/2015 1/20/2015 1/23/2015 1/26/2015 2/2/2015 2/4/2015 2/5/2015 2/15/2015 2/15/2015 2/15/2015 2/23/2015 3/9/2015 3/30/2015 4/2/2015 4/2/2015 4/4/2015 4/13/2015 4/17/2015 4/19/2015 4/22/2015 4/27/2015 5/4/2015 5/5/2015 5/12/2015 5/20/2015 5/24/2015 5/27/2015 6/4/2015

Ocala, FL Mobile, AL Hardeeville, SC Roseville, MN Mankato, MN Frederick, MD Columbia, SC Athens, GA Little Rock, AR Merced, CA Daytona Beach, FL Coon Rapids, MN Springfield, MA Beaver Falls, PA Jackson, TN Everett, WA Goldsboro, NC Seguin, TX Charlotte, NC Las Vegas, NV Lacey, WA Cleveland, OH Conyers, GA Tempe, AZ Robinson, TX Flint, MI Everglades City, FL Franklin, NC

Vanguard High School Williamson High School Royal Live Oaks Academy Hand in Hand Christian Montessori School Minnesota State University Frederick High School University of South Carolina University of Georgia Lawson Elementary School Tenaya Middle School Bethune-Cookman University Northwest Passage Alternative High School American International College Community College of Beaver County Lane College Everett Community College Wayne Community College Seguin High School Johnson C. Smith University Ruthe Deskin Elementary School North Thurston High School Willow Elementary School Conyers Middle School Corona del Sol High School Robinson High School Flint Southwestern Classical Academy Everglades City School South Macon Elementary School

K-12 K-12 K-12 K-12 College K-12 College College K-12 K-12 College K-12 College College College College College K-12 College K-12 K-12 K-12 K-12 K-12 K-12 K-12 K-12 K-12

Note: Incidents were classified as school shootings when a firearm was discharged inside a school building or on school or campus grounds, as documented in publicly reported news accounts. This includes assaults, homicides, suicides, and accidental shootings. Incidents in which guns were brought into schools but not fired there, or were fired off school grounds after having been possessed in schools, were not included. Incidents reported above were identified through media reports, so this is likely an undercount of the true total. The list above does not report gun violence that took place outside school or college premises. Source: Everytown (http://everytown.org/article/schoolshootings; web access date: 28 June 2015)

Page - 28

APPENDICES

COEDITORS Marianne Bertrand Martin Eichenbaum Hilary Hoynes Luigi Pistaferri Debraj Ray Larry Samuelson Andrzej Skrzypacz

The American Economic Review Published by the American Economic Association

Pinelopi Koujianou Goldberg, Editor

July 19, 2013 Managing Editor Steven M. Stelling BOARD OF EDITORS Mark Aguiar Pol Antràs Sandra Black Simon Board Craig Burnside Ariel Burstein Steven Callander Gary Charness Sylvain Chassang Dora Costa Miguel Costa-Gomes Dirk Engelmann Hanming Fang Timothy Feddersen Michael Fishman William Fuchs Gautam Gowrisankaran David Green Veronica Guerrieri Igal Hendel Ali Hortaçsu Shachar Kariv Navin Kartik Brian Knight Botond Kőszegi Ilan Kremer Arvind Krishnamurthy Jonathan Levin Gilat Levy Hamish Low Shelly Lundberg Matthew Mitchell Dilip Mookherjee Giuseppe Moscarini Philip Oreopoulos Rohini Pande Jonathan Parker Parag Pathak Nina Pavcnik Fabrizio Perri Ricardo Reis Jesse Rothstein Fiona Scott Morton Rajiv Sethi Jón Steinsson Amir Sufi Christopher Timmins Sarah Turner Eric Verhoogen Lise Vesterlund Leeat Yariv

American Economic Association Publications 2403 Sidney Street, Suite 260 Pittsburgh, PA 15203 412-432-2300 Fax: 412-431-3014

Luitel, Hari Sharan Algoma University - Business and Economics 1520 Queen Street East Sault Ste. Marie, Ontario P6A 2G4 Canada

RE: AER-2013-0867: Causes of State Tax Amnesties: A Review

Dear Professor Luitel, Thank you for submitting the paper “Causes of State Tax Amnesties: A Review” to the American Economic Review. I have now had a chance to read the manuscript. I am afraid that the paper is not a good fit for the AER. The paper reads like a comment on Dubin, Graetz and Wilde’s 1992 QJE paper. While we publish comments in the AER, we only consider comments on work that has been published in the AER. The Dubin et al. paper does not satisfy this condition. In an effort to achieve quick turnaround, I did not solicit the opinion of referees. It is our editorial policy to refund the submission fee in such cases. I am sorry that the news is not positive, but due to space limitations we can accept less than 8% of all submitted papers. I hope that this outcome will not prevent you from submitting your work to the American Economic Review in the future. Best Regards, Penny Goldberg

COEDITORS Mark Aguiar Roland Bénabou Marianne Bertrand Hilary Hoynes John Leahy Luigi Pistaferri Debraj Ray Larry Samuelson Managing Editor Steven M. Stelling BOARD OF EDITORS Nageeb Ali Manuel Amador Marco Bassetto Simon Board Leah Boustan Craig Burnside Ariel Burstein Steven Callander Sylvain Chassang Arnaud Costinot Matthias Doepke Dave Donaldson Jeffrey Ely Dirk Engelmann Timothy Feddersen Roland Fryer Gautam Gowrisankaran Veronica Guerrieri Erik Hurst Seema Jayachandran Navin Kartik Brian Knight Arvind Krishnamurthy Gilat Levy Bart Lipman Hamish Low Jens Ludwig Dilip Mookherjee Giuseppe Moscarini Ted O’Donoghue Philip Oreopoulos Jonathan Parker Parag Pathak Nina Pavcnik Fabrizio Perri Jesse Rothstein Edward Schlee Rajiv Sethi Jón Steinsson Amir Sufi Christopher Timmins Sarah Turner Eric Verhoogen Leeat Yariv

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The American Economic Review Published by the American Economic Association

Pinelopi Koujianou Goldberg, Editor

July 6, 2015 Luitel, Hari Algoma University – Business and Economics 1520 Queen Street East Sault Ste. Marie Ontario PSA 2G4 Canada RE: AER-2015-0866: Why Most Published Results on Unit Root and Cointegration Are False Dear Professor Luitel, I am writing about the paper “Why Most Published Results on Unit Root and Cointegration Are False” that you have submitted to the American Economic Review. I am afraid that the paper is not a good fit for the AER. The paper takes on the entire cointegration literature. Given that your critique refers to a well-established econometric methodology, a more methodologically oriented journal in Econometrics would be more appropriate. In your submission letter, you also mention our previous correspondence regarding an earlier paper you submitted to the AER. As I wrote in that letter, we do consider comments on earlier work published in the AER, but such comments typically regard a specific paper and not an entire literature. In an effort to achieve quick turnaround, I did not solicit the opinion of referees. It is our editorial policy to refund the submission fee in such cases. Best Regards, Penny Goldberg