Any series of observations ordered along a single dimension, such as time, may be thought of as a time series. The emphasis in time series analysis is on studying the dependence among observations at different points in time. What distinguishes time series analysis from general multivariate analysis is precisely the temporal order imposed on the observations. Many economic variables, such as GNP and its components, price indices, sales, and stock returns are observed over time. In addition to being interested in the contemporaneous relationships among such variables, we are often concerned with relationships between their current and past values, that is, relationships over time.

Time Series Analysis

Many panel data sets encountered in macroeconomics, international economics, regional science, and finance are characterized by cross-sectional or “spatial” dependence. Standard techniques that fail to account for this dependence will result in inconsistently estimated standard errors. In this paper we present conditions under which a simple extension of common nonparametric covariance matrix estimation techniques yields standard error estimates that are robust to very general forms of spatial and temporal dependence as the time dimension becomes large. We illustrate the relevance of this approach using Monte Carlo simulations and a number of empirical examples.

Consistent Covariance Matrix Estimation with Spatially Dependent Panel Data

Simple diagnostic tests for spatial dependence

We examine the influence of venture capital on patented inventions in the United States across twenty industries over three decades. We address concerns about causality in several ways, including exploiting a 1979 policy shift that spurred venture capital fundraising. We find that increases in venture capital activity in an industry are associated with significantly higher patenting rates. While the ratio of venture capital to R&D averaged less than 3% from 1983-1992, our estimates suggest that venture capital may have accounted for 8% of industrial innovations in that period.(Publication abstract)

Assessing the Contribution of Venture Capital to Innovation

Forecast evaluation often compares a parsimonious null model to a larger model that nests the null model. Under the null that the parsimonious model generates the data, the larger model introduces noise into its forecasts by estimating parameters whose population values are zero. We observe that the mean squared prediction error (MSPE) from the parsimonious model is therefore expected to be smaller than that of the larger model. We describe how to adjust MSPEs to account for this noise. We propose applying standard methods (West (1996)) to test whether the adjusted mean squared error difference is zero. We refer to nonstandard limiting distributions derived in Clark and McCracken (2001, 2005a) to argue that use of standard normal critical values will yield actual sizes close to, but a little less than, nominal size. Simulation evidence supports our recommended procedure.

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Approximately Normal Tests for Equal Predictive Accuracy in Nested Models

A Very Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix

This study investigates the causal links between trade, economic growth and inward foreign direct investment (FDI) in China at the aggregate level. The integration and cointegration properties of quarterly data are analysed. Long-run relationships between growth, exports, imports and FDI are identified in a cointegration framework, in which this paper finds bi-directional causality between economic growth, FDI and exports. Economic development, exports and FDI appear to be mutually reinforcing under the open-door policy.

Relationships between economic growth, foreign direct investment and trade: evidence from China

A TEST for spatial correlation in regression disturbances has been given by Cliff and Ord (1973). In their treatment, the test is defined by analogy with that first advanced by Durbin and Watson (1950) in the context of serial correlation. It is then shown that the asymptotic efficiency of the Cliff-Ord statistic relative to any other of the same functional form is not less than unity. An informal argument is then employed to demonstrate the convergence of their test statistic, when the spatial correlation parameter approWaches zero, to a quadratic form appearing in the likelihood ratio. The derivation given below enables their argument to be by-passed, as Silvey's (1959) general results on the asymptotic equivalence of Lagrange Multiplier, and likelihood ratio tests can now be invoked. Consider the usual linear regression model,

On the Cliff-Ord Test for Spatial Correlation

Three asymptotically equivalent tests for the presence of a common factor in a spatial autoregression model are presented. When such a common factor exists, the model reduces to the simple regressi...

Testing for a Common Factor in a Spatial Autoregression Model

Government- and charity-funded medical research and private sector research and development (RD 44 % of that additional private sector expenditure occurs within 1 year, with the remainder accumulating over decades. This spillover effect implies a real annual rate of return (in terms of economic impact) to public biomedical and health research in the UK of 15–18 %. When combined with previous estimates of the health gain that results from public medical research in cancer and cardiovascular disease, the total rate of return would be around 24–28 %. Overall, this suggests that government and charity funded research in the UK crowds in additional private sector R&D in the UK. The implied historical returns from UK government and charity funded investment in medical research in the UK compare favourably with the rates of return achieved on investments in the rest of the UK economy and are greatly in excess of the 3.5 % real annual rate of return required by the UK government to public investments generally.

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Quantifying the economic impact of government and charity funding of medical research on private research and development funding in the United Kingdom

Peter Burridge

Papers

A Very Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix

Relationships between economic growth, foreign direct investment and trade: evidence from China

On the Cliff-Ord Test for Spatial Correlation

Testing for a Common Factor in a Spatial Autoregression Model

Quantifying the economic impact of government and charity funding of medical research on private research and development funding in the United Kingdom